Stochastic Dynamic Load Identification on an Uncertain Structure With Correlated System Parameters

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Shaoqing Wu ◽  
Yanwei Sun ◽  
Yanbin Li ◽  
Qingguo Fei
Keyword(s):  
Dynamic System ◽  
Dynamic Load ◽  
Polynomial Chaos ◽  
Identification Problem ◽  
Stochastic Dynamic ◽  
Load Identification ◽  
Random System ◽  
System Parameters ◽  
Stochastic Load ◽  
Uncertain Dynamic System

A stochastic dynamic load identification algorithm is proposed for an uncertain dynamic system with correlated random system parameters. The stochastic Green's function is adopted to establish the relationship between the Gaussian excitation and the response. The Green's function is approximated by the second-order perturbation method, and orthogonal polynomial chaos bases are adopted to replace the corresponding bases in the Tayler series. The stochastic system responses and the stochastic forces are then represented by the polynomial chaos expansion (PCE) and the Karhunen–Loève expansion (KLE), respectively. A unified probabilistic framework for the stochastic dynamic problem is formulated based on the PCE. The stochastic load identification problem of an uncertain dynamic system is then transformed into a stochastic load identification problem of an equivalent deterministic system with the orthogonality of the PCE. Numerical simulations and experimental studies with a cantilever beam under a concentrate stochastic force are conducted to estimate the statistical characteristics of the stochastic load from the stochastic structural response samples. Results show that the proposed method has good accuracy in the identification of force's statistics when the level of uncertainty in the system parameters is not small. Large errors in the identified statistics may occur when the correlation in the random system parameters is neglected. Different correlation lengths for the random system parameters are investigated to show the effectiveness and accuracy of the proposed method.

scholarly journals A Novel Improved Maximum Entropy Regularization Technique and Application to Identification of Dynamic Loads on the Coal Rock

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Chunsheng Liu ◽  
Chunping Ren
Keyword(s):  
Maximum Entropy ◽  
Dynamic Load ◽  
Regularization Parameter ◽  
Estimation Method ◽  
Identification Problem ◽  
Iteration Algorithm ◽  
Load Identification ◽  
Signal Processing Algorithm ◽  
Rock Structure ◽  
Coal Rock

A new signal processing algorithm was proposed to identify the dynamic load acting on the coal-rock structure. First, the identification model for dynamic load is established through the relationship between the uncertain load vector, and the assembly matrix of the responses was measured by the machinery dynamic system. Then, the entropy item of maximum entropy regularization (MER) is redesigned using the robust estimation method, and the elongated penalty function according to the ill-posedness characteristics of load identification, which was named as a novel improved maximum entropy regularization (IMER) technique, was proposed to process the dynamic load signals. Finally, the load identification problem is transformed into an unconstrained optimization problem and an improved Newton iteration algorithm was proposed to solve the objective function. The result of IMER technique is compared with MER technique, and it is found that IMER technique is available for analyzing the dynamic load signals due to higher signal-noise ratio, lower restoration time, and fewer iterative steps. Experiments were performed to investigate the effect on the performance of dynamic load signals identification by different regularization parameters and calculation parameters, pi, respectively. Experimental results show that the identified dynamic load signals are closed to the actual load signals using IMER technique combined with the proposed PSO-L regularization parameter selection method. Selecting optimal calculated parameters pi is helpful to overcome the ill-condition of dynamic load signals identification and to obtain the stable and approximate solutions of inverse problems in practical engineering. Meanwhile, the proposed IMER technique can also play a guiding role for the coal-rock interface identification.

A Reliability-Based Formulation for Simulation-Based Control Co-design Using Generalized Polynomial Chaos Expansion

2021 ◽  
pp. 1-15
Author(s):  
Mohammad Behtash ◽  
Michael J. Alexander-Ramos
Keyword(s):  
Dynamic System ◽  
Design Optimization ◽  
Reliability Analysis ◽  
Polynomial Chaos ◽  
Probabilistic Constraints ◽  
Stochastic Dynamic ◽  
Generalized Polynomial Chaos ◽  
Generalized Polynomial ◽  
And Control ◽  
Stochastic Dynamic Systems

Abstract Combined plant and control design (control co-design, or CCD) methods are often used during product development to address the synergistic coupling between the plant and control parts of a dynamic system. Recently, a few studies have started applying CCD to stochastic dynamic systems. In their most rigorous approach, reliability-based design optimization (RBDO) principles have been used to ensure solution feasibility under uncertainty. However, since existing reliability-based CCD (RBCCD) algorithms use all-at-once (AAO) formulations, only most-probable-point (MPP) methods can be used as reliability analysis techniques. Though effective for linear/quadratic RBCCD problems, the use of such methods for highly nonlinear RBCCD problems introduces solution error that could lead to system failure. A multidisciplinary feasible (MDF) formulation for RBCCD problems would eliminate this issue by removing the dynamic equality constraints and instead enforcing them through forward simulation. Since the RBCCD problem structure would be similar to traditional RBDO problems, any of the well-established reliability analysis methods could be used. Therefore, in this work, a novel reliability-based MDF formulation of multidisciplinary dynamic system design optimization (RB-MDF-MDSDO) has been proposed for RBCCD. To quantify the uncertainty propagated by the random decision variables, Monte Carlo simulation has been applied to the generalized polynomial chaos (gPC) expansion of the probabilistic constraints. The proposed formulation is applied to two engineering test problems, with the results indicating the effectiveness of both the overall formulation as well as the reliability analysis technique for RBCCD.

Stochastic Dynamic Analysis and Reliability of a Vessel Rolling in Random Beam Seas

2015 ◽  
Vol 59 (02) ◽  
pp. 113-131
Author(s):  
Wei Chai ◽  
Arvid Naess ◽  
Bernt J. Leira
Keyword(s):  
Dynamic System ◽  
Markov Property ◽  
Planck Equation ◽  
Linear Filter ◽  
Stochastic Dynamic ◽  
Theoretical Principle ◽  
Pi Method ◽  
Beam Seas ◽  
Stochastic Dynamic Analysis ◽  
High Level

This article presents a four-dimensional (4D) path integration (PI) approach to study the stochastic roll response and reliability of a vessel in random beam seas. Specifically, a 4D Markov dynamic system is established by combing the single-degree-of freedom model used to represent the ship rolling behavior in random beam seas with a second-order linear filter used to approximate the stationary roll excitation moment. On the basis of the Markov property of the coupled 4D dynamic system, the response statistics of roll motion can be obtained by solving the Fokker-Planck equation of the dynamic system via the 4D PI method. The theoretical principle and numerical implementation of the current state of the art 4D PI method are presented. Moreover, the numerical robustness and accuracy of the 4D PI method are evaluated by comparing with the results obtained by the application of Monte Carlo simulation (MCS). The influence of the restoring terms and the damping terms on the stochastic roll response are investigated. Furthermore, based on the well-known Poisson assumption and the response statistics yielded by the 4D PI technique, evaluation of the reliability associated with high-level response is performed. The performance of the Poisson estimate for different levels of external excitations is evaluated by the versatile MCS technique.

Stochastic Dynamic Analysis of Structures with Spatially Uncertain Material Parameters

2014 ◽  
Vol 14 (08) ◽  
pp. 1440029 ◽  
Author(s):  
Kheirollah Sepahvand ◽  
Steffen Marburg
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Polynomial Chaos ◽  
Element Model ◽  
Stochastic Dynamic ◽  
Stochastic Field ◽  
Structural Dynamic ◽  
Material Parameters ◽  
Material Uncertainties ◽  
Stochastic Dynamic Analysis

This paper investigates the uncertainty quantification in structural dynamic problems with spatially random variation in material and damping parameters. Uncertain and locally varying material parameters are represented as stochastic field by means of the Karhunen–Loève (KL) expansion. The stiffness and damping properties of the structure are considered uncertain. Stochastic finite element of structural modal analysis is performed in which modal responses are represented using the generalized polynomial chaos (gPC) expansion. Knowing the KL expansions of the random parameters, the nonintrusive technique is employed on a set of random collocation points where the structure deterministic finite element model is executed to estimate the unknown coefficients of the polynomial chaos expansions. A numerical case study is presented for a cantilever beam with random Young's modulus involving spatial variation. The proportional damping constants are estimated from the experimental modal analysis. The expected value, standard deviation, and probability distribution of the random eigenfrequencies and the damping ratios are evaluated. The results show high accuracy compared to the Monte-Carlo (MC) simulations with 3000 realizations. It is also demonstrated that the eigenfrequencies and the damping ratios are equally affected from material uncertainties.

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