In the development of soft sensors for an industrial process, the colinearity of the predictor variables and the time-varying nature of the process need to be addressed. In many industrial applications, the partial least-squares (PLS) has been proven to capture the linear relationship between input and output variables for a local operating region; therefore, the PLS model needs to be adapted to accommodate the time-varying nature of the process. In this paper, a fast moving window algorithm is derived to update the PLS model. The proposed approach adapted the parameters of the inferential model with the dissimilarities between the new and oldest data and incorporated them into the kernel algorithm for the PLS. The computational loading of the model adaptation was therefore independent of the window size. In addition, the prediction performance of the model is only dependent on the retained latent variables (LVs) and the window size that can be predetermined from the historical data. Since a moving window approach is sensitive to outliers, the confidence intervals for the primary variables were created based on the prediction uncertainty. The inferential model would not be misled by the outliers from the online analyzers, whereas the model could be updated during the transition stage. The prediction performance of a soft sensor is not only dependent on the capability of the inferential model, but also relies on the data quality of the input measurements. In this paper, the input sensors were validated before performing a prediction. The deterioration of the prediction performance due to the failed sensors was removed by the reconstruction approach. A simulated example of a continuous stirred tank reactor (CSTR) with feedback control systems illustrated that the process characteristics captured by the PLS could be adapted to accommodate a nonlinear process. An industrial example, predicting oxygen concentrations in the air separation process, demonstrated the effectiveness of the proposed approach for the process industry.

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A novel process monitoring method based on modified Bayesian classification on PCA subspace is proposed. Fault detection and identification are the major steps to diagnose root causes of a process fault. However, before the faulty variables from the abnormal operations are identified, the different operating states need to be clustered from the historical data. The proposed approach modifies the Bayesian classification method to cluster data into groups. Therefore, a new fault identification index is derived based on cluster center and covariance. An industrial compressor process is used to demonstrate the effectiveness of the proposed approach. In the example, process-insight-based variables were monitored along with the measured variables. The capability of fault diagnosis has been improved, since the fault identification indices are directly related to the variables with process characteristics.

Fault isolation based on data-driven approaches usually assume the abnormal event data will be formed into a new operating region, measuring the differences between normal and faulty states to identify the faulty variables. In practice, operators intervene in processes when they are aware of abnormalities occurring. The process behavior is nonstationary, whereas the operators are trying to bring it back to normal states. Therefore, the faulty variables have to be located in the first place when the process leaves its normal operating regions. For an industrial process, multiple normal operations are common. On the basis of the assumption that the operating data follow a Gaussian distribution within an operating region, the Gaussian mixture model is employed to extract a series of operating modes from the historical process data. The local statistic T 2 and its normalized contribution chart have been derived for detecting abnormalities early and isolating faulty variables in this article. V

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