JSAE 20030248 SAE 2003-01-1853
Genetic Algorithms Optimization of Diesel Engine Emissions and Fuel Efficiency with Air Swirl, EGR, Injection Timing and Multiple Injections Hiro Hiroyasu and Haiyan Miao Kinki University
Tomo Hiroyasu, Mitunori Miki, Jiro Kamiura and Sinya Watanabe Doshisha University Copyright © 2003 Society of Automotive Engineers of Japan, Inc.
ABSTRACT The present study extends the recently developed HIDECS-GA computer code to optimize diesel engine emissions and fuel economy with the existing techniques, such as exhaust gas recirculation (EGR) and multiple injections. A computational model of diesel engines named HIDECS is incorporated with the genetic algorithm (GA) to solve multi-objective optimization problems related to engine design. The phenomenological model, HIDECS code is used for analyzing the emissions and performance of a diesel engine. An extended Genetic Algorithm called the ‘Neighborhood Cultivation Genetic Algorithm’ (NCGA) is used as an optimizer due to its ability to derive the solutions with high accuracy effectively. In this paper, the HIDECS-NCGA methodology is used to optimize engine emissions and economy, simultaneously. The multiple injection patterns are included, along with the start of injection timing, and EGR rate. It is found that the combination of HIDECS and NCGA is efficient and low in computational costs. The Pareto optimum solutions obtained from HIDECSNCGA are very useful to the engine designers. They show that it is possible to reduce emissions without increasing the fuel consumption by the optimization of exhaust gas recirculation (EGR) and multiple injections.
INTRODUCTION Diesel engines have considerable advantages in the aspect of engine power, fuel economy and durability. They are widely applied in vehicles from small to large. In order to meet increasing environmental concerns and more stringent emission regulations, currenttly researches are carried out aiming the reduction of soot
and nitric oxide (NOx) emissions simultaneously while maintaining reasonable fuel economy. The combustion in diesel engines can be improved by designing a good injection system to control characteristics of spray air entrainment. However, to carry out parameter studies for developing a good injection system through experiments, huge expenses and huge time are needed. For this reason, the optimization of parameters by the aid of computer simulation is very useful for design purposes. When the parameters are optimized by simulation, the minimization of fuel efficiency, the amounts of NOx, and soot becomes interesting to many engine designers [1, 2, 3]. Efforts were carried out to solve this optimization problem [4, 5, 6, 7]. However, in these studies, the optimization was treated as a single objective problem. In our current research, the parameter study to optimize the diesel engine design is treated as a Multi-objective Optimization Problem (MOP). To perform engine design optimization by simulation, an optimizer (which determines the next searching point) and an analyzer (which evaluates searching points) are needed. Several types of the models of diesel combustion exist [8] and can be used as an analyzer. Those models are roughly divided into three categories: thermodynamic models, phenomenological models and detailed multidimensional models. As the thermodynamic model only predicts the heat release rate and the calculation cost is considerably high to use detailed multi-dimensional models, the phenomenological model is chosen as an analyzer in this work. Many optimization algorithms are developed and implemented into several commercial code [9, 10]. The
Genetic Algorithm (GA) is an algorithm that simulates the heredity and evolution of creatures [11]. As a robust algorithm, it is capable to find an optimum solution even when the objective function has many local optimums. The GA is especially suitable for solving MOPs, since the GA is a multi-point search. Hence, we use GAs to minimize fuel efficiency, the amounts of NOx, and soot. In this paper, the phenomenological diesel engine model, the concept of MOPs and the GA method are illustrated briefly at first. Then, the optimization system is discussed. In this study, the target purpose functions are specific fuel consumption (SFC) and emissions (NOx and soot). The design variables are the shape of injection rate, the start of injection timing and EGR rate. The effectiveness of the GA for solving the engine design problems and the importance of the phenomenological model in GA optimization are clarified.
fuel mixes with fresh air and combustion products as the spray continues to burn. Ø No-Intermixing among the packages is assumed. Ø Spray tip penetration is defined by the experimental equations. Injected at the Start of Injection Package of Spray, P(L,M,N) N M
L Breakup Length Spray Tip Penetration
Figure 1: Schematic of the package distribution Air Entralnment
Expansion & Air Entralnment
SYSTEM DESCRIPTION Injection
PHENOMENOLOGICAL MODEL: HIDECS In the past 30 year, the most sophisticated phenomenological spray-combustion model, HIDECS has shown great potential as a predictive tool for both performance and emissions in a wide range of direct injection diesel engines. It was originally developed at the University of Hiroshima and was named ‘HIDECS’ recently. A detailed discussion of this model, and the examples of its successful applications were given in references [12-19]. Only a brief description of the model is provided in this article. In HIDECS, the spray injected into the combustion chamber from the injection nozzle is divided into many small packages of equal fuel mass as shown in Figure 1. No intermixing among the packages is assumed. The spray characteristics are defined by the empirical equations of spray penetration. For example, the shaded regions shown in Figure 1 are the fuel packages injected at the start of injection that constitute the spray tip during penetration. Air entrainment into a package is controlled by the conservation of momentum, that is, the amount of entrained air is proportional to the decrease in package velocity. The fuel, which is mixed with the air, begins to evaporate as drops, and ignition occurs after a ignitiondelay period. The air-fuel mixing processes within each package are illustrated in Figure 2. Each package, immediately after the injection, involves many fine drops and a small amount of air. As a package moves away from the nozzle, air entrains into the package and the fuel drops evaporate. Thus, the package consists of liquid drops, vaporized fuel, and air. After a short period of time after the start of injection, ignition occurs in the gaseous mixture, resulting in the rapid expansion of the package. Therefore, more fuel drops evaporate, and more fresh air entrains into the package. The vaporized
Fuel Evaporation & Mixing
Ignition & Evaporation Mixing & C o m b u stion Mixing & C o mbustion Combustion
Figure 2: Schematic of the mass system during combustion Figure 3 shows two possible combustion processes inside each package. The Case (A) is called evaporation-rate-controlled combustion, while Case (B) is called the entrainment-rate-controlled combustion. When ignition occurs, the combustion mixture that is prepared before ignition burns in a small increment of time. The fuel-burning rate in each package is calculated by assuming stoichiometric combustion. When there is enough air in the package to burn all of the vaporized fuel, there are combustion products, liquid fuel and fresh air remaining in the package after combustion. This process is shown in Figure 3 as Case (A). In the next small increment of time, more fuel drops evaporate and fresh air entrains into the package. At this point, if the amount of air in the package is enough to burn all the vaporized fuel under stoichiometric conditions, the same combustion process (Case A) is repeated. If the amount of air is not enough to burn all the vaporized fuel, however, the fuel-burning rate is dictated by the amount of air present. This process is shown in Figure 3 as Case (B). Therefore, the combustion processes in each package always precede under one of the conditions shown in Figure 3. The heat release rate in the combustion chamber is calculated by summing the heat releases of each package. The cylinder pressure and bulk-gas temperature in the cylinder are then calculated. Since the time history of temperature, vaporized fuel, air and combustion products in each package are known, the equilibrium concentrations of gas composition in each package can be calculated. The concentration of NOx is calculated by using the extended Zeldovich mechanism. The formation of soot is calculated by assuming first-order reaction of fuel vapor. The
oxidation of carbon is calculated by assuming secondorder reaction between carbon and oxygen. During the past 30 years, the code, HIDECS has been validated against wide ranges of engine rig experiments.
Pareto optimum solution is called a Pareto front. In MOPs, to find Pareto optimum solutions is one of the goals.
Pareto Optimum Solution Non Pareto Optimum Solution
Injection
: Liquid Fuel : Vaporized Fuel : Air
minimize
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Ignition
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Figure 4: The Pareto optimum solutions Figure 3: Schematic of the package combustion process MULTI-OBJECTIVE OPTIMIZATION PROBLEMS
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Problems to find design variables x that minimize or maximize k objective functions within m constraints are called Multi-objective Optimization Problems (MOPs). Usually, MOPs can be formulated as follows[20,21]:
r r r r r r r r min f ( x ) = ( f 1 ( x ), f 2 ( x ),..., f k ( x )) T
r r = {x ∈ R n g j ( x ) ≤ 0, ( j = 1,..., m )
(1)
Objective functions and constraints are consisting of design variables as follows,
r f i ( x ) = f i ( x1 , x 2 ,..., x n ), i = 1,..., k r g j ( x ) = g j ( x1 , x 2 ,..., x n ), j = 1,..., m
(2)
When the objective functions are in the trade-off relationship, it is difficult to minimize or maximize all objective functions at the same time. Therefore, the concept of the Pareto optimum Solution shall be introduced. It is defined as: For
r x0 ∈ R n ,
(a) If there is no solution dominates
r x ∈ R n that
r r x 0 , x 0 is a strong Pareto optimum
solution.
r x* ∈ R n that r r r satisfies f i ( x*) < f i ( x0 ) (∀ i = 1,..., k ) , x 0 is a (b) If there is no solution
weak Pareto optimum solution. Usually, there is not only one Pareto optimum solution but plural solutions in MOPs. In Figure 4, the concept of the Pareto optimum solutions is illustrated in the case of two objectives. In this figure, the line of the
GENETIC ALGORITHMS FOR MOPS The Genetic Algorithm (GA) is an algorithm that simulates creatures’ heredity and evolution [11]. Since the GA is one of the multi-point search methods, an optimum solution can be determined even when the landscape of the objective function is multi modal. Moreover, GAs can be applied to problems whose search space is discrete. Therefore, the GA is one among the very powerful optimization tools. In multiobjective optimizations, GAs can find a Pareto optimum set with one trial because the GA is a multi point search. As a result, the GA is a very effective tool especially in solving multi-objective optimization problems. In the GAs, a searching point is called an individual. Usually, an individual is expressed as a bit string. As shown in Figure 5, the basic procedure of the GAs for MOPs is as follows: If there are m individuals, there are m search points. These individuals are initialized at first. Then, the fitness value of each individual is determined. This operation is called ‘Evaluation’. In MOPs, the Pareto ranking is often used for determining the fitness value. After the evaluation operation, an individual is checked to remain for the next iteration. The individual with large evaluation value has a high possibility of remaining in the next iteration. This operation is called ‘Selection’. Usually, the roulette selection method is performed. If the terminal condition is not satisfied, new search points are required. To generate new search points, operations of ‘crossover’ and ‘mutation’ are carried out. Figure 6 and Figure 7 illustrate the concepts of crossover and mutation, respectively. In GA, the routine mentioned above is called a ‘Generation’. Usually, many generations are needed to find an optimum solution. There are many algorithms of the multi-objective GA [22, 23]. These algorithms are roughly divided into two
categories; those are the algorithms that treat the Pareto optimum solution implicitly or explicitly. Most of the latest methods treat the Pareto optimum solution explicitly. Typical algorithms are SPEA2 [24] and NSGA-II [25].
Initialization Evolution Derive the Pareto ranking Of each individual Pi. Derive the fitness value of Each individual Fi = 1/Pi
End
Mutation Figure 5: Flowchart of GA
Crossover Point 1
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Step 3: Generate new search population: Pt=At-1. Step 4: Sorting: Individuals of Pt are sorted according to the values of focused objective. The focused objective is changed at every generation. For example, when there are three objectives, the first objective is focused in this step in the first generation. The third objective is focused in the third generation. Then the first objective is focused again in the fourth generation. Step 5: Grouping: Pt is divided into groups which consist of two individuals. These two individuals are chosen from the top subsequently toward the bottom of the sorted individuals. Step 6: Crossover and Mutation: In a group, the crossover and mutation operations are performed. From two parent individuals, two child individuals are generated. Here, parent individuals are eliminated.
Terminal Check no yes Crossover
Step 2: Start new generation: Set t = t +1.
Step 7: Evaluation: All of the objectives of individuals are derived. According to the values of objectives, the Pareto ranking of each individual is decided. Using the Pareto ranking, the fitness value of each individual is decided. This operation is the same as step 2 in the former section. Step 8: Assembling: The all individuals are assembled into one group and this becomes new Pt.
Parent 1
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Step 9: Renewing archives: Assemble Pt and At-1. Then N individuals are chosen from 2 individuals. To reduce the number of individuals, the same operation of the SPEA2 (Environment Selection) is also performed.
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Step 10: Termination: Check the terminal condition. If it is satisfied, the simulation is terminated. If it is not satisfied, the simulation returns to Step 2.
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Figure 6: Crossover
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To demonstrate the searching ability of the NCGA, the NCGA is applied to the typical test function, KUR [27]. The results are compared with those of the typical GAs [28]. It was found that the NCGA derived better solutions than the other methods and the mechanism of the neighborhood crossover acts effectively to derive the solutions with high accuracy. SYSTEM DESIGN
Figure 7: Mutation In this paper, an extended GA called the Neighborhood Cultivation Genetic Algorithm (NCGA) is used. The NCGA was named because most of the genetic operations are performed in a group that consists of two individuals in this method. Its mechanism is beside that of SPEA2 and NSGA-II. The following steps show how NCGA works. (P t : search population at generation t, At : archive at generation t .) Step 1: Initialization: Generate an initial population P0.
The overview of the system is illustrated in Figure 8. In this system, the GA is used as an optimizer and the HIDECS is used as an analyzer. Between optimizer and analyzer, text files are exchanged. Basically, different types of the GAs and engine models can be used. In this study, a phenomenological model (HIDECS) and an extended GA called the Neighborhood Cultivation Genetic Algorithm (NCGA) was applied. The engine running with traditional diesel injection method is set as a baseline case for the GA optimization. The specification of the diesel engine is
summarized in Table 1. HIDECS code was evaluated by engine test results [19].
performed. Therefore, 20200 simulations of the HIDECS are performed. The average execution time of one trial of the HIDECS is 11.86 s. The total execution time is 11425 s and the total execution time for the GA operation is 525 s. Therefore, the parallel efficiency is more than 95 %. Table 2: PC Cluster specification CPU Memory Operating System Network Communication Library
Figure 8: System design Table 1: Engine specification Bore Stroke Compression Ratio Engine Speed Swirl Ratio Nozzle Hole Diameter Nozzle Hole Number Injected Fuel Mass Injection Timing Injection Duration
102 mm 105 mm 17 1800 rpm 1.0 0.2 mm 4 40.0 mg/st -5 deg. ATDC 18 deg.
To optimize the fuel consumption and emissions, the start time of diesel injection, the shape of the fuel injection, swirl ratio and EGR rate are chosen to be the design variables. In all the calculation, the total amount of fuel injection is kept as a constant. The objectives of this simulation are the amount of SFC, NOx and soot. The output, for the baseline case running with the traditional single injection is: 213.5 g/kWh of specific fuel consumption, 0.194 g/kWh of NOx emission and 0.413 g/kWh of soot emission. These values are used as baseline to compare with GA optimization results. In this simulation, the following NCGA parameters are used. The length of the chromosome is 8 bit per one design variable. The population size is 100 and the number of sub population is 10. The crossover rate and mutation rate are 1.0 and 1/96 respectively. At the same time, migration rate and migration interval are 0.4 and 10 respectively. COST OF CALCULATION This system runs on a PC cluster, summarized in Table 2. There are 32 CPUs in the PC cluster, 31 slaves and one master. HIDECS simulation is performed on each slave individually. The GA operations are performed on the master. For example, there are 100 individuals and 200 generations are
Pentium III (1 GHz) * 32 512 MB Linux 2.4.4 FastEthernet TCP/IP LAM
In this simulation, the NCGA needs a lot of iterations to find optimum solutions. However, because of the small calculation cost of the HIDECS, the Pareto optimum solutions are derived within three hours using the PC cluster. Compared to detailed multidimensional models, the phenomenological models have more advantageous, especially, when using genetic algorithms to solve MOPs, such as engine designs.
OPTIMIZATION RESULTS In this section, the derived Pareto optimum solutions are described first. Then characteristics of the derived shape of injection rate are discussed. The most important aspect of the multi-objective optimization problems is that the designers can find their design alternatives with the aid of optimizers. Hence, the optimization results are discussed from different aspects to illustrate how the designers find new design strategies from the derived Pareto optimization solutions. Some design alternatives are also discussed. PARETO-OPTIMUM SOLUTIONS The derived Pareto solutions from the HIDECS-NCGA system are plotted in Figure 9. It shows that all the plotted solutions are dominant and there are no nondominant solutions derived during the search. It would be very costly and time-consuming to perform all the engine tests to obtain the data shown in Figure 9. Hence, the computational test system described here shows great advantage. For better understanding of these solutions, the derived Pareto solutions are projected onto SFC-NOx, SFCSoot and NOx-Soot surface, respectively, as shown in Figure 10, 11 and 12. The trade-off relationships to reduce fuel consumption, NOx emission and soot emission simultaneously are clearly observed. There exist conflicts between economy and emissions control (see in Figure 10 and 11) and between the control of NOx and soot emissions (see in Figure 12). It is then realized that a compromise has to be made to meet more and more strict emission regulations while keeping acceptable fuel consumption.
In the following sections, the derived Pareto solutions will be discussed from different point of view, such as these solutions to bring the best fuel economy or to bring the minimum emissions, ect. Details of different design strategies are illustrated in this paper as well. Soot, g/kWh
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Figure 9: Derived Pareto solutions (SFC, NOx and Soot) 10
MINIMUM FUEL CONSUMPTION STRATEGY One solution is found among the derived Pareto solutions, which can bring the minimum value of fuel consumption (shown in Figure 9). The injection pattern, start of injection (SOI) time and EGR rate of this solution are illustrated in Figure 13. By analyzing the injection pattern, we found that most fuel is injected at the beginning of injection before top dead centre. It may be explained by the facts that the early injection causes better fuel-air mixing during the combustion process, which results in higher maximum in-cylinder pressure and hence engine output.
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Figure 10: Pareto solutions of SFC and NOx
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Figure 13: Injection rate strategy and engine output for the minimum fuel consumption MINIMUM NOX EMISSION STRATEGY
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Figure 11: Pareto solutions of SFC and Soot 1
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The Pareto solution which can bring the minimum value of NOx emissions is shown in Figure 14, its injection pattern, start of injection (SOI) time and EGR rate together with the engine output data. By analyzing them, we found that the diesel is injected at two steps. In practical multiple injection systems, this double step injection is known as ‘pilot injection’ and ‘main injection’ respectively. In this solution, EGR technique is used as well to reduce the NOx emission. Therefore, multiple injection strategy together with EGR can reduce the NOx emission remarkably. This is due to the medium in-cylinder pressure obtained in this strategy. MINIMUM SOOT EMISSION STRATEGY
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Figure 12: Pareto solutions of NOx and Soot
Figure 15 illustrate the injection pattern, start of injection (SOI) time and EGR rate of the optimization solution which brings the minimum soot emissions.
By analyzing this figure, we found that to reduce the soot emission, the injection is retarded. It is noticed that there is a very small amount of fuel injected at top dead center. The fuel is too small to bring the intensive in-cylinder combustion. However, this small amount of fuel may be helpful to the complete combustion of the fuel injected later, either by providing fully vaporized fuel or by increasing the in-cylinder temperature through chemical reactions at the beginning of main fuel injection.
Injection Rate
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another. Therefore, we need to find a compromise solution among the derived Pareto solutions. Figure 10, 11 and 12 were re-examined for this purpose. The solutions that provide the most interesting design strategies to engine designers are distributed along the edge of the plotted solutions. These edge solutions are redrawn respectively. (see the black square symbols in Figure 16, 17 and 18 ) In this study, ten strategies are selected among them. These selected strategies are illustrated as gray round symbols in Figure 16, 17 and 18, nominated from A to J. The strategies from A to J and their outputs are also plotted. The injection pattern, start of injection (SOI) time and EGR rate of each strategy are illustrated. The engine designers may find corresponding injection pattern, EGR rate and swirl ratio according to their target engine outputs. RECOMMENDED STRATEGIES
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Figure 14: Injection rate strategy and engine output for the minimum NOx emission
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The target solution should have lower emission values at similar specific fuel consumption as the baseline value of 213.5 g/kWh. Therefore, Figure 10 and 11 were redrawn, as shown in Figure 19. The first design candidate was found with the help of Figure 19. The injection rate strategy of design candidate (1) is illustrated in Figure 20. By comparing the output of design candidate (1) with that of the baseline value, it was found that emissions and the specific fuel consumption were reduced simultaneously. By using the similar method, design candidate (2) was found (illustrated in Figure 21). The specific fuel consumption was a little higher than the baseline case (less than 3%), but both NOx and soot were reduced. Especially, NOx emission was reduced remarkably (up to 60%). DISCUSSION
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In the system described in this paper, the diesel engine design was treated as a multi-objective problem using genetic algorithms. In this study, two design candidates were found. Design candidate (1) can reduce emissions and fuel consumption simultaneously compared with the baseline case, which uses the traditional injection rate without exhaust gas recirculation. Design candidate (2) can further decrease the NOx emission up to 60%. But this increases fuel consumption about 3%.
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Figure 15: Injection rate strategy and engine output for the minimum soot emission DESIGN STRATEGY DATABASE The Pareto solution which can bring the minimum value of fuel consumption and emissions (NOx and soot) are shown in Figure 13, 14 and 15 respectively. By analyzing these strategies, we found that the early diesel injection can obtain the best fuel economy. Multiple injection strategy together with EGR can reduce the NOx emission remarkably. To reduce the soot emission, the injection should be retarded. It is clear that these strategies are in conflict to one
Although the injection rate strategies obtained in this research are not practicable with the existing injection systems, they do give clues. It can be seen that the multiple injection is quite likely to be the solution to reduce NOx and soot emissions simultaneously while at the same time keeping good fuel economy. Further research should be carried out focusing on the multiple injection and therefore, find more practicable injection rate strategies by the aid of the HIDECS-NCGA system developed in this research.
Figure 16: Selected Pareto solutions of SFC and NOx
Figure 17: Selected Pareto solutions of SFC and soot
Figure 18: Selected Pareto solutions of NOx and soot
CONCLUSION
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It is made clear that the phenomenological model is suitable for optimization by using genetic algorithms, as the phenomenological model does not run with high calculation costs. This research also showed that the NCGA can successfully derive the Pareto optimum solutions. The information from these Pareto optimum solutions is provided in details for engine designers.
0.15 NOx, g/kWh
In this paper, the multi-objective optimization system is established for engine design by using the diesel engine computational model and genetic algorithms. The phenomenological model named HIDECS is used for analyzing the diesel engine. An extended genetic algorithm, Neighborhood Cultivation Genetic Algorithm (NCGA) is applied as an optimizer. In this simulation, the amount of SFC, NOx and soot are minimized simultaneously by changing the rate of fuel injection, the start of injection time and EGR rate. It was found that by adding EGR, the NOx emission is reduced. For soot formation, the late fuel injection should be involved.
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ACKNOWLEDGMENTS
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This work was supported by Japan Society for the Promotion of Science and a grant to RCAST at Doshisha University from the Ministry of Education, Science, Sports and Culture, Japan.
Injection Rate
Figure 19: Illustration the choose of design candidate 1 50 40 30 20 10 0
SOI time = -4 CA ATDC EGR rate = 0.04
REFERENCES 1.
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Output: SFC = 211.6 g/kWh NOx = 0.16 g/kWh Soot = 0.4 g/kWh Figure 20: Injection rate strategy and engine output of design candidate 1
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5.
SOI time = -3 CA ATDC EGR rate = 0.07
30 20 10 0 -2.5
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Output: SFC = 220 g/kWh NOx = 0.067 g/kWh Soot = 0.38 g/kWh Figure 21: Injection rate strategy and engine output of design candidate 2
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8.
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CONTACT Hiro Hiroyasu*: Professor, Research Institute of Industrial Technology, Kinki University, Takaya, Umenobe, Higashi-Hiroshima, 739-2116, Japan. Email Address:
[email protected] Haiyan Miao: Visiting researcher, Research Institute of Industrial Technology, Kinki University, Takaya, Umenobe, Higashi-Hiroshima, 739-2116, Japan. Email Address:
[email protected] Tomo Hiroyasu: Associate Professor, Department of Knowledge Engineering and Computer Science, Doshisha University, 1-3 Tatara Miyakodani, Kyotanabe-shi, Kyoto, 610-0321, Japan. Email Address:
[email protected] Mitunori Miki: Professor, Department of Knowledge Engineering and Computer Science, Doshisha University, 1-3 Tatara Miyakodani, Kyotanabe-shi, Kyoto, 610-0321, Japan. Jiro Kamiura: Graduate student, Department of Knowledge Engineering and Computer Science, Doshisha University, 1-3 Tatara Miyakodani, Kyotanabe-shi, Kyoto, 610-0321, Japan.
