Research On Optimal Placement Of Cable Sensor Based On Spatial Correlation And Prediction Of Cable Force Of Full-bridge

As an important load-bearing structure in cable-stayed bridge,the cable has become an important factor in the safety evaluation of bridge structures,of which the monitoring has become an indispensable content in a structural health monitoring(SHM)system of long-span cable-stayed bridges.A reasonable monitoring scheme,particularly,sensor placement related to accurate safety assessment and cost-saving budget of the SHM system.A method of optimal sensor placement is proposed in this paper considering the spatial correlativeness existing in the cable group,and an extreme learning machine based on particle swarm optimization(PSO_KELM)is employed to estimate the cable force at unsupervised position by the cable force at the optimal measurement point.Thus,the limited sensors would be utilized for maximizing useful information from the monitored bridges.Firstly,the trend of cable force caused by environmental factors is taken as research object,which is extracted by B-spline interpolation method from time-varying cable force.Pearson correlation coefficient,maximum information coefficient(MIC)and mutual information coefficient(MI)is respectively applied to detect the internal relationship of load response in cable group.Pearson correlation coefficient can only describe the linear relationship between variables,but the complexity of the bridge structure is far more than linear correlation;Maximum information coefficient is difficult to play its advantages in the relevance of exploration because of noise,but scatter diagram between cable show "broadband" characteristics;In contrast,mutual information coefficient based on kernel density estimation can explore the nonlinear relationship among the cable groups and is selected as correlation measure.Secondly,the bond energy algorithm(BEA)is used to cluster the correlation coefficient matrix of the cable group,and the classification of the sensor points and the selection of the optimal measurement points are carried out according to the arrangement order of cable points in the cluster correlation matrix.Taking 84 cables in upstream of Nanjing No.3 Yangtze River Bridge as an example,different optimal placement strategies are discussed with different correlation thresholds from 0.9 to 0.6 with 0.05 as space.The optimization results demonstrated that near 1/2 cables are selected as monitoring objects as threshold is 0.9,and the number of the optimal measurement points decreases with the decrease of the correlation threshold,verifying the effectiveness of the proposed method.Finally,a kernel extreme learning machine based on particle swarm optimization(PSO_KELM)is proposed to estimate the cable force at unsupervised position.The performance in the cable force inversion of extreme learning machine model(ELM)with different activation function and kernel function,multiple linear regression model(MLR)and adaptive regression spline model(MARS)are compared from the perspective of prediction accuracy and error distribution.Extreme learning machine with RBF kernel function(RBF_KELM)is found to have higher prediction accuracy and generalization ability.The maximum RMS of estimated force is 2.79 among all cables and the probability of absolute error falls in the range of [-3,3] is 99.54%,which satisfies the requirements of practical engineering.The MARS model is also used to verify the rationality of the optimal sensor placement method and correlation measure.