Integral Sensor Fault Detection and Isolation for Railway Traction Drive

sensors Article

Integral Sensor Fault Detection and Isolation for Railway Traction Drive Fernando Garramiola *

ID

, Jon del Olmo, Javier Poza, Patxi Madina and Gaizka Almandoz

Faculty of Engineering, Mondragon Unibertsitatea, 20500 Arrasate - Mondragón, Spain; [email protected] (J.d.O.); [email protected] (J.P.); [email protected] (P.M.); [email protected] (G.A.) * Correspondence: [email protected]; Tel.: +34-943-79-47-00 Received: 20 March 2018; Accepted: 11 May 2018; Published: 13 May 2018







Abstract: Due to the increasing importance of reliability and availability of electric traction drives in Railway applications, early detection of faults has become an important key for Railway traction drive manufacturers. Sensor faults are important sources of failures. Among the different fault diagnosis approaches, in this article an integral diagnosis strategy for sensors in traction drives is presented. Such strategy is composed of an observer-based approach for direct current (DC)-link voltage and catenary current sensors, a frequency analysis approach for motor current phase sensors and a hardware redundancy solution for speed sensors. None of them requires any hardware change requirement in the actual traction drive. All the fault detection and isolation approaches have been validated in a Hardware-in-the-loop platform comprising a Real Time Simulator and a commercial Traction Control Unit for a tram. In comparison to safety-critical systems in Aerospace applications, Railway applications do not need instantaneous detection, and the diagnosis is validated in a short time period for reliable decision. Combining the different approaches and existing hardware redundancy, an integral fault diagnosis solution is provided, to detect and isolate faults in all the sensors installed in the traction drive. Keywords: sensor fault diagnosis; diagnostic observer; fault injection; railway traction drive; frequency analysis

1. Introduction In the last few decades, electric drives have become more important with the increase of machinery electrification and electric vehicles. Moreover, in Railway applications, the availability of the traction drive is directly linked to the availability of the complete system, as a train could stop in case of a failure in the traction drive. Maintenance activities have an important influence on the availability of the system, being an ideal maintenance the one which prevents a failure [1], based on the health of the system. A Fault Diagnosis is needed in order to detect faults and implement a Condition-Based Maintenance. Fault diagnosis functionalities or tools can differentiate between some industrial applications and companies from others. With fault diagnosis, we refer to the sequence of actions needed to detect, locate, and identify the fault mode in a system. Moreover, the severity of the fault can be obtained. This is known in the literature as Fault Detection and Diagnosis (FDD) [2,3]. If the fault is only being detected and located, the approach is called Fault Detection and Isolation (FDI) [4]. In this case, the specific fault mode or the severity is not established. Different FDI approaches have been presented in the literature. In [5], a classification between model-based and model free approaches is done. Quantitative model-based FDI approaches, also referred as Model-based FDI, are based on an analytical redundancy, so the measured value is compared Sensors 2018, 18, 1543; doi:10.3390/s18051543

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to a value obtained from the model. The difference between both values is called residual, and it should be close to zero in fault-free cases. A comparison among the different Model-based FDI approaches is presented in [6]. In this research, on-board Model-based FDI approaches are proposed and implemented in a commercial Traction Control Unit (TCU) for a tram. In complex systems, a fault can concern several signals, being a Model-Based FDI a suitable solution to improve detection sensitivity [7]. The model of the traction drive is already available, as it is defined at the beginning of the design phase for performance simulation, so a Model-based FDI can be validated during this period too. In addition, the design of FDI approaches based on models can benefit from the knowledge and models gathered during the common design phase of the system. On the other hand, as model-free approaches need a large quantity of historical data, on-board diagnosis has limitation due to computational requirements [8]. On-board diagnosis is closer to physical systems, improving the diagnosis celerity and reducing the data communications costs. Moreover, in moving systems, the communication to remote diagnosis cannot be executed at high frequencies and on-board data storage is limited. Thus, this research is focused on Model-based FDI approaches implemented in a commercial TCU for a tram. Once a fault occurs, system performance deteriorates from the nominal zone to the degraded zone. Thus, a Model-based FDI for early detection of faults in traction drive elements, before the system passes from degraded mode to failure, is an important point to increase the availability and reliability of the system. The types of faults in traction drives can be classified as sensor, actuator, and process faults [9]. Fault Detection and Isolation (FDI) approaches have been implemented in electric drives, mainly for sensors [10,11], electric machines [12,13] and power converters [14,15]. Traction control strategy needs the sensor feedback for properly operation, so a faulty sensor can suppose a loss of availability and performance deterioration [16]. This research is focused on sensor fault detection and isolation in a traction drive. In [9] a review of FDI methods for sensor faults in aerospace applications is presented. Recently, an integrated diagnosis for aerospace application was presented in [17], which includes a sensor fault diagnosis and performance degradation estimation. There are several recent publications in sensor diagnosis for different applications in electric and hybrid vehicles [18–20], mainly in order to increase safety and availability. However, the publications in Railway systems are reduced and limited to test benches without commercial control units, observer-based FDI for sensor faults are proposed in [2,21,22]. The aim of this article is to propose an integral FDI solution for sensors in a Railway Traction drive, based on different FDI approaches. The applied approaches do not imply any hardware change. Railway applications are not safety-critical systems as aerospace systems. In aerospace applications, it is critical to react instantaneously to the fault, in order to activate a fault tolerant solution. On the other hand, in Railway applications, the control system can stop and restart the traction unit in seconds maintaining the motion of the train. Thus, the proposed approaches in this article for Railway application should be evaluated during a short time period in order to confirm the fault detection. The most suitable FDI approach for each sensor has been selected, based on the following factors: algorithm complexity, hardware and software resources available in the traction drive, tuning difficulty due to parameter variation/uncertainties and reliability. A simple model for an observer, avoiding several motor parameter variation during operation [23], the available hardware redundancy and low computational algorithms, which can be executed in the TCU without demanding an increase of the execution period, are the preferred choices. Among the FDI solutions for DC-link voltage and catenary current sensor, an observer-based FDI approach based on the input filter is proposed. In [21], a similar solution is presented, as an adequate solution for real time implementation, which avoids problems in the modelling of the power converter or the need of a FPGA-based FDI [24], allowing an easier implementation in the Digital Signal Processor available in the TCU. In [25], an Extended Kalman Filter is implemented for FDI, based on induction

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motor model. The author concludes that the performance of the approach deteriorates at very low speeds and it is affected by parameter variation. The proposed solution in this article does not require demanding hardware and software resources for real time implementation, due to the simplicity of the model of the input filter, in comparison to models including a power converter or an electric machine. Furthermore, among the observer-based approaches, Luenberger observer could be more adequate for industrial applications due to the possibility to simplify its algorithms [26]. In conclusion, the proposed solution is justified due to lower algorithm complexity, lower parameter variation and uncertainties of the input filter in comparison to more complex motor model, capability of the TCU and reliability of Luenberger observer. In the Railway Traction drive studied, only two phase measurements are available. Thus, low computational cost FDI approaches for phase current sensor, such as those based on the sum of three current measurements cannot be applied [27]. There are few studies with just two phase measurements which analyze offset and gain faults, as is summarized in [28]. This work proposes a bank of observers for an induction motor based drive, using a Sliding Mode Observer and a High Gain Observer. In [29] a Sliding Mode observer is proposed for phase current sensor fault reconstruction for a Permanent Magnet Synchronous motor based drive. Both research works use the motor model and they assume that motor parameters are known and constants. On the other hand, in [30], a compensation of the oscillation generated due to phase current sensor fault is presented. Moreover, the frequency of the oscillation allows to the ability to distinguish between offset and gain fault. The extraction of the oscillation can be done by applying to current components id and iq , a low pass filter and a passband filter. The passband filter will be centered in the fundamental frequency of motor stator current for offset faults, or at twice this frequency for gain faults. Despite the limitations of this approach, as it is not possible to isolate faults between both phase current sensors, it allows to reutilize filters and control strategy algorithm already implemented in the traction control unit. Thus, it requires lower computational resources compared to the aforementioned observer-based approaches. On the other hand, as it does not depend on the motor model, it does not need an online motor parameter adaptation to avoid performance deterioration, as these parameters change during operation [23]. In conclusion, the proposed solution is considered the most suitable for the Railway Traction drive, due to lower algorithm complexity in comparison to a bank of observers or a Kalman filter, the reutilization of available control and filter algorithms, capability of the TCU, and the reliability of the detection. Finally, in case of the speed sensor, due to the hardware redundancy already available in the Railway Traction drive configuration, observer-based FDI approaches for speed sensor faults [31], have not been implemented. Mainly, due the reliability of the hardware redundancy, being the detection decoupled from parameter variation and uncertainties, as well as the low computational cost and TCU capability, the solution based on hardware redundancy has been proposed. Previous works in sensor FDI in Railway applications have been validated in simulation [2,32] or in an experimental test bench [21,22], but without commercial TCU, and they do not include all the sensors installed in a railway traction drive. In contrast to previous works, a commercial Railway control unit was used for Hardware-in-the-loop simulation (HIL). The HIL platform is composed of a Real Time Simulator and a Traction Control Unit (TCU) for a Railway application. The TCU is a commercial unit for a tram developed by CAF Power & Automation (Spain). Thus, the FDI algorithms were implemented together with the same control software utilized for a real tram application. The paper has the following structure: Section 2 presents the Railway traction drive description and problem statement. Section 3 presents the integral sensor fault diagnosis structure. Section 4 proposes a FDI approach for DC-link voltage and catenary current sensors. Section 5 presents a FDI approach for motor phase current sensors. In Section 6, an approach for speed sensor based on hardware redundancy is presented. In Section 7 the validation in a HIL platform is presented. Finally, the discussion and conclusions are given.

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2. Railway Railway Traction Traction Unit Unit Description Description and and FDI 2. FDI Strategy Strategy Objectives Objectives There are are different different traction traction unit unit topologies topologies but but this this research research has has been been applied applied to to the the traction traction unit unit There shown in Figure 1. shown in Figure 1. Traction unit

750 Vdc

LF

K1 K3

RF

icat

iinv

RP

T1

T7 vbus

vcat

T3

iu

u CB

RDP

T5 iv

v

icrw

IM M

w IM M

T2

T4

T6

iret Input filter

Inverter

Suvw Encoder 1 Sensors

Traction control unit

Encoder 2

Figure 1. Railway traction unit. Figure 1. Railway traction unit.

• •• • • •• •• •

The traction unit is supplied from a 750 V DC catenary. The traction unit can be divided into: The traction unit is supplied from a 750 V DC catenary. The traction unit can be divided into: Main and pre-charge contactors, represented as K1 and K3. Main and pre-charge contactors, as K1functions and K3 . being the catenary current ripple Input filter, composed of LF, Crepresented B and RF, with Input filter,protection composedagainst of LF , Ccatenary with functions being catenaryvoltage currentsetting. ripple reduction, B and RF ,voltage reduction, changes, andthe a DC-link protection against catenary voltage changes, and a DC-link voltage setting. Braking unit given by IGBT T7 and braking resistor. Braking unitinverter given bythat IGBT T7 andtwo braking resistor. IGBT-based supplies induction motors in parallel. Traction control unit, where software for the control strategies, IGBT-based inverter that supplies two induction motors in parallel. protections and alarms, is executed. Traction control unit, where software for the control strategies, protections and alarms, is executed.

The The list list of of sensors sensors in in the the traction traction unit unit is is given given in in Table Table 1. 1. The The objective objective of of the theintegral integral supervision supervision is to present FDI approaches based on hardware and analytical redundancy, without is to present FDI approaches based on hardware and analytical redundancy, without including including additional additional sensors. sensors. Table 1. Summary of sensors in the Railway unit. Table

Sensor Sensor

Description Description

vcat

Catenary voltage sensors Catenary voltage sensors Catenary current sensor Catenary current sensor Return current catenarysensor sensor Return current to to catenary DC-link voltage sensor DC-link voltage sensor Braking unit current sensor Braking unit current sensor Motor phase current sensors Motor phase sensors Motor current speed sensors Motor speed sensors

vcat icaticat iretiret vbus vbus icrw icrw iu,v iu,v1,2 Encoder

Encoder 1,2

3. Integral Sensor Fault Diagnosis Structure 3. Integral Sensor Fault Diagnosis Structure The proposed Integral Sensor Fault Diagnosis strategy provides the most suitable solution for The proposed Integral Sensor Fault Diagnosis strategy provides the most suitable solution for each sensor, based on the architecture of the traction unit shown in Figure 1. In some cases, the addition each sensor, based on the architecture of the traction unit shown in Figure 1. In some cases, the of an additional sensor might be a new solution, more suitable, but it can have drawbacks too, due to addition of an additional sensor might be a new solution, more suitable, but it can have drawbacks new hardware or software requirements for the Traction control unit. Thus, approaches which provide too, due to new hardware or software requirements for the Traction control unit. Thus, approaches analytical or hardware redundancy without hardware changes are proposed. which provide analytical or hardware redundancy without hardware changes are proposed. Among the several FDI strategies developed for the traction drive, the ones presented in this Among the several FDI strategies developed for the traction drive, the ones presented in this article are shown in Figure 2, and explained in following sections. These strategies are centered in article are shown in Figure 2, and explained in following sections. These strategies are centered in the the FDI for DC-link voltage, catenary current, motor phase current and speed sensors. Solutions FDI for DC-link voltage, catenary current, motor phase current and speed sensors. Solutions for the rest of sensor (catenary voltage, return current, and crowbar current) are not discussed here, as they

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for the rest of sensor (catenary voltage, return current, and crowbar current) are not discussed here, as they areonbased onFDI similar FDI approaches. voltage sensor can beusing isolated using are based similar approaches. CatenaryCatenary voltage sensor faults can faults be isolated hardware hardware redundancy, than one sensor isin installed in Return the train. Return current sensor redundancy, since moresince thanmore one sensor is installed the train. current sensor faults are faults are isolated using the redundancy with catenary current sensors. Finally, crowbar current isolated using the redundancy with catenary current sensors. Finally, crowbar current sensorsensor fault fault detection canperformed be performed during braking with observer basedFDI FDIapproach approachpresented presented in in detection can be during braking with thethe observer based Section 4. 4. With With the the combination combination of Section of different different FDI FDI approaches, approaches, sensor sensor faults faults can can be be isolated. isolated.

DC- link voltage and catenary current sensors

Motor phase current sensors

Motor speed sensors

FDI: Observer based residual

FDI: Current components frequency analysis

FDI: Hardware redundancy

Severity of faults: Fault injection and enhanced FMEA. Likelihood ratio of residual

Severity of faults: Fault injection and enhanced FMEA Likelihood ratio of residual

Severity of faults: Comparison among motor speed sensors and train speed

Maintenance Decision-Making

Figure Figure 2. 2. Integral Integral Sensor Sensor Fault Fault Diagnosis Diagnosis structure structure for for traction traction unit. unit.

The different FDI strategies are executed in parallel. A suitable feedback gain selection for The different FDI strategies are executed in parallel. A suitable feedback gain selection for observer based FDI, makes residual for detecting catenary current sensor faults sensitivity low to DCobserver based FDI, makes residual for detecting catenary current sensor faults sensitivity low to link voltage sensor faults, and residual for detecting DC-link voltage sensor faults sensitivity low to DC-link voltage sensor faults, and residual for detecting DC-link voltage sensor faults sensitivity low catenary current sensor faults. Thus, both residuals are decoupled. to catenary current sensor faults. Thus, both residuals are decoupled. In order to avoid any false detection, as observer based residual sensitivity depends on observer In order to avoid any false detection, as observer based residual sensitivity depends on observer gains selection, a procedure is proposed to implement the integral diagnosis strategy for FDI in gains selection, a procedure current and voltage sensors.is proposed to implement the integral diagnosis strategy for FDI in current and voltage sensors. The estimation of fault severity is not deeply described in this article. In case of current and Thesensors estimation of afault severity is not deeply described this article. Inan case of current and voltage faults, previous fault injection and analysis,infor developing enhanced Failure voltage sensors a previous injection developing anofenhanced mode and effectsfaults, analysis (FMEA) fault is needed [33].and Thisanalysis, analysis for links the amount deviationFailure of the mode and effects analysis (FMEA) is needed [33]. This analysis links the amount of deviation of the sensor with the root failure mode. Then statistical tools as likelihood ratio are applied in order to sensor with the root failure mode. Then statistical tools as likelihood ratio are applied in order to estimate the fault severity. estimate the fault severity. 4. FDI Approach for DC-Link Voltage Sensor and Catenary Current Sensor 4. FDI Approach for DC-Link Voltage Sensor and Catenary Current Sensor Several FDI approaches were presented for DC-link sensors. In [34], a comparison between Several FDI approaches were presented for DC-link sensors. In [34], a comparison between power power and estimated motor input power is used for DC-link sensor fault FDI. This method has and estimated motor input power is used for DC-link sensor fault FDI. This method has limitations limitations for low speed and it depends on the stator resistance and inverter losses estimation. In for low speed and it depends on the stator resistance and inverter losses estimation. In [25] an [25] an Extended Kalman filter is proposed for DC-link voltage sensor FDI. This method is based on Extended Kalman filter is proposed for DC-link voltage sensor FDI. This method is based on the motor the motor model, which needs accurate parameter configuration and has high computational costs. model, which needs accurate parameter configuration and has high computational costs. On the other On the other hand, [21] proposes an Observer-based FDI method, which is not dependent on the hand, [21] proposes an Observer-based FDI method, which is not dependent on the motor model. It is motor model. It is based on a Luenberger observer [35] applied to a single phase PWM rectifier input based on a Luenberger observer [35] applied to a single phase PWM rectifier input filter. These kind of filter. These kind of strategies has the advantage of modelling the input LC filter of the traction drive, strategies has the advantage of modelling the input LC filter of the traction drive, which has a linear which has a linear model, based on manageable first order differential equations. In [22], a Sliding mode observer (SMO) is proposed instead of a linear gain observer. Taking into account the solutions presented in the literature and their advantages and drawbacks, a FDI approach that is independent of motor parameters and based on the input filter of the traction unit was proposed.

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model, based on manageable first order differential equations. In [22], a Sliding mode observer (SMO) is proposed instead of a linear gain observer. Taking into account the solutions presented in the literature and their advantages and drawbacks, a FDI approach that is independent of motor parameters and based on the input filter of the traction unit was proposed. 4.1. Input Filter System Model Similar to previous publications is presented in h i h[36], the model of ithe input filter h in state space i

(1), being xT = icat vbus , uT = vcat iinv icrw and yT = icat vbus . The iinv value is not directly measured, but it is calculated from T1, T3, and T5 switches states and iu and iv current sensors measurements. " # # " RF 1 1 0 0 − − L dx LF LF F u x+ 1 dt = 0 − C1B − C1B 0 CB " # (1) 1 0 y= x. 0 1 Before designing the observers, the observability and controllability of the system, given by (1) was checked. The controllability for a linear system is given if Expression (2) was fulfilled, n being the dimension of the state vector x. The rank obtained was 2, so it can be concluded that the system is fully controllable.   .. rank B . AB = n (2) The next step was to check the observability of the system, given if Expression (3) is fulfilled. The rank is 2, so it can conclude that the system is fully observable. 

 C   rank  · · ·  = n AC

(3)

Based on [37], the detectability and isolability analysis was done for the configuration represented in (1). It was assumed that the fault modes were additive and constant during the time window. In Table 2, the x in the detectable column represents that the fault mode was detectable. The x in each fault column represents that the fault is isolable respect to each row, whereas the 0 represents that the fault mode is not isolatable. Table 2. Diagnosability analysis for sensor faults for a time window of two samples.

ficat fvbus fvcat ficrw finv

Detectable

ficat

fvbus

fvcat

ficrw

finv

x x x x x

0 0 0 0 0

0 0 0 0 0

x 0 0 x x

x x x 0 0

x x x 0 0

Thus, from the results presented in Table 2, it can be concluded for example that it is not possible to isolate an additive fault in sensor vbus from an additive fault in sensor vcat . The same happens for isolating a fault in sensor icrw from a fault in iinv , or isolating a fault in sensor vbus from a fault in sensor icat without any other redundancy apart from the system given in state space representation (1). In the following subsection, a FDI approach based on a bank of observers for vbus and icat was proposed [36], providing analytical redundancy to solve one of the previously mentioned isolation

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problems. Although the diagnosability analysis has been done for additive fault modes, in the following FDI strategy both fault modes, additive and multiplicative, will be analysed, as offset and gain faults will be injected. 4.2. FDI Strategy for DC-Link Voltage and Catenary Current Sensors order isolate two SensorsIn 2018, 18, xtoFOR PEERDC-Link REVIEW voltage sensor faults from catenary current sensor faults, a bank of 7 of 19 Luenberger observers was proposed. Observers are based on the model of input filter system in (1), and (1), and in consequence, the strategy is independent themodel. motor The model. Thefilter input filterismodel is in consequence, the strategy is independent from thefrom motor input model simpler simpler motor and ituncertainties has fewer uncertainties andsoparameters, the observer than the than motorthe model andmodel it has fewer and parameters, the observerso implementation implementation and it had lessrequirements. computational requirements. was easier and itwas hadeasier less computational A A different different feedback feedback strategy strategy for for each each observer observer isis used used depending depending on on the the fault fault that that isis being being detected. detected. IfIfthe thedetection detectionisisfocused focusedon on DC-Link DC-Link sensor sensor faults, faults, the the observer observer equations equations for for DC-link DC-link voltage 𝑪1𝟏 = = [1 andy1𝑦1==icat 𝑖𝑐𝑎𝑡 voltage are are given given in in (4), (4), for for C .. [1 00]] and 𝑥̂. ̇ (𝑡) = 𝑨𝑥̂(𝑡) + 𝑩𝑢(𝑡) + 𝑳(𝑦1 (𝑡) − 𝑪𝟏 𝑥̂(𝑡)) xˆ (t) = Axˆ (t) + Bu(t) + L(y1 (t) − C1 xˆ (t)) (4) (4) 𝑦̂1 (𝑡) = 𝑪𝟏 𝑥̂(𝑡). yˆ1 (t) = C1 xˆ (t). In Figure 3, the observer model for DC-link voltage sensor FDI is presented. As it can be seen in In Figure 3, the observer model DC-linkthe voltage FDI isso presented. it can be seen in (4), the observer does not take intoforaccount 𝑣𝑏𝑢𝑠 sensor measured, the 𝑣̂𝑏𝑢𝑠Asestimated is not (4), the observer not take into sensor accountfault. the vThus, so the is not influenced by bus measured, bus estimated influenced by thedoes DC-link voltage in the case of avˆfaulty 𝑣𝑏𝑢𝑠 sensor, the fault will 𝑖𝑐𝑎𝑡 of a faulty v bus sensor, the fault will be detected and the DC-link voltage sensor fault. Thus, in the case be detected and isolated in the residual 𝑟𝑣𝑏𝑢𝑠 = 𝑣̂𝑏𝑢𝑠 − 𝑣𝑏𝑢𝑠 . On the other hand, the observer icat = vˆ isolated in is theinfluenced residual rvbus − vbus . fault, On the hand,redundancy the observerof estimation is influenced by bus sensor estimation by a 𝑣𝑐𝑎𝑡 soother hardware this sensor, available in a v sensor fault, so hardware redundancy of this sensor, available in distributed railway traction cat distributed railway traction configurations in the train should be used to discard the 𝑣𝑐𝑎𝑡 sensor configurations in the train should be used to discard the vcat sensor fault. fault. L icat

iu,iv vcat icrw

B

+

+ +

∫

icat vbus

icat C

+

+

+

icat ricat icat rvbus

vbus +

vbus A D Figure 3. Diagnostic observer for DC link voltage sensor FDI. Figure 3. Diagnostic observer for DC link voltage sensor FDI.

The system dynamic is given by the poles obtained solving the equation presented in (5). The system dynamic given byfixed the poles the six equation (5).open Normally Normally the closed loop is poles are to beobtained betweensolving three and times presented faster thaninthe loop the closed loop poles are fixed to be between three and six times faster than the open loop poles [22]. poles [22]. Higher dynamics make the observer more sensitive to measurement noises. Thus, the 𝑳 Higher dynamics make with the observer more sensitive to measurement noises. L gain matrix gain matrix is obtained the poles placement method. Closed loop polesThus, havethe been chosen to beis obtained the poles placement method. Closed loop poles have been chosen to be five times faster five timeswith faster than open loop poles. than open loop poles. |𝑠𝑰 − ((𝑨 + 𝑳𝑪)| (5)(5) A+ LC)| = = 0. 0. |sI − The traction system systemand and sensor faults injection blocks havemodelled been modelled in MatlabThe traction thethe sensor faults injection blocks have been in Matlab-Simulink. Simulink. Based on the most common sensor fault modes [9] and information from the CAF Power Based on the most common sensor fault modes [9] and information from the CAF Power & Automation & Automation maintenance team, gain (scaling), and offset (bias and drift) faults have been modelled, maintenance team, gain (scaling), and offset (bias and drift) faults have been modelled, as shown in as shown in Figure 4. Disconnection were not considered, since the drive protection system Figure 4. Disconnection faults were notfaults considered, since the drive protection system shuts itself down shuts itself down as quickly as possible, when overcurrents and overvoltages, due to hard faults, are as quickly as possible, when overcurrents and overvoltages, due to hard faults, are detected. The detected. The available time interval between the fault occurrence and system shut down does not available time interval between the fault occurrence and system shut down does not allow for any allow for any FDI task execution. The fault injection model allows injecting different sensor fault modes easily and quickly. Fault injection has been previously used in electric drives applications [38]. The aim of FDI in this work was early detection, before the system passes from degraded zone to failure. The real 𝑣𝑏𝑢𝑠 , obtained from the modelled system, the sensor measured 𝑣𝑏𝑢𝑠 , and the observer estimated 𝑣̂ are displayed for an offset sensor fault in Figure 5 and gain sensor fault in Figure 6.

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FDI task execution. The fault injection model allows injecting different sensor fault modes easily and quickly. Fault injection has been from previously in measurement, electric drives applications [38]. Theisaim FDI for in estimated value is decoupled 𝑣𝑏𝑢𝑠 used sensor as measured value notofuse this work loop, was early detection, beforeisthe system passes from degraded zone to failure. feedback so the faulty sensor easily detected. Fault selection

Fault -free sensor signal

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Faulty sensor signal

Gain

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estimated value is decoupled from 𝑣𝑏𝑢𝑠 sensor measurement, as measured value is not use for estimatedloop, value from 𝑣𝑏𝑢𝑠 sensor measurement, as measured value is not use for feedback soisthedecoupled faulty sensor is easily detected. feedback loop, so theNoise faulty sensor is easily detected. Fixed value

Fault -free sensor Fault -free signal sensor signal

Figure 4. Sensor fault injection. Figure 4. Sensor fault injection.

Fault selection Fault selection

The real vbus , obtained from the modelled system, the sensor measured vbus , and the observer estimated vˆ bus are displayed for an offset sensor fault in Figure 5 and gain sensor fault in Figure 6. Faulty Gain Offset Despite the faulty measurement of vbus sensor, the estimated vˆ bus follows sensor the real value, as the Faulty signal icat Gain sensor estimation does notOffset depend on this sensor. Furthermore, the filtered residual signalr vbus is shown too. icat Residual rvbus is obtained from comparison of vbus measurement and estimated vˆ bus . Thus, the increase of the residual can beNoise seen when offset or gain faultsFixed arevalue injected in vbus sensor, because the estimated Noise Fixed value value is decoupled from vbus sensor measurement, as measured value (b) is not use for feedback loop, (a) so the faulty sensor is easily detected. Figure 4. Sensor fault injection. Figure 5. (a) Direct current (DC)-link voltage for 20fault V offset fault injection in 𝑣𝑏𝑢𝑠 sensor at 6 s; (b) Figure 4. Sensor injection. 𝑖𝑐𝑎𝑡 |𝑟𝑣𝑏𝑢𝑠 | filtered from difference between measured and estimated 𝑣𝑏𝑢𝑠 .

(a) (b) (a) (b) Figure 5. (a) Direct current (a)(DC)-link voltage for 20 V offset fault injection (b)in 𝑣𝑏𝑢𝑠 sensor at 6 s;icat(b)

Figure voltage forfor 20 20 V offset faultfault injection in vbus at 6 s; (b) 𝑖𝑐𝑎𝑡 5. Figure 5. (a) (a)Direct Directcurrent current(DC)-link (DC)-link voltage V offset injection in sensor 𝑣𝑏𝑢𝑠 sensor at 6 rs;vbus (b) |𝑟 𝑣𝑏𝑢𝑠 | filtered from difference between measured and estimated 𝑣𝑏𝑢𝑠 . 𝑖𝑐𝑎𝑡 𝑖𝑐𝑎𝑡 filtered from betweenfor measured andfault estimated vbusin. 𝑣𝑏𝑢𝑠 Figure 6. (a)difference DC-link voltage +10% measured gain injection at 6 s; (b) |𝑟𝑣𝑏𝑢𝑠 | filtered |𝑟 | filtered from difference between and estimated 𝑣 sensor . 𝑣𝑏𝑢𝑠

from difference between measured and estimated 𝑣𝑏𝑢𝑠 .

𝑏𝑢𝑠

Once, the fault is detected, the isolability of the sensor is analysed. It has to be taken into account 𝑖𝑐𝑎𝑡 that a faulty DC-Link voltage sensor is not the only one that can change the value of 𝑟𝑣𝑏𝑢𝑠 . Different 𝑖𝑐𝑎𝑡 fault modes are injected in other sensors in the system, and the residual 𝑟𝑣𝑏𝑢𝑠 is monitored. Thus, an offset fault in phase current sensor 𝑖𝑢 , generates an oscillation in system variables, but the estimated 𝑣̂𝑏𝑢𝑠 keeps on following the real value, and the effect on the average residual is negligible compared to faulty 𝑣𝑏𝑢𝑠 sensor measurement. (a) (b) In case of an offset fault as it is (a) injection in sensor 𝑖𝑐𝑎𝑡 , an oscillation arises (b) during a transient, 𝑖𝑐𝑎𝑡 Figure 6. (a) DC-link voltage gain fault 𝑣𝑏𝑢𝑠 sensor at The 6 s; (b) |𝑟𝑣𝑏𝑢𝑠 | the filtered shown in Figure 7, but after 50 for ms,+10% estimated 𝑣̂𝑏𝑢𝑠injection followsinthe real value. effect on residual 𝑖𝑐𝑎𝑡 | filtered Figure 6. (a) DC-link voltage for +10% gain fault injection in 𝑣𝑏𝑢𝑠 sensor at 6 s; (b) |𝑟 𝑖𝑐𝑎𝑡 from difference between andfault, estimated 𝑣𝑏𝑢𝑠 . icat 𝑣𝑏𝑢𝑠 𝑟𝑣𝑏𝑢𝑠 is low, a measured 𝑣𝑏𝑢𝑠forsensor so ainjection suitable false 𝑣𝑏𝑢𝑠 sensor Figure 6. compared (a) DC-link to voltage +10% gain fault inthreshold vbus sensorcan at 6avoid s; (b) r from fault vbus filtered from difference between measured and estimated 𝑣𝑏𝑢𝑠 . detection andbetween isolation. Furthermore, the fault difference measured and estimated vbus . detection and isolation decision is taken after the Once, the fault isthe detected, the isolability of the sensor analysed. It has toso bethis taken into account residual overpasses threshold continuously during a is short time period, allows filtering 𝑖𝑐𝑎𝑡 Once, the fault is detected, the isolability of the sensor is analysed. It has to be taken into account that a faulty DC-Link voltage sensor is not the only one that can change the value of 𝑟 . Different 𝑣𝑏𝑢𝑠 transient values in the residual. 𝑖𝑐𝑎𝑡 𝑖𝑐𝑎𝑡value of 𝑟𝑣𝑏𝑢𝑠 that amodes faulty are DC-Link voltage sensor is not the system, only oneand thatthe can change 𝑟the . Different fault injected in other in the is monitored. Thus,and an 𝑣𝑏𝑢𝑠needs The only shortcoming of thissensors approach occurs when a 𝑣𝑐𝑎𝑡residual sensor fault to be detected 𝑖𝑐𝑎𝑡 fault modes are injected in other sensors in the system, and the residual 𝑟 is monitored. Thus, an 𝑣𝑏𝑢𝑠 offset fault in phase current sensor 𝑖 , generates an oscillation in system variables, but the estimated 𝑖𝑐𝑎𝑡 isolated. The effect in the estimated 𝑢𝑣̂𝑏𝑢𝑠 and 𝑟𝑣𝑏𝑢𝑠 , shown in Figure 8, is similar to the one generated offset fault in phase current sensor 𝑖 , generates an oscillation in system variables, but the estimated 𝑢 and the effect on the average residual is negligible compared 𝑣̂𝑏𝑢𝑠 keeps on following the real value, 𝑣̂𝑏𝑢𝑠 keeps on sensor following the real value, and the effect on the average residual is negligible compared to faulty 𝑣𝑏𝑢𝑠 measurement. to faulty 𝑣 sensor measurement.

Sensors 2018, 18, x FOR PEER REVIEW

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Sensors 2018, 18, 1543

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by a 𝑣𝑏𝑢𝑠 sensor fault. In this case, information coming from other traction drives in the distributed railway traction system should be analysed, to avoid wrong decisions. In addition to this information, Once, is detected, the isolability sensor is analysed. It occur has toin becase taken in case of 𝑣the sensor fault, a transient in the of 𝑖̂𝑐𝑎𝑡thearises, which does not of into 𝑣𝑏𝑢𝑠account sensor 𝑐𝑎𝑡 fault icat overpasses that faulty DC-Link voltage9.sensor is notsensor the only one that can change the value of rvbus . Different fault,a as it is shown in Figure The faulty logic decision is taken when the residual icat This fault modes are injected in other sensors in the system, and the residualtime. rvbus is monitored. the threshold, which should be above it permanently during a predefined produces a Thus, delay an offset fault in phase sensor iu , in generates an oscillation in system the variables, but the estimated in the detection, whichcurrent is not so critical this application, but decreases false detection risk due ˆ busabrupt vto keepschanges on following real value, and theby effect on the average residual is negligible compared to in thethe residuals, produced measurement noises. faultyBased vbus sensor on themeasurement. residual obtained during fault injection in steady state, and the likelihood ratio calculation, possible to estimate theinfault severity. Thus, in Table 3, theduring likelihood ratio obtained In case it ofisan offset fault injection sensor icat , an oscillation arises a transient, as it is shown in Figure 7,fault but after 50 ms, vˆ bus follows the real value. Thebeen effect on the residual for different injection in 𝑣estimated The likelihood ratio has calculated offline, 𝑏𝑢𝑠 is presented. Sensors 2018, 18,offset x FOR PEER REVIEW 9 of 19 icat for a 0.5 s time interval in steady state. The likelihood ratio is represented as 𝑠, being the subscript rand is low, compared to a v sensor fault, so a suitable threshold can avoid false v sensor fault bus bus vbus detection and isolation. Furthermore, the fault detection and isolation is likelihood taken afterratio the theafault reference, superscript thecoming different faulty cases. Adecision negative by 𝑣𝑏𝑢𝑠 free sensor fault. Inand thisthe case, information from other traction drives in the distributed indicatestraction that the fault casebeisanalysed, more probable, whereas a positive value indicates that the faulty residual overpasses thefree threshold continuously during a short time period, so this allows filtering railway system should to avoid wrong decisions. In addition to this information, case is more The higher the value thearises, more probable is the transient in thefault, residual. in case of values 𝑣𝑐𝑎𝑡probable. sensor a transient in theis,𝑖̂𝑐𝑎𝑡 which does notcase. occur in case of 𝑣𝑏𝑢𝑠 sensor fault, as it is shown in Figure 9. The faulty sensor logic decision is taken when the residual overpasses the threshold, which should be above it permanently during a predefined time. This produces a delay in the detection, which is not so critical in this application, but decreases the false detection risk due to abrupt changes in the residuals, produced by measurement noises. Based on the residual obtained during fault injection in steady state, and the likelihood ratio calculation, it is possible to estimate the fault severity. Thus, in Table 3, the likelihood ratio obtained for different offset fault injection in 𝑣𝑏𝑢𝑠 is presented. The likelihood ratio has been calculated offline, and for a 0.5 s time interval in steady state. The likelihood ratio is represented as 𝑠, being the subscript (a)the superscript the different faulty cases.(b) the fault free reference, and A negative likelihood ratio indicates that the fault free case is more probable, whereas a positive value indicates that the faulty Figure 7. (a) Measured, real and estimated 𝑣𝑏𝑢𝑠 for 20 A offset fault injection in 𝑖𝑐𝑎𝑡 sensor at 6 s; (b) Figure 7. probable. (a) Measured, real and estimated vthe 20 A offset fault injection in icat sensor at 6 s; bus for case is more The higher the value is, more probable is the case. 𝑖𝑐𝑎𝑡 |𝑟 | filtered from difference between measured and estimated 𝑣 . icat 𝑏𝑢𝑠 (b)𝑣𝑏𝑢𝑠 rvbus filtered from difference between measured and estimated vbus .

The only shortcoming of this approach occurs when a vcat sensor fault needs to be detected and icat , shown in Figure 8, is similar to the one generated isolated. The effect in the estimated vˆ bus and rvbus by a vbus sensor fault. In this case, information coming from other traction drives in the distributed railway traction system should be analysed, to avoid wrong decisions. In addition to this information, in case of vcat sensor fault, a transient in the iˆcat arises, which does not occur in case of vbus sensor fault, as it is shown in Figure 9. The faulty sensor logic decision is taken when the residual overpasses the (a) (b) threshold, which should be(a) above it permanently during a predefined time. (b) This produces a delay in the detection, which is not so critical in this application, but decreases the false detection risk due to 𝑖𝑐𝑎𝑡 at 6 s; (b) Figure real and 𝑣𝑏𝑢𝑠 forinjection 20 A offset 𝑖𝑐𝑎𝑡(b) sensor Figure 7. 8. (a) (a)Measured, DC-link voltage forestimated 20 V offset fault in fault 𝑣𝑐𝑎𝑡 injection sensor atin6 s; |𝑟𝑣𝑏𝑢𝑠 | filtered 𝑖𝑐𝑎𝑡 abrupt changes in from the residuals, by measurement noises. |𝑟𝑣𝑏𝑢𝑠 | filtered differenceproduced between measured and estimated 𝑣𝑏𝑢𝑠 . from difference between measured and estimated 𝑣𝑏𝑢𝑠 .

(a) (a)

(b) (b)

(b) |𝑟 𝑖𝑐𝑎𝑡 | filtered Figure 8. (a) (a) Catenary DC-link voltage for 20 V V offset offsetfault faultinjection injectioninin𝑣𝑣𝑐𝑎𝑡 sensor sensor at 6s; s; icat 𝑣𝑏𝑢𝑠 current Figure 8. 9. currentfor for20 20 (b) Catenary Figure (a) DC-link voltage V offset fault injection in vcat𝑏𝑢𝑠 sensor at 6ats;6 (b) rvbus filtered from from difference between measured and estimated 𝑣𝑏𝑢𝑠 . for 20 V offset fault injection in 𝑣 sensor at 6 s. difference between measured and𝑐𝑎𝑡 estimated vbus .

(a)

(b)

Figure 9. (a) Catenary current for 20 V offset fault injection in 𝑣𝑏𝑢𝑠 sensor at 6 s; (b) Catenary current

(a)

(b)

𝑖𝑐𝑎𝑡 8. 1543 (a) DC-link voltage for 20 V offset fault injection in 𝑣𝑐𝑎𝑡 sensor at 6 s; (b) |𝑟𝑣𝑏𝑢𝑠 | filtered SensorsFigure 2018, 18, 10 of 20

from difference between measured and estimated 𝑣𝑏𝑢𝑠 .

(a)

(b)

Figure 9. (a) Catenary current for 20 V offset fault injection in 𝑣 sensor at 6 s; (b) Catenary current Figure 9. (a) Catenary current for 20 V offset fault injection in v𝑏𝑢𝑠 bus sensor at 6 s; (b) Catenary current for 20 V offset fault injection in 𝑣𝑐𝑎𝑡 sensor at 6 s. for 20 V offset fault injection in vcat sensor at 6 s.

Based on the residual obtained during fault injection in steady state, and the likelihood ratio calculation, it is possible to estimate the fault severity. Thus, in Table 3, the likelihood ratio obtained for different offset fault injection in vbus is presented. The likelihood ratio has been calculated offline, and for a 0.5 s time interval in steady state. The likelihood ratio is represented as s, being the subscript the fault free reference, and the superscript the different faulty cases. A negative likelihood ratio indicates that the fault free case is more probable, whereas a positive value indicates that the faulty case is more probable. The higher the value is, the more probable is the case. Table 3. Likelihood ratio calculation for 10 V and 20 V offset fault in different scenarios. fault 10 V

fault 20 V

vbus Measured Scenario

sfault free

sfault free

Fault-free Offset fault 10 V Offset fault 15 V Offset fault 20 V

−45.73 50.57 100.33 154.13

−191.23 1.41 100.98 208.66

Similar to the DC-link voltage sensor, a second Luenberger observer h i can be proposed for icat T sensor fault detection, as shown in (6), being C2 = [0 1], x = icat vbus and y2 = vbus . .

xˆ (t) = Axˆ (t) + Bu(t) + L(y2 (t) − C2 xˆ (t)) yˆ (t) = Cxˆ (t).

(6)

The observer model is presented in Figure 10. In this case, only the residual due to the difference between estimated and measured vbus is used for the feedback, so the iˆcat estimation does not depend vbus is used for FDI in current sensor i , as shows on the icat sensor measurement. The residual ricat cat Figure 11. vbus arises under v Although, a transient in iˆcat and ricat bus sensor fault, as it is shown in Figure 12, this residual sensitivity is low to vbus sensor faults in steady state. On the other hand, a ripple arises in the residual when a motor phase current sensor fault occurs, shown in Figure 12, so it can be used as additional information for phase current sensors FDI, which will be analysed in the following section. vbus , and it is easily isolated as it only occurs during braking. A fault in icrw sensor, is detected in ricat In conclusion, if no fault is detected in this residual during traction, but a fault is detected during braking, there is a fault in icrw sensor.

𝑥̂̇ (𝑡) = 𝑨𝑥̂(𝑡) + 𝑩𝑢(𝑡) + 𝑳(𝑦2 (𝑡) − 𝑪𝟐 𝑥̂(𝑡)) (6) (6) 𝑦̂(𝑡) = 𝑪𝑥̂(𝑡). 𝑦̂(𝑡) = 𝑪𝑥̂(𝑡). The observer model is presented in Figure 10. In this case, only the residual due to the difference The observer model is presented in Figure 10. In this case, only the residual due to the difference between estimated and measured 𝑣𝑏𝑢𝑠 is used for the feedback, so the 𝑖̂𝑐𝑎𝑡 estimation does not between estimated and measured 𝑣𝑏𝑢𝑠 is used for the𝑣𝑏𝑢𝑠 feedback, so the 𝑖̂𝑐𝑎𝑡 estimation does not depend on 18, the1543 𝑖𝑐𝑎𝑡 sensor measurement. The residual 𝑟𝑖𝑐𝑎𝑡 is used for FDI in current sensor 𝑖𝑐𝑎𝑡 , as Sensors 2018, 11 of 20 𝑣𝑏𝑢𝑠 depend on the 𝑖𝑐𝑎𝑡 sensor measurement. The residual 𝑟𝑖𝑐𝑎𝑡 is used for FDI in current sensor 𝑖𝑐𝑎𝑡 , as shows Figure 11. shows Figure 11. L L

iu,iv viucat ,iv ivcrw cat icrw

+ + + ++

B B

+

∫∫

icat vibus cat vbus

icat i

C C

+ ++

+

cat vbus icat - + ricat vbus + ricat i cat

vbus vbus -

+ v+

vbus rvbus vbus rvbus

bus

vbus

A A D D

Figure 10. Diagnostic observer for catenary current sensor FDI. Figure 10. Diagnostic observer observer for for catenary catenary current Figure 10. Diagnostic current sensor sensor FDI. FDI.

(a) (a)

(b) (b)

𝑣𝑏𝑢𝑠 Figure 11. (a) Catenary current for 20 A offset fault injection in 𝑖𝑐𝑎𝑡 at 6 s; (b) |𝑟𝑖𝑐𝑎𝑡 | filtered from 𝑣𝑏𝑢𝑠 | filtered from Figure 11. (a) Catenary current for 20 A offset fault injection in 𝑖𝑐𝑎𝑡 at 6 s; (b) |𝑟 vbus filtered from difference measured andfor estimated 𝑖𝑐𝑎𝑡 .fault injection in icat at 6 s; (b) r𝑖𝑐𝑎𝑡 Figure 11.between (a) Catenary current 20 A offset icat difference between measured and estimated 𝑖𝑐𝑎𝑡 . difference between measured and estimated icat . 𝑣𝑏𝑢𝑠 Although, a transient in 𝑖̂𝑐𝑎𝑡 and 𝑟𝑖𝑐𝑎𝑡 arises under 𝑣𝑏𝑢𝑠 sensor fault, as it is shown in Figure SensorsAlthough, 2018, 18, x FOR PEER REVIEW 11 of 19 𝑣𝑏𝑢𝑠 a transient in 𝑖̂𝑐𝑎𝑡 and 𝑟𝑖𝑐𝑎𝑡 arises under 𝑣𝑏𝑢𝑠 sensor fault, as it is shown in Figure

12, this residual sensitivity is low to 𝑣𝑏𝑢𝑠 sensor faults in steady state. On the other hand, a ripple 12, this residual sensitivity is low to 𝑣𝑏𝑢𝑠 sensor faults in steady state. On the other hand, a ripple arises in the residual when a motor phase current sensor fault occurs, shown in Figure 12, so it can arises in the residual when a motor phase current sensor fault occurs, shown in Figure 12, so it can be used as additional information for phase current sensors FDI, which will be analysed in the be used as additional information for phase current sensors FDI, which will be analysed in the 𝑣𝑏𝑢𝑠 following section. A fault in 𝑖𝑐𝑟𝑤 sensor, is detected in 𝑟𝑖𝑐𝑎𝑡 , and it is easily isolated as it only occurs 𝑣𝑏𝑢𝑠 following section. A fault in 𝑖 sensor, is detected in 𝑟 , and it is easily isolated as it only occurs during braking. In conclusion,𝑐𝑟𝑤if no fault is detected in 𝑖𝑐𝑎𝑡 this residual during traction, but a fault is during braking. In conclusion, if no fault is detected in this residual during traction, but a fault is detected during braking, there is a fault in 𝑖𝑐𝑟𝑤 sensor. detected during braking, there is a fault in 𝑖𝑐𝑟𝑤 sensor.

(a)

(b)

|𝑟 𝑣𝑏𝑢𝑠 | filtered 𝑣𝑏𝑢𝑠 Figure 12. (a) |𝑟vbus vbus𝑖𝑐𝑎𝑡 𝑖𝑐𝑎𝑡 | filtered for 20 V offset fault injection in 𝑣𝑏𝑢𝑠 sensor at 6 s; (b) Figure 12. (a) ricat filtered for 20 V offset fault injection in vbus sensor at 6 s; (b) ricat filtered for for 20 A offset fault injection in 𝑖𝑢 at 6 s. 20 A offset fault injection in iu at 6 s.

5. FDI Approach for Phase Current Sensors 5. FDI Approach for Phase Current Sensors With regard to phase current sensor FDI in electric drives, in [39] a bank of observers is proposed. With regard to phase current sensor FDI in electric drives, in [39] a bank of observers is proposed. Each observer has just one of the phase current sensors as input, so based on the estimation, it is Each observer has just one of the phase current sensors as input, so based on the estimation, it is possible the detection and isolation of faulty sensor. In contrast to this application, the system under possible the detection and isolation of faulty sensor. In contrast to this application, the system under study in this article uses only two phase current sensors, and the third current is calculated from the study in this article uses only two phase current sensors, and the third current is calculated from other two. Another bank of observers is proposed in [40] for a Double Fed Induction generator, the other two. Another bank of observers is proposed in [40] for a Double Fed Induction generator, normally used in wind turbines. In this case, only two phase currents are measured, but rotor current normally used in wind turbines. In this case, only two phase currents are measured, but rotor current measurements are needed for stator current estimations, and stator current measurements for rotor measurements are needed for stator current estimations, and stator current measurements for rotor current estimations. current estimations. On the other hand, in [40] a FDI approach based on the analysis of the probability density On the other hand, in [40] a FDI approach based on the analysis of the probability density functions (pdf) of the sensor current signal is proposed. A phase current sensor fault generates a functions (pdf) of the sensor current signal is proposed. A phase current sensor fault generates a change in the pdf of 𝑖𝑑 current, obtained from the application of the Park transformation. change in the pdf of id current, obtained from the application of the Park transformation. Finally, in [30,41] a compensation of the phase current sensor fault effect is proposed. Based on the frequency of the oscillations generated due to the sensor fault, it is possible to distinguish offset and gain faults. These approaches do not allow the fault isolation, but there are not dependent on motor model. Based on the actual traction drive configuration, where only two phase current sensor are available and there is not any phase voltage sensor, the approach selected in this work was the

normally used in wind turbines. In this case, only two phase currents are measured, but rotor current measurements are needed for stator current estimations, and stator current measurements for rotor current estimations. On the other hand, in [40] a FDI approach based on the analysis of the probability density Sensors 2018, 18, 1543of the sensor current signal is proposed. A phase current sensor fault generates 12 of 20a functions (pdf) change in the pdf of 𝑖𝑑 current, obtained from the application of the Park transformation. Finally,in in[30,41] [30,41]aacompensation compensationof ofthe thephase phasecurrent currentsensor sensorfault faulteffect effectisisproposed. proposed.Based Based on on Finally, the frequency of the oscillations generated due to the sensor fault, it is possible to distinguish offset the frequency of the oscillations generated due to the sensor fault, it is possible to distinguish offset and gain gain faults. faults. These These approaches approaches do do not not allow allow the the fault fault isolation, isolation, but but there there are are not not dependent dependent on on and motor model. motor model. Basedon onthe the actual traction drive configuration, only twocurrent phase sensor current are Based actual traction drive configuration, wherewhere only two phase aresensor available available and is notvoltage any phase voltage sensor, the approach in this work was the and there is notthere any phase sensor, the approach selected in thisselected work was the analysis of the analysis of the oscillations in the current components 𝑖 and 𝑖 , generated by offset and gain faults. 𝑑 by offset 𝑞 oscillations in the current components id and iq , generated and gain faults. This approach is This approach is simple compared to other strategies, which are dependent on the model the motor simple compared to other strategies, which are dependent on the model of the motor andofparameter and parameter variability. Moreover, 𝑖 and 𝑖 are already calculated for the control strategy the 𝑑 𝑞 variability. Moreover, id and iq are already calculated for the control strategy of the traction motor.ofThe traction motor. The only shortcoming is that it is not possible to isolate the faulty phase current only shortcoming is that it is not possible to isolate the faulty phase current sensor, and both sensors sensor,be and both sensors should be checked to complete diagnosis. should checked to complete diagnosis. The residual generation process divided into three different steps, is shown in Figure 13. The residual generation process is is divided into three different steps, as itas is it shown in Figure 13. The The first step consists in eliminating the average value of the current components 𝑖 and 𝑖 . An 𝑞 first step consists in eliminating the average value of the current components id and iq . An𝑑 Exponential Exponential Smoother filter (ES) is used for this task [42]. The filter discrete transfer function is given Smoother filter (ES) is used for this task [42]. The filter discrete transfer function is given by (7), being 1 − 𝑏 . Itfilter is a with recursive filter withponderation, an exponential ponderation, decreasing the aby = (7), 1 − being b. It is 𝑎a = recursive an exponential decreasing the influence of past influence pastgoes samples samples asoftime by. as time goes by. b𝑏 H𝐻(𝑧) . (7) (z) == (7) −1 ∙ 11− − az 𝑎𝑧 −1 fs 2fs

[ids,iqs]

-

Step 1: Mean value

+

[rids-fs,riqs-fs] [rids-2fs,riqs-2fs]

[Δids-fs,Δiqs-fs] [Δids-2fs,Δiqs-2fs] Step 2: Harmonic extraction

Step 3: Envelope

Figure andiq𝑖𝑞components componentsfiltering filtering residual generation. Figure13. 13. Current Current 𝑖i𝑑d and forfor residual generation.

The second step is based on two passband filters [42], centered in f s and 2 f s , being f s the fundamental frequency of motor stator current, which is obtained from flux and torque estimation. From previous analysis [30], it is known that offset deviations produce an additional oscillation in the current components id and iq , at f s . Gain deviations generate the oscillation at 2 f s . Due to the oscillation generated, the first one allows to detect offset faults, whereas the second one detects gain faults. The discrete transfer function of the passband filter is given by (8), being w0 and b, parameters to calculate in function of bandpass and sample frequency. Finally, the oscillation envelope is obtained in step 3.
(1 − b ) 1 − z −2 H (z) = . (8) 1 − 2bcos(w0 )z−1 + (2b − 1)z−2 The residuals generated for different motor phase current sensor fault modes injection are shown next, being the references for torque and speed 600 Nm and 600 rpm, respectively. In Figure 14, the residuals based on a passband filter centered in f s , and 2 f s for offset fault in sensor iu are presented. The residual based on a filter centered in f s , is able to detect injected offset faults, whereas the residual based on 2 f s is not sensitive. As it is shown in Figure 15, the residual based on a passband filter centered in 2 f s , is able to detect gain faults in iu sensor, whereas the one based on a filter centred in f s , is not sensitive. The fault severity estimation should be done as it was explained in previous sections, using information obtained from FMEA analysis and statistical tools.

The residuals generated for different motor phase current sensor fault modes injection are shown next, being the references for torque and speed 600 Nm and 600 rpm, respectively. In Figure 14, the next, being the references for torque and speed 600 Nm and 600 rpm, respectively. In Figure 14, the residuals based on a passband filter centered in 𝑓𝑠 , and 2𝑓𝑠 for offset fault in sensor 𝑖𝑢 are residuals based on a passband filter centered in 𝑓𝑠 , and 2𝑓𝑠 for offset fault in sensor 𝑖𝑢 are presented. The residual based on a filter centered in 𝑓𝑠 , is able to detect injected offset faults, whereas presented. The residual based on a filter centered in 𝑓𝑠 , is able to detect injected offset faults, whereas the residual based on 2𝑓𝑠 is not sensitive. As it is shown in Figure 15, the residual based on a the residual based on 2𝑓𝑠 is not sensitive. As it is shown in Figure 15, the residual based on a passband centered in 2𝑓𝑠 , is able to detect gain faults in 𝑖𝑢 sensor, whereas the one based a Sensors 2018,filter 18, 1543 13on of 20 passband filter centered in 2𝑓𝑠 , is able to detect gain faults in 𝑖𝑢 sensor, whereas the one based on a filter centred in 𝑓𝑠 , is not sensitive. filter centred in 𝑓𝑠 , is not sensitive.

(a) (a)

(b) (b)

Figure 14. (a) Residual generated for offset faults injected in sensor 𝑖𝑢 and filtering frequency 𝑓𝑠 ; (b) Figure 14. 14. (a) (a)Residual Residualgenerated generated offset faults injected in sensor iu and filtering frequency fs ; Figure forfor offset faults injected in sensor 𝑖 and filtering frequency 𝑓𝑠 ; (b) Residual generated for offset faults injected in sensor 𝑖𝑢 and filtering𝑢 frequency 2𝑓𝑠 . (b) Residual generated for offset faults injected in sensor i and filtering frequency 2 f . u Residual generated for offset faults injected in sensor 𝑖𝑢 and filtering frequency 2𝑓𝑠 . s

(a) (a)

(b) (b)

Figure 15. (a) Residual generated for gain faults injected in sensor 𝑖𝑢 and filtering frequency 𝑓𝑠 ; (b) Figure 15. (a) Residual generated for gain faults injected in sensor 𝑖𝑢 and filtering frequency 𝑓𝑠 ; (b) Residual for gain faults injected in faults sensor injected 𝑖𝑢 and filtering frequency 2𝑓𝑠 . Figure 15.generated (a) Residual generated for gain in sensor iu and filtering frequency f s ; Residual generated for gain faults injected in sensor 𝑖𝑢 and filtering frequency 2𝑓𝑠 . (b) Residual generated for gain faults injected in sensor iu and filtering frequency 2 f s .

The fault severity estimation should be done as it was explained in previous sections, using The fault severity estimation should be done as it was explained in previous sections, using information obtained from FMEA analysis and statistical tools. 6. FDI for Speed Sensor information obtained from FMEA analysis and statistical tools. Analytical redundancy for speed sensor diagnosis, based on observers, has been previously used 6. FDI for Speed Sensor 6. for Speed Sensor in FDI railway applications [31], but normally hardware redundancy for speed sensors is already available Analytical redundancy for speed sensor diagnosis, based on observers, has been previously used in distributed systems. Thus, sensor based diagnosis, on the twobased speedon sensor measurements available in the Analyticaltraction redundancy for speed observers, has been previously used in railway applications [31], but normally hardware redundancy for speed sensors is already presented traction drive, and the average train speed calculated from different axes, a FDI algorithm in railway applications [31], but normally hardware redundancy for speed sensors is already available in distributed traction systems. Thus, based on the two speed sensor measurements was proposed. available in distributed traction systems. Thus, based on the two speed sensor measurements available in the presented traction drive, and the average train speed calculated from different axes, The FDI structure is shown in drive, Figureand 16. the The sensor fault and isolation based on the available in the presented traction average traindetection speed calculated from is different axes, a FDI algorithm was proposed. difference among three linear speeds, two calculated form the encoders and the third one calculated a FDI algorithm was proposed. The FDI structure is shown in Figure 16. The sensor units. fault detection and isolationresiduals is based (9) on the as anThe average linear speed of all in theFigure distributed Thus, three are FDI structure is shown 16. Thetraction sensor fault detection anddifferent isolation is based on the difference among three linear speeds, two calculated form the encoders and the third one calculated proposed. of the residuals overpasses the threshold during an amount successive samples, difference Once, amongany three linear speeds, two calculated form the encoders and theofthird one calculated the corresponding logic indicator f is activated:

r12 = |v1 − v2 | r1 = |vtrain − v1 |

(9)

r2 = |vtrain − v2 |. Depending on the combination of indicators, the faulty sensor is isolated. A relevant vtrain measurement deviation is not probable, as it depends on multiple sensor measurements, gathered from a variety of traction units. Anyway, if f 1 and f 2 indicators are given, it is recommendable to check the encoder sensors of another traction drive, in order to discard a multiple speed sensor fault (both encoders of one traction drive) at the same time. In Table 4, the combination of indicators for speed sensor isolation is shown.

2 𝑡𝑟𝑎𝑖𝑛 2 proposed. Once, any of the residuals overpasses the threshold during an amount of successive samples, the corresponding logic indicator 𝑓 is activated:

𝑟12 = |𝑣1 Residual − 𝑣2 | evaluation

Residual generation ωm1

ωm2

𝑟1 = |𝑣𝑡𝑟𝑎𝑖𝑛r1− 𝑣1 |

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𝑟2 = |𝑣𝑡𝑟𝑎𝑖𝑛 − 𝑣2 |. v2

Conversion Residual generation

vtrain ωm1

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Fault detection Residual evaluation r r112

r2 Residual Fault Figure 16. FDI for speed sensor. generation detection

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f f112

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Fault isolation

Depending on the combination of indicators, rthe faulty sensor is fisolated. A relevant 𝑣𝑡𝑟𝑎𝑖𝑛 12 12 vtrain measurement deviation is not probable, as it depends on multiple sensor measurements, gathered from a variety of traction units. Anyway, if 𝑓1 and 𝑓2 indicators are given, it is recommendable to check the encoder sensors of another tractionFDI drive, speed in order to discard a multiple speed sensor fault Figure Figure 16. 16. FDIfor for speedsensor. sensor. (both encoders of one traction drive) at the same time. In Table 4, the combination of indicators for speed sensor isolation shown. Depending on theiscombination of indicators, the faulty sensor is isolated. A relevant 𝑣𝑡𝑟𝑎𝑖𝑛 measurement deviation probable, ofasindicators it depends on multiple sensor measurements, gathered Tableis4.not Combination for speed sensor fault isolation. Table 4. Combination of if indicators sensorare fault isolation. from a variety of traction units. Anyway, 𝑓1 and for 𝑓2 speed indicators given, it is recommendable to check theFlag encoder sensors ofinanother traction drive, in orderw𝒘 to discard multiple sensor fault Flag Fault Sensor wm1 Fault Fault Sensor Faultain Sensor vspeed m2 train𝒗𝒕𝒓𝒂𝒊𝒏 Fault in Sensor 𝒘𝒎𝟏 ininSensor 𝒎𝟐 Fault in Sensor (both encoders of one traction drive) at the same time. In Table 4, the combination of indicators for f1 1 1 1 𝑓1 1 00 speed sensor is shown. f2 0 1 1 𝑓 isolation 0 11 2

𝑓12

f 12

1 1 0 1 1 0 Table 4. Combination of indicators for speed sensor fault isolation.

7. Hardware-in-the-Loop Validation Validation for FDI 7. Hardware-in-the-Loop FDI Approaches Approaches Flag Fault in Sensor 𝒘𝒎𝟏for Fault in Sensor 𝒘𝒎𝟐 Fault in Sensor 𝒗𝒕𝒓𝒂𝒊𝒏 The HIL platform used used for validation validation is is composed composed of aa Real Real Time Time Simulator, Simulator, from OPAL-RT OPAL-RT 𝑓1 platform 1 for 0 1 The HIL of from Company, and a commercial Traction Control Unit, develop by CAF Power & Automation, for aa 𝑓 0 1 1 Company,2and a commercial Traction Control Unit, develop by CAF Power & Automation, for Railway application, as it is shown in Figure 17. 𝑓 1 0 12 Railway application, as it is1 shown in Figure 17. 7. Hardware-in-the-Loop Validation for FDI Approaches The HIL platform used for validation is composed of a Real Time Simulator, from OPAL-RT Company, and a commercial Traction Control Unit, develop by CAF Power & Automation, for a SUPERVISION COMPUTER Railway application, as it is shown in Figure 17.

CONDITIONING MODULES

REAL TIME SIMULATOR

SUPERVISION COMPUTER

RB 750 Vdc

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icrw

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MODEL OF THE PLANT REAL TIME SIMULATOR

CONDITIONING MODULES

EMBEDDED CODE

Figure 17. Hardware-in-the-loop platform. Figure 17. Hardware-in-the-loop platform.

RB 750 Vdc

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The TCU is externally connected to the Real Time Simulator through analog and digital ports. Conditioning modulesMODEL to adapt the inputs and outputs OF THE PLANT CONTROLbetween & DIAGNOSIS TCU and Real Time Simulator are needed. This platform allows injecting faults, easily and quickly, in order to test the different Figure 17. Hardware-in-the-loop platform. FDI approaches. The simulation step for model running in the Real Time Simulator is 15 µs. The TCU has a DSP for high speed execution. The sensor measurements are captured and monitored every 120 µs for validation purposes. Input filter

Inverter

7.1. FDI Validation for DC-Link Voltage and Catenary Current Sensors The Hardware-in-the-loop simulation results for DC-link voltage and catenary current sensors are shown in Figure 18. First, the residuals for normal operation are shown. The 𝓛∞ norm (10) is Sensors 1543 15 of of 20 chosen2018, for18, threshold setting, so residual thresholds should be higher than the maximum value 𝑣𝑏𝑢𝑠 residual during normal operation. Then, the residuals 𝑟𝑖𝑐𝑎𝑡 for FDI in catenary current sensor and 𝑖𝑐𝑎𝑡 𝑟 for FDI in DC-link voltage sensor are validated. 𝑣𝑏𝑢𝑠 7.1. FDI Validation for DC-Link Voltage and Catenary Current Sensors ‖𝑢‖results |𝒖(𝑘)|, 𝑠𝑢𝑝 ∞,𝑠 = for (10) The Hardware-in-the-loop simulation DC-link voltage and catenary current sensors are 𝑖∈[𝑘,𝑘+𝑠] shown in Figure 18. First, the residuals for normal operation are shown. The ∞ norm (10) is chosen If the diagnostic dynamic is fastshould enough, transients aremaximum appreciated in the residual for threshold setting, observer so residual thresholds beonly higher than the value of residual 𝑣𝑏𝑢𝑠 𝑖𝑐𝑎𝑡 𝑟𝑣𝑏𝑢𝑠 and 𝑟𝑖𝑐𝑎𝑡 operation. . If slowerThen, dynamic is chosen, in order the robustness vbus icat for FDI during normal the residuals ricat for FDItoinincrease catenary current sensor to andmeasurement rvbus 𝑣𝑏𝑢𝑠 𝑣𝑏𝑢𝑠 noises, steady state error appears in 𝑟 , so the threshold 𝑟 should be increased to avoid false 𝑣𝑏𝑢𝑠 𝑖𝑐𝑎𝑡 in DC-link voltage sensor are validated. detections. Finally, it has to be taken into account that a phase current fault injection generates an 𝑣𝑏𝑢𝑠 oscillation in the catenary current andkuink the=residual for sup |u𝑟𝑖𝑐𝑎𝑡 (k)|,, which can generate a false alarm(10) ∞,s ∈[k,k+s] sensors should be checked too, before taking catenary current sensor FDI, so the FDI for phase icurrent decision. A low pass filter can be implemented too, in order to eliminate the oscillation in the residual.

(a)

(b)

(c)

(d)

(e)

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𝑖𝑐𝑎𝑡 Figure 18. (a) Measured, and estimated 𝑣𝑏𝑢𝑠 and |𝑟icat 𝑣𝑏𝑢𝑠 | for fault-free operation; (b) Measured, and Figure 18. (a) Measured, 𝑣𝑏𝑢𝑠 and estimated v bus and r vbus for fault-free operation; (b) Measured, 𝑖𝑐𝑎𝑡 and estimated 𝑖𝑐𝑎𝑡 and |𝑟𝑖𝑐𝑎𝑡 |𝑟 | for | for fault-free operation; (c) Measured, and estimated 𝑣𝑏𝑢𝑠 and 𝑣𝑏𝑢𝑠 vbus icat for fault 𝑣𝑏𝑢𝑠 v estimated icat and operation; Measured, estimated and rvbus ricatsensor; for fault-free in 𝑖𝑐𝑎𝑡 fault injected in 𝑣𝑏𝑢𝑠 (d) Measured, and(c) estimated 𝑖𝑐𝑎𝑡and and |𝑟𝑖𝑐𝑎𝑡 | for busfault-injected 𝑣𝑏𝑢𝑠 vbus sensor; (e) |𝑟𝑖𝑐𝑎𝑡 | ifor fault-injection in 𝑖𝑢 phase current injected in Measured, vbus sensor;and (d) estimated Measured,𝑖𝑐𝑎𝑡 andand estimated in icat sensor; sensor; cat and ricat for fault-injected vbus (e) Measured, and estimated icat and ricat for fault-injection in iu phase current sensor; (f) Oscillation vbus generated in catenary current and ricat due to fault-injection in iu phase current sensor.

If the diagnostic observer dynamic is fast enough, only transients are appreciated in the residual icat . If slower dynamic is chosen, in order to increase the robustness to measurement noises, and ricat vbus , so the threshold r vbus should be increased to avoid false detections. steady state error appears in rvbus icat Finally, it has to be taken into account that a phase current fault injection generates an oscillation in the vbus , which can generate a false alarm for catenary current sensor catenary current and in the residual ricat FDI, so the FDI for phase current sensors should be checked too, before taking decision. A low pass filter can be implemented too, in order to eliminate the oscillation in the residual. vbus rvbus

𝑣𝑏𝑢𝑠 (f) Oscillation generated in catenary current and |𝑟𝑖𝑐𝑎𝑡 | due to fault-injection in 𝑖𝑢 phase current sensor.

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7.2. FDI Validation for Phase Current Sensors

𝑣𝑏𝑢𝑠 Oscillation generated in implemented catenary currentinand | due fault-injection in 𝑖𝑢HIL phase current The FDI approach was the|𝑟𝑖𝑐𝑎𝑡 TCU andtovalidated in the platform. The Sensors(f) 2018, 18, 1543 16 of 20

sensor.results are obtained for a torque reference of 600 Nm and motor speed of 600 rpm. The following average value of the envelope depends on the operating point, so for a severity estimation of the fault, 7.2. FDI FDI Validation Validation for for Phase Phase Current Current Sensors 7.2. Sensorsaverage value and the fault injected for different operating a previous relation between the envelope points should be obtained inimplemented HIL simulation. Thus, adaptive threshold based on 𝑖𝑑,𝑞platform. components, The FDI was in the TCU and validated in the HIL platform. The following The FDIapproach approach was implemented in the an TCU and validated in the HIL The motor torque and speed are needed to estimated fault severity. In the case of fixed threshold, the results are obtained for a torque reference of 600 Nm and motor speed of 600 rpm. The average value following results are obtained for a torque reference of 600 Nm and motor speed of 600 rpm. The sensibility of the FDI approach will be different depending on the operating point. For example, for of the envelope on the operating point, so for point, a severity estimation the fault,of a previous average value ofdepends the envelope depends on the operating so for a severityof estimation the fault, a previous torquebetween reference ofenvelope 600 Nm, aenvelope threshold of 20the A willand detect +50% gain operating deviation, whereas the thebetween average value and fault injected for different points should arelation relation the average value the afault injected for different operating threshold needs to be decrease to 16 A, to detect the same fault for a torque reference of 200 Nm. be obtained in HIL simulation. Thus, an adaptive threshold based on i components, motor torque points should be obtained in HIL simulation. Thus, an adaptive threshold d,q based on 𝑖𝑑,𝑞 components, Intorque Figure 19 the results deviations injected,Infault asthe filtering presented, oscillations inthe (a) and speed are and needed to estimated fault severity. case ofsteps fixed threshold, sensibility of the motor speed areof needed to estimated severity. In are the case of the fixed threshold, and envelopes in (b). Different offset faults are injected into the 𝑖 sensor current. The current FDI approach will be different depending on the operating point. For example, for a torque reference 𝑢 sensibility of the FDI approach will be different depending on the operating point. For example, for component theAoscillation due ato+50% the offset fault injectedwhereas are shown. 600 Nm, aaverage threshold of 20 will detectfiltered, a of +50% gain whereas the threshold needs tothe be aof torque reference ofvalue, 600 Nm, a threshold 20 generated A willdeviation, detect gain deviation, The 𝑓𝑠 centred extracts the oscillation to same an offset Moreover, the envelope of the decrease toneeds 16 A,filter detect the same fault adue torque reference of Nm. reference threshold totobe decrease to 16 A, tofor detect the fault fault. for200 a torque of 200 Nm. oscillation, which will be used as residual to compare to the threshold, is shown. In Figure 19 the results of deviations injected, as filtering steps are presented, oscillations in (a) In Figure 19 the results of deviations injected, as filtering steps are presented, oscillations inand (a) envelopes in (b).inDifferent offset faults injected into the iinto The currentThe component u sensor and envelopes (b). Different offsetare faults are injected the current. 𝑖𝑢 sensor current. current average value, the oscillation filtered, generated due to thedue offset fault injected are shown. The f s component average value, the oscillation filtered, generated to the offset fault injected are shown. centred filter extracts the oscillation due to an offset fault. Moreover, the envelope of the oscillation, The 𝑓𝑠 centred filter extracts the oscillation due to an offset fault. Moreover, the envelope of the which will be usedwill as residual to compare the threshold, shown. is shown. oscillation, which be used to as compare residual to to theisthreshold,

(a)

(b)

Figure 19. Residual generation for a +20 A, +50 A, and +100 A offset faults injected in phase current sensor, oscillation in (a) and envelope in (b).

(a) (b) in 𝑖𝑢 sensor current are In Figure 20, the different filtering steps for a gain fault injected presented, oscillation in (a) and envelope in (b). In this case, the oscillation is extracted by the 2𝑓𝑠 Figure 19. Residual generation for a +20 A, +50 A, and +100 A offset faults injected in phase current Figure 19. Residual generation for a +20 A, +50 A, and +100 A offset faults injected in phase current centred filter. sensor, oscillation in (a) and envelope in (b). sensor, oscillation of in (a) envelope in (b). The sensibility theand FDI approach is better for low speeds, being higher in 𝑖𝑞 than in 𝑖𝑑 current component. On the other hand, 𝑖 is more to torque changes, the filtering of this In Figure 20, the different filtering𝑞 steps forsensitive a gain fault injected in 𝑖𝑢sosensor current are In Figure 20, the different filtering steps for a gain fault injected in i sensor current are presented, u componentoscillation can be more complicated. The in FDI is able differentiate between by offset presented, in (a) and envelope (b).approach In this case, thetooscillation is extracted the and 2𝑓𝑠 oscillation in (a) and envelope in (b). In this case, the oscillation is extracted by the 2 f centred filter. s gain fault modes, but it is not possible to isolate between faults in one phase or the other. centred filter. The sensibility of the FDI approach is better for low speeds, being higher in 𝑖𝑞 than in 𝑖𝑑 current component. On the other hand, 𝑖𝑞 is more sensitive to torque changes, so the filtering of this component can be more complicated. The FDI approach is able to differentiate between offset and gain fault modes, but it is not possible to isolate between faults in one phase or the other.

(a)

(b)

Figure 20. Residual generation for a 120% gain fault injected in phase current sensor, oscillation in (a) Figure 20. Residual generation for a 120% gain fault injected in phase current sensor, oscillation in (a) and envelope in (b). and envelope in (b).

(b) 7.3. FDI Validation for Speed (a) Sensors The sensibility of the FDI approach is better for low speeds, being higher in iq than in id current Figure 20. generation a 120% gain fault phase current in (a) component. OnResidual the other hand, iq for is more sensitive toinjected torque in changes, so the sensor, filteringoscillation of this component andmore envelope in (b). can be complicated. The FDI approach is able to differentiate between offset and gain fault modes, but it is not possible to isolate between faults in one phase or the other. 7.3. FDI Validation for Speed Sensors

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7.3. FDI Validation for Speed Sensors In Figure 21 the results for the FDI approach for speed sensors are shown. A gain fault In Figure to 21 an theincrease resultsoffor approach foran speed sensors fault corresponding 27 the rpmFDI is set at 59 s and increase of 54are rpmshown. at 66 s inA 𝑤gain 𝑚1 speed corresponding to an increase of 27 rpm is set at 59 s and an increase of 54 rpm at 66 s in w speed sensor. sensor. In both cases, the residuals 𝑟1 and 𝑟12 overpass the thresholds, so the flags m1 𝑓1 and 𝑓12 will In cases,Based the residuals r14,and r12 be overpass the thresholds, so is theinflags f 1 and willFDI be approach activated. be both activated. on Table it can concluded that the fault sensor 𝑤𝑚1 .f 12 This Based on Table 4, it can be concluded that the fault is in sensor w . This FDI approach just analyses m1 just analyses steady state residuals, whereas an anti-sliding algorithm processes transient differences steady state residuals, whereas an anti-sliding algorithm processes transient differences among speed among speed measurements. This kind of algorithms is commonly found in railway traction control measurements. This kind of algorithms is commonly found in railway traction control systems. systems.

Figure 21. 21. Speed and speed speed residuals. residuals. Figure Speed measurements measurements and

8. Discussion 8. Discussion In this article, different FDI approaches have been presented to build an Integral Sensor Fault In this article, different FDI approaches have been presented to build an Integral Sensor Fault Detection and Isolation for a Railway traction drive. Furthermore, a proposal for the fault severity Detection and Isolation for a Railway traction drive. Furthermore, a proposal for the fault severity estimation has been presented too. An observer based FDI approach has been used for DC-link estimation has been presented too. An observer based FDI approach has been used for DC-link voltage voltage and catenary current sensors, a signal analysis based FDI approach for phase current sensors and catenary current sensors, a signal analysis based FDI approach for phase current sensors and a and a hardware redundancy based FDI for speed sensors. Each approach has been justified as the hardware redundancy based FDI for speed sensors. Each approach has been justified as the most most suitable one for the traction drive presented. The FDI approach selection has been done based suitable one for the traction drive presented. The FDI approach selection has been done based on the on the following factors: algorithm complexity, hardware and software resources available in the following factors: algorithm complexity, hardware and software resources available in the traction traction drive, tuning difficulty due to parameter variation/uncertainties and reliability. The drive, tuning difficulty due to parameter variation/uncertainties and reliability. The observer-based observer-based FDI for DC-link voltage and catenary current sensor uses the input filter model FDI for DC-link voltage and catenary current sensor uses the input filter model instead of the motor instead of the motor model. As input filter model is simpler, the influence of parameter variations model. As input filter model is simpler, the influence of parameter variations and uncertainties and uncertainties is lower. Furthermore, a Luenberger observer is proposed, due to lower algorithm is lower. Furthermore, a Luenberger observer is proposed, due to lower algorithm complexity in complexity in comparison to other solutions. The signal analysis based FDI for phase current sensors comparison to other solutions. The signal analysis based FDI for phase current sensors need low need low computational resources, as some algorithms are already available in the control strategy. computational resources, as some algorithms are already available in the control strategy. Furthermore, Furthermore, as it is not based on a motor model, motor parameter estimation during operation is as it is not based on a motor model, motor parameter estimation during operation is not needed. not needed. Finally, a redundant hardware based FDI is proposed for speed sensor faults, due to Finally, a redundant hardware based FDI is proposed for speed sensor faults, due to reliability and low reliability and low computational cost. computational cost. Furthermore, the approaches developed in Matlab-Simulink have been simulated and Furthermore, the approaches developed in Matlab-Simulink have been simulated and implemented in a HIL platform with a real Railway TCU, designed for a tram. FDI approaches have implemented in a HIL platform with a real Railway TCU, designed for a tram. FDI approaches been implemented in the DSP of the TCU, being the execution period 20 µ s. have been implemented in the DSP of the TCU, being the execution period 20 µs. The presented fault severity calculation was not implemented in real time, in order to reduce the The presented fault severity calculation was not implemented in real time, in order to reduce the computational requirements for the DSP. The Integral Sensor Fault Detection and Isolation presented, computational requirements for the DSP. The Integral Sensor Fault Detection and Isolation presented, allows detecting and isolating faults in all the sensors presented in the traction drive. allows detecting and isolating faults in all the sensors presented in the traction drive. The FDI for the DC-link voltage and catenary current sensors is based on the input filter model of the traction drive, and it is not dependent on the motor model. The uncertainties and variability of parameters in the input filter are lower than in the motor model, which makes this solution easier to implement in a real application. Moreover, this FDI approach is not influenced by the operating point

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The FDI for the DC-link voltage and catenary current sensors is based on the input filter model of the traction drive, and it is not dependent on the motor model. The uncertainties and variability of parameters in the input filter are lower than in the motor model, which makes this solution easier to implement in a real application. Moreover, this FDI approach is not influenced by the operating point of the motor. The balance between the robustness and the sensitivity of the strategy is given by the observer feedback gain. Higher gains allow setting lower thresholds to increase the detection sensitivity, but this implies a lower robustness due to false alarms caused by measurement noises or other sensor faults. This work has set as a threshold of 20 A for current residual and 20 V for voltage residual, based on fault free behavior, so lower values should not be considered as a degraded zone. This FDI approach in combination with hardware redundancy, allows detecting and isolating faults in catenary current, crowbar current, return current, DC-link voltage and catenary voltage sensors. The fault severity estimation is calculated offline, based on previously obtained relations between the injected faults and generated residuals. Then a likelihood ratio is calculated with the residual values obtained in real time to estimate the most probable fault severity. The FDI strategy for phase current sensors is able to detect two fault modes, offset and gain. Its main limitation is that, it is not possible to isolate between the two available phase current sensors, so both should to be checked to isolate the faulty sensor. Phase current sensors faults generate an oscillation which depends on the operating point, so in case of fixed threshold, the sensitivity for the same threshold is different depending on the operating point. An adaptive threshold to maintain the same sensibility is recommended, based on current components, estimated torque and motor speed. Residual envelope and fault relation is obtained by fault injection. The oscillation extraction is subject to motor electrical frequency estimation and bandwidth around it. The extraction filter should be redesign in case of a change in the execution period. The FDI algorithm for speed sensors is the least demanding solution in terms of computational cost for traction drives where more than one speed measurement is available. The main contribution of this work is the definition of an Integral Sensor Fault Detection and Isolation for a Railway traction drive, in opposite to most of the research works, which focus on only one or two kind of sensors. Moreover, it has been validated in a real Railway traction control unit, whereas the previous works have been validated in test benches without commercial control units, in rapid control prototyping devices. Further research should be done with regard to fault severity estimation and fault reconstruction, in combination with information coming from other available tools in industry as FMEA. Fault injection and performance analysis under faults can provide information for an enhanced FMEA. This enhanced FMEA combines with FDI approaches, can provide reliable fault severity estimation. Furthermore, an adaptive threshold automation should be developed to optimize the sensibility of the detection and robustness for the different operating points of the motor. 9. Conclusions This article has presented an Integral Sensor Fault Detection and Isolation for a Railway traction drive. The research aim was to implement an early fault detection in sensors, which allows improving the availability of traction drives. Taking into account that the strategy has to be executed by an embedded commercial traction control unit, low computational cost FDI approaches have been selected, due to commercial traction control unit limitations. Moreover, the use of easy to tune FDI algorithms for each application is a key point to obtain a successful industrial acceptance. The FDI approaches presented here, as well as the proposed Integral Sensor Fault Detection and Isolation, can be adapted to electric drives in other applications. Author Contributions: F.G. and J.d.O. conceived and designed the experiments; F.G., P.M. and J.d.O. performed the experiments; J.P. and G.A. analysed the data; F.G. wrote the paper.

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Acknowledgments: This research work was supported by CAF Power & Automation. The authors are thankful to the colleagues from CAF Power & Automation, who provided material and expertise that greatly assisted the research. Conflicts of Interest: The authors declare no conflict of interest.

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