A pole-residue polynomial-chaos neural network for stochastic frequency response of MDOF systems

The statistics of the frequency response of an uncertain structure are most demanding to compute near lightly damped resonances. As the parameters vary, the resonant frequencies migrate, so at a fixed frequency the response depends sharply on the parameters, and a polynomial surrogate converges slowly there. We propose to work on its partial-fraction representation characterized by poles and residues. The surrogate is an encoder–decoder with a physical bottleneck, in which an encoder maps the random parameters into the spectral data and a fixed analytic pole–residue layer decodes them into the response. We introduce two encoders of the spectral data, a direct polynomial-chaos map, PR-PCE, and a neural-network encoder that takes the chaos basis as its feature map, PR-PCNN. We develop the construction for a random vector indexed by the frequency. A complementary route learns the same spectral code from sampled responses alone, independently of the system matrices. The framework is verified on two systems, a three-degree-of-freedom structure and a clamped–free beam whose flexural rigidity is a random field. On both, the linear PR-PCE map is the most accurate, the neural encoders follow it, and a frequency-wise chaos expansion trails them. The representation is also benchmarked against a stochastic frequency transformation and a per-realisation vector fit. For these smooth spectral data the linear map stays the more accurate, and the value of the neural encoder lies in its flexibility, since it also learns the code end-to-end and from sampled responses alone.