The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
Kai Goebel - One of the best experts on this subject based on the ideXlab platform.
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Uncertainty quantification in remaining useful life prediction using first-order reliability methods
IEEE Transactions on Reliability, 2014Co-Authors: Swaminathan Sankararaman, Matthew J. Daigle, Kai GoebelAbstract:In this paper, we investigate the use of first-order reliability methods to quantify the uncertainty in the remaining useful life (RUL) estimate of components used in engineering applications. The prediction of RUL is affected by several sources of uncertainty, and it is important to systematically quantify their combined effect on the RUL prediction in order to aid risk assessment, risk mitigation, and decision-making. While sampling-based algorithms have been conventionally used for quantifying the uncertainty in RUL, analytical approaches are computationally cheaper, and sometimes they are better suited for online decision-making. Exact analytical algorithms may not be available for practical engineering applications, but effective approximations can be made using first-order reliability methods. This paper describes three first-order reliability-based methods for RUL uncertainty quantification: first-order second moment method (FOSM), the first-order reliability method (Form), and the Inverse first-order reliability method (Inverse-Form). The Inverse-Form methodology is particularly useful in the context of online health monitoring, and this method is illustrated using the power system of an unmanned aerial vehicle, where the goal is to predict the end of discharge of a lithium-ion battery. [ABSTRACT FROM AUTHOR]
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Uncertainty Quantification in Remaining Useful Life of Aerospace Components using State Space Models and Inverse Form
54th AIAA ASME ASCE AHS ASC Structures Structural Dynamics and Materials Conference, 2013Co-Authors: Shankar Sankararaman, Kai GoebelAbstract:This paper investigates the use of the Inverse first-order reliability method (Inverse- Form) to quantify the uncertainty in the remaining useful life (RUL) of aerospace components. The prediction of remaining useful life is an integral part of system health prognosis, and directly helps in online health monitoring and decision-making. However, the prediction of remaining useful life is affected by several sources of uncertainty, and therefore it is necessary to quantify the uncertainty in the remaining useful life prediction. While system parameter uncertainty and physical variability can be easily included in Inverse-Form, this paper extends the methodology to include: (1) future loading uncertainty, (2) process noise; and (3) uncertainty in the state estimate. The Inverse-Form method has been used in this paper to (1) quickly obtain probability bounds on the remaining useful life prediction; and (2) calculate the entire probability distribution of remaining useful life prediction, and the results are verified against Monte Carlo sampling. The proposed methodology is illustrated using a numerical example.
Elisabeth M Werner - One of the best experts on this subject based on the ideXlab platform.
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functional affine isoperimetry and an Inverse logarithmic sobolev inequality
Journal of Functional Analysis, 2012Co-Authors: Shiri Artsteinavidan, Boaz Klartag, Carsten Schutt, Elisabeth M WernerAbstract:Abstract We give a functional version of the affine isoperimetric inequality for log-concave functions which may be interpreted as an Inverse Form of a logarithmic Sobolev inequality for entropy. A linearization of this inequality gives an Inverse inequality to the Poincare inequality for the Gaussian measure.
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Functional affine-isoperimetry and an Inverse logarithmic Sobolev inequality
arXiv: Functional Analysis, 2011Co-Authors: Shiri Artstein-avidan, Boaz Klartag, Carsten Schuett, Elisabeth M WernerAbstract:We give a functional version of the affine isoperimetric inequality for log-concave functions which may be interpreted as an Inverse Form of a logarithmic Sobolev inequality inequality for entropy. A linearization of this inequality gives an Inverse inequality to the Poincar'e inequality for the Gaussian measure.
Jin Cheng - One of the best experts on this subject based on the ideXlab platform.
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Application of the response surface methods to solve Inverse reliability problems with implicit response functions
Computational Mechanics, 2008Co-Authors: Jin ChengAbstract:The Inverse first-order reliability method (Form) is considered to be one of the most widely used methods in Inverse reliability analysis. It has been recognized that there are shortcomings of the Inverse Form in solving Inverse reliability problems with implicit response functions, primarily inefficiency and difficulties involved in evaluating derivatives of the implicit response functions with respect to random variables. In order to apply the Inverse Form to structural Inverse reliability analysis, response surface methods can be used to overcome the shortcomings. In the present paper, two different response surface methods, namely the polynomial-based response surface method and the artificial neural network-based response surface method, are developed to solve the Inverse reliability problems with implicit response functions, and the accuracy and efficiency of the two response surface methods are demonstrated through two numerical examples of steel structures. It is found that the polynomial-based response surface method is more efficient and accurate than the artificial neural network-based response surface method. Recommendations are made regarding the suitability of the two response surface methods to solve the Inverse reliability problems with implicit response functions.
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a new approach for solving Inverse reliability problems with implicit response functions
Engineering Structures, 2007Co-Authors: Jin Cheng, Jie Zhang, C S Cai, Rucheng XiaoAbstract:The Inverse first-order reliability method (Form) is one of the most widely used methods in Inverse reliability analysis. However, this method has two drawbacks in the solution of Inverse reliability problems with implicit response functions. First, it requires the evaluation of the derivatives of the response functions with respect to the random variables. When these functions are implicit functions of the random variables, derivatives of these response functions are not readily available. Second, it usually involves repeated deterministic response analyses of complicated structures due to the variation of the basic variables, and therefore requires a relatively long computation time. To overcome these drawbacks of the Inverse Form, an artificial neural network (ANN)-based Inverse Form is proposed in this paper. In this method, an ANN model is used to approximate the structural response function so that the number of deterministic response analyses can be dramatically reduced. The explicit Formulation of structural response is derived by using the parameters of the ANN model. After the explicit response function is determined, the Inverse Form is applied to solve the Inverse reliability problem. The accuracy and efficiency of the proposed method is demonstrated through two numerical examples. Some important parameters in the proposed method are also discussed.
Paul Steinmann - One of the best experts on this subject based on the ideXlab platform.
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Recent Progress in Inverse Form Finding for Metal Forming Applications
2018Co-Authors: Paul Steinmann, Philipp Landkammer, Michael CaspariAbstract:Inverse Form finding determines the optimal material configuration (i.e. the un-deFormed work-piece geometry) for a desired spatial configuration (i.e. the deFormed work-piece geometry) for the case of prescribed boundary conditions. Previous approaches are either only available for two- dimensional problems, computationally expensive, not applicable for path dependency or suffer from a cumbersome derivation. Hence, there is an urgent need for efficient and flexible approaches applicable to elasto-plastic materials and especially to Forming processes. Here, we propose two different strategies to approach these difficulties. On the one hand, we focus on an algorithm based on an Inverse mechanical Formulation. It deter- mines the sought material configuration e.g. for orthotropic elasto-plasticity at large deFormations. Here we invoke a material modelling approach based on logarithmic strains for our investigations due to its modular Formulation. Then the algorithmic procedure starts at the given spatial target configuration. We compute the sought material configuration by a parametrization of the deFormation map in terms of spatial coordinates and a Formulation based on Inverse kinematics. We by-pass path dependency by alternating between a solution based on a direct and an Inverse boundary value problem and mapping the computed plastic variables to the target configuration. For selected benchmark problems, this approach turns out to be more stable and efficient than traditional shape optimization methods. On the other hand, we present a novel, node-based and non-invasive optimization algorithm. Its derivation relies on gradient-based optimization theory and an analysis of the deFormation stage. There- fore, the algorithm avoids a cumbersome derivation as needed for the Inverse mechanical Formulation. Furthermore, the advocated optimization approach is entirely independent from the constitutive modelling and straightforwardly applicable to frictional contact problems. We couple our algorithm non-invasively to arbitrary (also commercial) simulation environments. By applying a line-search strategy, testing the mesh quality and controlling inner nodal positions through an additional fictitious elastic problem, we enhance the stability of the algorithm. A convergence analysis of benchmark problems shows excellent results. Comparing both strategies indicates that the non-invasive optimization approach is better suited for an application to Forming processes. In order to demonstrate its practicability, we apply the method to improve the results of sheet and sheet-bulk metal Forming processes (cup deep drawing, local bulk-Forming operations with stamping of a sheet by tooth geometries, a combined process of drawing and upsetting). Furthermore, we verify the numerical results through Forming experiments.
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A non-invasive Form finding method with application to metal Forming
Production Engineering, 2016Co-Authors: Philipp Landkammer, Paul Steinmann, Thomas Schneider, Robert Schulte, Marion MerkleinAbstract:Inverse Form finding aims in determining the optimal material configuration of a workpiece for a specific Forming process. A gradient- and parameter-free (nodal-based) Form finding approach has recently been developed, which can be coupled non-invasively as a black box to arbitrary finite element software. Additionally the algorithm is independent from the constitutive behavior. Consequently, the user has not to struggle with the underlying optimization theory behind. Benchmark tests showed already that the approach works robustly and efficiently. This contribution demonstrates that the optimization algorithm is also applicable to more sophisticated Forming processes including orthotropic large strain plasticity, combined hardening and frictional contact. A cup deep drawing process with solid-shell elements and a combined deep drawing and upsetting process to Form a functional component with external teeth are investigated.
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Application of a Non-Invasive Form Finding Algorithm to the Ring Compression Test with Varying Friction Coefficients
Key Engineering Materials, 2015Co-Authors: Philipp Landkammer, Paul SteinmannAbstract:It is a great challenge in the development of functional components to determine the optimal blank design (material configuration) of a workpiece according to a specific Forming process, while knowing the desired target geometry (spatial configuration). A new iterative non-invasive algorithm, which is purely based on geometrical considerations, is developed to solve Inverse Form finding problems. The update-step is perFormed by mapping the nodal spatial difference vector, between the computed spatial coordinates and the desired spatial target coordinates, with a smoothed deFormation gradient to the discretized material configuration. The iterative optimization approach can be easily coupled non-invasively via subroutines to arbitrary finite element codes such that the pre-processing, the solving and the post-processing can be perFormed by the habitual simulation software. This is exemplary demonstrated by an interacting between Matlab (update procedure for Inverse Form finding) and MSC.MarcMentat (metal Forming simulation). The algorithm succeeds for a parameter study of a ring compression test within nearly linear convergence rates, despite highly deFormed elements and tangential contact with varying friction parameters.
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a comparison between a recursive method based on an Inverse mechanical Formulation and shape optimization for solving Inverse Form finding problems in isotropic elastoplasticity
Pamm, 2014Co-Authors: Sandrine Germain, Philipp Landkammer, Paul SteinmannAbstract:In this paper we compare two methods, a recursive method based on an Inverse mechanical Formulation and a method based on a recursive shape optimization Formulation, in order to solve Inverse Form finding problems in isotropic elastoplasticity. Both methods are succinctly presented and a numerical example is given. It was found that no difference could be found between the node coordinates on the undeFormed configurations computed with both methods. However the convergence to the solution is faster with the recursive method based on an Inverse mechanical Formulation than with the method based on shape optimization. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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On a recursive Formulation for solving Inverse Form finding problems in isotropic elastoplasticity
Advanced Modeling and Simulation in Engineering Sciences, 2014Co-Authors: Sandrine Germain, Philipp Landkammer, Paul SteinmannAbstract:Background Inverse Form finding methods allow conceiving the design of functional components in less time and at lower costs than with direct experiments. The deFormed configuration of the functional component, the applied forces and boundary conditions are given and the undeFormed configuration of this component is sought. Methods In this paper we present a new recursive Formulation for solving Inverse Form finding problems for isotropic elastoplastic materials, based on an Inverse mechanical Formulation written in the logarithmic strain space. First, the Inverse mechanical Formulation is applied to the target deFormed configuration of the workpiece with the set of internal variables set to zero. Subsequently a direct mechanical Formulation is perFormed on the resulting undeFormed configuration, which will capture the path-dependency in elastoplasticity. The so obtained deFormed configuration is furthermore compared with the target deFormed configuration of the component. If the difference is negligible, the wanted undeFormed configuration of the functional component is obtained. Otherwise the computation of the Inverse mechanical Formulation is started again with the target deFormed configuration and the current state of internal variables obtained at the end of the computed direct Formulation. This process is continued until convergence is reached. Results In our three numerical examples in isotropic elastoplasticity, the convergence was reached after five, six and nine iterations, respectively, when the set of internal variables is initialised to zero at the beginning of the computation. It was also found that when the initial set of internal variables is initialised to zero at the beginning of the computation the convergence was reached after less iterations and less computational time than with other values. Different starting values for the set of internal variables have no influence on the obtained undeFormed configuration, if convergence can be achieved. Conclusions With the presented recursive Formulation we are able to find an appropriate undeFormed configuration for isotropic elastoplastic materials, when only the deFormed configuration, the applied forces and boundary conditions are given. An initial homogeneous set of internal variables equal to zero should be considered for such problems.
Swaminathan Sankararaman - One of the best experts on this subject based on the ideXlab platform.
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Uncertainty quantification in remaining useful life prediction using first-order reliability methods
IEEE Transactions on Reliability, 2014Co-Authors: Swaminathan Sankararaman, Matthew J. Daigle, Kai GoebelAbstract:In this paper, we investigate the use of first-order reliability methods to quantify the uncertainty in the remaining useful life (RUL) estimate of components used in engineering applications. The prediction of RUL is affected by several sources of uncertainty, and it is important to systematically quantify their combined effect on the RUL prediction in order to aid risk assessment, risk mitigation, and decision-making. While sampling-based algorithms have been conventionally used for quantifying the uncertainty in RUL, analytical approaches are computationally cheaper, and sometimes they are better suited for online decision-making. Exact analytical algorithms may not be available for practical engineering applications, but effective approximations can be made using first-order reliability methods. This paper describes three first-order reliability-based methods for RUL uncertainty quantification: first-order second moment method (FOSM), the first-order reliability method (Form), and the Inverse first-order reliability method (Inverse-Form). The Inverse-Form methodology is particularly useful in the context of online health monitoring, and this method is illustrated using the power system of an unmanned aerial vehicle, where the goal is to predict the end of discharge of a lithium-ion battery. [ABSTRACT FROM AUTHOR]
