Study On Optimal Sensor Placement For Structural Health Monitoring With Modal Measurements

Optimal sensor placement is one of key problems of designing stuctural health monitoring system,because it has an essential effect on the availability of the data collection. Due to field conditions and cost considerations,a given number of sensors are limitted.The goal is to use a minimum number of sensors,placed at the right locations,so that both presence and extent of damage of the structure system can be identified effectively.The author has systematically studied several problems of optimal sensor placement in structural health monitoring,such as the inconsistency between modal observability and damage identifiability,the adaptability of performance matrix and optimization criterion,ill-posed characteristic of system inverse problem,reasonable selection of mode numbers,the contradiction between sensitivity of structural response and system robustness,optimal sensor placement for structures with torsional degrees of freedom.The detail research contents of paper are as follows:Firstly,a Fisher information matrix(FIM) based on coordination of modal observability and damage identifiability is put forward,and the adaptability of the matrix and optimization criterion is investigated.Considering the structural response changes that result from damage, the relationship between the structural response and damage was deduced from the structural motion equation by a quasi-analytical mode.According to the information entropy,an object function was set up including the information of mode independence and damage sensitivity. Then,the difference between three FIMs is examined by a quasi-analytical mode.In addition, the relation of these matrixes is derived.Numerical example of three-dimensional scaffold is applied to explore the adaptability between the three FIMs and several evaluation criterions.Secondly,a novel criterion with the sensitivity of structural response and system robustness coordinated and a heuristic search algorithm are developed.In nature,optimal sensor placement for structural damage detection is an inverse problem,which the ill-posed characteristic is manifested as condition number of the identification equation(CNIE).The results of the sensor optimization are dependent upon not only FIM but also CNIE.However, the large CNIE due to the degree-of-freedom(DOF) deletion,which leads to the ill-poseness of the inverse problem,are commonly ignored in previous literatures.The main object of this paper is to develop a novel criterion for sensor optimization that can remedy the ill-poseness due to DOF deletion and simultaneously maintain FIM as maximum as possible.Thus,the optimization criterion of simultaneously maximizing FIM and minimizing CNIE is proposed. And a heuristic search algorithm is developed to delete DOFs until to the given number of the sensors.The proposed approach is numerically studied by Two-dimensional truss structure. The results of sensor placement and structural damage detection are compared with effective independence algorithm and damage sensitivity method.The usefulness and feasibility of the algorithm is illustrated through the dynamic test for free spanning submarine pipeline.Thirdly,a method of selecting suitable number of modes for damage sensitivity is put forward,and the two corresponding evaluating criterions are established.The rate of change of 2- norm of the FIM between the first i modes and the first i+1 modes is taken as the index of selecting the number of modes,which is described by the rate of change curve chart. According to the two evaluating criterions of the consistency of information feature and the results of damage detection before and after optimal sensor placement,the effectiveness and universality of the method are verified by three numerical examples:two-dimensional truss with two DOFs on node,three-dimensional shell with three DOFs on node,three-dimensional submarine pipleline with six DOFs on node.Fourthly,considering the effect of structural rotational response on optimum sensor placement and structural damage detection,a method of optimium sensor locations for structures with torsional DOFs is studied.Utlizing the improved reduced system(IRS) method,the rotational response is calculated by the translational response.Then,a new FIM is designed.Finally,combined with the method of selecting mode number,the modified optimum sensor placement method is developed.The riser of offshore platform numerical example shows that the modified method is effective and the influence and relative error of reconstruction of rotational response by the methods of Guyan and IRS are both different.The numerical example of suspension arch bridge shows that the modified optimum sensor placement method based on IRS method is superior to empirical method.