Mathematical Problems in Engineering

Volume 2015, Article ID 317142, 10 pages

http://dx.doi.org/10.1155/2015/317142

## Fault Tolerance Automotive Air-Ratio Control Using Extreme Learning Machine Model Predictive Controller

^{1}Department of Electromechanical Engineering, University of Macau, Macau^{2}Department of Computer and Information Science, University of Macau, Macau

Received 7 August 2014; Revised 27 September 2014; Accepted 28 September 2014

Academic Editor: Jiuwen Cao

Copyright © 2015 Pak Kin Wong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Effective air-ratio control is desirable to maintain the best engine performance. However, traditional air-ratio control assumes the lambda sensor located at the tail pipe works properly and relies strongly on the air-ratio feedback signal measured by the lambda sensor. When the sensor is warming up during cold start or under failure, the traditional air-ratio control no longer works. To address this issue, this paper utilizes an advanced modelling technique, kernel extreme learning machine (ELM), to build a backup air-ratio model. With the prediction from the model, a limited air-ratio control performance can be maintained even when the lambda sensor does not work. Such strategy is realized as fault tolerance control. In order to verify the effectiveness of the proposed fault tolerance air-ratio control strategy, a model predictive control scheme is constructed based on the kernel ELM backup air-ratio model and implemented on a real engine. Experimental results show that the proposed controller can regulate the air-ratio to specific target values within a satisfactory tolerance under external disturbance and the absence of air-ratio feedback signal from the lambda sensor. This implies that the proposed fault tolerance air-ratio control is a promising scheme to maintain air-ratio control performance when the lambda sensor is under failure or warming up.

#### 1. Introduction

Vehicular emissions are the major source of gaseous pollutants that contribute to the harmful and negative effects on environment and human health. It has been reported in [1–4] that the increasing amount of vehicular emissions has led to hundred thousands of mortalities and billions of economic loss every year. To reduce the amount of toxic elements in vehicular emissions, three-way catalytic converter is currently the most effective after-treatment device. This device reduces the unburned hydrocarbons and carbon monoxide by oxidization and nitrogen oxides by reduction [5]. The conversion efficiency of the catalytic converter, however, depends highly on the air-ratio (also known as lambda). When the air-ratio is at the stoichiometric value (i.e., air-ratio = 1.0), the conversion efficiency can reach as high as 98%, but derivation of only 1% from stoichiometry can already result in 50% degradation on the converter. Therefore, for environmental purpose, the air-ratio is usually regulated to 1. Meanwhile, as an important engine parameter, the air-ratio should also be controlled to different values for other situations [6]. For instance, if emissions are not concerned, the air-ratio can be regulated to around 0.95 to achieve the best engine power performance, whilst it is 1.05 to achieve the best brake-specific fuel consumption. Consequently, an effective air-ratio control system is necessary for engine system to maintain its best performance under various operating conditions.

Over the past decades, car manufacturers and researchers have developed many air-ratio control strategies [7–12]. Examples include the sliding mode control [7, 8], proportional-integral-derivative (PID) control [9], and neural-network-based model predictive control (MPC) [10–12]. Sliding mode control requires a very accurate mathematical definition of the engine model, but in general it is impossible to derive an exact engine dynamics model due to its highly nonlinear nature [13]. In most sliding mode air-ratio control studies, many assumptions have been made in the model derivation, and many coefficients are difficult to determine for a real engine, so this strategy may not be suitable for practical use. Although PID control is the most widely used approach in practice, the calibration and tuning of the control parameters are very time-consuming and engine dependent. The tuned PID controller cannot deal with steady disturbance or any change in the engine conditions either. Thus, among these researches, the most appropriate and promising technique for air-ratio control is the neural-network-based MPC, due to its robustness to multivariable, time-varying, and delay systems like modern engine systems [12]. It is well-known that a reliable prediction model is the core component of the MPC, but the engine models developed in [10, 11] were only surrogate models. That is, the models were trained from the data generated by empirical equations rather than a real engine. Therefore, similar to the deficiency of sliding mode control approach, the neural-network prediction models in [10, 11] derived from data generated by empirical equations cannot effectively reflect the actual performance of real engines. In the most recent study of MPC air-control strategy [12], the prediction model for the controller was constructed based on experimental data rather than numerical data. Experimental results in [12] showed that the controller performance is superior to those of [10, 11] in real application. Nevertheless, one major concern for the control strategy in [12] is that the prediction model must rely on the real-time air-ratio signal measured from the lambda sensor located at the exhaust pipe of the engine. When the sensor is under failure or warming up during cold start, the controller becomes ineffective, resulting in poor control performance.

In fact, for most of the current available air-ratio control approaches, the air-ratio measurement must be acquired as the feedback to the controllers. Hence, the problem of lambda sensor failure must be addressed. Although on-board diagnostics for the lambda sensor has been a requirement for more than two decades [14] and any fault of the lambda sensor must be reflected through the “check engine” light on the instrument panel, the driver may not be aware of such fault and may not be willing to replace the lambda sensor when the car can still be driven without significant defect. In that case, the emissions and fuel consumption of that car are already significantly deteriorated. Therefore, maintaining a satisfactory air-ratio control performance when the lambda sensor is under failure or warming up during cold start is of great significance. This paper proposes to build a supplementary air-ratio model to compensate the lambda sensor, in which the measured air-ratio signal is not required as the model input.

From the open literature [15, 16], it is possible to predict the air-ratio without using the previous air-ratio signal. For instance, Gassenfeit and Powell [15] compared two algorithms that can predict the air-ratio from either the cylinder pressure time history patterns or the ratio of the cylinder pressure before and after combustion. Another example is the method described by Asik et al. [16], in which the air-ratio can be roughly estimated from induced crankshaft speed fluctuations. However, the quantities used in these algorithms, say, the in-cylinder pressure and delicate crankshaft speed fluctuation, are usually unavailable in normal vehicle engines because expensive sensors are required. Moreover, as mentioned, empirical equations may not be suitable for real applications. Thus, by following the framework in [12], this study attempts to construct the air-ratio model from experimental data. Extreme learning machine (ELM) [17] is currently a popular and effective algorithm for training model from sample data. Many recent studies [18, 19] already showed that ELM is superior to other famous methods, such as neural-networks, least squares support vector machines, and relevance vector machine, in terms of generalization performance and computational load. ELM has been employed for various practical applications too [20, 21]. Thus, ELM is selected in this study to develop the supplementary air-ratio model.

Among so many variants of ELM, kernel-based ELM is adopted in this study to build the model. It is because, in kernel ELM, the random feature mapping is replaced with a kernel function, so randomness does not occur and the chance of result variations could be reduced [22]. In fact, the model built in [12] was based on an online variant of ELM, whose backbone is simply a basic ELM (i.e., the model is still an ELM with random feature mapping but can be updated when online data is provided). The reason why offline version of ELM is used in this paper instead of the online one is that the real-time data of air-ratio will not be available when the lambda sensor is malfunctioning. As both the air-ratio model from [12] and the proposed air-ratio model are made from the same basis (kernel ELM), a fair comparison can be made to evaluate their performances.

In order to verify the effectiveness of the ELM supplementary air-ratio model, this paper also proposes a nonlinear MPC algorithm for air-ratio control, which utilizes a switch to toggle between the lambda sensor signals and the ELM supplementary air-ratio model predictions. When the lambda sensor works well, the air-ratio measurement will be used; when the lambda sensor is under failure, the backup air-ratio model will be used. The MPC under such strategy is called fault tolerance controller (FTC), which is a novel nontrivial application of ELM. Based on the multiple-step-ahead air-ratio predictions, a control signal is obtained to regulate the air-ratio to trace the desired values. The proposed FTC is also compared with the typical air-ratio control techniques, including online sequential extreme learning machine model predictive controller (OEMPC) [12], diagonal recurrent neural-network model predictive controller (DNMPC) [10], and traditional open-loop air-ratio control system, to evaluate its performance. The concept of kernel-based ELM is provided in Section 2. The construction and evaluation of the ELM supplementary air-ratio model are given in Section 3. The detail of the FTC design is presented in Section 4. Experimental implementation and evaluation of the proposed FTC and OEMPC are provided in Section 5.

#### 2. Kernel-Based Extreme Learning Machine

Kernel-based ELM is a learning scheme for single-hidden-layer feedforward network, with the use of kernel [17]. Considering a set of training samples , with each being a dimensional input vector and as the target scalar output, a single-hidden-layer feedforward network with hidden nodes can be written aswhere is the feature mapping output with respect to and is the output weight vector. In kernel-based ELM, this weight vector is determined by minimizing both the norm of the weight vector and the training error. The corresponding optimization problem is where is a user-specified penalty term for regularization purpose.

Then, based on the Karush-Kuhn-Tucker theorem, optimizing (2) is equal to solving the following dual optimization problem:where is the Lagrange multiplier.

By taking derivatives on (3), the following conditions are obtained:where

By combining the conditions in (4) and eliminating the Lagrange multipliers , the optimal weight vector could be calculated as where and is the identity matrix.

With (6), the output function of the network for an unknown input becomes

Finally, by defining a kernel matrix satisfying Mercer’s conditions as(7) becomes

In this study, the function is the supplementary air-ratio model.

#### 3. Supplementary Air-Ratio Model

##### 3.1. Model Construction

The objective of the ELM supplementary air-ratio model is to predict the future air-ratio when the lambda sensor is under failure or during cold start. Previous air-ratio measurement must not be used as the inputs to the model. Three engine parameters related closely to the air-ratio performance were carefully selected as the model inputs: fuel injection time (FI), engine speed (ES), and throttle position (TP). The order of the system dynamics was chosen to be 2 (i.e., second-order system with 2 past time steps), which gives the minimum prediction error [12]. The structure of the supplementary air-ratio model is shown in Figure 1.