Influence Of Random Parameters Research Articles

Probabilistic Seismic Response Prediction of Three-Dimensional Structures Based on Bayesian Convolutional Neural Network

Seismic response prediction is a challenging problem and is significant in every stage during a structure’s life cycle. Deep neural network has proven to be an efficient tool in the response prediction of structures. However, a conventional neural network with deterministic parameters is unable to predict the random dynamic response of structures. In this paper, a deep Bayesian convolutional neural network is proposed to predict seismic response. The Bayes-backpropagation algorithm is applied to train the proposed Bayesian deep learning model. A numerical example of a three-dimensional building structure is utilized to validate the performance of the proposed model. The result shows that both acceleration and displacement responses can be predicted with a high level of accuracy by using the proposed method. The main statistical indices of prediction results agree closely with the results from finite element analysis. Furthermore, the influence of random parameters and the robustness of the proposed model are discussed.

Damage identification in offshore jacket structures based on modal flexibility

A modal flexibility-based method using finite element model updating technique for damage detection purposes is presented. The motivation for choosing modal flexibility is explained and the objective function for an iterative optimization process is formulated. The simulated platform FE model is established with single and triple damage cases where noise contamination and model uncertainty are considered. Monte Carlo simulation is used for random parameter study. A substructure optimization algorithm is proposed together with a threshold to lower the number of design variables. When the flexibility-based method employs only the first order modal parameter and translational degree of freedoms on merely 4 nodes, satisfactory results can still be derived under high level of contaminated noise and random errors on elemental elasticity modulus and mass density. The influence of random parameters, spatial-incompleteness and tiny damage cases are discussed with several important conclusions summarized. The proposed substructure optimization algorithm and crucial problems during optimization process are described. The algorithm is applied to two numerical examples including a simply-supported beam and a jacket-platform, the study based on equivalent model reveals better accuracy and efficiency of the proposed algorithm, even with 3% measurement noise and model uncertainty.

Study on Nonlinear Vibration Analysis of Gear System with Random Parameters

In order to study the dynamic characteristics of gear nonlinear vibration system and the influence of random parameters, firstly, a nonlinear stochastic vibration analysis model of gear 3-DOF is established based on Newton’s Law. And the random response of gear vibration is simulated by stepwise integration method. Secondly, the influence of stochastic parameters such as meshing damping, tooth side gap and excitation frequency on the dynamic response of gear nonlinear system is analyzed by using the stability analysis method such as bifurcation diagram and Lyapunov exponent method. The analysis shows that the stochastic process can not be neglected, which can cause the random bifurcation and chaos of the system response. This study will provide important reference value for vibration engineering designers.

Probabilistic Analysis Of A Space Truss By Means Of A Multidimensional Variable Description

AbstractProbabilistic analysis of a space truss is presented in the paper. Reliability of such a structure is sensitive to geometrical and material imperfections. The objective of this paper is to present a variant of the point estimate method (PEM) to determine mean values and standard deviations of limit loads of engineering structures. The main advantage presented by this method is the small number of sample calculations required to obtain estimators of investigated parameters. Thus the method is straightforward, requiring only preliminaries of probability theory. This approach is illustrated by limit state analysis of a space truss, considering geometric and material imperfections. The calculations were performed for different random models, so the influence of random parameters on the limit load of the truss can be determined. A realistic snow load was imposed.

Dynamic Reliability Analysis of Gear Transmission System of Wind Turbine in Consideration of Randomness of Loadings and Parameters

A dynamic model of gear transmission system of wind turbine is built with consideration of randomness of loads and parameters. The dynamic response of the system is obtained using the theory of random sampling and the Runge-Kutta method. According to rain flow counting principle, the dynamic meshing forces are converted into a series of luffing fatigue load spectra. The amplitude and frequency of the equivalent stress are obtained using equivalent method of Geber quadratic curve. Moreover, the dynamic reliability model of components and system is built according to the theory of probability of cumulative fatigue damage. The system reliability with the random variation of parameters is calculated and the influence of random parameters on dynamic reliability of components is analyzed. In the end, the results of the proposed method are compared with that of Monte Carlo method. This paper can be instrumental in the design of wind turbine gear transmission system with more advantageous dynamic reliability.

Multicriterion reliability-oriented optimization of structural systems by stochastic programming

Papers deals with multicriterion reliability-oriented optimization of truss structures by stochastic programming. Deterministic approach to structural optimization appears to be insufficient when loads acting upon a structure and material properties of the structure elements have a random nature. The aim of this paper is to show importance of random modelling of the structure and influence of random parameters on an optimal solution. Usually, quality of engineering structure design is considered in terms of displacements, total cost and reliability. Therefore, optimization problem has been formulated and then solved in order to show interaction between displacement and a total cost objective function. The examples of 4-bar and 25-bar truss structures illustrate our considerations. The results of optimization are presented in the form of diagrams.

The random attractor of the stochastic Lorenz system

We study the existence of attractors for dynamical systems under the influence of random parameters. Such a random attractor is a measurable multi-function with compact images fulfilling particular invariance and attracting properties. In particular, this uniquely determined attractor attracts measurable multi-functions. Under certain conditions we estimate the Hausdorff dimension of the attractor. These results will be applied to the Lorenz system under the influence of a random external parameter perturbation.

Spin‐1 Random‐Bond Transverse Ising Model with Competing Interactions

AbstractThe longitudinal magnetization, the transverse magnetization, and the order parameter y of the spin‐1 random‐bond transverse Ising model with competing interactions on a diamond lattice are discussed within the framework of the effective‐field theory. The phase diagrams of the system are obtained. The possible reentrant phenomena displayed by the system and the influence of random parameters α and p̄ on the behavior of the system are investigated.

Statistical theory on optical directional couplers with random parameters

Statistical coupling characteristics of optical directional couplers subject to random irregularities are studied theoretically by means of coupled mode theory. A new method is used for solving coupled mode equations in which random components of coupling coefficients and phase constants are assumed to be Gaussian random processes with an arbitrary correlation length. Mean values, variances, and probability distributions of coupled powers in 0‐dB and 3‐dB directional couplers are presented. The influence of random parameters is made clear. It is seen that tolerance requirements can be relaxed by a proper choice of the average parameters. Discussions about the film waveguide couplers for integrated optics applications are presented.