Automotive engine idle speed control optimization ...

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598 Received 22 May 2008 Revised 19 August 2008 Accepted 25 August 2008

Automotive engine idle speed control optimization using least squares support vector machine and genetic algorithm P.K. Wong, L.M. Tam, K. Li and H.C. Wong Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Macau Abstract Purpose – Nowadays, automotive engines are controlled by electronic control units (ECUs), and the engine idle speed performance is significantly affected by the setup of control parameters in the ECU. The engine ECU tune-up is done empirically through tests on a dynamometer (dyno). In this way, a lot of time, fuel and human resources are consumed, while the optimal control parameters may not be obtained. The purpose of this paper is to propose a novel ECU setup optimization approach for engine idle speed control. Design/methodology/approach – In the first phase of the approach, Latin hypercube sampling (LHS) and a multi-input/output least squares support vector machine (LS-SVM) is proposed to build up an engine idle speed model based on dyno test data, and then a genetic algorithm (GA) is applied to obtain optimal ECU setting automatically subject to various user-defined constraints. Findings – The study shows that the predicted results using the estimated model from LS-SVM are in good agreement with the actual test results. Moreover, the optimization results show a significant improvement on idle speed performance in a test engine. Practical implications – As the methodology is generic it can be applied to different vehicle control optimization problems. Originality/value – The research is the first attempt to integrate a couple of paradigms (LHS, multi-input/output LS-SVM and GA) into a general framework for constrained multivariable optimization problems under insufficient system information. The proposed multi-input/output LS-SVM for modelling of multi-input/output systems is original, because the traditional LS-SVM modelling approach is suitable for multi-input, but single output systems. Finally, this is the first use of the novel integrated framework for automotive engine idle-speed control optimization. Keywords Electromechanical devices, Control technology Paper type Research paper

International Journal of Intelligent Computing and Cybernetics Vol. 1 No. 4, 2008 pp. 598-616 q Emerald Group Publishing Limited 1756-378X DOI 10.1108/17563780810919140

1. Introduction Nowadays, automotive engines are controlled by the electronic control unit (ECU) and the engine idle speed performance is significantly affected by the setup of control parameters in the ECU. In modern spark ignition (SI) engines, an efficient idle-speed performance is required to fulfil the ever-increasing requirements on fuel consumption, vehicle driveability and pollutant emissions. Conventional SI engine idle-speed tune-up relies on the engineer’s experience and the tune-up process normally spends a few months. As a result, a lot of time, fuel and human resources are consumed, while the optimal parameter may not be obtained. The goal of idle speed control (ISC) is to enable the engine with closed throttle to run at low enough engine speed to minimize fuel

consumption but not so low that the engine noise, vibration and harshness quality is compromised. The worst-case scenario is that the engine speed falls low enough to cause engine stall. In the modern engine ECU setup, there are four main control variables affecting idle speed and disturbance rejection ability; they are fuel injection, manifold absolute pressure (MAP),valve timing and spark advance. Figure 1 shows a typical engine control system. The fuel injection is controlled by adjusting the injection time of the fuel injector to change the amount of fuel injected into the manifold. At idle, the MAP is usually controlled by altering the air flow from the environment to the intake manifold through adjustment of an air control valve. The air control valve is either a by-pass air valve (BPAV) or electronic throttle. Valve timing refers to when the valves open and close in relation to piston position that controls the air-fuel mixture to enter the combustion chamber. The spark advance is adjusted by advancing or retarding the ignition time before top dead centre (BTDC). From the control point of view, a typical engine ISC system usually consists of look-up table control system, that mainly provides a steady-state control action, and idle air valve controller, which regulates the transient characteristic. Both control parts should match with each other. The primary difficulty with the control problem is that the engine at idle is subject to step disturbances from unknown external loads and accessory loads such as air-conditioning or power-steering loads, etc. The disturbance decreases engine speed rapidly and it must be rejected. Recently, researches have described the use of online proportional-integralderivative (PID) tuning controller (Howell and Best, 2000), adaptive control algorithm (DaeEun and Jaehong, 2007), colonial competitive approach for PID controller (Esmaeil et al., 2008), predictive control algorithm (Manzie and Watson, 2003) and robust control algorithm (Petridis and Shenton, 2003) to regulate the air control valve to achieve satisfying idle speed response. However, these intelligent controllers are still under investigation. No matter how advance of the algorithms, the development of the control systems must call for exact engine model and base system parameters (e.g. base fuel 6 4

2

Idle speed control optimization 599

7 8

5

12

3

10 9 11 13

1 12

14 Notes:(1)ECU; (2)Throttle valve and bypass air valve; (3)Intake manifold; (4)Manifold absolute pressure sensor; (5)Fuel injector; (6)Intake valve; (7)Ignition spark; (8)Camshaft position sensor (9)Engine temperature sensor; (10)Knocking sensor; (11)Crankshaft position sensor; (12)Oxygen senso; (13)Fuel pressure sensor; (14)Acceleration pedal. Reproduced from the only available original

Figure 1. Typical engine control system

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injection time, valve timing and ignition timing in idle speed range) for system simulation, dynamic analysis and identification of operating parameters. An engine model is a complex multi-variable nonlinear function, which is very difficult to be determined, so the models used in these sophisticated controllers are all empirical models, which are derived from resorting to some simple physical laws combined with identification procedures for estimation of several unknown parameters (Christian et al., 2006). However, this kind of engine model is quite simple as compared with the real engine system (DaeEun and Jaehong, 2007). In fact, many coefficients in the empirical models are also difficult to be determined. Therefore, the empirical models cannot reflect the true performance of the controller and let the engineer truly optimize the controller parameters. Apart from engine model and controller issues, there is no research working on the ECU lookup table setup for ISC problem. Moreover, the ISC objectives in the available literatures only focus on idle speed response subject to external disturbance, there is no discussion on fuel consumption and emission quality, but these two factors are very important in ISC problem. Therefore, development of a comprehensive ISC optimization method is an important research to automotive engineering. In developing an effective optimization method, an exact engine model is also necessary. To exactly model a complicate system whose domain information is insufficient like an engine, black-box identification techniques are usually employed. These techniques can quickly derive models from experimental data (So¨derstro¨m and Stoica, 1989). The most common black-box modelling technique in automotive engineering is neural networks. It is well known that a neural network is a universal estimator. Recent researches have described the use of neural networks for modelling some engine performances (Liu and Fei, 2004; Celik and Arcaklioglu, 2005) based on experimental data. It has in general, however, two main drawbacks for neural networks (Haykin, 1999): (1) The architecture, including the number of hidden neurons, has to be determined a priori or modified while training by heuristic, which results in a non-necessarily optimal network structure. (2) The training process (i.e. the minimization of the residual squared error cost function) in neural networks can easily be stuck by local minima. Various ways of preventing local minima, like early stopping, weight decay, etc. are employed. However, those methods greatly affect the generalization of the estimated function, i.e. the capacity of handling new input cases. With an emerging technique of least squares support vector machines (LS-SVM) (Suykens et al., 2002) combining the advantages of neural networks (handling large amount of highly nonlinear data) and nonlinear regression (high generalization), the previous drawbacks from neural networks are overcome. The main advantages of LS-SVM over neural networks are: . good generalization; . guarantee of global solution having minimal fitting error; and . the architecture of the model has not to be determined before training (Liu et al., 2005).

In view of the advantages of LS-SVM and the deficiencies of the current ISC problem, this paper proposes a new ISC optimization methodology based on LS-SVM and genetic algorithm (GA), which considers the problem variables and constraints comprehensively. In the proposed approach, LS-SVM is employed to model the multi-variable engine ISC system. The model then serves as an objective function for optimization. A schematic illustration of the framework and overall methodology is shown in Figure 2. The upper branch in Figure 2 shows the steps required to build up the LS-SVM model. The experiments are still required, but only to provide sufficient data for LS-SVM training. Design of experiments is used for additionally streamline the process of creating representative sampling data points to train the LS-SVM model. Once the engine idle speed performance model obtained is evaluated, it is then possible to use a computer-aided technique to search the best engine control parameters automatically based on the model. As the model obtained by LS-SVM is a non-differentiable function, only direct search techniques are suitable for optimization. GA is a widely used direct search technique, so GA is proposed for this constrained multi-variable ISC optimization problem. The optimal set points are then sent back to the ECU to carry out evaluation tests, which can exam the feasibility and efficiency of the proposed optimization approach. The main purpose of this paper is to demonstrate the effectiveness of the proposed LS-SVM þ GA method. It is important to note that there are no apparent limits or

601

Data preprocessing

X3

Design of Experiments Latin (DOE) Hypercube

Idle speed control optimization

X2

X1

DOE Sampling

Dyno experiments GA optimizer

Fuel injection time

Load disturbance

Spark advance

Air valve controller parameters

Valve timing

Multi-input-output LS-SVM model Predicted engine performance

Optimization objective & constraints

Satisfy?

No

Update control parameters

Yes No De-normalization

Valid? Yes Tests & validation

Optimal control setting

Figure 2. Framework for optimization of engine ISC parameters

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constrains in the number of input-output variables, idle speed controller types and the formulation of the optimization objective function. Hence, the methodology is generic and, its effectiveness is demonstrated in the latter sections through a case study of ISC optimization problem. It is believed that the proposed method can be applied to different vehicle control optimization problems.

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2. Idle speed model identification This section describes the model identification phase. A multi-input/output LS-SVM for idle speed modelling is firstly introduced. Then experimental set up for collecting the sampling data is presented. In the final part of this section, the accuracy of this LS-SVM model is examined by test data set and the prediction results are discussed. 2.1 LS-SVM formulation for multi-variable function estimation Consider a training dataset, D ¼ {ðxk ; y k Þ}Nk¼1 , with N data points where xk Î R n represents the kth engine setup, yk Î R m is the kth engine output based on the engine setup xk, k ¼ 1 to N. Here, yk is an m dimension output vector, y k ¼ ½y k ; 1. . .y k ; m. For example, yk, 1 could be the minimum idle speed and yk,m could be the fuel consumption. For the automotive engine, each output performance in the data set yk is usually an individual variable and able to be measured separately, so the training dataset D can be arranged as: D ¼ {d 1 ; . . .d h ; . . . ; dm }

ð1Þ

where dh ¼ {ðxk ; y k;h Þ}Nk¼1 ; h e [1, m ]. In this case, for each single output dimension in the output yk, it forms a new training data set dh. Consequently, the multi-input/output training data set D is separated into m multi-input but single-output sub-training data set dh. For each multi-input single-output dataset dh, LS-SVM deals with the following optimization problem in the primal weight space: 2 3 N 1 T 1X 2 6 minJ P ðw;eÞ ¼ w w þ g 7 e 6 w;b;e 7 2 2 k¼1 k ð2Þ 4 5 T such that ek ¼ y k;h 2 ½w fðxk Þ þ b; k ¼ 1; ...;N where w [ R nh is the weight vector of the target function, e ¼ [e1;..., eN] is the residual vector, and w : R n ! R nh is a nonlinear mapping, b is a bias, n is the dimension of xk, and nh is the dimension of the unknown feature space. The model of the estimated function is considered as: y h ¼ M h ðxÞ ¼ w T fðxÞ þ b:

ð3Þ

However, w may be in very high or even infinite dimensions that cannot be solved directly. In order to resolve the problem, the Lagrangian of equation (2) is constructed to derive the dual problem and the Lagrangian is as follows: Lðw;b;e; aÞ ¼ J p ðw;eÞ 2

N X

ak {w T fðxk Þ þ b þ ek 2 y k;h }

k¼1

where ak ea are Lagrange multipliers. The conditions for optimality are given by:

ð4Þ

8 N X > > > ››wL ¼ 0 ! w ¼ ak fðxk Þ > > > > k¼1 > > > > N > X < ›L ¼ 0 ! ak ¼ 0 ›b > k¼1 > > > > ›L > > > ›ek ¼ 0 ! ak ¼ gek ; > > > > : ››aL ¼ 0 ! w T fðxk Þ þ b þ ek 2 yk;h ¼ 0; k ¼ 1; ...;N k

Idle speed control optimization ð5Þ

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After elimination of the variables w and e in equation (4) using the results from equation (5), the LS-SVM dual formulation of nonlinear function estimation is then expressed as follows (Suykens et al., 2002): 2

3" # " # 3 0 b 5 4Solve in a;b : 4 5 ¼ 1 1v V þ g I N yh a 2

1Tv

0

ð6Þ

where IN is an N-dimensional identity matrix, y h ¼ ½y 1;h ; ...;y N ;h T , 1v is an N-dimensional vector ¼ [1, ..., 1]T, a ¼ [a1, ..., aN]T, and g [ R is a scalar for regularization factor (which is a hyper-parameter for tuning). The kernel trick is employed as follows: Vk;l ¼ wðxk ÞT wðxl Þ ¼ Kðxk ;xl Þk;l ¼ 1; ...;N :

ð7Þ

where K is a predefined kernel function. The resulting LS-SVM modelPfor function estimation is constructed by substituting the results of equation (5), i.e. w ¼ Nk¼1 ak fðxk Þ into equation (3) and becomes: y h ¼ M h ðxÞ ¼

N X

ak fðxk ÞT fðxÞ þ b ¼

k¼1 N X

kxk 2 xk ¼ ak exp 2 s2 k¼1

N X k¼1

2

!

ak Kðxk ;xÞ þ b ð8Þ

þb

where ak, b [ R are the solutions of equation (6), xk is the training data; x is the new input setup for engine idle performance prediction, and radial basis function (RBF) is chosen as the kernel function K, which is the common choice for modelling. In the RBF, s specifies the kernel sample variance, which is also a hyperparameter for tuning, and k· k means Euclidean distance. After inferring m pairs of hyperparameters (g, s) by a well-known technique, Bayesian inference (Suykens et al., 2002), m individual training data sets are used for calculating m individual sets of support vectors ak and threshold values b. Finally, m individual sets of Mh(x) can be constructed based on equation (8). The whole multi-input/output modelling algorithm is shown in Figure 3.

Engine models

xN,1

..

..

x1,1

x y ... x1,n y1,m ... ... xN,n yN,m ..

dm

Figure 3. Multi-input/output LS-SVM modelling framework

. .

. . .

M1(x)

LS-SVM-h (gh, sh)

Mh(x) . .

xN,1

LS-SVM-1 (g1, s1)

. . .

..

..

x1,1

x y ... x1,n y1,h ... ... xN,n yN,h ..

dh

. .

xN,1

..

..

x1,1

Training Data D x y ... x1,n y1,1 ... y1,m ... ... ... xN,n yN,1 ... yN,m ..

604

. .

xN,1

..

..

x1,1

x y ... x1,n y1,1 ... ... xN,n yN,1 ..

d1

..

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Mm(x)

LS-SVM-m (gm, sm)

In Figure 3, a set of LS-SVM models are generated to predict the engine response under different combinations of control variables. Each LS-SVM model represents one engine output performance which is included in the objective function for optimization. 2.2 Experimental setup and data sampling for case study The test engine used in the case study is a Honda Type-R 2.0 liter i-VTEC engine. The engine technical specification is given in Table I. The MAP of the engine is controlled by a BPAV. Although the use of electronic throttle becomes more and more prevalent, the method is equally applicable to both electronic throttle and BPAV. Taking the practical and demonstration purposes into account, a typical aftermarket programmable ECU- MoTeC M800 is selected as the optimization test bed. The fuel injection time, valve timing and ignition control signals are stored in the look-up tables of the ECU. Moreover, a PID controller using engine idle speed as feedback signal is applied to the BPAV. The control schemes of MoTeC M800 ECU are shown in Table II. To check the robustness of the control settings, the test car is loaded on a 500 Hp chassis dyno (Figure 4), and a constant step load provided by the dyno is applied to the car, and then the engine speed and l variations are measured. The engine idle performance data is also recorded by the ECU at a logging rate of 20 Hz. Figure 5

Table I. Technical specification for the test engine

Engine

Honda Type-R K20A i-VTEC

Capacity (cc) Cylinders Max power kW (PS) at RPM Max torque Nm (Kgm) at RPM Fuel system Variable valve timing system Idle system Ignition system

1998 4 in line 162 (220)/8,000 206 (21)/7,000 Multipoint electronic fuel injection Servo-hydraulic system BPAV Multiple-coil direct ignition

shows the constant step load applied by the dyno in the course of data sampling. The aim engine idle speed is set to be 1,200 rpm in the case study. In this case study, the following engine idle speed parameters are selected to be the input and output variables of the LS-SVM model: x ¼, F i;j ; I i;j ; V j ; Pro; Int; Der; Nor; L . and


X y ¼, IAER ; IAEl ; F; Rmin ; T rise .

Control variable

Type of control scheme

Fuel injection time Valve timing Ignition advance MAP

Open loop 3D look-up table Open loop 2D look-up table Open loop 3D look-up table PID BPAV controller

Table II. Control schemes of MoTeC M800

Test engine

Programmable ECU

Dyno

Figure 4. Experimental setup for data sampling and programmable ECU

25

Load L (%)

20 15 10 5 0

0

1

2

3

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7 8 9 Time (s)

10 11 12 13 14 15

Figure 5. Constant step load applied by the dyno in the case study

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2.2.1 Input variables. Fi, j: Fuel injection time at the corresponding MAP i and idle speed j (ms, i ¼ [20, 30, 40, 50], j ¼ [500, 1,000, 1,500]). Table III shows an example of fuel look-up table in the ECU.

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Ii, j:

Ignition advance at the corresponding MAP i and idle speed j (degree BTDC, i ¼ [20, 30, 40, 50], j ¼ [500, 1,000, 1,500]). Table IV shows an example of ignition advance look-up table in the ECU.

Vj :

Intake valve opening time at the corresponding idle speed j (degree BTDC, j ¼ [500, 1,000, 1,500]). Table V shows an example of valve timing look-up table in the ECU.

Pro: Proportional gain of idle air valve controller. Int:

Integral gain of idle air valve controller.

Der: Derivative gain of idle air valve controller. Nor: Normal position of idle air valve (percentage of wide open); L:

Table III. An example of fuel injection time look-up table

Table IV. An example of ignition advance look-up table

Table V. An example of valve timing look-up table

Constant step load applied to engine (percentage of the dyno full load).

MAP (kPa)

500

RPM 1,000

1,500

50 40 30 20

4.02 3.36 3.24 3.04

4.06 3.39 3.27 2.89

4.09 3.36 3.31 3.04

MAP (kPa)

500

RPM 1,000

1,500

50 40 30 20

10 9.4 8.6 7.9

16 15.7 15 14.5

18 17.3 16.8 15.9

RPM

500

1,000

1,500

2

6

8


2.2.2 Output variables. . IAER – integral absolute error of engine idle speed, which is calculated by: IAER ¼

tf X

ð9Þ

j Rt 2 Raim j

t¼0

.

where tf – data recording time; tf ¼ 15 s; Rt – engine idle speed; Raim – aim idle speed; Raim ¼ 1,200 rpm. IAEl – integral absolute error of l: IAEl ¼

tf X

607

ð10Þ

jlt 2 laim j

t¼0

.

.

.

where lt – engine l value; laim – target l; laim – 1. SF – overall fuel consumption (ms), it is equal to the sum of fuel consumption from t ¼ 0 to tf ¼ 15 s with sampling time ¼ 0.05 s. Rmin – minimum idle speed in which the engine falls to when a step load is applied (rpm). Trise – recovery time to aim speed when a step load is applied (s).

1,400

8,000

1,300

7,000

1,200

6,000

1,100 Engine idle speed

1,000

Aim idle speed

4,000

Idle speed IAE value Rmin = 589 Trise = 2.3 IAER = 7,350

3,000

900 800

Rmin

700 Trise

600 500

0

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5,000

7 8 9 Time (s)

2,000

Idel speed IAER value

Engine speed (rpm)

A design of experiment technique – Latin hypercube sampling (LHS) (Lunani et al., 1995) is employed to choose a representative set of operating points for generating training samples. A total of 200 sets of representative combinations of input variables are selected and downloaded to the ECU to produce 200 sets of output performance data. Figures 6-8 show an example of output performance data in the 30th sampling data set D30. In order to have a fair comparison with the engine idle performances under different input setups, all the engine training data are recorded 5 s before the load is applied and 10 s after that point. Figure 6 shows the load rejection performance in D30. When the

1,000

0 10 11 12 13 14 15

Figure 6. Load rejection performance in D30

1.2

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1.15

16

1.1

14

608

Lambda

1.05

12

1

10

0.95 8

0.9

6

0.85

IAEl = 16.68 Lambda Aim Lambda IAE value of Lambda

0.8 0.75

Figure 7. Lambda performance in D30

0.7

0

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Lambda IAEl value

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0 7 8 9 10 11 12 13 14 15 Time (s)

load is applied, the engine speed firstly falls to 589 rpm and then takes 2.3 s to recover. The IAE value, which represents the load rejection ability, in 15 s test period is 7,350. Meanwhile, the engine l value as shown in Figure 7 rises first, it is due to the fact that if the engine speed suddenly drops, the fuel injection time is also dropped accordingly (Figure 8). When the PID BPAV controller starts to take action, it tends to open widely to increase the MAP, resulting in increasing the amount of fuel injected into the intake manifold. In this way, more air-fuel mixture can be inbreathed into the combustion chamber to generate more torque to cancel the load and regain to the aim speed. It is noted that there is a time delay between the fuel injection and the l value. It is because the l value is measured by an oxygen sensor in the exhaust pipe and the value can only present the stoichiometric ratio in the previous combustion cycle.

4.5

500

4

450

3.5

400

3

350 300

2.5

250

2 ∑F = 466.6

1.5

Fuel injection

1

∑F

0.5

Figure 8. Fuel consumption in D30

0

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200 150 100 50

0 7 8 9 10 11 12 13 14 15 Time (s)

∑F (ms)

Fuel injection (ms)

2.3 Application of multi-input/output LS-SVM and modelling results In the current application, Mh(x), h ¼ [1, 2, 3, 4, 5] in equation (8) stands for the performance functions of IAER, IAEl, SF, Rmin, Trise, respectively. After collection of

sample data set D, for every data subset dh ¼ D, it is randomly divided into two sets: TRAINh for training and TESTh for testing, where TRAINh contains 80 per cent of dh and TESTh holds the remaining 20 per cent. Then TRAINh is sent to the LS-SVM module for training, which has been implemented using LS-SVMlab 1.5 (Pelckmans et al., 2003), a MATLAB toolbox under MS Windows XP. In order to have a more accurate modelling result, the input data of the training data set is conventionally normalized before training (Pyle, 1999). This prevents any input parameter from domination to the output value. For all input values, it is necessary to be normalized within the range [0, 1], i.e. unit variance, through equation (11). For example, v e [7, 39], vmin ¼ 7 and vmax ¼ 39. The limits for each input engine control parameter should be predetermined via a number of experiments or expert knowledge or manufacturer data sheets. After obtaining the optimal setting, each set point should go through a de-normalization using the inverse of N 2 1of equation (11) in order to obtain the actual value v. The process flow of the normalization and de-normalization is shown in Figure 2: N ðvÞ ¼ v * ¼

v 2 vmin vmax 2 vmin


ð11Þ

To verify the accuracy of each function of Mh(x), an error function has been established. For a certain function Mh (x), the corresponding validation error is: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u 1 X yk 2 M h ðxk Þ2 ð12Þ Eh ¼ t N k¼1 yk where xk is the engine input parameters of kth data point in TESTh, yh is the actual output value in the data point dk (dk ¼ (xk,yk) represents the kth data point in dh) and N is the number of data points in the test set. The error Er is a root-mean-square of the difference between the true value yk of a test point dk and its corresponding estimated value Mh (xk). The difference is also divided by the true value yk, so that the result is normalized within the range [0, 1]. Hence, the accuracy rate for each output function Mh (x) is calculated using the following formula: Accuracyh ¼ ð1 2 E h Þ £ 100%

ð13Þ

All the output functions are evaluated one by one against their own test sets TESTh using equation (13). According to the accuracy shown in Table VI, the predicted results are in good agreement with the actual experiment results under their hyperparameters (gh, sh) inferred using Bayesian inference. However, it is believed that the function Engine output function Mh(x) M1(x) M2(x) M3(x) M4(x) M5(x) Overall average

gh

sh

Average accuracy with TESTh (per cent)

2796.4 190.53 1546.34 2426.72 3349.90

70.04 53.54 1264.26 61.86 44.69

95.7 96.1 94.5 95.4 93.5 95.1

Table VI. Accuracy of different output functions Mh and its corresponding hyperparameters

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accuracy could be improved by increasing the number of training data. An example of comparison between the predicted and actual engine IAER value and its error under the same ECU configuration is shown in Figure 9. As shown in Table VI, the LS-SVM model prediction accuracy is very good. Hence, the idle-speed system model built can be trusted and used for GA optimization. 3. Idle speed control optimization After obtaining the idle speed model, it is then possible to use GA technique to search the best engine setup automatically. Nowadays, GA has already been a well-known technique for solving many engineering optimization problems. The GA used in this research starts by generating randomly a set of solutions called population P. Each candidate solution in P is called a chromosome, which is composed of the input variables. Successive populations are called generations. The population P of n individuals {I1, . . . ,In} interacts with an environment and constraints, which returns a fitness f1,. . ., fn for an individual. The basic operation of a GA is to evolve a new population P0 from P by the operations of selection, crossover, mutation and elitism in each generation. The selection operation picks individuals from P based on an objective/fitness function, such as equation (14) in this paper. Individuals with better fitness are cloned more times than those with worse fitness. The crossover operation takes random pairs of selected individuals as parents and allows them to produce children containing genetic information for both parents. The mutation changes some random portions of the chromosome of an individual. The elitism preserves the best individual in the previous generation while replacing the worst individual in the current generation. Therefore, the best individual in all generations can be found. Successive generations produce

IAER value

18,000

12,000

6,000

Actual IAE value Predicted IAE value by LS-SVm

0

0

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25

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Figure 9. Comparison between predicted IAER values and the IAER values in TESTh

Predicted IAER error (%)

κ 18 16 14 12 10 8 6 4 2 0

1

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19

22 κ

increasingly fit individuals. The process is repeated until optimal solution is generated. The transition rules used by GAs are probabilistic. There are mainly two coding methods for chromosomes in GA: binary (0 and 1), and real (floating point). In contrast with binary-coded GA, real-coded GA does not require coding between real world data (usually floating point values). As real-coded GA directly uses floating-point values as the chromosomes, real-coded GA has been selected in this project. 3.1 Objective function for engine ISC optimization An objective function is designed to evaluate the idle performance under different control setups. In the case of engine ISC optimization, a complete ISC evaluation function should encompass (Thornhill and Thompson, 1999): . Idle speed regulation. The engine idle speed must be capable of maintaining close to the aim point with less deviation as possible. Essentially, the better the idle speed regulation and disturbance rejection ability, the lower the aim idle speed can be set. . Robustness of load disturbance. In a vehicle, the disturbance is due to electrical loads (e.g. switching on of air-conditioning, window heating, light, etc.), power steering and low-speed manoeuvring. These are events, when they occur, the engine may stall. . Fuel economy and emissions. On average, vehicles consume about 30 per cent of their fuel in idling during city driving (Jurgen, 1995), so minimization of fuel consumption and pollutant emissions in idle speed is very important.


Hence, a well-considered objective function for ISC problem is formulated as follows: Objective function ¼ max½2wIAER arctanðM 1 ðxÞÞ 2 wIAEl arctanðM 2 ðxÞÞ 2 wPF arctanðM 3 ðxÞÞ þ wRmin arctanðM 4 ðxÞÞ 2 wT rise arctanðM 5 ðxÞÞ

ð14Þ

Subject to: 2 % F i;j % 5 ms

0 % I i;j % 30 degree BTDC

2 30 % V j % 30 degree BTDC

where M1(x) represents the idle speed regulation quality; M2(x) represents the idle speed emission quality, ideally when the stoichiometric ratiol ¼ 1 the catalytic converter gets the maximum conversion efficiency of the exhaust gas; M3(x) is employed to assess the idle speed fuel consumption; M4(x) and M5(x) are used together for assessing the idle speed load rejection ability; wIAER , wIAEl , wPF , wRmin , wT rise are the user-defined weights of engine idle speed regulation, emission, fuel economy and load rejection ability, respectively. Table VII shows the user-defined weights in the case study. Each performance index is also transformed to a scale of (0, p/2) in equation (14). This ensures each index has the same contribution to the objective function. wIAER 3

wIAEl

wPF

wRmin

wTrise

2

3

4

1

Table VII. User-defined weights in the case study

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The objective function is manipulated by the GA optimization algorithm for generating the best ISC setting. The optimization framework has been implemented using Matlab. After testing various crossover and mutation methods for this application, the following GA operators and parameters have been selected for maximum efficiency and accuracy: . number of generation ¼ 1,000; . population size ¼ 50; . selection method: standard proportional selection; . crossover method: simple crossover with probability Pc ¼ 80 per cent; and . mutation method: hybrid static Gaussian and uniform mutation with probability Pm ¼ 40 per cent and standard deviation ¼ 0.2. 3.2 Optimization results The optimal set points recommended by the GA algorithm are shown in Tables VIII-XI. The predicted engine performance using the optimal setting is shown in Table XII. A comparison between the optimization results and Dbest, which is the best fitness among the 200 sample data sets, is also presented in the same table. Table XII shows that the optimization results produce significant improvement over Dbest.

Table VIII. Optimized fuel injection look-up table

Table IX. Optimized ignition advance look-up table

MAP (kPa)

500

RPM 1,000

1,500

50 40 30 20

3.39 2.23 2.11 1.99

3.34 2.25 2.13 1.91

3.55 2.25 2.25 2.12

MAP(kPa)

500

RPM 1,000

1,500

50 40 30 20

13.2 12.6 11.9 11.1

14.9 15.4 14 13

18.5 17.8 16.9 16.6

Table X. Optimized valve timing look-up table

RPM

Table XI. Optimized PID BPAV controller parameters

Pro 0.097

500

1,000

1,500

0.4

8.1

10.3

Int

Der

Nor

0.072

0.081

34.4

3.3 Evaluation of results To check the feasibility and efficiency of the methodology, the optimal setting is then sent back to the ECU and an evaluation test is carried out using the dyno. Figures 10-12 show the actual engine idle performance based on the optimal setting. Figure 10 shows the load rejection performance using the optimal setting. Before the load is applied, the engine idle speed runs steady and closely to the aim speed. When the load is applied, the engine falls to a minimum speed of 683 rpm and then takes 1.8 s to recover. Figure 11 shows the engine l performance using the optimal setting. It is noted that the l performance is very close to the aim value. When the load is applied, only a small deviation occurs and then the l value quickly returns to the aim value. SF

Rmin

Trise

Fitness

5007 6754 25.8

3.4 8.6 60.5

353.9 404.4 12.5

721 615 17.2

1.6 1.2 2 33

2 6.7197 2 6.9263 3

8,000

1,300

7,000

1,200

6,000

1,100

5,000

1,000 4,000 900

Engine idle speed Aim idle speed Idle speed IAE value

Rmin

800 700

Trise

600 0

1

2

3

4

5

6

7 8 9 Time (s)

1,000

0 10 11 12 13 14 15

Figure 10. Actual load rejection performance using the optimal setting

3

1.2

2.5

1

2

0.8 0.6

Lambda Aim Lambda IAE value of Lambda

0.4

IAEl = 2.85

0.2 0

2,000

Rmin = 683 Trise = 1.8 IAER = 5,412

Table XII. Optimization results against results of Dbest

0

1

2

3

4

5

6

1.5 1 0.5

0 7 8 9 10 11 12 13 14 15 Time (s)

Lambda IAEl value

500

3,000

613

Idel speed IAER value

IAEl

1,400

Lambda

Engine speed (rpm)

Optimization results Results of the best point of 200 sample sets, Dbest Overall improvement (per cent)

IAER


Figure 11. Actual lambda performance using the optimal setting

4

400

3.5

350

3

300

2.5

250 200

2 Fuel injection 1.5

150

∑F (ms) ∑F = 377.4

1

100 50

0.5

Figure 12. Actual fuel consumption using the optimal setting

0

0 0

1

2

3

4

5

6

7 8 9 10 11 12 13 14 15 Time (s)

IAER Table XIII. Comparison between optimization results and actual test results and Dbest

∑F (ms)

614

Fuel injection (ms)

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IAEl

SF

6,754 8.62 404.4 Dbest Optimization results (OP) 5,007 3.41 353.9 Actual test results (Da) 5,412 2.85 377.4 Accuracy of results (OP relative to Da) (per cent) 92.51 80.70 93.77 Actual improvement (Da relative to Dbest) 19.8 66.9 6.67

Rmin

Trise

Fitness

615 1.2 2 6.9263 721 1.6 2 6.7197 683 1.8 2 6.6693 94.43 88.88 99.24 11.1 250 3.7

Table XIII shows a comparison among the optimization results, actual test results and the results of Dbest. The actual test results in Table XII show that the ECU setting recommended produces the best performance. Table XIII indicates that the optimization results are in good agreement with the actual test results. This verifies again that the engine idle-speed model built by the LS-SVM is accurate and reliable. With the optimal ECU setup generated by the GA, the actual idle speed regulation quality is 19.8 per cent better than that of Dbest. Especially, the engine emission quality, the engine fuel consumption and the minimum idle speed outperform 66.9, 6.67 and 11.1 per cent, respectively. The recovery time of the idle speed is sacrificed in the objective function, wTrise is set to be the lowest value in this case study, so the recovery time based on the optimal setting is 50 per cent longer than that of Dbest. However, the recovery time is still acceptable. 4. Conclusions This paper proposes a novel methodology for modelling the idle speed performance of a high degree-of-freedom automotive engine and determining the best engine setup for ISC. The approach uses a new multi-input/output LS-SVM framework for modelling and a multi-objective GA framework to manipulate the engine model for determining the best combination of control parameters automatically. A case study demonstrates its application to a real automotive engine. The study illustrates the optimization of fuel injection time, spark timing, valve timing and PID BPAV controller parameters for maximizing engine idle speed regulation quality, load rejection ability, emission

quality and fuel economy. Evaluation tests show that the model accuracy is very good and an impressive improvement on engine idle performance is achieved using the optimal setting generated. Both prediction and experimental results indicate that the proposed methodology can really produce accurate and high-quality engine ISC performance. As compared with the conventional manual tuning, the proposed approach can greatly reduce the number of expensive dyno tests, which saves not only the time taken for optimal setup, but also a large amount of resources. It is also believed that the optimization results can be further improved if more training data are added to the LS-SVM model. From the perspective of automotive engineering, the integrated modelling and optimization methodology is a new approach and it can be applied to the other engine setup problems. In terms of scientific contribution, the research successfully integrates a couple of paradigms (LHS, multi-input/output LS-SVM and GA) into a general framework for constrained multivariable optimization problems under insufficient system information. References Celik, V. and Arcaklioglu, E. (2005), “Performance maps of a diesel engine”, Applied Energy, Vol. 81, pp. 247-59. Christian, B., Thomas, B., Aik, S. and Petra, M. (2006), “A nonlinear model for design and simulation of automotive idle speed control strategies”, Proceedings of the 2006 American Control Conference Minneapolis, pp. 14-16. DaeEun, K. and Jaehong, P. (2007), “Application of adaptive control to the fluctuation of engine speed at idle”, Information Science, Vol. 177, pp. 3341-55. Esmaeil, A.G., Farzad, H., Ramin, R. and Caro, L. (2008), “Colonial competitive algorithm: a novel approach for PID controller design in MIMO distillation column process”, International Journal of Intelligent Computing and Cybernetics, Vol. 1 No. 3, pp. 337-55. Haykin, S. (1999), Neural Networks: A Comprehensive Foundation, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ. Howell, M.N. and Best, M.C. (2000), “On-line PID tuning for engine idle-speed control using continuous action reinforcement learning automata”, Control Engineering Practice, Vol. 8, pp. 147-54. Jurgen, R. (1995), Automotive Electronics Handbook, 1st ed., McGraw-Hill, New York, NY. Liu, B., Su, H.Y. and Chu, J. (2005), “New predictive control algorithms based on least squares support vector machines”, Journal of Zhejiang University Science, Vol. 5, pp. 440-6. Liu, Z. and Fei, S. (2004), “Study of CNG/diesel dual fuel engine’s emissions by means of RBF neural network”, Journal of Zhejiang University Science, Vol. 5, pp. 960-5. Lunani, M., Sudjianto, A. and Johnson, P.L. (1995), “Generating efficient training samples for neural networks using Latin hypercube sampling”, Proceedings of the 1995 Artificial Neural Networks in Engineering, pp. 209-14. Manzie, C. and Watson, H.C. (2003), “A novel approach to disturbance rejection in idle speed control towards reduced idle fuel consumption”, IMechE Part D: J. Automobile Engineering, Vol. 217, pp. 677-90. Pelckmans, K., Suykens, J., Van, G., de Brabanter, J., Lukas, L., Hanmers, B., De Moor, B. and Vandewalle, J. (2003), LS-SVMlab: A MATLAB/C Toolbox for Least Square Support Vector Machines, available at: www.esat.kuleuven.ac.be/sista/lssvmlab Petridis, A.P. and Shenton, A.T. (2003), “Inverse-NARMA: a robust control method applied to SI engine idle-speed regulation”, Control Engineering Practice, Vol. 11, pp. 279-90.


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Pyle, D. (1999), Data Preparation for Data Mining, 1st ed., Morgan Kaufmann Press, San Mateo, CA. So¨derstro¨m, T. and Stoica, P. (1989), System Identification, 1st ed., Prentice-Hall, Cambridge. Suykens, J., Gestel, T., Brabanter, J., Moor, B. and Vandewalle, J. (2002), Least Squares Support Vector Machines, 1st ed., World Scientific Press, Singapore. Thornhill, M. and Thompson, S. (1999), “A comparison of idle speed control schemes”, Control Engineering Practice, Vol. 8, pp. 519-30. About the authors P.K. Wong is currently an Associate Professor in the Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau. He received his PhD degree in Mechanical Engineering from The Hong Kong Polytechnic University in 1997. His research interests include automotive engineering, fluid power transmission and control and engineering applications of artificial intelligence. P.K. Wong is the corresponding author and can be contacted at: [email protected] L.M. Tam, Full Professor, is the Department Head of Electromechanical Engineering, Faculty of Science and Technology, University of Macau. He received his PhD degree in Mechanical Engineering from the Oklahoma State University, USA, in 1995. He is also the President of the Institute for the Development and Quality, Macau. His research interests include heat transfer, chaos, and energy saving. K. Li is a PhD student in Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau. His research interests include fluid power engineering, variable valve timing and lift control and engineering applications of artificial intelligence.

H.C. Wong is an MSc student in the Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau. His research interest is automotive engineering.

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