Journal of Mechanical Science and Technology 27 (7) (2013) 2171~2179 www.springerlink.com/content/1738-494x
DOI 10.1007/s12206-013-0536-6
Optimization algorithm for diesel engine operating parameters based on a vehicle driving test cycle† Daebong Jung1, Junghwan Bang1, Seungmok Choi1, Hoimyung Choi2 and Kyoungdoug Min1,* 1
School of Mechanical and Aerospace Engineering, Seoul National University, Seoul, 151-742, Korea 2 Advanced Institutes of Convergence Technology, Suwon-si, Gyeonggi-do, 443-270, Korea (Manuscript Received June 23, 2011; Revised January 29, 2013; Accepted March 23, 2013)
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Abstract For compliance with stringent exhaust emissions regulations, diesel engines have been equipped with electronically controlled components. Hence, there are various engine operating parameters that must be optimized, however optimization of these parameters is complicated. The objective of this research is to provide a new optimization algorithm for the diesel engine operating parameters with consideration of the vehicle control strategy. To optimize engine operating parameters, the concept of the vehicle-based optimization has been introduced. The engine response functions for performance and emissions were determined using the design of experiments, the response surface method and regression method with various engine operating parameters. Then, the engine operating points of the vehicle during the test cycles were analyzed, and the fuel consumption and emissions were estimated. Consequently, the engine operating parameters at each operating point were optimized to reduce the fuel consumption and the emissions such as NOx and PM by using the gradient method. Moreover, a new optimization algorithm enables to optimize engine operating parameters in various test cycle without additional engine experiment. Keywords: Diesel engine; Optimization; Response function; Central composite design (CCD); Polynomial regression; Vehicle simulation ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1. Introduction Recently, there has been strong worldwide demand for the reduction of greenhouse gases and harmful exhaust emissions due to the serious nature of global warming and pollutant emissions. Because internal combustion engines for automobiles have been acknowledged to be a significant source of greenhouse gases and pollutant emissions, demands for a reduction in exhaust emissions and fuel consumption have increased. With this trend, the need for the development of a low emission and low fuel consumption vehicle has greatly increased. The diesel engine has been used as a power source for various types of vehicles due to its high thermal efficiency. With the recent introduction of electronically controlled high speed direct injection (HSDI) technology, there has been considerable advancement in diesel engine technology. Nevertheless, diesel engines still have drawbacks, such as the relatively high production of NOx and PM emissions. It is expected that these emissions will be reduced with the exhaust aftertreatment technologies, which are the subject of active research among automotive industry [1-7]. *
Corresponding author. Tel.: +82 2 880 1661, Fax.: +82 2 883 0719 E-mail address:
[email protected] Recommended by Associate Editor Man-Yeong Ha © KSME & Springer 2013 †
In the research of diesel engines, the method of determining the engine operating parameters is as important as the engine design and exhaust after-treatment technologies for achieving low fuel consumption and reducing exhaust emissions [4, 810]. This is because fuel consumption and emission characteristics vary significantly according to the engine operating parameters [11-15]. In an HSDI engine, numerous control parameters exist, such as the number of injection (main, pilot and post), the injection time, the injection duration, the rail pressure, the exhaust gas recirculation (EGR) rate, and the boost pressure [16-18]. The goal associated with the determination of the engine operating parameters for diesel engine mapping is to minimize the fuel consumption and the emissions simultaneously. Because the fuel consumption and the emissions generally have a trade-off relationship, it is contradictory to minimize the two simultaneously [12]. Thus, a more realistic goal for engine mapping is to minimize the fuel consumption while meeting emissions regulations during vehicle emission test cycles, such as the FTP-75 or NEDC. When a vehicle is driven in an emission test cycle, the diesel engine operates over a wide range of speeds and loads. Hence, control parameters should be optimized for all engine operating points. It is difficult to determine the appropriate levels that will meet the goal of minimizing fuel consumption and meeting emissions requirements. Moreover, it becomes more com-
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plicated for the case of diesel hybrid vehicles, which have an operating point and time that vary significantly according to the vehicle driving strategy. Previous studies focused on one or several operating points for a diesel engine [9, 12, 19, 20]. Fuel consumption and exhaust emission levels vary significantly according to the engine operating parameters and the operating time interval at each operating point. The driving control strategy, such as the shifting of the transmission, is closely coupled with the determination of the engine operating parameters. Therefore, it is highly desirable to develop the algorithm which can optimize the engine operating parameters and the driving control strategy simultaneously. However, because this is too complicated in reality, the scope of this study is limited to the development of an algorithm for the optimization of the engine operating parameters for a fixed control strategy. In other word, this optimization algorithm provides a method to improve fuel consumption, emissions, and other performance factors for the fixed driving control strategy. Therefore, in a conventional diesel vehicle, the primary effectible parameters can be optimized for the fixed driving control strategy, and the vehicle driving control strategy in the development process can be improved using these results. In addition, this algorithm can be applied to the development process of hybrid electric vehicles (HEV). During the development process of an HEV with a conventional engine, no additional experiments or 1-D engine simulations are required because the suggested algorithm can optimize the engine operating parameters and the control strategies of the HEV to satisfy the requirements. To optimize the engine operating parameters, the fuel consumption and emission level according to various combinations of that for all conditions should be obtained. However, it is not cost-effective to perform a full factorial test. For example, for four main engine operating parameters, 20 cases of engine speed, 20 engine loads, and 3 levels would require 32,400 engine test cases [8]. It is highly desirable to reasonably predict the full factorial test by performing a reduced number of engine test cases. The objective of this study was to develop a new optimization algorithm for the engine operating parameters. This algorithm derives the engine response functions using a costeffective experimental design, analyzes the engine operating points of a vehicle driving mode using vehicle simulations, and minimizes vehicle fuel consumption with meeting required emission levels.
2. Optimization algorithm for the diesel engine considering the vehicle driving control strategy The optimization algorithm suggested in this paper is described in Fig. 1. First, experiments for obtaining the response functions for the responses were executed using the design of experiment (DOE) method or other methods. The engine experiment can be substituted with a 1-D engine simulation if the 1-D engine model guarantees reliability and has been vali-
Fig. 1. Flow chart of optimization process.
dated. Then the response functions, which reflect the influences of each operating parameter, were derived from the experimental data using a response surface analysis and a second order regression analysis. For the vehicle simulation with a driving pattern, such as NEDC, the time weighting factor of the engine operating point was calculated to determine the target-operating points, which need to be optimized. Optimization of the engine operating parameters at the selected operating points was completed using a gradient method, which determines the optimal direction of change for the engine operating parameters from the minimum bsfc map case. Through this process, the engine operating parameters were optimized to reduce the fuel consumption and emissions simultaneously. 2.1 Engine test using a design of experiment method Among the types of design of experiment methods, the Central Composite Faced method was applied to the engine test because it can derive accurate response functions with a reduced number of test cases. For example, in the case of 3 engine operating parameters, which have 3 levels (-1, 0, 1), the full factorial test required 27 cases, while only 15 tests are required for the central composite faced method. Thus, the engine experiment was conducted based on the test cases, which were constructed by the Central Composite Faced method. If there are reliable 1-D engine simulation models that can predict the fuel consumption and emissions accurately, a simulation is conducted to obtain data instead of experiments.
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2.2 Response function The response surface analysis represents the statistical methodology used to analyze the response surfaces when various factors influence the response values through complex interactions. There has been some research on the optimization of diesel engines using the response surface analysis with a second-order polynomial regression model that adapts the central composite design [13, 21-23]. From the engine experiment data, second order polynomial functions, which represent the relationship between the engine responses and the engine operating parameters, were derived using a response surface analysis and a second order regression analysis. The response surface analysis is suitable to derive the function of the engine operating parameters and to explain the interaction between various operating parameters. In addition, it is convenient to determine the maximum or minimum value of the response. The relationship between the engine operating parameters and the engine responses are defined as Eq. (1). R = f ( x1 , x2 , x3 ,…, xn ) .
(1)
In Eq. (1), R is the engine response, and xn is an engine operating parameter. The response function, as Eq. (1), is generally unknown. Although the response function is known within a limited range, it is too complex to apply. Therefore, the response function is simplified using a multiple regression model. It is requirement that the response function is satisfied within a limited range. In other words, the response function should describe the relationship between the engine operating parameters and the engine responses precisely in a specific range. 2.3 Gradient method The gradient method was applied to optimize the engine operating parameters. The gradient method is used to determine the optimal global point. First, the comparison of the gradient values, which were calculated between the reference point and the other points, was performed. Then, the optimum gradient value was selected, which represents the minimum increase in the fuel consumption with the maximum reduction of emissions. Because the objective of this study was to reduce the fuel consumption and the emissions, such as NOx and PM, the gradient that was associated with the optimal direction was defined as Eqs. (2)-(4). G1 =
∆NOx ×∆PM ∆bsfc
(2)
(if, ∆NOx
