Theoretical Study On Optimal Sensor Placement Considering Uncertainty Of Structural Modal Identification

Structural modal identification is to analyze the response data at the measuring point positions for obtaining the frequency,damping ratio,mode shape and other parameters that reflect the dynamic characteristics of the structure.Sensor placement is the first step in structural health monitoring.The number of measuring points and the quality of the data directly affect the effect of modal identification.In actual tests,economic cost,data storage,and other restrictions make the number of sensors to be deployed limited,and sensors cannot be placed in certain parts of the structure.As a result,complete structural information cannot be obtained.In addition,measurement noise pollution,insufficient sampling frequency,and the difference between theoretical models and actual situations will affect the accuracy of the obtained data.Therefore,the lack or error of structural modal information will cause uncertainty in modal identification results.It is important to selecting the sensor positions reasonably to reduce the uncertainty of modal identification by obtaining as much accurate modal information as possible on the premise of a limited number of sensors.This dissertation addresses three major issues affecting the uncertainty of modal identification results:the interference of measurement noise on the true response of the structure,the model error between the finite element model and the real structure,and the well-posed assumptions of the modal estimation method that do not match the actual situation.Research on sensor placement methods to reduce the uncertainty of modal identification has been carried out,and the main works are as follows:(1)The measurement noise will cause the deviation between the measurement data and the real response of the structure,and then cause the uncertainty problem of modal identification.In order to describe the uncertainty problem of modal identification,the transformation matrix was used to rewrite the theoretical formula form of Bayesian modal identification method in frequency domain,and a probability model of modal identification considering the arrangement of sensors is established.Information entropy is used to quantify the uncertainty of modal parameter identification,and a sensor placement criterion is developed to reduce the influence of measurement noise on modal identification.The example analysis shows that the proposed method can effectively reduce the interference of measurement noise on modal identification,and can reduce the uncertainty of identified structural frequency,damping ratio and mode shape results.The identification uncertainty of different modal parameters is affected by the sensor placement differently.In comparison,the uncertainty of frequency and damping ratio identification is less affected by the sensor placement,and the uncertainty of mode shape identification is more affected by the sensor placement.(2)The derivation of the sensor placement criteria is usually based on the finite element model of the structure.The model error between the finite element model and the real structure will cause uncertainty in modal identification.In the various sensor placement methods for structural modal identification,the prediction error caused by model error and measurement noise is usually assumed to be a Gaussian vector for research.Here,the stiffness variation of the structure is taken as the model error,and the measurement noise and the model error in the prediction error are separated,and the influence of the model error on the sensor placement is specifically considered.When quantifying the uncertainty of modal parameter identification,because the Fisher information matrix is uncertain,the traditional information entropy index is no longer applicable,and a conditional information entropy index is proposed to quantify the uncertainty.Theoretically,the existing information entropy index is a special case of the proposed conditional information entropy index.In the numerical example,various forms of prediction errors are used,and the influence of model error on the sensor placement method is analyzed,and a qualitative theoretical explanation is given.(3)In structural health monitoring systems,strain sensors are often used to obtain structural information about large local deformations,and the overall modal information of the structure contained in the dynamic strain data is usually ignored.In order to make full use of the displacement modal information contained in the strain data,based on the finite element theory,a displacement modal estimation method in the local coordinate system is proposed.The displacement mode shapes at the node positions of the unit are estimated using the strain modal shapes at the positions of the strain sensors.In order to describe the uncertainty of the estimation results,a probability model for displacement mode estimation is established,and the Cramer-Rao lower bound of the mode shape estimator is used to represent the smallest covariance boundary.Based on the geometric meaning of the confidence ellipsoid,different norm forms of Fisher information matrix are used to quantify the uncertainty of the estimation result.The numerical example analyzes the influence of different positions of the strain sensor on the uncertainty of the displacement modal estimation for the plane and space beam elements,and gives some discussions on the optimal placement of the strain sensor.(4)For the multi-type sensor placement of strain,displacement,velocity and acceleration sensors,the existing sensor placement methods usually arrange each type of sensor independently,without considering the relationship among different types of responses,which will cause the underdetermined problem of modal identification due to insufficient acceleration counts.The underdetermined problem can be solved by using the displacement modal information contained in the strain data.The displacement modal estimation method mentioned above is improved to make it suitable for the displacement modal estimation in the global coordinate system.The influence of different strain sensor locations and the degrees of freedom to be estimated on the uncertainty of the modal estimation is analyzed,and the optimal strain gage placement is determined in combination with the positions of the large deformation locations of the structure.The modal assurance criterion and the redundancy criterion are used to evaluate the displacement mode shapes obtained through the integration of multiple types of sensors,and the positions of such sensors are selected based on the value of the optimal criterion function.The research results show that the proposed sensor placement method can obtain more complete modal information,can effectively reduce the uncertainty of modal identification,and make the comprehensively acquired displacement modal shapes have better distinguishability and smaller redundancy.