Reliability of statically indeterminate timber structures: Modelling approaches and sensitivity study

In statically indeterminate timber structures, the stiffness of the members and the semi-rigid behaviour of joints influence the force distribution in the structure, affecting its performance and reliability. This paper aims at identifying the impact of connections on the reliability of such structures by performing a study of a simple statically indeterminate system, i.e. a simple beam with rotational springs at its supports. Using UQlab, a Matlab-based toolbox, a parametric study varying the stiffness and the level of ductility of connections was performed. Different methods such as Subset, Importance Sampling and Adaptive Kriging with Subset simulation were applied and compared in terms of efficiency and computational time. The results showed that an increment in reliability is gained increasing the level of ductility of joints of intermediate and high stiffness.

Passive systems, which completely depend on natural phenomena such as gravity, conduction and convection to accomplish the safety functions, are increasingly being used in new generation nuclear reactor designs. However, since the driving forces of passive systems are weak, they are more vulnerable to associated uncertainties and there may be a non-zero probability for the system to deviate from the intended behavior and leads to functional failure. Methods for quantification of the functional failure include Monte-Carlo simulation of the system uncertainties using a validated mechanistic code. Generally, the mechanistic codes used for complex system modeling are computationally expensive and Monte- Carlo simulation for estimating small failure probabilities requires more time and often become prohibitive. In this respect, recently, functional reliability methodologies including advanced simulation techniques such as subset simulation, Markov chain Monte-Carlo, importance sampling, and response conditioning method are reported in open literature. Unlike in the case of direct Monte Carlo simulation, for the probability estimates obtained using these advanced simulations, analytical formulas are not available to estimate standard error and confidence interval. In this paper, the estimation of standard error and confidence interval of functional reliability estimates using computationally efficient re-sampling methods based on bootstrap technique are described. Numerical application of these methods, to quantify the variability of functional reliability estimates, is also explained.

In the practical engineering, to solve the small failure probabilities with correlated high-dimensional variables, the subset simulation (SS) is combined together with the Monte Carlo and importance sampling (IS) method. The samples from the probability density functions (PDF) of the importance sampling are used to construct the intermediate failure events, by which the small failure probabilities are turned into a Markov chain (MC), which is a continuous product made of a series large failure probability or conditional failure probability (CFP) which is easily answered, on which the structural reliability can be efficiently simulated by directly obtaining the samples with correlated ones. Finally, the 3 planet carriers of 3 grade planetary reducers in shield tunneling machine(STM) are as examples to check the algorithm above, the results show that the SS of the IS with correlated variables can highly simulate failure probability.

The importance of design robustness and reliability is a well-established notion and practice in today’s industry. Manufacturing companies strive to achieve Six-Sigma quality measures. While Virtual Prototyping is a key-factor in accelerating the product development process while reducing development costs; it has not contributed in the quest for improved product reliability and robustness performance since it is based on deterministic approaches. This paper provides a systematic approach to design for sixsigma simultaneously addressing variability and uncertainty present in real life on most design parameters. The first step is the ability to flexibly integrate and federate best-of-class virtual prototyping simulation software programs -most based on Finite Element Modeling techniques- thus, capturing existing engineering processes. These engineering processes provide the deterministic calculation engines for assessing design performance outputs of interest, such as -but not limited to- stress, structural impact, eigenfrequencies, forced response functions, fatigue life. Second is the assessment of design parameter variability on the design performance outputs. Analytical methods for the efficient calculation of dynamic response variability examined in this work include reliability-based methods such as First and Second Order Reliability methods, the Importance Sampling Monte Carlo (ISMC) method and the Transformed Importance Latin Hypercube Sampling (TILHS) method. They have been assessed for their ability to accurately predict the failure probability in a reasonable amount of time. The latter criterion is paramount for successful application to large industrial FE models, where the computation time is the main bottleneck. The accuracy has been examined with the comparison of the aforementioned methods with classical and advanced Monte-Carlo methodologies. Uncertainty is treated with the use of Transformation Method based on Fuzzy arithmetic concepts. Fuzzy arithmetic is an attractive mathematical concept to solve problems with uncertain parameters. The Transformation Method (TM) follows a fuzzy approach based on the concept of α-cuts, i.e. discretization of the parameter’s magnitude into a number of intervals. Uncertainty is then assessed by solving the problem in a systematic way: for each combination of the values attained by the uncertain parameters a deterministic computation of the response is performed. In this paper, the TM is demonstrated on an airplane FE model, to assess the effect of material stiffness uncertainty on the FRF from wing tip to pilot seat. A second demonstration example on this model aims to ensure a certain frequency difference between two free-free modes that may result in flutter at certain air speed; several reliability methods are applied for this purpose, namely Monte Carlo simulations, FORM and Importance Sampling.

본 논문은 오류 마루 영역에서 우수한 성능을 가지는 비이진 LDPC (low-density parity-check) 부호의 설계 방법을 제안하고 성능을 검증한다. 제안된 설계 방법은 비이진 LDPC 부호의 이진 최소 거리(binary minimum distance)를 최대화하도록 패리티 검사 행렬의 비이진 원소 값들을 결정한다. BPSK (binary phase-shift keying) 변조 방식 하에서 제안된 방법으로 설계된 비이진 LDPC 부호가 오류 마루(error floor) 영역에서 우수한 성능을 가지는 것을 Monte Carlo 시뮬레이션과 중요도 표본 추출(importance sampling) 기법을 사용하여 검증한다. In this paper we propose a design algorithm for nonbinary LDPC (low-density parity-check) codes with low error-floors. The proposed algorithm determines the nonbinary values of the nonzero entries in the parity-check matrix in order to maximize the binary minimum distance of the designed nonbinary LDPC codes. We verify the performance of the designed nonbinary LDPC codes in the error-floor region by Monte Carlo simulation and importance sampling over BPSK (binary phase-shift keying) modulation.

The surrogate model-based sampling method has been an active area of research due to its evident efficiency over direct sampling method. The fusion of the adaptive kriging (AK) model with the adaptive radial-based importance sampling (ARBIS) method is developed as an improvement of the AK model combined with Monte Carlo simulation (MCS) method especially for estimating the small failure probabilities. In the AK–ARBIS method, the number of candidate samples in each updating process of the kriging model is reduced through partitioning the whole MCS sample domain into different subdomains and removing the samples inside the last subdomain from the participating candidate sampling pool, which can avoid the time-consuming matrix operation involved in kriging predictions in order to find the best training sample in each updating step. In the existing AK–ARBIS method, kriging model stops updating according to the learning function-based stopping criterion, which cannot directly reflect the error of the estimated failure probability. In this regard, this paper proposes the error-based stopping criterion (ESC) enhanced AK–ARBIS method, where the processes of finding the optimal hypersphere and accurately identifying the sign of candidate samples are decoupled in order to successfully embed the ESC. In addition to embedding the ESC into the AK–ARBIS method, two target-oriented candidate sampling reduction strategies are investigated, respectively, to improve the efficiency of finding the optimal hypersphere and accurately identifying the sign of the participating candidate samples. Based on the candidate sampling pool reduction strategies and ESC, both the computational time and the required number of calls to the real limit state function are reduced over the existing AK–ARBIS method. Three case studies are analyzed to demonstrate the accuracy and efficiency of the proposed enhanced AK–ARBIS method, especially for estimating the small failure probabilities.

Computation of failure probability via hierarchical clustering

At the multiplexer of an ATM network, the admissible cell loss probability is less than 10−12 for some service categories. Ordinary Monte Carlo (MC) simulation requires considerable computation time to obtain such a small probability. The importance sampling (IS) technique is effective in accclerating the MC simulation. In an IS simulation, the underlying distribution is biased so as to generate more samples in the target event. In order to achieve a fast simulation, it is important to have a simulation distribution that yields an estimate with minimum variance. This is called the optimal simulation distribution. In this paper, we investigate the survivor function P(Q > q) of a stationary queue length Q in ATM queuing and obtain an IS estimate of P(Q > q) at about 10−2 by means of the optimal simulation distribution. Conventional methods [1, 2] for determining the optimal distribution require a lot of computation time. We apply the large deviation theory to this problem to obtain the optimal simulation distribution analytically and carry out an IS simulation. We present some numerical results for M/D/1 and 2-state MMPP/D/1 which demonstrate that our estimates are obtained in a very small computation time and are accurate when compared to MC simulation. © Scripta Technica, Inc. Electron Comm Jpn Pt 1, 80(12): 28–37, 1997

In this paper, Crude Monte Carlo method and importance sampling are utilized to determine the reliability of long-term changes in groundwater level. Furthermore, different data analysis methods are used to determine the abnormal patterns and to investigate the cause of spatial variations of failure probability. For this purpose, three methods including robust covariance, one-class SVM, and Isolation Forest are applied to define the decision function. In the preliminary detection of the outliers, DFFITS and COOK measures are used to confirm the existence of abnormal plains in a two-dimensional space. The validity of prediction results is verified through the developed method of uncertain monitoring by selecting the most significant outlier points. In addition, the abnormal pattern detection methods are compared using non-random pattern discovery decision functions. The reliability analysis of groundwater is conducted during the two periods from 1994 to 2007 and 2008 to 2021. In the second period, parts of the eastern part of the northwest, central parts of the desert of Iran, and areas from west-southwest and east-south-east to other regions exposed to a lower probability of passing through the critical conditions. In contrast, the outcomes confirm the occurrence of drought with probability more than 80% for most of the plains. Eventually, the importance sampling method showed the closest relation in the correct distribution of the decision function. In contrast, due to the cluster shape and density of the outliers, the upper part of the decision function was determined with high certainty in the discovery of abnormal plains.

The problem of pricing a continuous barrier option in a jump-diffusion model is studied. It is shown via an effective combination of importance sampling and analytic formulas that substantial speed ups can be achieved. These techniques are shown to be particularly effective for computing deltas.

An efficient time-dependent (TD) Monte Carlo (MC) importance sampling method has recently been developed [G. Tao and W. H. Miller, J. Chem. Phys. 135, 024104 (2011)] for the evaluation of time correlation functions using the semiclassical (SC) initial value representation (IVR) methodology. In this TD-SC-IVR method, the MC sampling uses information from both time-evolved phase points as well as their initial values, and only the "important" trajectories are sampled frequently. Even though the TD-SC-IVR was shown in some benchmark examples to be much more efficient than the traditional time-independent sampling method (which uses only initial conditions), the calculation of the SC prefactor-which is computationally expensive, especially for large systems-is still required for accepted trajectories. In the present work, we present an approximate implementation of the TD-SC-IVR method that is completely prefactor-free; it gives the time correlation function as a classical-like magnitude function multiplied by a phase function. Application of this approach to flux-flux correlation functions (which yield reaction rate constants) for the benchmark H + H(2) system shows very good agreement with exact quantum results. Limitations of the approximate approach are also discussed.

The design of complex systems often requires reliability assessments involving a large number of uncertainties and low probability of failure estimations (in the order of 10−4). Estimating such rare event probabilities with crude Monte Carlo (CMC) is computationally intractable. Specific numerical methods to reduce the computational cost and the variance estimate have been developed such as importance sampling or subset simulation. However, these methods assume that the uncertainties are defined within the probability formalism. Regarding epistemic uncertainties, the interval formalism is particularly adapted when only their definition domain is known. In this paper, a method is derived to assess the reliability of a system with uncertainties described by both probability and interval frameworks. It allows one to determine the bounds of the failure probability and involves a sequential approach using subset simulation, kriging, and an optimization process. To reduce the simulation cost, a refinement strategy of the surrogate model is proposed taking into account the presence of both aleatory and epistemic uncertainties. The method is compared to existing approaches on an analytical example as well as on a launch vehicle fallout zone estimation problem.

This dissertation focuses on the importance sampling (IS) variance reduction technique in the Monte Carlo simulation of the performance of digital communication systems over a memoryless, additive Gaussian noise channel. The result is a unbiased estimate of the decision error with significantly smaller estimation variance than conventional Monte Carlo simulation provides. Several common digital (n, k) block codes are used to illustrate the importance sampling approach. Bounds on the variance of the error estimate are developed where the channel description is simple, but where the multiple dimension decision regions are potentially complex. Coherent detection is used as a venue for the comparison of these IS techniques with respect to increasing dimension. Bounds based on the union bound are presented for several IS techniques. An overlap stratification variance reduction technique is introduced and extended with the application of IS. A mixed IS biasing function is employed for concentrating more samples in a particular error region and is employed for several of the common lower rate ([special characters omitted] < 1) block codes. For the random phase channel the IS biasing function is developed as a 2n dimensional pdf consisting of n Rayleigh-Rician pdf pairs. The error performance of several common lower rate block codes is presented. An alternate formulation, having the potential advantage of being able to use both mean translation and variance scaling, is presented. This approach is based on a commonly used technique to numerically generate a single Rayleigh-Rician pdf pair.

In recent years, the increasing integration of renewable energy and electric vehicles has exacerbated uncertainties in power systems. Operators are interested in identifying potential violation events such as overvoltage and overload via probabilistic power flow calculations. Evaluating the violation probabilities requires sufficient accuracy in tail regions of the output distributions. However, the conventional Monte Carlo simulation and importance sampling typically require numerous samples to achieve the desired accuracy. The required power flow simulations result in substantial computational burdens. This study addresses this challenge by proposing a surrogate-assisted importance sampling method. Specifically, a high-fidelity radial basis function-based surrogate is constructed to approximate the nonlinear power flow model. Subsequently, the surrogate is embedded in the conventional importance sampling technique to evaluate the rare probabilities with high efficiency and reasonable accuracy. The computational strengths of the proposed method are validated in the IEEE 14-bus, 118-bus, and realistic 736-bus systems through comparisons with several well-developed methods. The comparisons provide a reference for system operators to select the appropriate method for evaluating violations based on the intended applications.

Importance sampling (IS) is a powerful method for reducing simulation run times when estimating the probabilities of rare events in communication systems using Monte Carlo simulation and is made feasible and effective for the simulation of networks of queues by regenerative techniques. However, using the most favorable IS settings very often makes the length of regeneration cycles infinite or impractically long. To address this problem, a methodology that uses IS dynamically within each regeneration cycle to drive the system back to the regeneration state after an accurate estimate has been obtained is discussed. A statistically based technique for optimizing IS parameter values for simulations of queueing systems, including complex systems with bursty arrival processes, is formulated. A deterministic variant of stochastic simulated annealing (SA), called mean field annealing (MFA), is used to minimize statistical estimates of the IS estimator variance. The technique is demonstrated by evaluating blocking probabilities.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>