<p>This study investigates the probabilistic response prediction of high-dimensional strongly nonlinear fractional-order systems subject to both intrinsic parameter uncertainties and stochastic excitations. Such systems present significant challenges due to their high dimensional nature and complex coupling effects, which conventional methods struggle to address effectively. To tackle these challenges, a physics-data fusion-driven dimensionality reduction theory is employed for stochastic dynamic analysis of fractional-order systems. The framework comprises three key steps. First, a memoryless transformation is introduced to convert the original fractional-order system into an augmented high-dimensional integer-order memoryless system. Second, by combining the total probability principle with subspace decomposition techniques, the governing unconditional Fokker–Planck-Kolmogorov (FPK) equation is effectively decoupled, significantly reducing computational complexity. Third, a deep neural network (DNN) is employed to learn the equivalent drift coefficient (EDC) or equivalent diffusion function (EDF) from a small set of Monte Carlo simulation (MCS) data of the augmented system, and a radial basis function neural network (RBFNN) is then used to predict the probability density function (PDF) of the target state variables. Finally, numerical validation through three illustrative examples demonstrates excellent agreement with MCS while maintaining superior computational efficiency.</p>

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Random vibration of high-dimensional strongly nonlinear fractional-order systems with parametric uncertainties

  • Hong Han,
  • Lincong Chen

摘要

This study investigates the probabilistic response prediction of high-dimensional strongly nonlinear fractional-order systems subject to both intrinsic parameter uncertainties and stochastic excitations. Such systems present significant challenges due to their high dimensional nature and complex coupling effects, which conventional methods struggle to address effectively. To tackle these challenges, a physics-data fusion-driven dimensionality reduction theory is employed for stochastic dynamic analysis of fractional-order systems. The framework comprises three key steps. First, a memoryless transformation is introduced to convert the original fractional-order system into an augmented high-dimensional integer-order memoryless system. Second, by combining the total probability principle with subspace decomposition techniques, the governing unconditional Fokker–Planck-Kolmogorov (FPK) equation is effectively decoupled, significantly reducing computational complexity. Third, a deep neural network (DNN) is employed to learn the equivalent drift coefficient (EDC) or equivalent diffusion function (EDF) from a small set of Monte Carlo simulation (MCS) data of the augmented system, and a radial basis function neural network (RBFNN) is then used to predict the probability density function (PDF) of the target state variables. Finally, numerical validation through three illustrative examples demonstrates excellent agreement with MCS while maintaining superior computational efficiency.