A Study On The Method Of Force Identification Based On Equivalent Excitation Source With An Optimized Sensor Placement

The knowledge of the dynamic force is of great importance for a large number of industrial applications such as the system dynamics optimization,fault diagnosis,noise reduction,and vibration control as well as response prediction.Due to the complexity of the structure and the dynamic load,the direct measurement of forces is always relatively hard or even cannot be achieved in many cases.Thus,it is very necessary to develop the indirect methods by which the forces can be identified from the measured dynamic responses of the structure.Different indirect methods,also known as force identification methods,have been developed in recent years.For most of them,the identification accuracy largely depends on the signal-to-noise ratio of response and the sensor placement.This work proposes a method which has a good anti-noise performance to identify the structural dynamic force with the use of the distributed response in measurement region.Moreover,an optimal selection method on measurement region is further investigated in order to improve the identification precision of the force.In addition,the design of low noise equipment is usually based on the force identification method.For this type of excitation evaluation problem,some innovative researches based on the equivalent excitation source model are carried out.Then a technique of internal excitation source inversion on machinery is presented by combining the sensor optimization with the equivalent excitation source method.The technique is studied through theoretical modeling,numerical simulation and experimental test.The primary works are summarized as follows:(1)The errors of the force identification vary with different spatial locations of the response measurements as well as the noise level.This work presents a method to identify the force based on the reconstruction of distributed response by transferring the problem from discrete points to the whole region which can smooth the noise in the measured response.An optimized sensor placement is obtained by using a set of local orthogonal polynomials to approximate the response distribution of the chosen region and choosing the Gaussian quadrature points as the sensor locations.Numerical simulations of models with planar and curved surfaces are presented to validate the method.It is found that the proposed method can effectively reduce the influence of noise and improve the precision of the force identification.The method is also validated by an experiment and an accurate recognition of the forces is observed.(2)The selection of measurement region directly affects the sensor placement,and ultimately affects the identification accuracy.This work presents an optimization model which uses the regional coherent factor as the objective function to select measurement region in analysis region.Based on the coherent analysis of the transfer function for discrete points at a frequency,the coherent analysis for region is derived and the regional coherent factor is defined.For a multi-frequency optimization problem,the 3D transfer function matrix of the system can be converted into a 2D form and then reassembled to be a new matrix.The optimization model can be established from the new matrix.Numerical simulations are carried out on a simply supported beam model,the results show that the coherence factor can reflect the ill pose of the transfer function matrix.Compared with the condition number method,the optimal measurement region can be selected quickly and effectively and the problem of multi-frequency optimization is easy to deal with in coherent factor method.(3)According to the idea of equivalent source in acoustics,a force identification method based on equivalent excitation source model is established.The technique is developed based on the response similarity principle and can obtain the equivalent excitation distribution results,simplifying the process of test and estimation.Then the method of determining the number and position of equivalent excitation source is further studied.Through an experiment,the recognition error is analyzed and the validity and accuracy of the technique are verified.(4)Combining the sensor placement optimization method with the equivalent excitation source method,an internal excitation source inversion technique on machinery is presented.The technique is applied on a modular electromotor.Experiments of the electromotor to identify the bearing force and electric magnetic force are performed.At the peak frequencies of the response spectrum,compared with the sensors' actual measurement results,the identification errors are satisfied.This technique is promising to be used in the engineering application.