(625c) Model-Based Fault Detection for Nonlinear Process Systems Using Multiparametric Programing for Parameter Estimation

Early detection and diagnosis of faults are essential to minimise the economic losses and fatal damage of the operators and the equipment. Several techniques have been developed to detect and localize the fault. With the aid of process models, estimation and decision methods, faults can be detected and monitored by process states, model parameters and characteristic quantities [1]. Model-based fault detection techniques can be categorised into observer-based, parity relation and parameter estimation methods. The observed-based uses the outputs of the system from the measurements by using some type of observer, and then constructs the residual by an output estimate error and the parity relation approach uses the parity check on the consistency of parity equation to generate residuals (parity vector). The inconsistency in the parity relations indicates the presence of faults. On the other hand, in the parameter estimation approach, the model parameters of the actual process are repeatedly estimated on-line and the results are compared with the reference model [2-7]. The key limitation however is that it requires solving an optimization problem online at regular time interval. The key issue with solving an online optimization problem is not only that it is time consuming, but also that the solution may not converge in a reasonable time.

Thus, this work presents a model based fault detection and diagnosis approach using parameter estimation for process systems using multiparametric programming. Multiparametric programming provides the optimization variables as an explicit function of the parameter [8]. In this work, a square system of parametric nonlinear algebraic equations is obtained by formulating optimality condition. These equations are then solved symbolically using Mathematica to obtain model parameters as an explicit function of measurement [9]. This allows computation of parameter estimates by simple function evaluation. The diagnosis of fault is carried out by monitoring the changes of the residual of model parameters. The estimated parameters should be close to observed parameters when no fault is present. Any substantial discrepancy between estimated model parameters and the observed model parameters may be interpreted as a fault, i.e., if the discrepancy goes above a certain threshold.

Case studies of fault detection and diagnosis for single stage evaporator system [10] and quadruple tank system [11] are presented. A number of faulty and fault free scenarios are considered to show the effectiveness of the presented approach of parameter estimate and faults can be detected by monitoring the residual of model parameters. The proposed approach successfully estimates the model parameters and detects the faults in the systems

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