Uncertainties In Structural Analysis Research Articles

Deep Learning-based Metamodeling Technique for Nonlinear Seismic Response Quantification

Classical physics-based numerical techniques such as finite element method (FEM) usually takes a huge computational resource and time for simulation-based uncertainties in structural analysis. Especially, it is expensive when nonlinear time history analysis is involved. The metamodeling technique becomes an alternative with an ability to predict the time history response of both elastic and inelastic structural system in a data-driven fashion. Various machine learning and deep learning-based techniques have been attempted to have their limitations in handling huge and sequential data while it comes to predict the whole response time history given stochastic ground motion acceleration. In this regard, Long Short Term Memory (LSTM) approach is found to be useful. The present study used LSTM deep learning network based metamodeling approach for nonlinear seismic response history approximation. The novelty of the approach lies in its capability of capturing record to record variability even for an inelastic structure. This metamodel can work with the desired level of accuracy with very limited data. The proposed approach has shown satisfactory results to approximate seismic response of a nonlinear single degree of freedom system.

A Non-Probabilistic Measure of Structural Reliability Based on Convex Model

The problem of the non-probabilistic reliability is investigated in this paper, in which the convex model is used to deal with uncertainties in structural analysis and design. The limitation on the current non-probabilistic reliability is discussed. Then a novel non-probabilistic reliability model is proposed, and its computational procedure is given. Two numerical examples are conducted to illustrate the feasibility and validity of the proposed non-probabilistic reliability model.

Probabilistic fracture mechanics with uncertainty in crack size and orientation using the scaled boundary finite element method

The geometry of cracks in a structure are often difficult to determine accurately, leading to uncertainties in structural analysis. This paper presents a probabilistic fracture mechanics (PFM) approach to evaluate the reliability of cracked structures considering the uncertainty in crack geometry. The shape sensitivity analysis of the stress intensity factor (SIF) is performed efficiently using the scaled boundary finite element method (SBFEM). No remeshing is required as the size and orientation of a crack vary. Reliability is estimated using various probabilistic techniques. Numerical examples demonstrate the accuracy and simplicity of the present method.

The encounter of interval and probabilistic approaches to structural reliability at the design point

The consideration of uncertainties in structural analysis has traditionally been made in the field of structural reliability within the framework of classical probability theory. In many cases, however, there is no sufficient probabilistic information to substantiate such an approach. In recent years several non-probabilistic methods have been proposed as alternatives. One of them is the interval analysis, oriented to estimate the range of variation of output structural variables given the ranges of the input ones. The method, however, requires the use of special arithmetics which renders its application unpractical for structural analysis based on finite elements or other numerical techniques. In this paper a Monte Carlo method that can be applied to probabilistic as well as to interval approaches to reliability analysis is proposed. It is based on the optimal properties of the classical design point of probabilistic structural reliability. In particular, it is shown that the order statistics of the output variable is concealed in a plot defined by the design point vector. This facilitates the selection of the relevant samples for either interval or probability-based analysis. The examples show that the desired interval of the response or the failure probability can be accurately estimated on such a basis. The paper also discusses the use of Monte Carlo methods for both reliability and interval analysis from the point of view of the proposed representation.

Identification of random shapes from images through polynomial chaos expansion of random level set functions

AbstractIn this paper, an efficient method is proposed for the identification of random shapes in a form suitable for numerical simulation within the extended stochastic finite element method (X‐SFEM). The method starts from a collection of images representing different outcomes of the random shape to identify. The key point of the method is to represent the random geometry in an implicit manner using the level set technique. In this context, the problem of random geometry identification is equivalent to the identification of a random level set function, which is a random field. This random field is represented on a polynomial chaos (PC) basis and various efficient numerical strategies are proposed in order to identify the coefficients of its PC decomposition. The performance of these strategies is evaluated through some ‘manufactured’ problems and useful conclusions are provided. The propagation of geometrical uncertainties in structural analysis using the X‐SFEM is finally examined. Copyright © 2009 John Wiley & Sons, Ltd.

The effects of uncertainties in structural analysis

Model-based predictions of structural behavior are negatively affected by uncertainties of various type and in various stages of the structural analysis. The present paper focusses on dynamic analysis and addresses the effects of uncertainties concerning material and geometric parameters, mainly in the context of modal analysis of large-scale structures. Given the large number of uncertain parameters arising in this case, highly scalable simulation-based methods are adopted, which can deal with possibly thousands of uncertain parameters. In order to solve the reliability problem, i.e., the estimation of very small exceedance probabilities, an advanced simulation method called Line Sampling is used. In combination with an efficient algorithm for the estimation of the most important uncertain parameters, the method provides good estimates of the failure probability and enables one to quantify the error in the estimate. Another aspect here considered is the uncertainty quantification for closely-spaced eigenfrequencies. The solution here adopted represents each eigenfrequency as a weighted superposition of the full set of eigenfrequencies. In a case study performed with the FE model of a satellite it is shown that the effects of uncertain parameters can be very different in magnitude, depending on the considered response quantity. In particular, the uncertainty in the quantities of interest (eigenfrequencies) turns out to be mainly caused by very few of the uncertain parameters, which results in sharp estimates of the failure probabilities at low computational cost.

Uncertainty identification by the maximum likelihood method

To incorporate uncertainty in structural analysis, a knowledge of the uncertainty in the model parameters is required. This paper describes efficient techniques to identify and quantify variability in the parameters from experimental data by maximising the likelihood of the measurements, using the well-established Monte Carlo or perturbation methods for the likelihood computation. These techniques are validated numerically and experimentally on a cantilever beam with a point mass at an uncertain location. Results show that sufficient accuracy is attainable without a prohibitive computational effort. The perturbation approach requires less computation but is less accurate when the response is a highly nonlinear function of the parameters.

Fuzzy structural analysis using α-level optimization

In this paper new concepts and developments are presented for structural analysis involving uncertain parameters. Based on a classification of the uncertainties in structural analysis the uncertainty “fuzziness” is identified and its quantification is demonstrated. On the basis of fuzzy set theory a general method for fuzzy structural analysis is developed and formulated in terms of the α-level optimization with the application of a modified evolution strategy. Every known analysis algorithm for the realistic simulation of load-bearing behavior may be applied in the fuzzy structural analysis in the sense of a deterministic fundamental solution. By way of example, geometrically and physically nonlinear algorithms are adopted in the presented study as a deterministic fundamental solution for the analysis of steel and reinforced concrete structures. The paper also describes coupling between α-level optimization and the deterministic fundamental solution.

Nondeterministic "Possibilistic" Approaches for Structural Analysis and Optimal Design

The development of methods to take Into account uncertainties in structural analysis and in design optimization is attracting both the scientific and the industrial communities. In this domain possibilistic methods in which uncertainties are defined by fuzzy numbers appear as an alternative to the classical probabilistic methods such as the Monte Carlo simulations or the stochastic finite element method. The principal difficulty of possibilistic methods is that they lead to the resolution of systems of equations in which the coefficients are defined by intervals. Several approaches for the direct solution of such interval linear equations systems are presented and compared. The vertex method is taken as reference. It is shown that the problems that are solved are mathematically different according to the method used. For static linear analysis a cost-effective iterative solution of the vertex is proposed. It is based on Neumann series expansions and solves an optimization subproblem to compute extrema of the structural responses. The effectiveness of the method is illustrated by the solution of truss problems, classical in the optimization literature. Extension of the method to inverse problems of design is also considered.