Abstract: An inverse method based on λ-probability distribution function(PDF) and first order second moment is developed to effectively evaluate the influence of the uncertainty of measured response on the identified results of structural parameters. The quadric derivative of λ-PDF is used to model the PDF of the identified uncertain variable. The method includes a double-loop procedure. In the inner-loop the performance function is solved by first order second moment method to obtain the computational PDFs of the responses. In the outer-loop the uncertain inverse problem is transformed into an optimization problem by minimizing the moment errors of the measured and computational responses, and the optimization problem is solved by intergeneration projection genetic algorithm. The method proposed can not only effectively estimate the PDFs of the unknown structure variables, but also have a higher computational efficiency compared with the traditional statistical method. Two numerical examples and an engineering problem are used to demonstrate the feasibility and effectiveness of the proposed method.

Key words: first order second moment, parameters identification, probability distribution function(PDF) estimation, uncertain inverse problem, λ-PDF