Stochastic force identification for uncertain structures based on matrix equilibration and improved Tikhonov regularization method

•A novel stochastic force identification method is developed for uncertain structures.•A two-side equilibration method is proposed to reduce the condition number of the FRF matrix.•An improved Tikhonov regularization method is proposed to identify the force PSD.•The probability integral equation for the identified force PSD is established and solved.•The PDFs and the confidence intervals of force PSD can be effectively identified. Accurate identification and estimation of stochastic forces applied to in-service engineering structures play a vital role in structural safety assessments. This study devised an effective force power spectral density (PSD) identification method to address the challenge of identifying multipoint stationary stochastic forces in uncertain structures. Initially, a probability model was employed to characterize structural uncertainties. Subsequently, an integral relationship was established between the probability density function (PDF) of the random structural parameters and that of the stochastic force PSD. By employing a point-selection technique based on the generalized F-discrepancy and a smoothing method, the uncertainty problem was transformed into a finite number of stochastic force PSD identification problems for deterministic structures. Simultaneously, based on the inverse pseudo-excitation method, a matrix equilibration approach and an improved Tikhonov regularization method were used to address the problem of large identification errors near structural natural frequencies. In comparison to the traditional weighting matrix method, the proposed method further reduces the condition number of frequency response function matrices, thereby enhancing the accuracy of force PSD identification. Finally, numerical examples were presented to validate the effectiveness of the proposed method in solving the stochastic force identification problem.