A FREQUENCY-DOMAIN PROBABILITY DENSITY RECONSTRUCTION METHOD BASED ON CHARACTERISTIC FUNCTIONS

To overcome the limited accuracy of conventional sample-space-based statistical inference methods in representing data distributions, this paper proposes a general frequency-domain probability density reconstruction method based on the characteristic function. First, a numerical formulation of the characteristic function is derived based on complex fractional moment theory, which effectively suppresses the high-frequency oscillations inherent in empirical characteristic functions. Second, closed-form analytical expressions of Gaussian basis functions in the frequency-domain are obtained, and a consistent mapping between frequency-domain parameters and their corresponding sample-space counterparts is established. On this basis, a deterministic initialization strategy based on amplitude spectrum peak detection is developed, enabling direct identification of initial model parameters through spectral feature analysis. Finally, a full-frequency-domain least-squares objective function is constructed, and parameter optimization is performed via global waveform matching between analytical and numerical characteristic functions. Owing to the analytical formulation in the frequency domain, the optimized frequency-domain parameters can be directly employed to reconstruct the probability density function in the sample space, thereby avoiding computationally intensive numerical inverse transformations. Numerical examples demonstrate that the proposed method achieves superior accuracy and enhanced modeling flexibility in reconstructing univariate extreme value distributions and multivariate joint distributions, highlighting its potential for engineering structural reliability assessment and risk analysis.