Elsevier

Swarm and Evolutionary Computation

Volume 8, February 2013, Pages 54-68
Swarm and Evolutionary Computation

Regular Paper
Practical multi-objective controller for preventing noise and vibration in an automobile wiper system

https://doi.org/10.1016/j.swevo.2012.08.004Get rights and content

Abstract

This paper presents an approach using a multi-objective controller to prevent noise and vibration generated by the wiper blade during its wiping operation. Firstly, this paper focuses on the experimental approach to collect noise and vibration data from a car wiper system during its operation and secondly, to develop black box model of the wiper system using nonparametric approach of system identification known as nonlinear auto regressive exogenous Elman neural network (NARXENN). Finally, a novel closed loop iterative input shaping controller whose parameters are tuned simultaneously by a Pareto based multi objective genetic algorithm (MOGA) are proposed and simulated in such a way that it can prevent unwanted noise and vibration in the wiper system. The main contribution of this work rather the previous studies of automobile wiper system is to develop a novel multi-objective control strategy whereby an automobile wiper blade is moved within its sweep workspace in the least amount of time with minimum noise and vibration.

Introduction

A good wiping performance of an automobile wiper system is not only to provide a clear vision through the windscreen but also to operate silently. In order to meet these two important aspects it is typically relied on the wiper physical attributes such as blade rubber, windscreen glass material, friction between blade tip and windscreen, windscreen curve shape and attack angle of the blade. A computational modeling validated by experimental test which considered attack angle and friction coefficient influence carried out by Chevennement et al. [1]. The effects of wiping speed and windscreen wetness on noise generated of wiper blade was investigated by Zhang [2] and was shown that wiping noise is strongly affected by windshield wetness, while less affected by wiping speed. It is frequently happened that the wiper system generates low frequency noise and vibration known as chatter [3]. In the open literature it is evidenced that chattering noise in the wiper system is due to deformation of wiper blade during the wiper turnover. This chatter noise is not only annoying to the occupants but also causes vision disturbance to the driver.

To date, there are a number of published articles concerning on noise and vibration in the wiper system. Abu Bakar et al. [4] conducted model testing to determine the natural frequencies of a wiper and conducted experiments to investigate vibration and noise of a wiper. They found that the wiper produces chatter noise below 100 Hz. The windscreen also experiences streaking visual deterioration effect during the experiment. They inferred that non-uniform water films on the windscreen may disturb contact between the rubber blade and the windscreen interfaces that lead to vibration. Goto et al. [5], Grenouillat et al. [6] and Okura and Oya [7] investigated squeal noise reduction using 2D and 3D mathematical models. Stallaert et al. [8] and Chevennement et al. [9] developed a finite element model to support the optimization of the control configuration, study the dynamic instability of a flexible wiper system and suppressing wiper squeal noise. Fujii and Yamaguchi [10] suggested a new method for dynamic behavior of wiper blade using an optical approach. Chang et al. [11] worked on control of the chaotic motion of an automotive wiper system by using bifurcation diagram and Lyapunov exponent. Various Control methods have also been adopted for other purposes in the wiper system. An experimental study has been carried out in order to compensate the delay caused by various environmental conditions as well as other intelligent operations of a smart wiper. Three different sensory devices which measure the rain intense according to auditory, tactile and vision parameters are determined. A fuzzy logic controller is employed for position control of wiper and eliminates uncertainties [12]. Park et al.[13] developed an intelligent method comprising of image processing technique and fuzzy logic decision maker to assign the interval of wiper movement and its speed based on rain intensity without driver's intervention. An accurate control of wiper blade for an independent wiper system in opposition sides which are actuated via two separate motors are investigated by Lévine [14]. A feedback PID controller is employed in collaboration with a sort of feed-forward controller called flatness in order to avoid collision and obtain more precise trajectory tracking of each wiper.

The various techniques of system identifications are broadly used as a fundamental requirement in engineering and scientific applications such as time series prediction, pattern recognition, symbolic regression or prediction of dynamic model of a system. Due to hyper nonlinear characteristic of a wiper system accurate nonlinear system identification is required for extracting black box of system. Hence, A nonlinear auto regressive exogenous (NARX) in cascade with Elman neural network (ENN) is utilized for the purpose of system identification of nonlinear wiper system.

NARX is one the well-known system identification models which proved to be greatly efficient and accurate for nonlinear system identification [15], [16], [17], [18], [19]. There have been a number of popular techniques which developed and applied to identify NARX models that best estimate output behavior of a nonlinear system based on the input state. These techniques are classified into two major sorts of parametric and non-parametric approaches of system identifications. Although parametric identification approach such as least square (LS) or recursive least squares (RLS) algorithms have got broad applications for parameter estimation in modeling slowly varying dynamic systems [20], the technique does not work efficiently for a system whose characteristics change abruptly with time [21]. Parameter estimation constitutes a procedure that makes it possible to adjust a model with a specific structure. For this purpose, it is necessary to determine the appropriate order and parameters for the model that best fits input–output data obtained during the experiment. This task can be very time consuming indeed and it is very important to choose a correct order for the model, since a lower order may imply that the model could not adequately describe the real dynamics of the process, while a higher order could increase model uncertainties [22]. In order to control vibration and noise of wiper system which is considered as a flexible manipulator with several modes of frequencies it was proven that nonparametric approaches and specifically NN performed better at higher resonant modes than conventional RLS even in problems associated with non-minimum phase characteristics of the system [20]. Once the system is not sufficiently excited, the covariance matrix of the RLS algorithm may grow, which leads to the covariance “windup” that may cause a breakdown of the algorithm. In order to overcome these shortcomings of parametric identification methods, some modified techniques for adjusting the forgetting factor or combining different techniques have been investigated [23], [24] the use of which a forgetting factor could cause the predicted values of parameter to tend to fluctuate rather than to converge to a certain value. The level of fluctuation depends on the value of forgetting factor so that a smaller value of forgetting factor leads to a larger fluctuation in the parameter values. Furthermore, several comparisons which signified outperform of nonparametric techniques over parametric ones in the area of the flexible manipulators and plates modeling can be found in [25], [26], [27].

MLP neural network applied to power system dynamic load identification is not usually desirable, as its static of structure is non-dynamic. In ENN unlike MLP which merely uses feedforward connections there is a set of carefully chosen feedback connections that allow the network remember cues from the recent past. Besides, the distinct self-connections of the context nodes in the Elman network make it sensitive to the history of input data, which is essentially useful in dynamical system modeling with white noise input. All these as well as the authors previous investigations on using different intelligence modeling for the purpose of nonlinear flexible system identification and control [26], [27], [28] justified that the memory function with a dynamic feedback of neural network can effectively solve this sort of problems. Hence, a modified type of ENN is used in this study for dynamic modeling of wiper blade system with Bang–Bang input and end-point acceleration and hub displacement as outputs.

Iterative learning (IL) method is an intelligent learning algorithm for mechanisms which perform repetitive operations within a period of time to improve the system's performance. The first idea of IL control (ILC) formulations were proposed by Uchiyama in Japanese language and translated by Arimoto et al. in English and later mathematically formulated by Arimoto et al. in English [29], [30]. A comprehensive survey on IL control and its applications can be found in [26], [31], [32], [53].

Input shaping (IS) technique as an advisable feed-forward controller cancels the residual vibration in flexible structures if the amplitudes and instances of convolved impulses are identified accurately [33], [34], [35]. On the other hand, inaccurate application of Impulse instances can cause significant degradation in system performance. One way to overcome this shortcoming of open-loop input shaping is using closed-loop input shaping (CLIS) [36].

Since control of wiper system's noise and vibration involves several conflict objectives which should be in command and optimized simultaneously a need for an effective multi objective optimization is necessary in this study. The main advantage of MOGA is its versatility for including a variety of objectives and constraints while designing the controller. Generally, it can be said that it is not an analytical approach which deals with Pareto set problem. So, evolutionary computations are employed commonly in order to find the Pareto fronts of different objectives of problem. Pareto approaches for first time has been proposed by Goldberg in order to figure out Schaffer's VEGA problem [37]. Fitness sharing is introduced to keep diversity of solutions over the Pareto line by Fonseca and Fleming, 1993 [38]. Up to present several multi objective problems have been studied by researchers in control field [39], [40], [41].

A novel combination of CLIS and IL controllers is developed while a Pareto multi objective genetic algorithm (MOGA) is utilized to estimate the most appropriate values of controller gains to design a robust controller for vibration and noise reduction of automobile's wiper blade without sacrificing its speed of response. In fact the proposed controller applies a hybrid of an open loop controller which overcomes the unwanted vibration of wiper due to its high elasticity characteristic in one hand and closed loop part of controller is tasked to deal with the external disturbance which are likely to influence the operation of wiper system in both time and frequency domain simultaneously.

Section snippets

Experimental model preparation

The wiper model used in this study is the uni-blade type wiper which is typically found in the Proton Iswara. A pipe hose with running water on the top of windscreen facilitated that simulates a rainy or wet condition for operating wiper at speed of Bang–Bang input. In the experiment, a 16 input channels PAK MK II Muller BBM signal analyzer, a Kistler Type 8794A500 tri-axial accelerometer and a shaft encoder were used to measure the acceleration of end point and displacement of hub angle of the

NARX model

The NARX model structure is defined byy(k)=F(y(k1),,y(kny),u(k1),,u(knu))+ε(k)in which the effect of noise is assumed additive at output of the model. F(.) is a nonlinear function, yk, uk and εk are output, input, and noise respectively where ny, nu and are maximum lags on observations and exogenous inputs [42]. In order to identify the NARX model; the corresponding F(.) function should be approximated first; so that in this study the nonlinear function F(.) is estimated by ENN.

Elman neural network algorithm

Elman

System modeling

In order to validate the capability of applied system identification model for acceptable extent of uncertainty and nonlinearity a uniformly distributed white noise signal in the same frequency range of system was generated in the path of the output of system. The mentioned noise input in the time and frequency domains are illustrated in Fig. 9.

For the modeling process, input–output data were collected for a wiper system. Then, performing the one value at the moment the best maximum lag of the

Establish the cost functions

Three cost functions of wiper system's dynamic characteristics are defined to be considered in this study. Integral of absolute end-point acceleration (IAEA), maximum overshot of hub displacement and rise time of hub displacement response are objectives that aimed to be minimized and defined as

  • Integral absolute value of end-point acceleration (IAEA):IAEA=0T|yEA(t)|dt,where |yEA(t)| singnifies the acquired signal of end-point acceleration of wiper lip. IAEA in the merely states the integral of

Conclusion

This study centered a practical multi disciplinary control of a flexible structure particularly for an automotive wiper blade system. A model characterizing a flexible wiper structure has been devised using identification system. A dynamic model based experiment is developed at initial stage of the work. Then, the inputs and outputs of the wiper system are used to model the dynamic characteristics of the structure using a modified nonparametric approach called NARXENN. With attaining the

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