Load-Dependent Structural State Reconstruction-Oriented and Reliability-Based Sensor Placement Optimization Method

This paper investigates a novel time-dependent reliability model to optimize load-dependent sensor placement (LDSP) for dynamic inverse problems using the set-theory-based uncertainty quantification method. To accurately realize prediction, unbiased estimators of the uncertain bounds of the modal coordinates between the reduced dynamic system and full structure are regarded as the two nominal optimization objectives. The uncertainties are treated as interval numbers, and their propagations are introduced using the dimensionwise analysis method. Enlightened by the orthogonal polynomial to estimate continuous functions in an enclosed interval, this study uses the first type of Chebyshev polynomial to obtain the interval of modal coordinates in dynamic systems, which is more accurate than the traditional interval perturbation methods. To quantify the matching states between reduced and full dynamics, this paper develops a novel time-dependent reliability-based model comprising two fields of interval process models regarded as the constraint, where the intersection denotes the physics meaning of the failure. The method of time-dependent reliability-based LDSP consists of two optimization objectives with reliability constraints, which can be presented by a flowchart and effectively solved by an advanced algorithm. The accuracy of the given method is assessed by sensor placement configurations in the application of large spacecraft.