OCReP: An Optimally Conditioned Regularization for Pseudoinversion Based Neural Training

In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such cases, so that we introduce, in the framework of Tikhonov regularization, a matricial reformulation of the problem which allows us to use the condition number as a diagnostic tool for identification of instability. By imposing well-conditioning requirements on the relevant matrices, our theoretical analysis allows the identification of an optimal value for the regularization parameter from the standpoint of stability. We compare with the value derived by cross-validation for overfitting control and optimisation of the generalization performance. We test our method for both regression and classification tasks. The proposed method is quite effective in terms of predictivity, often with some improvement on performance with respect to the reference cases considered. This approach, due to analytical determination of the regularization parameter, dramatically reduces the computational load required by many other techniques.Comment: Published on Neural Network

A Fault Diagnosis Scheme for Gearbox Based on Improved Entropy and Optimized Regularized Extreme Learning Machine

The performance of a gearbox is sensitive to failures, especially in the long-term high speed and heavy load field. However, the multi-fault diagnosis in gearboxes is a challenging problem because of the complex and non-stationary measured signal. To obtain fault information more fully and improve the accuracy of gearbox fault diagnosis, this paper proposes a feature extraction method, hierarchical refined composite multiscale fluctuation dispersion entropy (HRCMFDE) to extract the fault features of rolling bearing and the gear vibration signals at different layers and scales. On this basis, a novel fault diagnosis scheme for the gearbox based on HRCMFDE, ReliefF and grey wolf optimizer regularized extreme learning machine is proposed. Firstly, HRCMFDE is employed to extract the original features, the multi-frequency time information can be evaluated simultaneously, and the fault feature information can be extracted more fully. After that, ReliefF is used to screen the sensitive features from the high-dimensional fault features. Finally, the sensitive features are inputted into the optimized regularized extreme learning machine to identify the fault states of the gearbox. Through three different types of gearbox experiments, the experimental results confirm that the proposed method has better diagnostic performance and generalization, which can effectively and accurately identify the different fault categories of the gearbox and outperforms other contrastive methods.</p