Research On Optimal Sensor Placement Method Oriented To Structural Response Reconstruction

With the development of science and technology and the progress of human civilization,modern engineering is putting forward more and more strict requirements to the solution of structure dynamics problem.In this process,structural dynamics and other disciplines have intercrossed and interacted gradually,and many new research fields have been spawned,such as structural vibration control,parameter identification,load identification,diagnosis prediction,fault diagnosis and damage identification,etc.For the research in the above areas,the response information of the structure is of vital importance.The structural dynamic response reconstruction technology is to obtain the information of the unmeasured part of the structure through the information of the measured part of the structure,which has important practical significance and application prospect in many engineering fields.On the other hand,restricted by economic factors and other aspects,the number of sensors which can be deployed in the structural health monitoring system is limited.The problem of optimal sensor placement is how to use as few sensors as possible to obtain as much information as possible about the structure.Optimal sensor placement has received extensive attention from the academic circle in recent years.Different types of optimal sensor placement criteria and methods are emerging one after another.However,there are few studies on the optimal sensor placement methods for structural response reconstruction.In view of the above,the following research work was carried out in this thesis:Aiming at the uncertain response reconstruction problem of linear structure,the definition of Kalman problem was introduced,the state space equation of structure was established,and the derivation and summary of the traditional Kalman filter algorithm was carried out.Combined with the backward sequential algorithm,the optimal sensor placement method based on Kalman filter was presented.The presented method was verified using two-dimension truss model under two different working conditions.Aiming at the problem that the traditional Kalman filter algorithm can not be used under unknown excitation,a scheme of using excitation identification Kalman filter(EIKF)algorithm to simultaneously predict the structural response and excitation was proposed,and comparison was made between EIKF and robust two-step Kalman filter(RTSKF).By using binary encoding,a firefly algorithm which can solve discrete problem was proposed,and it was applied to solve the optimal placement of sensors.The effectiveness of the backward sequential algorithm and the firefly algorithm was verified by comparison using numerical example.In order to solve the filtering divergence problem of EIKF under the single sensor type measurement,a two-stage reconstruction method of structural response was proposed combining the modal method and the EIKF.The backward sequential algorithm was used to optimize the placement of sensors,and numerical example was carried out to verify the two-stage reconstruction method for the structural response.At the same time,a cantilever beam model was tested,and the sensor placement scheme obtained by the proposed method was successfully used to reconstruct the structural response of the unmeasured part and predict the unknown excitation.The results of test examples are in good agreement with those of numerical examples.