Biased Estimation Method Based On Neumann Series And Its Application In Damage Assessment

Biased estimation is one of the effective methods to solve ill conditioned linear equations Ridge estimation is one of the most common biased estimation methods,which has been widely used in many engineering problems.However,there are still some problems in the existing ridge estimation or generalized ridge estimation methods,such as difficult to select the ridge parameters accurately and too much computation.For this reason,this paper studies a new method of biased estimation based on Neumann series,which is used to solve ill conditioned linear equations,and applies this method to structural damage assessment calculation to reduce the adverse effect of data noise on calculation accuracy.The main research contents include:By using Neumann series expansion,a new calculation formula of biased estimation for linear equations is derived.The proposed method can unify the existing formulas of least square estimation,ridge estimation and generalized ridge estimation,establish the essential relationship between biased estimation and unbiased estimation,and can extend a series of new biased estimation forms.Taking the ill conditioned linear equations as an example,it shows that in this series,the In the new form of partial estimation,there is a solution which is closer to the true value than ridge estimation or generalized ridge estimation.Furthermore,the Neumann biased estimation method is applied to structural damage assessment to solve the problem of data noise pollution.In the calculation process,the particularity of damage assessment is fully utilized.According to the calculation results of the first biased estimation,a new disturbance diagonal matrix is designed and the second biased estimation is carried out to obtain more accurate damage assessment Estimate the result.Simple supported beam and plane truss structure are used as numerical examples to simulate various damage conditions to verify the feasibility of the proposed method.The results show that under the interference of data noise,the Neumann series biased estimation method with feedback calculation can obtain better damage evaluation results,and the second and third biased estimation solutions are more accurate than the first biased estimation solutions.Finally,this paper analyzes the shortcomings of the proposed method,and makes prospects for the future research work.