Metamodeling and robust minimization approach for the identification of elastic properties of composites by vibration method

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This paper describes a method for determination of elastic parameters (elastic moduli and Poisson's ratio) of orthotropic composite plate‐type structural elements using the results of natural frequency measurements. The identification of parameter values is provided by minimization of weighted squared difference (discrepancy) between physically measured frequencies and natural frequencies calculated by Finite Element Method. The metamodels for the frequency dependence on the elastic parameters and other geometrical and physical parameters of test specimens, including parameters with uncertainty (“noisy constants”) are built using experimental designs optimized according to the Mean Squared Error space filling criterion and third‐order polynomial approximations. The minimum of weighted squared difference between measured and calculated frequencies is found using the multistart random search method. The expressions for standard deviations of identified parameters depending on deviations of “noisy constants” are derived using linearized metamodels. The expressions for identification errors allow the statement of the identification task as a robust minimization problem by simultaneous minimization of the discrepancy function and standard deviations of the identified values by varying the values of unknown elastic parameters and weighting coefficients for different frequencies. The partial scaling of natural frequencies is used for the reduction of the uncertainty impact on the identification error. This allows reducing the identification error of elastic moduli about two times and Poisson's ratio about 20 times in comparison with the results obtained by using dimensioned frequencies.