Product quality modelling and prediction based on wavelet relevance vector machines

In order to predict product quality and optimize production process, the product quality models need to be built. However, there are complex nonlinear relationship among the product quality parameters and the production process variables. The common methods cannot model the production process with high accuracy and the prediction intervals cannot be given by those methods. In contrast, the kernel methods can transform the original input data into a feature space via kernel function, and then the linear methods can be used to resolve the nonlinear problem accurately. Moreover, the relevance vector machine as a kernel method can give the prediction intervals, and wavelet kernel can inherit the ability of local analysis and feature extraction from the wavelet function. The product quality models based on wavelet relevance vector machine are proposed in this paper. A simulation data set, two chemistry data sets and a real field data set of zinc coating weights from strip hot-dip galvanizing are used to validate the model. The results demonstrate that the model based on wavelet relevance vector machines has a higher prediction precision than the common methods such as partial least squares(PLS), orthogonal signal correction-partial least squares(OSC-PLS), Quadratic-PLS, kernel partial least squares(KPLS), orthogonal signal correction-kernel partial least squares(OSC-PLS), least squares-support vector machines (LS-SVM) and ordinary relevance vector machines(RVM). The prediction intervals are also given by the presented model. Mexican, Morlet and Difference of Gaussian (DOG) wavelet relevance vector machines (WRVMs) for multi-group data show superior prediction performance compared to other methods mentioned above.

► A product quality model based on wavelet relevance vector machine (WRVM) is proposed.
► Wavelet relevance vector machine model can give the exact prediction interval.
► Zinc coating weights from strip hot-dip galvanizing are predicted to validate the model.
► WRVM has a higher prediction precisions than PLS, Q-PLS KPLS, SVM and RVM.