Dynamic Load Identification Based On The Wavelet Shape Function

Accurate dynamic load information can provide the basis for structural operational condition easement and safety maintenance.Dynamic load is often difficult to measure directly for technical or economic reasons.Thus load identification by using the structural dynamic response is an important approach to obtain external load.Shape function and deconvolution based dynamic force identification methods has attracted more and more attention in recent years as they can reduce the number of unknowns and enhance the identification efficiency significantly.However,there are still some problems to be solved in selecting appropriate shape function and determining the optimum time unit length.In this paper,multi-scale wavelet function is introduced into the field of dynamic force identification.Based on the time domain deconvolution concept,the Lagrange wavelet and Trigonometric wavelet are employed as shape function,and the corresponding dynamic force identification is proposed by using the structural response and model.The feasibility and effectiveness of the proposed method are verified by numerical and experimental examples.The main work and conclusions are as follows:1.Lagrange wavelet shape function based dynamic force identification method is proposed.The local force in each time unit is approximated by wavelet scale functions,and corresponding multi-scale force-response equation is established for dynamic force identification.Further the scale of force-response equation is lifted by adding high-scale wavelets to improve the identification accuracy gradually.Numerical examples of a simply bean and a two-story frame indicate that the proposed method can identify the dynamic force effectively and the identification accuracy can be enhanced by lifting the scale of the force-response equation gradually.2.As only finite sampling points information of the dynamic response are used in the aforementioned method,errors in individual sampling points data can lead to the relative large identification error.The least square method is introduced to fit all sampling point data in the time domain unit to improve the anti-noise performance.Numerical examples show that the least square method can effectively reduce the negative impact caused by errors in individual sampling points.3.In order to reduce the size of load-response equation,segment by segment real-time dynamic force calculation method is proposed based on the concept of moving time window.The entire time of dynamic force is dived into segments,and identified accordingly.Numerical examples indicate that the combined utilization of the segment by segment method and the shape function method can not only reduce the size of load-response equation and enhance the calculation efficiency,but also reduce the sensitivity to noise.Besides,online dynamic force identification can be realized.4.As Lagrange wavelet shape function is a linear function,it has inherent deficiency in approximate dynamic force.Therefore the trigonometric wavelet based force identification method is presented.The trigonometric wavelet with“wave? property is employed as shape function,and the corresponding multi-scale force-response equation is established to identify the dynamic force.Numerical example is carried out to verify the advantages of the trigonometric wavelet function based method,compared to the Lagrange wavelet function based method.5.An experimental cantilever beam test is designed to verify the effectiveness and superiority of the proposed dynamic force identification method.Concentrated dynamic force is applied via an exciter and the structural dynamic response is measured by displacement sensor.The results indicate that the proposed method can identify the dynamic force effectively.