One of the main obstacles in the solution of structural optimization problems is the need to repeat solutions of the analysis and sensitivity analysis equations. In large-scale structures, having complex analysis models, the computational effort may become prohibitive. To alleviate this difficulty a general approach for repeated analysis and repeated sensitivity analysis, called combined approximations, was developed during the last 15 years. The solution is based on the integration of several algorithms and methods. As a result, accurate results can be achieved efficiently. In previous studies, solution procedures for various particular problems were developed. This article summarizes the various formulations and solution procedures for reanalysis and sensitivity reanalysis of linear, nonlinear, static and dynamic systems. It is shown that the various solution procedures are based on applications of similar basic algorithms. Numerical examples demonstrate the efficiency of the calculations and the accuracy of the results.

Reanalysis and sensitivity reanalysis by combined approximations

The combined approximations method proposed by Kirsch is an efficient reanalysis method providing high-quality results. To integrate the Kirsch method into a structural optimization process, this paper presents a new adaptive Kirsch method to determine the minimum number of basis vectors using the K-condition number. Consequently, a closer relationship between the Kirsch method and structural optimization is bridged. Moreover, the effectiveness of the Kirsch method is improved for application in optimal design problems. The presented numerical results prove that the adaptive Kirsch method is significantly more efficient than the Kirsch method because of the advantage of adaptively determining the minimum number of basis vectors to satisfy the predefined reanalysis error.

New Adaptive Technique of Kirsch Method for Structural Reanalysis

Vibration reanalysis based on block combined approximations with shifting

The modal stability procedure for dynamic and linear finite element analysis with variability

Methods, systems, devices and computer program products for planning for failures of vehicular components are provided herein. A method includes obtaining a first set of data of maintenance events recorded for multiple vehicular components across multiple vehicles in a fleet; obtaining a second set of data of maintenance work orders performed on the vehicular components; obtaining a third set of data of measurements taken in connection with the vehicular components; analyzing (i) the first set of data and (ii) the second set of data to identify component failure events associated with the multiple vehicular components; determining failure indicators for each of the vehicular components in each of the vehicles in the fleet based on the second set of data, the third set of data, and the identified component failure events; and outputting the indicators in multiple visualized forms, each representing one of multiple levels of granularity.

Monitoring and Planning for Failures of Vehicular Components

: Finite element analysis (FEA) is a well-established methodology in structural dynamics. However, optimization and/or probabilistic studies can be prohibitively expensive because they require repeated FEA of large models. Various re-analysis methods have been proposed in order to calculate efficiently the dynamic response of a structure after a baseline design has been modified, without recalculating the new response. The parametric reduced-order modeling (PROM) and the combined approximation (CA) methods are two re-analysis methods, which can handle large model parameter changes in a relatively efficient manner. Although both methods are promising by themselves, they can not handle large FE models with large numbers of degrees of freedom (DOF) (e.g. 100,000) and design parameters (e.g. 50), which are common in practice. In this paper, a new re-analysis method is proposed where the original CA method is modified to further improve its efficiency, especially for problems where a large number of modes is required. The modified CA (MCA) method is then integrated with the PROM approach, in order to formulate a new efficient re-analysis method that is suitable for large FE models with many design parameters that vary in a wide range. A simple frame structure is used to explain all steps of the proposed method. Also, a vibro-acoustic analysis of a realistic vehicle FE model is presented to demonstrate the efficiency and accuracy of the new method. A design optimization study is also performed to highlight the accuracy and efficiency of the proposed re-analysis method.

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An Efficient Re-Analysis Methodology for Vibration of Large-Scale Structures (PREPRINT)

A system and a method of generating a reliability prediction for components of a vehicle. The system and the method include implementing importance sampling in dynamic vehicle systems when the vehicle is subjected to time-dependent random terrain input. Alternatively, simulation data may be implemented. The system and the method include determining a decorrelation length, scaling up the standard deviation of white noise, and calculation of a likelihood ratio.

System and method for importance sampling based time-dependent reliability prediction

Finite element (FE) analysis is a well-established methodology in structural dynamics. However, probabilistic studies can be prohibitively expensive because they require repeated FE analyses of large models. Various re-analysis methods have been proposed with the premise to effectively calculate the dynamic response of a structure after a baseline design has been modified, without recalculating the new response. Although they improve the computational efficiency considerably, they are not efficient enough for probabilistic analysis of large-scale vibration problems because they can only generate a relatively small number of sample points for a practically acceptable CPU time. In this paper, an efficient reanalysis method is used to generate a finite number of response sample points. Subsequently, tail modeling is used to estimate the right tail of the response PDF. This methodology enables us to accurately estimate high reliability values of vibratory problems with a relatively small number of analyses. A probabilistic vibration analysis of a realistic vehicle FE model is presented to demonstrate the advantages of the proposed probabilistic methodology.

Efstratios Nikolaidis

Papers

An Efficient Re-Analysis Methodology for Vibration of Large-Scale Structures (PREPRINT)

System and method for importance sampling based time-dependent reliability prediction

Reliability Estimation of Large-Scale Structural Vibration Problems