This paper proposes a hybrid algorithm based on the physics-informed kernel function neural networks(PIKFNNs)and the direct probability integral method(DPIM)for calculating the probability density function of stochast...This paper proposes a hybrid algorithm based on the physics-informed kernel function neural networks(PIKFNNs)and the direct probability integral method(DPIM)for calculating the probability density function of stochastic responses for structures in the deep marine environment.The underwater acoustic information is predicted utilizing the PIKFNNs,which integrate prior physical information.Subsequently,a novel uncertainty quantification analysis method,the DPIM,is introduced to establish a stochastic response analysis model of underwater acoustic propagation.The effects of random load,variable sound speed,fluctuating ocean density,and random material properties of shell on the underwater stochastic sound pressure are numerically analyzed,providing a probabilistic insight for assessing the mechanical behavior of structures in the deep marine environment.展开更多
This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochas...This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.展开更多
基金the National Natural Science Foundation of China,Grant Number:12372196,12302258,52325803,U22A20229,12402238State Key Laboratory of Ocean Engineering(Shanghai Jiao Tong University),Grant Number:GKZD010089+2 种基金the Six Talent Peaks Project in Jiangsu Province of China,Grant Number:2019-KTHY-009Jiangsu Funding Program for Excellent Postdoctoral Talent,Grant Number:2023ZB506Postdoctoral Fellowship Program of CPSF,Grant Number:GZC20230667。
文摘This paper proposes a hybrid algorithm based on the physics-informed kernel function neural networks(PIKFNNs)and the direct probability integral method(DPIM)for calculating the probability density function of stochastic responses for structures in the deep marine environment.The underwater acoustic information is predicted utilizing the PIKFNNs,which integrate prior physical information.Subsequently,a novel uncertainty quantification analysis method,the DPIM,is introduced to establish a stochastic response analysis model of underwater acoustic propagation.The effects of random load,variable sound speed,fluctuating ocean density,and random material properties of shell on the underwater stochastic sound pressure are numerically analyzed,providing a probabilistic insight for assessing the mechanical behavior of structures in the deep marine environment.
基金National Natural Science Foundation of China for Innovative Research Groups Under Grant No.50321803 & 50621062National Natural Science Foundation of China Under Grant No.50808113 & 10872148
文摘This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.
