Optimal Sensors Placement Based On Effective Independence-data Fusion Method

In the field of structural health monitoring,the goal of optimal placement of sensors is to obtain as much dynamic system information as possible,which is very important to the structural health monitoring system.These can determine the authenticity and accuracy of the overall and local running state information of structure.The number and position of sensors will affect the diagnosis of structural behavior and the accuracy of identified parameters.By facing with various forms of structure,traditional sensor optimization methods are difficult to work well.In general,the classical effective independent method can not only ensure the linear independence of the mode shape vector,by also obtain the position with higher vibration energy.In this paper,an effective independent-data fusion method is proposed,which combines the improved singular value decomposition method with the element modal strain energy to improve and modify the classical effective independent method.First of all,basing on the effective independent legislation,an effective independent-data fusion algorithm is presented,and the flexibility of proposed method is verified by a numerical example of a four-layer double frame structure.Among them,five evaluation criteria are used to evaluate the results of sensor location optimization.Then,one of the factors affecting the effective independent-data fusion algorithm,selection and parameter setting of modal analysis method is analyzed.The parameter setting of modal analysis solution block has influenced the output of singular value and vibration mode.Subsequently,to prove the reliability of parameter setting,another influence factor,the number of modes,is analyzed to avoidthe unexpected effect of the order superposition of modal strain energy.The number of modes in the optimal arrangement of sensors is determined according to the change rate of Fisher information matrix,damage sensitivity and entropy.Finally,the reasonable parameters and the determined number of modes are replaced into the effective independent-data fusion method to obtain the optimal measuring points,and the vibration modal experiments of the frame structure model are carried out in order to achieve good application performance.The conclusions of this paper in my work are as follow:1.Based on effective independent legislation,an effective independent-data fusion sensor placement method is proposed.The acceleration responses of all nodes are decomposed by improved singular value decomposition,and the effective independent components are modified combining with the modal strain energy coefficient.Five evaluation criteria are utilized to evaluate the performance of effective independent legislation,effective independentimproved modal strain energy method and effective independent-data fusion method.The results show that the independence between the modes obtained by the effective independentdata fusion method is more average and with good robustness,which is similar to the noise resistance and modal information yielded by existing effective independent legislation and effective independent-improved modal strain energy method.Having all these aspects into consideration,a great potential of engineering application is providing by the effective independent-data fusion method.Under different noise intensity,five evaluation indexes of the effective independent-data fusion algorithm can all remain stable,especially the number of modal conditions that characterize the anti-noise ability.It begins to decrease as the noise enhances,and then stabilizes at about 14 basically,showing a strong anti-noise performance of this method.2.Analyzes and studies the selection of modal analysis method and the feasibility of parameter setting.The modal parameters are set: the solution data are output by ANSYS,the time integration step of transient analysis is determined,and the modal parameters of node acceleration response are identified by enhanced frequency domain decomposition method.The results verify the effectiveness of the ANSYS command flow programming.The relative errors of the first three frequencies of the cantilever structure,calculating by the uniform mass matrix and the lumped mass matrix defined in the modal solution options,are less than 1%.What's more,the frequency calculation efficiency of the lumped mass matrix is higher than that of the uniform mass matrix.The frequency identification error of the enhanced frequency domain decomposition method(EFDD)is less than 1%,indicating that the identification method has strong applicability.3.Chooses different methods to determine the number of modes.The change rate of Fisher information matrix,damage sensitivity and entropy method are applied to select the number of modes in the optimal arrangement of sensors.The results show that the two norms and traces of Fisher information matrix can directly determine the number of modes.Among the methods of modes number determining based on damage sensitivity,the local mutation point of the curve is obvious while the overall change trend is hard to observe.For the modes number determination of the entropy method,the entropy value varies distinctly as the entropy value from 29 th to 52 th order is smaller and the others is larger.In addition,according to the definition of catastrophe point and catastrophe eigenfunction,it is known that the mode changes frequently between global vibration and local vibration..At least 12 sensors are needed for data fusion of the first 40 modes and the first 10 modes,which is determined by the information matrix trace according to the relationship between the number of sensors and the maximum non-diagonal elements of the modal confidence matrix MAC,as well as the rule that the maximum non-diagonal elements of the MAC matrix in complex structures should be over the threshold of 0.25 suggestion proposed by Carne.Overall,using the first 40 modes determined by the information matrix trace for data fusion is better than using only the first 10 modes,and the mode shape matrix,obtained from modal parameter identification,of the first 10 frequencies has the best orthogonality.4.Experimental verification and analysis.A frame experimental model is built to pick up the acceleration response signals of each node.In order to verify the performance of the effective independent-data fusion algorithm proposed in this paper,the modal parameters of the experimental data is identified by Matlab program and the frequencies and modal shapes obtained by the optimal placement methods of each sensor is compared.The results show that the frequencies and mode shapes of effective independent legislation and effective independentdata fusion method can obtain better identification resultsas the appropriate increase of the number of measuring points for the frame structure.Similarly,if an appropriate number of modes is selected,the parameters identified by the effective independent-data fusion method can be best estimated.