Principal component analysis (PCA) is a powerful fault detection and isolation method. However, the classical PCA, which is based on the estimation of the sample mean and covariance matrix of the data, is very sensitive to outliers in the training data set. Usually robust principal component analysis is applied to remove the effect of outliers on the PCA model. In this paper, a fast two-step algorithm is proposed. First, the objective was to find an accurate estimate of the covariance matrix of the data so that a PCA model might be developed that could then be used for fault detection and isolation. A very simple estimate derived from a one-step weighted variance-covariance estimate is used (Ruiz-Gazen, 1996). This is a "local" matrix of variance which tends to emphasize the contribution of close observations in comparison with distant observations (outliers). Second, structured residuals are used for multiple fault detection and isolation. These structured residuals are based on the reconstruction principle, and the existence condition of such residuals is used to determine the detectable faults and the isolable faults. The proposed scheme avoids the combinatorial explosion of faulty scenarios related to multiple faults to be considered. Then, this procedure for outliers detection and isolation is successfully applied to an example with multiple faults.
Principal component analysis (PCA) is a powerful fault detection and isolation method. However, the classical PCA which is based on the estimation of the sample mean and covariance matrix of the data is very sensitive to outliers in the training data set. Usually robust principal component analysis was applied to remove the effect of outliers on the PCA model. In this paper, a fast two-step algorithm is proposed. First, the objective was to find a robust PCA model that could be used for outliers detection and isolation. Hence a scale-M estimator [1] is used to determine a robust model. This estimator is computed using an iterative re-weighted least squares (IRWLS) procedure. This algorithm is initialized from a very simple estimate derived from a one-step weighted variancecovariance estimate [2]. Second, structured residuals are used for multiple fault detection and isolation. These structured residuals are based on the reconstruction principle and the existence condition of such residuals is used to determine the detectable faults and the isolable faults. The proposed scheme avoids the combinatorial explosion of faulty scenarios related to multiple faults to consider. Then, this procedure for outliers detection and isolation is successfully applied to an example with multiple faults.
Our work is devoted to the problem of multiple sensor fault detection and isolation using principal component analysis. Structured residuals are used for multiple fault isolation. These structured residuals are based on the principle of variable reconstruction. However, multiple fault isolation based on reconstruction approach leads to an explosion of the reconstruction combinations. Therefore instead of considering all the subsets of faulty variables, we determine the isolable multiple faults by removing the subsets of variables that have too high minimum fault amplitudes to ensure fault isolation. Unfortunately, in the case of a large number of variables, this scheme yet leads to an explosion of faulty scenarios to consider. An effective approach is to use multi-block reconstruction approach where the process variables are partitioned into several blocks. In the first step of this hierarchical approach, the goal is to isolate faulty blocks and then in the second step, from the faulty blocks, faulty variables have to be isolated. The proposed approach is successfully applied to multiple sensor fault detection and isolation of an air quality monitoring network.
Recovery boilers play a key role in chemical pulp mills. Early detection of defects, such as water leaks, in a recovery boiler is critical to the prevention of explosions, which can occur when water reaches the molten smelt bed of the boiler. Early detection is difficult to achieve because of the complexity and the multitude of recovery boiler operating parameters. Multiple faults can occur in multiple components of the boiler simultaneously, and an efficient and robust fault isolation method is needed. In this paper, we present a new fault detection and isolation scheme for multiple faults. The proposed approach is based on principal component analysis (PCA), a popular fault detection technique. For fault detection, the Mahalanobis distance with an exponentially weighted moving average filter to reduce the false alarm rate is used. This filter is used to adapt the sensitivity of the fault detection scheme versus false alarm rate. For fault isolation, the reconstruction-based contribution is used. To avoid a combinatorial excess of faulty scenarios related to multiple faults, an iterative approach is used. This new method was validated using real data from a pulp and paper mill in Canada. The results demonstrate that the proposed method can effectively detect sensor faults and water leakage.
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