Nonlinear system identification using Kautz basis expansion-based Volterra–PARAFAC model

“…Figure 7 is the framework of principal component analysis together with alternate least squares for vibration signal features extraction (PCA-ALS), which can be summarized as seven procedures. Step 1: Simulated signal is obtained using equation ( 16) to (17).…”

Section: Multi-fault Of Multi-channel Detection Based On Tensor Factorization a Procedures Of Multi-fault Of Multi-channel Detection Basementioning

confidence: 99%

“…In this paper, δ n is the standard deviation of the noise signal and it reflects the noise strength, and hence δ n n(t) represents Gaussian white noise signal. In the above equation, h(t) can be written as [26] h (t) = = e −βt sin (2πf r t) t ≥ 0 0 others (17) where β = 50Hz is a decay parameter. Sampling frequency and time are separately set to 20k Hz and 0.5s, and the data length is 10000.…”

Section: B Simulation Analysismentioning

confidence: 99%

“…In the past years, many researches have conducted surveys on the tensor decomposition, and the interesting readers can be referred to the review in [16]. PARAFAC model can be also successfully used to identify nonlinear system [17]. A multidimensional de-noising technique of rotating machinery based on the tensor factorization has been developed for multidimensional signal filtering [18].…”

Section: Introductionmentioning

confidence: 99%

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A Tensor-Based Approach for Identification of Multi-Channel Bearing Compound Faults

2019

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Vibration signal analysis is one of the most effective approaches for detecting faults in bearings. A bearing compound-fault signal always consists of multiple signatures and stochastic noise. The separation of multi-fault signals from them is not only crucial but also very challenging. In order to solve this issue, a novel multiple faults detecting technique has been developed based on tensor factorization. The original multi-channel vibration signals are formulated as a 3-way tensor via the temporal signal, spectra, and channel information in a high-dimensional space. The PARAFAC decomposition is used to analyze the tensor model, and then, principal component analysis (PCA) is introduced to find the numbers of the rankone tensor. Finally, the tensor model is solved by alternating least squares (ALSs) approach combined with PCA technique. The performance of the detection method has been proven by simulation analysis of the multi-channel compound faults signals. The experimental results obtained using the developed technique also demonstrated that compound-fault signatures can be effectively and clearly identified.INDEX TERMS PARAFAC, compound-fault, rolling element bearing, fault identification, tensor.

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“…As the transfer function of a linear system, Volterra kernel (including Volterra kernel time-domain kernel and Volterra kernel frequency-domain kernel) does not depend on the input and output of the system, which can characterize the essential properties of the nonlinear system and explain the special phenomena of the nonlinear system. It has advantages of clear physical meaning and rich information, which is widely used in electronic engineering, mechanical and electrical engineering, control engineering, and other fields [1][2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

An Intelligent Calculation Method of Volterra Time-Domain Kernel Based on Time-Delay Artificial Neural Network

Zhong

Chen

2020

Mathematical Problems in Engineering

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To solve the problems of high complexity and low accuracy in Volterra time-domain kernel calculation of a nonlinear system, this paper proposes an intelligent calculation method of Volterra time-domain kernel by time-delay artificial neural networks (TDANNs) and also designs a root mean square error (RMSE) index to choose the neuron number of the network input layer. Firstly, a three-layer TDANN is designed according to the characteristics of the Volterra model. Secondly, the relationship between parameters of TDANN and Volterra time-domain kernel is analyzed, and then three-order expressions of Volterra time-domain kernel are derived. The calculation of Volterra time-domain kernel is completed by network training. Finally, it is verified by a nonlinear system. Simulation results indicate that compared with traditional methods, the new method has higher accuracy, and it can realize the batch calculation of Volterra kernel, which not only improves the calculation efficiency but also provides accurate data for fault diagnosis based on Volterra kernel in further research work.

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Nonlinear system identification using Kautz basis expansion-based Volterra–PARAFAC model

Cited by 7 publications

References 39 publications

Two‐parameter Kautz network‐based LTV‐MPC for non‐linear standalone micro‐grid control

Two‐parameter Kautz network‐based LTV‐MPC for non‐linear standalone micro‐grid control

A Tensor-Based Approach for Identification of Multi-Channel Bearing Compound Faults

An Intelligent Calculation Method of Volterra Time-Domain Kernel Based on Time-Delay Artificial Neural Network

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