Research on optimized layout of bridge sensors based on MAC stepwise addition and subtraction algorithm

Abstract

The difference in the location and number of sensors induces the acquisition effect of structural state information in the bridge health monitoring system to a certain extent, which is also one of the most difficult problems restricting the development of bridge health monitoring technology. Based on the Modal Assurance Criterion, this paper took a cantilever simply supported beam as an example and adopted the Effective Independence method, Kinetic Energy method and QR decomposition method to optimize a sensor layout. Taking the number of sensors as 5, the layout and MAC matrix factors were analyzed by comparing the MAC matrix and its distribution diagrams obtained by different methods. The results showed that the stepwise subtraction method based on QR decomposition was the best. And by changing the number of sensor, it was found that the optimal number of sensor was 9. It was also found that the existing methods had the shortcomings of over-reliance on the selection of initial measuring points. In order to improve this defect, cyclic iteration of stepwise addition and subtraction was introduced, and an optimal layout method based on the stepwise addition and subtraction of the number of sensors was proposed. Through screening and optimization of this method, the average off-diagonal element in the calculation example was reduced from 0.118 to 0.006 to achieve the satisfactory optimization effect. At the same time, this method was employed to optimize the layout of a concrete continuous rigid-frame bridge with 9 and 19 sensors, and the results showed that the sensor layout was more uniform. Therefore, the proposed method provides the opportunity to obtain fair optimization results and to have a considerable engineering application value.