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Stochastic averaging, as an effective technique for dimension reduction, is of great significance in stochastic dynamics and control. However, its practical applications in industrial and engineering fields are severely hindered by its dependence on governing equations and the complexity of mathematical operations. Herein, a data-driven method, named data-driven stochastic averaging, is developed to automatically discover the low-dimensional stochastic differential equations using only the random state data captured from the original high-dimensional dynamical systems. This method includes two successive steps, that is, extracting all slowly varying processes hidden in fast-varying state data and identifying drift and diffusion coefficients by their mathematical definitions. It automates dimension reduction and is especially suitable for cases with unavailable governing equations and excitation data. Its application, efficacy, and comparison with theory-based stochastic averaging are illustrated through several examples, numerical or experimental, with pure Gaussian white noise excitation or combined excitations. [ABSTRACT FROM AUTHOR]

Inspired by the phenomenon of localized response intensification in wideband random vibration, a novel procedure is proposed to determine the optimal locations of piezoelectric patch attaching on wideband random point-driven beam for vibration energy harvesting application. The optimization objective is to maximize the mean output voltage, and the optimal locations lie on the vicinities of the excited point and its symmetric point. The optimal locations keep invariable regardless of typical symmetric boundary conditions (such as the clamped, simply supported, free, and torsional spring supports), the lower and upper cutoff frequencies of the band-limited white noise, and the external damping provided that the excited point is not too close to boundaries and the bandwidth of excitation covers enough modes of primary structure. The robustness of optimal locations is illustrated from an electromechanical coupling model and is qualitatively verified through experimental testing on a random-excited aluminum beam with piezoelectric patches attached on its surface. [ABSTRACT FROM AUTHOR]

The simplified governing equations of applied mechanics play a pivotal role and were derived based on ingenious assumptions or hypotheses regarding the displacement fields for specific problems. In this paper, we introduce a data-driven method by the name AI-Timoshenko in honor of Timoshenko, father of applied solid mechanics, to automatically discover simplified governing equations for applied mechanics problems directly from discrete data simulated by the three-dimensional (3D) finite element method. The simplified governing equations are in variational form, which is compact and advantageous for data-driven discovery. AI-Timoshenko liberates applied mechanicians from burdensome labor, including assumptions, derivation, and trial and error. The simplified governing equations for Euler-Bernoulli and Timoshenko beam theories are successfully rediscovered using the present AI-Timoshenko method, which shows that this method is capable of discovering simplified governing equations for applied mechanics problems. [ABSTRACT FROM AUTHOR]

The response control of nonlinear random dynamical systems is an important but also difficult subject in scientific and industrial fields. This work merges the decomposition technique of feedback control and the data-driven identification method of stationary response probability density, converts the constrained functional extreme value problem associated with optimal control to an unconstrained optimization problem of multivariable function, and determines the optimal coefficients of preselected control terms by an optimization algorithm. This data-driven method avoids the difficulty of solving the stochastic dynamic programming equation or forward-backward stochastic differential equations encountered in classical control theories, the miss of the conservative mechanism in the nonlinear stochastic optimal control strategy, and the difficulty of judging the integrability and resonance of the controlled Hamiltonian systems encountered in the direct-control method. The application and efficacy of the data-driven method are illustrated by the random response control problems of the Duffing oscillator, van der Pol system, and a two degrees-of-freedom nonlinear system. [ABSTRACT FROM AUTHOR]