Monitoring nonlinear profile data using support vector regression method

In today's manufacturing industries, if the quality characteristic of a product or a process is assumed to be represented by a functional relationship between the response variable and one or more explanatory variables, then the data generated from such a relationship are called profile data. Generally speaking, the functional relationship of the profile data rarely occurs in linear form, and the real data usually do not follow normal distribution. Thus, in this paper, the functional relationship of profile data is described via a nonparametric regression model and a nonparametric exponentially weighted moving average (EWMA) control chart is developed for detecting the process shifts for nonlinear profile data in the Phase II monitoring. We first fit the nonlinear profile data via a support vector regression model and use the fitted values to calculate the five metrics. Then, the nonparametric EWMA control chart with the five metrics can be constructed accordingly. Moreover, a simulation study is conducted to evaluate the detecting performance of the new control chart under various process shifts using the out‐of‐control average run length. Finally, a realistic nonlinear profile example is used to demonstrate the usefulness of our proposed nonparametric EWMA control chart and its monitoring schemes. It is expected that the proposed nonparametric EWMA control chart can enhance the monitoring efficiency for nonlinear profile data in the phase II study.     

Development and analyses of data-driven models for predicting the bed depth profile of solids flowing in a rotary kiln

Soft computing data-driven modeling (DDM) techniques have attracted the attention of many researchers across the globe as they do not require deep knowledge of the complex physical process. In the present research, data-driven based models have been developed using support vector regression (SVR), multilayer perceptron neural network (MLP), radial basis function neural network (RBFNN) and general regression neural networks (GRNN) techniques for predicting the bed depth profile of solids flowing in a rotary kiln. The performances of the developed models were compared and evaluated against the experimental results in terms of statistical measures such as coefficient of determination (R²), and average absolute relative error (AARE). The obtained results and findings from this research have revealed that data-driven models can predict the bed depth profile of solids flowing in a rotary kiln quite accurately. The SVR-based model exhibited the lowest AARE value of 1.72% and highest R² value of 0.9981 while GRNN, RBFNN, and MLP models gave corresponding values of AARE as 3.69%, 55.13%, 98.15% and those of R² as 0.9898, 0.0052 and 0.0081, respectively. Moreover, the developed DDM-based models i.e. GRNN, RBFNN, and MLP models overcame the limitations of the existing solutions which involved iterative numerical procedure entailing high degree of computational complexity.