Multivariate Alarm Monitoring for Non-Convex Normal Operating Zones Based on Search Cones

Abstract

Normal operating zones (NOZs) are the variation spaces of multiple related variables under normal conditions. This paper proposes a search-cone-based method to establish NOZ models and design dynamic alarm thresholds for multivariate alarm monitoring. First, mathematical models are established by exploiting search cones from historical normal data points to describe non-convex NOZs of multiple related process variables. Second, dynamic alarm thresholds of each process variable are designed based on the established NOZ models for new data points being inside or outside the NOZs. The proposed method extends from convex NOZs to non-convex ones, and the main contribution is to establish mathematical models of NOZs for monitoring abnormal conditions and design dynamic alarm thresholds for generating alarms. Continuous stirred tank reactors (CSTR) and industrial examples are provided to illustrate the effectiveness of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Alarm systems play critically important roles for safe and efficient operation of industrial plants. Many process variables are related so that their normal variation ranges formulate high-dimensional geometric spaces referred to as normal operating zones (NOZs). Hence, it is desirable to adopt the NOZs for alarm monitoring. By contrast, if relationships among process variables are ignored, missed and false alarms may occur to deteriorate the performance of alarm systems. This paper proposes a method to establish mathematical models for NOZs and design dynamic alarm thresholds. The established models can describe non-convex or convex NOZs; the dynamic alarm thresholds can quantify distances between NOZ boundaries and operating points of a multivariate process