Independent Component Analysis for Redundant Sensor Validation

Redundant sensors have been widely used in safety critical facilities such as nuclear power and chemical plants. As these industries strive to move towards condition-based sensor calibration practices, on-line calibration verification algorithms must be developed. Independent component analysis (ICA) can be applied for redundant sensor validation. Independent component analysis is a statistical model in which the observed data is expressed as a linear transformation of latent variables (‘independent components’) that are nongaussian and mutually independent. The ICA method is able to reduce the redundancy of the original dataset in order to predict the process parameter more accurately. The ICA prediction method is proven to be a robust method that can be used as a non-parametric approach to build a model that can detect faulty and drifted sensors so that they can be scheduled for maintenance. A slow sensor drift case study from a nuclear power plant is presented to show the usefulness of this technique. The ICA based system results are much better than other current methods. Independent component analysis is shown to be a new and effective approach for redundant sensor validation. 1.0 Introduction Redundant measurements are widely used in mission critical applications such as nuclear power plants, chemical facilities and the aerospace industry. Redundant information enhances the reliability of measurement. On the other hand, the redundant information can be utilized to check measurement channel integrity. On-line monitoring is the process of automatically checking component operation while the process is operating. EPRI formed the EPRI/Utility On-Line Monitoring Working Group in 1994 with the goal of obtaining NRC approval of on-line monitoring as a calibration reduction tool for safety-related instruments. Their On-Line Monitoring Cost-Benefit Guide estimates an industry wide cost savings of $40M to $290M over the next 20 years [EPRI 2002]. The report also claims the following benefits of on-line monitoring. • Helps eliminate unnecessary field calibrations. • Reduces associated labor costs. • Limits personnel radiation exposure. • Limits the potential for damaging equipment. Various on-line calibration monitoring algorithms have been developed. For example, the Instrument Calibration and Monitoring Program (ICMP) [Wooten 1993] was used for redundant sensor monitoring. It has been implemented at the V.C. Sumner Nuclear plant beginning in 1991 as a performance-monitoring tool. ICMP is a weighted average algorithm, which assigns a consistency value to each channel. If the measurement is consistent all the time, all measurements will be equally weighted and the algorithm is reduced to simple average. If one of the measurements differs from the others a lot, the weight of that measurement will be reduced due to inconsistency. Thus the parameter estimate will contains less drift due to reduced weight for the faulty channel. Other systems have been developed by suppliers such as Smartsignal Inc. (www.smartsignal.com), PCS (www.pcs-home.com), and EXPERT Microsystems (www.expmicrosys.com). These methods are geared towards the general monitoring of process sensors but not specifically towards redundant sensors. More sophisticated models can be built to fully utilize the redundant information contained in the measurement. A research program using Independent Component Analysis (ICA) shows that ICA model captured essential information in the redundant measurement method and is able to reduce the redundancy of the original dataset in order to predict the process parameter more accurately. ICA prediction is very robust in that faulty sensors do not adversely affect the status of good sensors [Ding, 2003]. In this paper, a slightly different approach using a non-regression ICA modeling for redundant sensor validation is presented using actual plant data set. The results are compared with ICMP. For a description of the ICMP algorithm, one can refer to Rasmussen [2002]. 2.0 Methodology 2.1 System Description A typical redundant sensor validation system is as follows: Parameter Estimate Residuals Sensor Status Figure 2.1 Redundant Sensor Validation System The functional description for each block is as follows: Estimator: the system receives redundant sensor values (redundancy of n = 2, 3, 4...) and processes them to provide a best estimate of the measured parameter. Residual Formation: the parameter estimates are compared to the actual sensor signals and residuals are formed. Fault Detection Algorithm: the residuals are processed to determine if they have significantly changed from zero. Redundant Sensor Measurements Estimator Residual Formation Fault Detection Algorithm 2.2 ICA model and algorithm Independent component analysis is a statistical model in which the observed data (X) is expressed as a linear transformation of latent variables (‘independent components’, S) that are nongaussian and mutually independent. We may express the model as