Convergence of adaptive mixed finite element method for convection-diffusion-reaction equations

We prove the convergence of an adaptive mixed finite element method (AMFEM) for (nonsymmetric) convection-diffusion-reaction equations. The convergence result holds from the cases where convection or reaction is not present to convection-or reaction-dominated problems. A novel technique of analysis is developed without any quasi orthogonality for stress and displacement variables, and without marking the oscillation dependent on discrete solutions and data. We show that AMFEM is a contraction of the error of the stress and displacement variables plus some quantity. Numerical experiments confirm the theoretical results.Comment: arXiv admin note: text overlap with arXiv:1312.645

Using Efficient Global Optimization with CFD for Aerodynamic Optimization

Machine learning and optimization are the stepping blocks in broad engineering areas, such as computational fluid dynamics (CFO) and CFO-based design optimization. Using the CFO-based optimization framework, MACH-Aero, we were able to use the SLSQP optimizer and compared the results with a reference case completed by the SNOPT optimizer. Results verified that our SLSQP optimizer was working properly. The solver created showed that our objective function had a difference in magnitude of 0.000019 allowing us to conclude that our solver was working as intended. However, there were several failed attempts before reaching a successful run that gave us a satisfactory result. Further work was done to attempt to make a solver that can handle cases of similar types to the failed one. Efficient global optimization will eventually be paired with the CFO solver, which is expected to result in successful runs using the previous unsuccessful conditions while alleviating computational costs

Active learning with generalized sliced inverse regression for high-dimensional reliability analysis

It is computationally expensive to predict reliability using physical models at the design stage if many random input variables exist. This work introduces a dimension reduction technique based on generalized sliced inverse regression (GSIR) to mitigate the curse of dimensionality. The proposed high dimensional reliability method enables active learning to integrate GSIR, Gaussian Process (GP) modeling, and Importance Sampling (IS), resulting in an accurate reliability prediction at a reduced computational cost. The new method consists of three core steps, 1) identification of the importance sampling region, 2) dimension reduction by GSIR to produce a sufficient predictor, and 3) construction of a GP model for the true response with respect to the sufficient predictor in the reduced-dimension space. High accuracy and efficiency are achieved with active learning that is iteratively executed with the above three steps by adding new training points one by one in the region with a high chance of failure

The Effect of Different Rollover Conditions of the Vibrator on Human Injury

Vibrator, as a crucial vehicle of oil and gas exploration, is challenged by the complex terrains. The probability of rollover accident is therefore high in bumpy terrain in which the drivers\u27 life is seriously threatened. Finite element numerical analysis was used to study the injury of the driver\u27s head, neck and chest in the rollover accidents of domestic KZ-28 type vibrator on different conditions. The injuries of three parts were evaluated based on the human injury criteria. Driver\u27s safety on different rollover conditions was comparatively analyzed. The results indicated that the injury degree of human head caused by vibrator rollover accident is at a low level. In comparison with head, the human neck is more likely to be injured than head and chest. In three different rollover accidents, the injury degree of drivers on the rollover condition of the vibrator colliding with slope multiply is most serious. Besides, the results demonstrated that the safety of driver can be enhanced by the rollover protective structures of KZ-28 type vibrator. This structure requires to be improved in energy absorption and isolation buffer. In addition, the safety belt and collision angle between the cab and the ground are also significantly associated with the injury degree. This research is of guiding significance to vibrator driver for taking safety protection measures

Second Order Reliability Method for Time-Dependent Reliability Analysis Using Sequential Efficient Global Optimization

Reliability depends on time if the associated limit-state function includes time. A time-dependent reliability problem can be converted into a time-independent reliability problem by using the extreme value of the limit-state function. Then the first order reliability method can be used but it may produce a large error since the extreme limit-state function is usually highly nonlinear. This study proposes a new reliability method so that the second order reliability method can be applied to time-dependent reliability analysis for higher accuracy while maintaining high efficiency. The method employs sequential efficient global optimization to transform the time-dependent reliability analysis into the time-independent problem. The Hessian approximation and envelope theorem are used to obtain the second order information of the extreme limit-state function. Then the second order saddlepoint approximation is use to evaluate the reliability. The accuracy and efficiency of the proposed method are verified through numerical examples

A Bayesian Approach to Recovering Missing Component Dependence for System Reliability Prediction via Synergy Between Physics and Data

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

High-Dimensional Reliability Method Accounting for Important and Unimportant Input Variables

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