The Research On The Load Identification Based On Condition Number Of Matrix

As one of the second inverse problem of structural dynamics,dynamic load identification plays a great important role in practical applications in engineering.Conventional methods of dynamic load identification mainly contain frequency domain method and time domain method.As a method of frequency domain method,frequency response function(FRF)inverse method has been widely used for this method can be easily to understand,and its theoretical basis is more mature,and be proposed at first.The basic principle of FRF inverse method is to establish frequency response function model of the vibration system in frequency domain,then by using the output of the system(the measured response of the system)in order to identify the input of the system(dynamic load).The key point of the method is how to select the response points to ensure the benign of the frequency response function matrix,to ensure the high identify accuracy of the dynamic load even if there exists a big measurement error.The condition number of matrix is the mark whether the matrix is ill-conditioned or not,and if the condition number is very large,the matrix is ill-conditioned,otherwise it is well-conditioned.So the problem turned to how to select the appropriate response points which can constitute a matrix with a small condition number and well-conditioned.Though it has the highest calculate accuracy to calculate the condition number of all response points combination in order to select the best combination,but the method is impractical.Because in practical engineering applications,the quantity of the response points is large,it will take a long time to calculate all the condition numbers.Therefore,it will be very meaningful to establish a response points selection method with high precision and high efficiency.In this paper,for there are a great deal response points in engineering,it studies the theory of condition number and draw a conclusion that the condition number is related to the row(column)of the matrix.We can select the row vector with this relationship,then can find the best combination of response points with smaller condition number.The existing response points selection method mainly use the optimization algorithm or transform the frequency response matrix.In this paper the response points selection method derived from the study the properties of the matrix and it has stronger theoretical support compared with other methods.Numerical experiment is also made in the paper,the result shows that the method can select the better combination of response points accurately and efficiently even there are a large number of response points and be valuable in practical application.