skip to main content


Search for: All records

Award ID contains: 1923799

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. Abstract

    Reliability analysis is usually a core element in engineering design, during which reliability is predicted with physical models (limit-state functions). Reliability analysis becomes computationally expensive when the dimensionality of input random variables is high. This work develops a high dimensional reliability analysis method by a new dimension reduction strategy so that the contributions of both important and unimportant input variables are accommodated by the proposed dimension reduction method. The consideration of the contributions of unimportant input variables can certainly improve the accuracy of the reliability prediction, especially where many unimportant input variables are involved. The dimension reduction is performed with the first iteration of the first order reliability method (FORM), which identifies important and unimportant input variables. Then a higher order reliability analysis, such as the second order reliability analysis and metamodeling method, is performed in the reduced space of only important input variables. The reliability obtained in the reduced space is then integrated with the contributions of unimportant input variables, resulting in the final reliability prediction that accounts for both types of input variables. Consequently, the new reliability method is more accurate than the traditional method, which fixes unimportant input variables at their means. The accuracy is demonstrated by three examples.

     
    more » « less
  2. Abstract

    Predicting system reliability is often a core task in systems design. System reliability depends on component reliability and dependence of components. Component reliability can be predicted with a physics-based approach if the associated physical models are available. If the models do not exist, component reliability may be estimated from data. When both types of components coexist, their dependence is often unknown, and the component states are therefore assumed independent by the traditional method, which can result in a large error. This work proposes a new system reliability method to recover the missing component dependence, thereby leading to a more accurate estimate of the joint probability density (PDF) of all the component states. The method works for series systems whose load is shared by its components that may fail due to excessive loading. For components without physical models available, the load data are recorded upon failure, and equivalent physical models are created; the model parameters are estimated by the proposed Bayesian approach. Then models of all component states become available, and the dependence of component states, as well as their joint PDF, can be estimated. Four examples are used to evaluate the proposed method, and the results indicate that the proposed method can produce more accurate predictions of system reliability than the traditional method that assumes independent component states.

     
    more » « less
  3. null (Ed.)
    Abstract

    Reliability-based design (RBD) identifies design variables that maintain reliability at a required level. For many routine component design jobs, RBD may not be practical as it requires nonlinear optimization and specific reliability methods, especially for those design jobs which are performed manually or with a spreadsheet. This work develops a practical approach to reliability-based component design so that the reliability target can be achieved by conducting traditional component design repeatedly using a deterministic safety factor. The new component design is based on the First Order Reliability Method, which iteratively assigns the safety factor during the design process until the reliability requirement is satisfied. In addition to a number of iterations of deterministic component design, the other additional work is the calculation of the derivatives of the design margin with respect to the random input variables. The proposed method can be used for a wide range of component design applications. For example, if a deterministic component design is performed manually or with a spreadsheet, so it the reliability-based component design. Three examples are used to demonstrate the practicality of the new design method.

     
    more » « less
  4. null (Ed.)
    Abstract

    System reliability is quantified by the probability that a system performs its intended function in a period of time without failure. System reliability can be predicted if all the limit-state functions of the components of the system are available, and such a prediction is usually time consuming. This work develops a time-dependent system reliability method that is extended from the component time-dependent reliability method that uses the envelop method and second order reliability method. The proposed method is efficient and is intended for series systems with limit-state functions whose input variables include random variables and time. The component reliability is estimated by the existing second order component reliability method, which produces component reliability indexes. The covariance between components responses are estimated with the first order approximations, which are available from the second order approximations of the component reliability analysis. Then the joint probability of all the component responses is approximated by a multivariate normal distribution with its mean vector being component reliability indexes and covariance being those between component responses. The proposed method is demonstrated and evaluated by three examples.

     
    more » « less
  5. null (Ed.)
    Abstract

    Average lifetime, or mean time to failure (MTTF), of a product is an important metric to measure the product reliability. Current methods of evaluating MTTF are mainly statistics or data based. They need lifetime testing on a number of products to get the lifetime samples, which are then used to estimate MTTF. The lifetime testing, however, is expensive in terms of both time and cost. The efficiency is also low because it cannot be effectively incorporated in the early design stage where many physics-based models are available. We propose to predict MTTF in the design stage by means of physics-based models. The advantage is that the design can be continually improved by changing design variables until reliability measures, including MTTF, are satisfied. Since the physics-based models are usually computationally demanding, we face a problem with both big data (on the model input side) and small data (on the model output side). We develop an adaptive supervised training method based on Gaussian process regression, and the method can then quickly predict MTTF with minimized number of calling the physics-based models. The effectiveness of the method is demonstrated by two examples.

     
    more » « less
  6. Abstract Reliability can be predicted by a limit-state function, which may vary with time and space. This work extends the envelope method for a time-dependent limit-state function to a time- and space-dependent limit-state function. The proposed method uses the envelope function of time- and space-dependent limit-state function. It at first searches for the most probable point (MPP) of the envelope function using the sequential efficient global optimization in the domain of the space and time under consideration. Then the envelope function is approximated by a quadratic function at the MPP for which analytic gradient and Hessian matrix of the envelope function are derived. Subsequently, the second-order saddlepoint approximation method is employed to estimate the probability of failure. Three examples demonstrate the effectiveness of the proposed method. The method can efficiently produce an accurate reliability prediction when the MPP is within the domain of the space and time under consideration. 
    more » « less
  7. Abstract Predicting system reliability is often a core task in systems design. System reliability depends on component reliability and dependence of components. Component reliability can be predicted with a physics-based approach if the associated physical models are available. If the models do not exist, component reliability may be estimated from data. When both types of components coexist, their dependence is often unknown, and therefore, the component states are assumed independent by the traditional method, which can result in a large error. This study proposes a new system reliability method to recover the missing component dependence, thereby leading to a more accurate estimate of the joint probability density function (PDF) of all the component states. The method works for series systems whose load is shared by its components that may fail due to excessive loading. For components without physical models available, the load data are recorded upon failure, and equivalent physical models are created; the model parameters are estimated by the proposed Bayesian approach. Then models of all component states become available, and the dependence of component states, as well as their joint PDF, can be estimated. Four examples are used to evaluate the proposed method, and the results indicate that the method can produce more accurate predictions of system reliability than the traditional method that assumes independent component states. 
    more » « less
  8. Abstract Reliability analysis is a core element in engineering design and can be performed with physical models (limit-state functions). Reliability analysis becomes computationally expensive when the dimensionality of input random variables is high. This work develops a high-dimensional reliability analysis method through a new dimension reduction strategy so that the contributions of unimportant input variables are also accommodated after dimension reduction. Dimension reduction is performed with the first iteration of the first-order reliability method (FORM), which identifies important and unimportant input variables. Then a higher order reliability analysis is performed in the reduced space of only important input variables. The reliability obtained in the reduced space is then integrated with the contributions of unimportant input variables, resulting in the final reliability prediction that accounts for both types of input variables. Consequently, the new reliability method is more accurate than the traditional method which fixes unimportant input variables at their means. The accuracy is demonstrated by three examples. 
    more » « less