Observability analysis for model-based fault detection and sensor selection in induction motors

Abstract

Sensors in different types and configurations provide information on the dynamics of a system. For a specific task, the question is whether measurements have enough information or whether the sensor configuration can be changed to improve the performance or to reduce costs. Observability analysis may answer the questions. This paper presents a general algorithm of nonlinear observability analysis with application to model-based diagnostics and sensor selection in three-phase induction motors. A bond graph model of the motor is developed and verified with experiments. A nonlinear observability matrix based on Lie derivatives is obtained from state equations. An observability index based on the singular value decomposition of the observability matrix is obtained. Singular values and singular vectors are used to identify the most and least observable configurations of sensors and parameters. A complex step derivative technique is used in the calculation of Jacobians to improve the computational performance of the observability analysis. The proposed algorithm of observability analysis can be applied to any nonlinear system to select the best configuration of sensors for applications of model-based diagnostics, observer-based controller, or to determine the level of sensor redundancy. Observability analysis on induction motors provides various sensor configurations with corresponding observability indices. Results show the redundancy levels for different sensors, and provide a sensor selection guideline for model-based diagnostics, and for observer-based controllers. The results can also be used for sensor fault detection and to improve the reliability of the system by increasing the redundancy level in measurements.

Comparison among Methods for Induction Motor Low-Intrusive Efficiency Evaluation Including a New AGT Approach with a Modified Stator Resistance

“…Then, the modified stator resistance estimation is performed offline applying (21) and (22) using these current and voltage data in (23) and (24).…”

“…The simulation tests have been performed with a 0.5-HP 2-pole IM. The rated values and parameters for the IM are presented in Table 1 [24]. The IM was simulated as a dynamic model based on the state-space equations, with inserted mechanical losses [1].…”

Observability analysis of biochemical process models as a valuable tool for the development of mechanistic soft sensors

“…The observability matrix O , is defined as the Jacobian of the Lie derivative vector q . For calculation of this Jacobian, a numerical differentiation method in complex domain was implemented which has the advantage of being indifferent to the scale of as described previously . The analytical computation of the Jacobian matrix would be impractical and time consuming for most applications because of the existence of highly nonlinear functions in the Lie derivative vector.…”

“…For calculation of this Jacobian, a numerical differentiation method in complex domain was implemented which has the advantage of being indifferent to the scale of x * as described previously. 20,21 The analytical computation of the Jacobian matrix would be impractical and time consuming for most applications because of the existence of highly nonlinear functions in the Lie derivative vector. The nonlinear system is observable if the rank of the observability matrix, O, is equal to the number of state variables, n. For enhancing the A 0 : growing biomass; A 1 : nongrowing biomass; PEN: penicillin concentration; A 2 : vacuoles; A 3 : degenerated biomass; A 4 : autolyzed biomass; r e : rate of extension; r b : rate of branching; r p : rate of penicillin production; r h : rate of penicillin hydrolysis; r d [1][2][3][4] : rates of differentiation of biomass from one type to another.…”

Optimal Sensor Configuration and Fault-Tolerant Estimation of Vehicle States

“…Nakhaeinejad et al [4] suggested a similar approach not only for analysis of the faults, but also for defining a guideline for model-based sensor selection for induction motors. Among all of the abovementioned methods, the condition number is more common and is frequently used in the literature [1], [5], [6].…”