A Novel Concept for Reliability Evaluation Using Multiple Deterministic Analyses (original) (raw)
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System Reliability Analysis by Monte Carlo Based Method and Finite Element Structural Models
Journal of Offshore Mechanics and Arctic Engineering, 2014
In principle, the reliability of complex structural systems can be accurately predicted by Monte Carlo simulation. This method has several attractive features for structural system reliability, the most important being that the system failure criterion is usually relatively easy to check almost irrespective of the complexity of the system. However, the computational cost involved in the simulation may be prohibitive for highly reliable structural systems. In this paper a new Monte Carlo based method recently proposed for system reliability estimation that aims at reducing the computational cost is applied. It has been shown that the method provides good estimates for the system failure probability with reduced computational cost. In a numerical example the usefulness and efficiency of the method to estimate the reliability of a system represented by a nonlinear finite element structural model is presented. To reduce the computational cost involved in the nonlinear finite element analysis the method is combined with a response surface model.
Comparative study of computational methods of structural reliability assessment
Safety is an essential requirement of a structural system. Reliability is an additional tool of growing importance in engineering, as it allows us to quantify uncertainties in the design. Thus, reliability assists us in making more suitable decisions regarding the safety of a structure. The present work compares and analyzes structural reliability methods applied to various examples of limit state functions. These methods are essential tools for this analysis because they identify and quantify uncertainties in random variables, allowing the evaluation of the probability of failure of the structure. Structural reliability methods were programmed and simulated in the Python language. The performance of these methods was analyzed through examples of linear, nonlinear, implicit, and explicit limit state functions. The results indicate that the simulation of Monte de Carlo brute force (MCBF) and importance sampling (MCAI) proved to be quite efficient for the examples studied in this work, with values equal to or very close to the reference values from the literature. The First Order and Second Moment Method (FOSM) presented limitations in some examples when the basic random variables do not have a normal distribution and the limit state function is nonlinear. The first-order reliability method (FORM) employs a failure surface linearization, which does not work well for highly nonlinear problems. The second-order reliability method (SORM) has improved the FORM results by including additional information about the curvature of the limit state function.
Numerical Approximation of Structural Reliability Analysis Methods
International Journal of Innovation and Applied Studies, 2017
We know that with the reliability structure, modeling is based on a deterministic physical system: the latter extract degradation mechanisms. Thus, mechanisms taken into account are crack propagations and are defects from thermal or vibratory fatigue, corrosion or erosion etc... The structure is submitted to some loadings in its environment; this, defines a finite number of modes of degradation. We can envision envisage two possible outcomes: failure or success. Therefore, we could consider the failure probability deterministic or probabilistic. According to the probabilistic approach, the risk will be evaluated without probability of failure. It is understood that this evaluation represents the entire problem of this work. In our study, we are going to be examining the development of two methods of structural reliability, which are the first order and second order: That is why we are going to use FORM and SORM method alongside with the Monte Carlo simulation, which are so effective...
A New Hybrid Reliability Analysis Method: The Design Point - Response Surface - Simulation Method
2008
Classical reliability methods such as First-and Second-Order Reliability Methods (FORM and SORM) have been important breakthroughs toward feasible and reliable integration of probabilistic information and uncertainty analysis into advanced design methods and modern design codes. These methods have been successfully used in solving challenging reliability problems. Nevertheless, caution should be used in the applications of these methods since their limitations and shortcomings in terms of applicability and accuracy are known and documented. Current research trends highlight the importance of structural reliability analysis methodologies that are able to provide improved estimates of the failure probability without excessive increase in computational cost when compared with ordinary FORM/SORM analyses. In this work, a new hybrid reliability analysis method, denoted as Design Point -Response Surface -Simulation (DP-RS-Sim) method is proposed and illustrated. This method innovatively combines the design point (DP) search used in FORM/SORM analyses with the response surface method and appropriate simulation techniques. The need for this combination has emerged from the results obtained through visualization of the limit state surfaces (LSSs) typically used in finite element reliability analysis. In particular, the visualization results show that these LSSs are often highly nonlinear in the neighborhood of their DPs. As application example, the time-invariant reliability analysis of a reinforced concrete frame structure subjected to horizontal pushover loads is considered. DP-RS-Sim-based estimations of the probability of limit state exceedance (expressed in terms of displacement thresholds) by the benchmark structure are compared with FORM, SORM, crude Monte Carlo and Importance Sampling results in terms of accuracy and computational cost. It is shown that the new DP-RS-Sim method can provide accurate failure probability estimates at low computational cost compared to other structural reliability methods.
Structural reliability analysis using deterministic finite element programs
Latin American Journal of Solids and Structures
The paper shows how structural reliability algorithms can be incorporated into deterministic (commercial) finite element codes and used to perform numerical structural reliability analysis based on finite element models of a structure. A structural reliability module is developed and linked to the ANSYS finite element program, creating a customized version of the program. Structural reliability analysis can be performed in the ANSYS environment, and involves construction of a parametric finite element model, definition of random parameter distributions, definition of a limit state function based on finite element results, and solution for the failure probability. Numerical examples involving truss and frame structures are studied. An application example -structural reliability analysis of an eye-bar suspension bridge -is also presented.
Moment methods for structural reliability
First-order reliability method (FORM) is considered to be one of the most reliable computational methods. In the last decades, researchers have examined the shortcomings of FORM, primarily accuracy and the diculties involved in searching for the design point by iteration using the derivatives of the performance function. In order to improve upon FORM, several structural reliability methods have been developed based on FORM, such as second-order reliability method (SORM), importance sampling Monte-Carlo simulation, ®rst-order third-moment reliability method (FOTM), and response surface approach (RSA). In the present paper, moment methods for structural reliability are investigated. Five moment method formulas are presented and investigated, and the accuracy and eciency of these methods are demonstrated using numerical examples. The moment methods, being very simple, have no shortcomings with respect to design points, and requires neither iteration nor the computation of derivatives, and thus are convenient to be applied to structural reliability analysis. #
A Proposed Method for Reliability Analysis in Higher Dimension
Abstract—In this paper, a new method is proposed to evaluate the reliability of stochastic mechanical systems. This technique is based on the combination of the probabilistic transformation methods for multiple random variables (MPTM) and the finite element method (FEM). The transformation technique evaluates the Probability Density Function (PDF) of the system response by the use of the Jacobian of the inverse mechanical function.
—The Response Surface Method (RSM) is not efficient to solve reliability analysis of complex and computationally high-demanding models. The Stochastic Response Surface Method (SRSM) was proposed recently. This paper adds some mathematics foundation for the SRSM, and compares the SRSM and RSM. The two approaches are applied to a nonlinear numerical example and a statically indeterminate beam problem respectively. The results show that the SRSM can be used for efficient, accurate estimate reliability.
A novel reliability evaluation method for large engineering systems
Ain Shams Engineering Journal, 2016
A novel reliability evaluation method for large nonlinear engineering systems excited by dynamic loading applied in time domain is presented. For this class of problems, the performance functions are expected to be function of time and implicit in nature. Available first-or second-order reliability method (FORM/SORM) will be challenging to estimate reliability of such systems. Because of its inefficiency, the classical Monte Carlo simulation (MCS) method also cannot be used for large nonlinear dynamic systems. In the proposed approach, only tens instead of hundreds or thousands of deterministic evaluations at intelligently selected points are used to extract the reliability information. A hybrid approach, consisting of the stochastic finite element method (SFEM) developed by the author and his research team using FORM, response surface method (RSM), an interpolation scheme, and advanced factorial schemes, is proposed. The method is clarified with the help of several numerical examples.