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

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.