Modeling switched circuits based on wavelet decomposition and neural networks

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Abstract

In this paper, switched circuits are modeled based on wavelet decomposition and neural network. Also describes the usage of wavelet decomposition and neural network for modeling and simulation of nonlinear systems. The switched circuits are piecewise-linear circuits. At each position of switch the circuit is linear but when considered all switching positions of the circuit it becomes nonlinear. An important problem which arises in modeling switched circuit is high structural complexity. In this study, wavelet decomposition is used for feature extracting from input signals and neural network is used as an intelligent modeling tool. Two performance measures root-mean-square (RMS) and the coefficient of multiple determinations (R2) are given to compare the predicted and computed values for model validation. The evaluated R2 value is 0.9985 and RMS value is 0.0099. All simulations showed that the proposed method is more effective and can be used for analyzing and modeling switched circuits. When we consider obtained performance, we can easily say that the proposed method can be used efficiently for modeling any other nonlinear dynamical systems.

Introduction

Switches are relatively common circuit components. One of the reasons for this is that many electronic and power electronic circuit components, modeled by using switches and other linear component, have been added to the non-linear component class in recent years. In addition, formulation and solution of the circuits containing such components and their modeling using a piecewise-linear approach is also common now. Switches are revealed in equivalent circuits by modeling them as non-linear components [1].

Switched circuits have found many applications areas in engineering like telecommunication networks and mechanical systems [2], [3]. These circuits can be categorized in three groups according to their clocking situations [4]. First group is consisting of externally clocked switched circuits, second group is consisting of internally clocked switched circuits and third group is consisting of externally and internally clocked switched circuits. In the last few decades, many researchers have studied about computer methods for analysis and design of nonlinear systems [5], [6], [7], [8]. One of these methods is piecewise linearization, in these methods nonlinear components in the circuits or systems are changed with their equivalent linear time invariant component or equivalent ideal linear switches [6], [7], [8], [9], [10], [11]. For analyzing switched circuits, time domain and frequency domain methods were also studied [3], [12]. In [1], the formulation of state and output equations and solutions of switched-systems were presented by using bond graph model with a new simple and more general switch definition. In [10] they were realized a study for modeling and simulating switched circuits by using artificial neural network and adaptive network based fuzzy inference systems. Wavelet transform also used in nonlinear analysis [7]. In [7], a novel method for the analysis and simulation of integrated circuits (ICs) with the potential to greatly shorten the IC design cycle was proposed. A highly efficient wavelet-based simulation technique for high-frequency circuits was presented. The multitime partial differential-equation system describing the circuit has been solved using a pseudowavelet collocation method. A nonlinear model-reduction process has been applied, leading to significant gains in efficiency, but without a complementary loss in accuracy.

Another method for modeling nonlinear system is black-box modeling. The black-box approach is used to model nonlinear dynamical systems when the input–output quantities are known. Neural network (NN) is one of the well known black-box approach and used in many different disciplines such as modeling, analyzing and control [9], [13], [14], [15], [16]. One of the problems which arise in modeling with NN is slow and difficult training. If the input signals are complex or similar to each other, then NN models are not able to learn systems dynamics fluently and training stages take more time.

In this paper, switched circuits are modeled based on wavelet decomposition and neural network. The wavelet and neural network approach allows solving the high structural complexity and slow and difficult training problems. The paper is organized as follows. In Section 2, we review some basic properties of the wavelet decomposition and neural networks. The proposed system is described in Section 3. The effectiveness of the proposed method is demonstrated in Section 4. Finally, conclusion is presented in Section 5.

Section snippets

Preliminaries

In this section, the theoretical foundations for the expert system used in the presented study are given in the following subsections.

Procedure

Different approaches have been used to model switched circuits. [1] used bond graph approach for modeling and analyzing switching circuits and [10] used neural and fuzzy-neural networks approaches for modeling and simulating of switched circuits, both of them had obtained desired performances. The aim of this study is to present the usage of wavelet for decomposing SCs signals and modeling SCs by composed signals. Fig. 5 shows the proposed expert system block diagram. It consists of two parts:

Modeling results

To determine the model validation, the wavelet and neural network model performance and mathematical model performance are compared graphically as shown in Fig. 8. In this stage, Vi=1sin(0.1t) is applied as an input to mathematical model and wavelet and neural network model. The outputs of these models are shown in Fig. 8. It clearly indicates that the nonlinear dynamics of switched circuit have been modeled accurately.

Some statistical methods, such as the root-mean squared (RMS), the

Conclusion

In this study, intelligent model for switched circuit is performed. The task of signal processing and modeling is performed using the wavelet and neural network, respectively. The obtained results show that the proposed intelligent model can make an efficient interpretation. The signal processing is motivated by a realization that wavelet essentially is a representation of a signal at a variety of resolutions. In brief, the wavelet decomposition has been demonstrated to be an effective tool for

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