A novel two-step strategy of non-probabilistic multi-objective optimization for load-dependent sensor placement with interval uncertainties

Conventional optimal sensor placement methods use structural dynamic characteristics such as mode shapes to determine sampling positions for extracting information. However, these approaches have not considered actual load cases or structural responses. Relevant mode shapes in the responses are important for sensor configurations and damage detection. Because the sensor layouts under specific load cases and free vibrations are completely different from them in free vibration, using current sensor placement theories may lead to errors or even failure. In studies that consider both the dynamic characteristics and load cases, a novel uncertain load-dependent sensor placement method is developed using the non-probabilistic theory for response reconstruction, which has a two-step strategy. Based on the unbiased estimate of modal coordinates with a reduced and full model in the deterministic case, this study treats uncertainties as interval numbers, and the propagation of uncertain modal coordinates is proposed based on non-probabilistic theory. Provided uncertain but bounded responses are obtained, the uncertain modal coordinates are calculated easily without requiring the complex process of uncertainty quantification using statistical methods. Furthermore, a two-step strategy is used to select the optimum displacement sensor configurations. The non-probabilistic multi-objective optimization consists of deterministic and uncertain parts that can be solved using NSGA-II (Non-dominated Sorting Genetic Algorithm II) to obtain the preliminary Pareto front in the first step. For conveniently determining the final sensor configuration from a large number of candidate solutions located at the Pareto front, a novel interval time series model is constituted based on the ratio of reduced and full intervals. Therefore, the obtained solutions can be applied to reconstruct responses of the full structures from the deterministic and uncertain parts simultaneously. Two engineering examples are applied to verify the effectiveness and accuracy of the proposed method, accompanied by comprehensive discussions.