Optimal Sensor Placement: a sensor density approach
Finding the optimal number and location of measurement points for modal tests and virtual sensing applications is a non-trivial task. The numerical mode shapes of the test object, if available, can assist in picking the optimal sensor number and locations. As in any optimization problem, an objective function is formulated. The typical objective functions are the determinant of the Fisher Information Matrix, the sum of the off-diagonal elements of the AutoMAC matrix, the condition number of the mode shape matrix, etc. The optimization problem is posed as distributing the given number of sensors in the candidate locations to maximize (or minimize) the chosen objective function. This binary optimization problem is typically solved by using sequential sensor placement or genetic algorithms. This study suggests the relaxation of the binary optimization problem by introducing sensor density: in each candidate location, the sensor is allowed to have a density varying from 0 (no sensor) to 1 (there is a sensor). In this case, the derivative of the objective function with respect to sensor configuration exists, and powerful gradient-based optimization algorithms can be employed. The study elaborates on the suggested method and demonstrates its advantages in application to test objects of different complexity.
Copyright (c) 2022 Dmitri Tcherniak
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