OPTIMIZATION OF VEHICLE SUSPENSION SYSTEM USING GENETIC ALGORITHM

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1 INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) International Journal of Mechanical Engineering and Technology (IJMET), ISSN (Print), ISSN (Print) ISSN (Online) Volume 6, Issue 2, February (2015), pp IAEME: Journal Impact Factor (2015): (Calculated by GISI) IJMET I A E M E OPTIMIZATION OF VEHICLE SUSPENSION SYSTEM USING GENETIC ALGORITHM Ranjeet kumar S. Gupta 1, Vilas Sonawane 2, Dr. D. S. S. Sudhakar 3 1 Asst. Prof., Mechanical Engg. Dept., D.J. Sanghvi College of Engineering, Mumbai, India, 2 SGGS Institute of Technology, Mechanical Dept., Nanded, India 3 HOD, Production Engg. Dept., Fr. Conceicao Rodrigues College of Engineering, Mumbai, India, ABSTRACT Modeling the suspension of an automobile is of interest for many automotive and vibration engineers. Of importance for these engineers is the ride quality of the vehicle traversing over broken roads and control of body motion. When traveling over rough terrain, the vehicle exhibits bounce (up and down), pitch (rotation about the center of gravity along the vehicle's length) and roll (rotation about the center of gravity along the vehicle's width) motions. Optimization of vehicle ride and handling performance must meet many competing requirements. For example, vibration in the frequency range that causes driver discomfort needs to be minimized, which requires decreasing suspension stiffness. Yet the suspension deflection should stay within travel constraints, so suspension stiffness needs to be increased. The traditional practice of relying on test cars for suspension development is time consuming and costly. In this paper, we will demonstrate a simulation-led design approach, which reduces reliance on test vehicles and produces optimal results. The approach starts with the development of a fast and accurate vehicle model in Matlab and Simulink combined for testing the parameters, and concludes by automated optimization of suspension parameters using Genetic Algorithm, to meet performance requirements specified. This would produce more applicable results of industrial and commercial merit. Keywords: Optimization, Vehicle Suspension, Genetic Algorithm, Matlab, Simulink 1. INTRODUCTION There is a clear trend in industry towards more complex products spanning over several engineering domains. Simultaneously, there is a pressure on developing products faster, at competitive prices, and to a high quality standard. In order to meet these demands, manufacturing 47

2 companies have been forced to focus their efforts on the development process. In that respect, one issue has been to ensure the efficiency of the development process, which has resulted in methods to analyze and manage the design process. Another issue has been to develop tools and techniques that support the design of complex products, which has produced a wealth of computerized engineering tools. As the computational capabilities of the computers increase, the scope for simulation and numerical optimization is enlarged. A great part of the design process will always be intuitive. However, analytical techniques, simulation models and numerical optimization could be of great value and can permit vast improvements in design. The first issue is to ensure an efficient design process. In this paper, a design process modeling approach is presented where simulation is employed in order to predict the performance of the design process in terms of lead-time and cost. Design process modeling gives enhanced understanding of the properties of the process, which is important as a thorough understanding of the design process forms the basis for further process improvements. With the help of design process models, different competing design processes can be compared and evaluated based on process leadtime and costs. The second issue focuses on how to improve the design of complex systems by employing simulation and optimization techniques. As widely recognized, engineering design is an iterative process where new design proposals are generated and evaluated. According to Roosenburg and Eekels[9], the iterative part of the design process consists of synthesis, simulation, evaluation and decision. For each provisional design, the expected properties are predicted using simulation models, which are then compared to the requirements on the system. If the design does not meet the requirements it is modified and evaluated again in the search for the best possible design. Based on this description, it could be seen that design is essentially an optimization process. In order to raise the level of automation, and thereby speed up parts of the process, the optimization could be formalized and an optimization algorithm introduced. The presence of several conflicting objectives is typical for engineering design problems. In many cases where optimization techniques are utilized, the multiple objectives are aggregated into one single objective function. Optimization is then conducted with one optimal design as the result. The result is then strongly dependent on how the objectives are aggregated. Here a multiobjective problem is solved aggregating it into a single objective genetic algorithm applied to support the design of a passenger vehicle suspension system. The outcome from this optimization is a set of Pareto optimal solutions that visualizes the tradeoffs between system performance and design. The solution is quickly achieved using GA tool of Matlab In real-world situations, system parameters will always include variations to some extent, and this fact is likely to influence the performance of the system. However, we want the system to be robust and perform well under a wide range of operational conditions. Therefore we need to answer not only the question What is best? but also What is sufficiently robust? Genetic algorithms (GAs) and the closely related evolutionary algorithms are a class of nongradient methods which has grown in popularity ever since Rechenberg [7] and Holland [1] first published their work on the subject in the early 70s. For a more comprehensive study of genetic algorithms, see Goldbergs [1] splendid book on the subject. Genetic algorithms are modeled after mechanisms of natural selection. Each optimization parameter (x n )is encoded by a gene using an appropriate representation, such as a real number or a string of bits. The corresponding genes for all parameters x 1...x n form a chromosome capable of describing an individual design solution. A set of chromosomes representing several individual design solutions comprises a population where the fittest are selected to reproduce. Mating is performed using crossover to combine genes from different parents to produce children. The children are inserted into the population and the procedure starts over again, thus creating an artificial Darwinian environment. 48

3 2. MATHEMATICAL MODEL A vehicle suspension system is a complex vibration system having multiple degrees of freedom [3]. The purpose of the suspension system is to isolate the vehicle body from the road inputs. Various aspects of the dynamics associated with the vehicle put different requirements on the components of the suspension system. Passenger ride comfort requires that the acceleration of the sprung mass be relatively smaller whereas the lateral dynamic performance requires good road holding which needs consistent normal force between the road and the tires. This all has to work within the maximum allowed deflection of the suspension spring and limitations of the dynamic tire deflection [6]. An automobile traveling along a level road at a constant speed v0 encounters a speed bump shown in (1). The vehicles suspension system (front and rear springs and shock absorbers) is modeled by linear springs and dampers, and the compliance of the tires is modeled by front and rear springs. The vehicle cab motion is limited to heave in the y-direction and a small amount of pitch ϴof the vehicles longitudinal axis [4]. The tires are assumed to remain in contact with the road surface at all times. The road profile is responsible for the systems input, the height of the road (with respect to some reference) underneath the front and rear tires, respectively. The system has three translational degrees of freedom, y, yf, yr which are the vertical displacements of the vehicle cab and both front and rear axles from their equilibrium positions. The lone rotational degree of freedom is the pitch angle ϴ. The model equations are listed as follows: M = K fs [y f -(y + L f ϴ)] + B f [ f - ( + L f )] + k rs [y r - (y - L r ϴ) + B r [ - ( - L r )](Eqn. 1) M = - (K fs + K rs )y - (B f + B r ) + K fs y f + B f f + K rs y r + B r + (K rs L r - K fs L f ) ϴ + (B r L r - B f L f ) (Eqn. 2) Figure 1: Moving vehicle and suspension system model. 49

4 M f = - K fs [y f - (y + L f ϴ)] - B f [ f - ( + )] + K ft (u f - y f ) = - (K fs + K ft )y f - B f f + K fs y + B f + K fs L f ϴ + B f L f + K ft u f (Eqn. 3) M r = - K rs [y r - (y - L r ϴ)] - B r [ - ( - L r )] + K rt (u r - y r ) = - (K rs + K rt )y r - B r + K rs y + B r - K rs L r ϴ - B r L r + K rt u r (Eqn. 4) l = K fs [y f - (y + L f ϴ)] + B f [ f - ( + L f )]L f - K rs [y r - (y - L r ϴ)] + B r [ - ( - L r )]L r (Eqn. 5) On this basis the following Simulink Model is created. 3. OPTIMIZATION Figure 2: Simulink Model. Optimization objective is to minimize the sprung mass acceleration of the quarter car model. So the required comfort is obtained from the system. For the above requirement we use the objective function which is tness function for Genetic Algorithm (GA) op-timization process [10]. According to James principal, the root mean square (RMS) of sprung mass acceleration can be expressed as:,,,, = [ + ](Eqn. 5) The optimization results are derived for a vehicle having front and rear as same congurations, travelling at the speed of 30 m/s on the road with an irregularity coefficient of power spectrum taking the value of 6.5x10-6 m 3. 50

5 4. RESULTS AND CONCLUSIONS The total number of generations to study was not determined before testing began. Because of the complex nature of the genetic algorithm and time limitations for the number of possible generations run, it was decided to start the genetic algorithm and observe how the genetic algorithm progressed before convergence criteria were set. In the end, the algorithm was terminated at the 51st generation. Provided the lower and upper bounds for the variables as per shown in the table followed: Table 1: Bounds for the Optimization Problem. Bounds Parameters Lower Upper m u (Kg) m s (Kg) K t (N/m) K (N/m) C (Ns/m) After running the GA Optimisation, the optimised values of the variables are as follows: m u = Kg. m s = Kg. K t = 435, N/m. K = 61,531 N/m. C = Ns/m. The plot of the optimization run is as shown: Figure 3: Plot of Average between Individuals and the Best, Worst and Mean values for each iteration. 51

6 Figure 4: Plot of Average Fitness of Individuals. Due to the overall conformity of the generation and the fact that the total error bars on the average parent variable values encompassed both the high parameter values and the average parameter values it was determined that further testing with a higher n generations was not likely to yield a stronger solution. While there is no guar-antee that the best solution found is indeed the optimal con guration, it is, with several other similar parameters, a very strong solution. In this regard, the time available was also a factor in the termination of the genetic algorithm. If more time were available more generations could have been tested to increase the level of con dence that the best solution had been found. One can see clearly that maximum, minimum, and average parameters values all ap-proach towards optimum in Figure with increasing generation number, indicating that the genetic algorithm was functioning correctly. Due to the overall conformity of the generation and the fact that the total error bars on the average parent variable values encompassed both the high parameter values and the average parameter values (see Fig. 3) it was determined that further testing with a higher n generations was not likely to yield a stronger solution. While there is no guarantee that the best solution found is indeed the optimal configuration, it is, with several other similar parameters, a very strong solution. In this regard, the time available was also a factor in the termination of the genetic algorithm. If more time were available more generations could have been tested to increase the level of confidence that the best solution had been found. One can see clearly that maximum, minimum, and average parameters values all approach towards optimum in Figure with increasing generation number, indicating that the genetic algorithm was functioning correctly. Figure 5: Plot of Stopping Criteria. 52

7 Figure 6: Termination of Optimization. The results that we are obtaining from GA optimization can be verified by checking the response of our Simulink Model. First we just take some arbitrary values from the ranges, and get the response for these values. Then we'll compare the results which we are getting from our GA optimized parameters. The output of the model are namely the body deflection, front deflection, rear deflection and the pitch. It is shown by the plot represented as in Fig. 5 and 6. The displacements is much reduced as compared to a that generated by arbitrary parameter values. Also there is subsequent reduction in the front and rear deflection of the vehicle; and the pitch (theta) is reduced as well. Figure 5: Response of the Model for the General Parameter Values. 53

8 Figure 6: Response of the Model for the Optimized Parameter Values. This proves that the parameter values that we are getting from GA optimization are actually optimized for the vehicles response. As GA is an discrete optimization technique, i.e. it comes out with a different set of results for the same optimization problem in every subsequent run. And also the objective function value is optimized to almost to the same extent. Hence for every run, with same set of parameters and conditions the optimized parameter values will be substantially different. Still it can be taken as an advantage that there are multiple set of solutions available through GA; unlike many other optimization technique that tend to give only one solution. 5. CONCLUSION The integration of the optimization algorithms with the vehicle model has been success-fully achieved allowing for an automated optimization process. It has been learnt that GA is verily suitable for such kind of iterative design problems. The number of parameters as applicable was appropriately selected by the algorithm for the optimized RMS of sprung mass acceleration. And also the parameters selected for optimization were infact ideal. Usage of Matlab for the application of the optimization algorithm i.e. GA made it very easy; else otherwise the massive amount of calculations to be carried for 'n' number of generations would have been practically impossible. It also gave the advantage of quickly adapting to the changes as per the algorithm to provide with the systems response. 6. REFERENCES 1. GOLDBERG D., 1989, Genetic Algorithms in Search and Machine Learning Reading, Addison Wesley. 2. BALL M., FLEISCHER M., CHURCH D., A Product Design System Employing Optimization-based Tradeoff analysis, in Proceedings of ASME DETC Design Theory and Methodology Conference, Baltimore, USA, September 10-13, ESCHENAUER H., KOSKI J., AND OSYCZKA A., "Multicriteria Design Optimization," Berlin: Springer-Verlag,

9 4. HORN J., "Multicriterion decision making", Handbook of Evolutionary Computation, T. Bck, D. Fogel, and Z. Michalewicz, Eds., IOP Publishing Ltd. and Oxford University Press, KEENEY R. AND RAIFFA H., "Decisions with multiple objectives preferences and value tradeoffs", John Wiley & Sons, New York, USA, MANETSCH T. J., "Toward effcient global optimization in large dynamic systems - The adaptive complex method", IEEE Transactions on Systems, Man &Cybernetics, vol. 20, pp , PAHL G. AND BEITZ W., Engineering Design A Systematic Approach, Springer-Verlag, London, PHADKE M. S., Quality Engineering Using Robust Design., Springer- Prentice Hall, ROOZENBURG N. AND EEKELS J., Product Design: Fundamentals and Methods, Springer- John Wiley & Sons Inc, PROF. D. A. HULLENDER., Modeling and Simulation of Engineering Systems, Springer- Course Notebook for Dynamic Systems Modeling. 11. Chaitanya Kuber, Modelling Simulation And Control of an Active Suspension System International Journal of Mechanical Engineering & Technology (IJMET), Volume 5, Issue 11, 2014, pp , ISSN Print: , ISSN Online: Alok Kumar Pandey and Dr R. P. Sharma, Simulation of Eight Wheeled Rocker Bogie Suspension System Using Matlab International Journal of Mechanical Engineering & Technology (IJMET), Volume 4, Issue 2, 2013, pp , ISSN Print: , ISSN Online: Flt Lt Dinesh Kumar Gupta, Linear Programming In Matlab International Journal of Industrial Engineering Research and Development (IJIERD), Volume 4, Issue 1, 2013, pp , ISSN Online: , ISSN Print: