| In structural health monitoring,the modal parameters of structure are generally determined based on structural vibration information that is obtained by sensors,and the operational status of the structure is determined accordingly.Optimal sensor placement is the first step in structural health monitoring..The placement of sensors has considerable influence on the identification of structural modal parameters.The ideal arrangement should meet the requirements of economy,identification and accuracy.At present,the research on the optimal sensor placement in structural health monitoring is mainly based on the single-objective criterion,and there are few studies on the deployment of multiple criteria.Therefore,in this paper,based on the traditional single sensor placement criteria,Pareto optimization theory is introduced to perform multi-objective optimization,and a multi-objective sensor placement method that can consider multiple placement criteria simultaneously is established.The contents are as follows:(1)The traditional sensor multi-objective placement methods include additive method,product method,deductive method,etc.These methods need to determine the weight coefficient.Only one placement scheme can be obtained at a time.Obtaining multiple placement plans requires multiple operations,and the computation is not efficient enough.In this paper,Pareto optimization is introduced into the multi-objective placement of sensors,and the Pareto front of the sensor placement is firstly solved.Then the final placement of sensors is selected from the Pareto solutions.(2)Considering the influence of sensor placement on parameter identification error,vibration response intensity,and modal independence,Pareto optimization method was used to establish three dual-objective optimal sensor placement criteria,and a non-dominated sorting genetic algorithm was used to obtain the Pareto front of sensor placement criteria.The proposed placement method is validated by an example of two-dimensional plane truss structure.The method can comprehensively consider the influence of the placement of sensors on the two targets.In the Pareto front,it can find a sensor placement scheme that is not inferior to the placement method that only considers a single target.(3)The Pareto optimization method is used to simultaneously consider the requirements of minimum parameter identification error,maximum vibration response,and modal independence.A three-objective sensor placement is established using the determinant of the Fisher information matrix,modal kinetic energy,and MAC non-diagonal element values.The paper proposes a comprehensive evaluation model to determine the final solution from the Pareto solutions.Comparing the final solution with six typical sensor placement methods,the proposed method can fully weigh the influence of sensor placement on the parameter identification error,vibration response intensity and modal independence.(4)Taking a engineering practice of the Run yang Yangtze River Bridge as an example,the finite element model of the main beam of the bridge was performed.The first six vertical mode shapes were selected to optimize the multi-objective sensor placement for the 93 nodes of the main beam.Based on the determinants of the Fisher information matrix,the sum of the average mode shapes values,and the maximum value of the MAC non-diagonal elements,a three-objective optimal sensor placement criterion that takes into account the small parameter error,vibration response,and modal independence is established.The Pareto front of the placement criterion was obtained by a non-dominated sorting genetic algorithm.The satisfied solution found in the Pareto front was compared with five typical sensor placement methods.The rankings of the parameter identification error index,vibration response strength index,and modal independence index of the satisfied solution were 3rd,3rd,and 1st,respectively.The feasibility of using Pareto optimization method for multi-objective sensor placement was verified. |
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