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Fault detection technique is essential for improving overall equipment efficiency of semiconductor manufacturing industry. It has been recognized that fault detection based on k nearest neighbor rule (kNN) can effectively deal with some characteristics of semiconductor processes, such as multimode batch trajectories and nonlinearity. However, the computation complexity and storage space involved in neighbors searching of kNN prevent it from online monitoring, especially for high dimensional cases. To deal with this difficulty, principal component-based kNN has also been presented in literature, in which dimension reduction is done by principal component analysis (PCA) before kNN rule implemented to fault detection. However, dimension reduction by PCA may distort the distances between pairs of samples (trajectories). Thus the false alarm and missing detection of kNN for fault detection may increase in principal component subspace because PCA fails to preserve pairwise distances in subspace. To overcome this drawback, we propose a new fault detection method based on random projection and kNN rule, which combines the advantages of random projection in distance preservation (in the expectation) and kNN rule in dealing with the problems of multimodality and nonlinearity that often coexist in semiconductor manufacturing processes. An industrial example illustrates the performance of the proposed method.Index Terms-Fault detection, k-nearest neighbor rule (kNN), random projection (RP), distance preservation.

Kernel principal component analysis (KPCA) has shown excellent performance in monitoring nonlinear industrial processes. However, model building, updating, and online monitoring using KPCA are generally time-consuming when massive data are obtained under the normal operation condition (NOC). The main reason is that the eigen-decomposition of a high-dimensional kernel matrix constructed from massive NOC samples is computationally complex. Many studies have been devoted to solving this problem through reducing the NOC samples, but a KPCA model constructed from the reduced sample set cannot ensure good performance in monitoring nonlinear industrial processes. The performance of a KPCA model depends on whether the results of the eigen-decomposition of the reduced kernel matrix can well approximate that of the original kernel matrix. To improve the efficiency of KPCA-based process monitoring, this paper proposes randomized KPCA for monitoring nonlinear industrial processes with massive data. The proposed method uses random sampling to compress a kernel matrix into a subspace which maintains most of the useful information about process monitoring. Then, the reduced kernel matrix is operated to obtain desired eigen-decomposition results. On the basis of these approximated eigen-decomposition results, the proposed randomized KPCA can enhance the performance in monitoring nonlinear industrial processes. This is because the commonly used monitoring statistics are related to the eigenvalues and eigenvectors of the kernel matrix. Finally, numerical simulation and the benchmark TE chemical process are used to demonstrate the effectiveness of the proposed method.

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Estimating the state of a dynamic system via noisy sensor measurement is a common problem in sensor methods and applications. Most state estimation methods assume that measurement noise and state perturbations can be modeled as random variables with known statistical properties. However in some practical applications, engineers can only get the range of noises, instead of the precise statistical distributions. Hence, in the framework of Dempster-Shafer (DS) evidence theory, a novel state estimatation method by fusing dependent evidence generated from state equation, observation equation and the actual observations of the system states considering bounded noises is presented. It can be iteratively implemented to provide state estimation values calculated from fusion results at every time step. Finally, the proposed method is applied to a low-frequency acoustic resonance level gauge to obtain high-accuracy measurement results.