Line Sampling Method Research Articles

A Curved Surface Integral Method for Reliability Analysis of Multiple Failure Modes System with Non-Overlapping Failure Domains

Abstract In the study of reliability of systems with multiple failure modes, approximations can be obtained by calculating the probability of failure for each state function. The first-order reliability method and the second-order reliability method are effective, but they may introduce significant errors when dealing with certain nonlinear situations. Simulation methods such as line sampling method and response surface method can solve implicit function problems, but the large amount of calculation results in low efficiency. The curved surface integral method (CSI) has good accuracy in dealing with nonlinear problems. Therefore, a system reliability analysis method (CSIMMS) is proposed on the basis of CSI for solving multiple failure modes system reliability problems with non-overlapping failure domains. The order of magnitude of the failure probability is evaluated based on the reliability index and the degree of nonlinearity, ignoring the influence of low order of magnitude failure modes, and reducing the calculation of the system failure probability. Finally, CSIMMS and other methods are compared by three numerical examples, and the results show the stability and accuracy of the proposed method.

Global sensitivity analysis for multiple importance sampling centres using a novel adaptive line sampling method

To achieve more efficient resolution of reliability analysis problems in engineering, it is essential to enhance the line sampling (LS) method, which is typically effective for rare events. This article proposes an enhanced method for rare events by combining LS with kriging. In this method, the updating of kriging is conducted from a one-dimensional perspective along the important direction. The samples used to assess the failure probability are obtained through importance sampling (IS) from multiple IS centres rather than Monte Carlo simulation (MCS). During each iteration, both upper and lower bounds of the failure probability are simultaneously evaluated to determine whether to halt the iteration process. Finally, global sensitivity analysis is conducted by filtering the samples generated at multiple IS centres, rather than generating MCS samples. By comparison with existing methods, this article demonstrates the efficiency and accuracy of the proposed method through three numerical examples and an engineering problem.

Stochastic collocation enhanced line sampling method for reliability analysis

Stochastic collocation enhanced line sampling method for reliability analysis

Estimation of small failure probabilities by partially Bayesian active learning line sampling: Theory and algorithm

Line sampling (LS) has proved to be a highly promising advanced simulation technique for assessing small failure probabilities. Despite the great interest in practical engineering applications, many efforts from the research community have been devoted to improving the standard LS. This paper aims at offering some new insights into the LS method, leading to an innovative method, termed ‘partially Bayesian active learning line sampling’ (PBAL-LS). The problem of evaluating the failure probability integral in the LS method is treated as a Bayesian, rather than frequentist, inference problem, which allows to incorporate our prior knowledge and model the discretization error. The Gaussian process model is used as the prior distribution for the distance function, and the posterior mean, and an upper bound of the posterior variance of the failure probability are derived. Based on the posterior statistics of the failure probability, we also put forward a learning function and a stopping criterion, which enable us to use active learning. Besides, an efficient algorithm is also designed to implement the PBAL-LS method, with the ability to automatically adjust the important direction and efficiently process the lines. Five numerical examples are studied to demonstrate the performance of the proposed PBAL-LS method against several existing methods.

Structural global failure probability function estimation based on adaptive augmented line sampling method

A global failure probability function estimation method based on the adaptive augmented line sampling method is proposed to solve the parameter failure probability functions in structural reliability analysis and design. The proposed method uses an adaptive strategy to carry out a series of local failure probability function estimations at specific values in the design parameter space by using the augmented line sampling method. Then an optimal combination algorithm based on the minimum variation of coefficient is proposed to integrate all the local failure probability function estimations into a global estimation. Compared with the existing methods, the proposed method further improves the accuracy and efficiency of estimating failure probability functions. Finally, numerical and engineering examples are provided to demonstrate the applicability and superiority of the proposed method in analyzing calculation accuracy and efficiency.

Line Sampling Procedure for Extensive Planetary Protection Analysis

Exploration missions to other planets have to satisfy planetary protection requirements to limit the probability of impacts between mission-related objects and celestial bodies, with the goal of reducing the risk of contaminating them with biological material coming from Earth. The verification of these requirements can become a lengthy and computationally expensive task when addressed with common methods such as Monte Carlo simulations, as they involve analysing the interplanetary trajectories and the uncertainties associated with them for time spans up to 100 years, and estimating small probabilities with strict confidence levels. This paper presents novel improvements of the line sampling method, already introduced for the verification of planetary protection requirements as a way to estimate the impact probabilities more efficiently and with greater accuracy than achieved with standard Monte Carlo. These newly developed techniques are presented, with the aim of making the analysis with Line Sampling more effective, and providing more information about the distribution of impacts in the initial uncertainty distribution: an algorithm to identify the time intervals where most close approaches are clustered, and an algorithm to improve the determination of the main sampling direction and increase the accuracy of the probability estimation.

An efficient method for estimating failure probability bounds under random‐interval mixed uncertainties by combining line sampling with adaptive Kriging

AbstractFor addressing the low efficiency of structural reliability analysis under the random‐interval mixed uncertainties (RIMU), this paper establishes the line sampling method (LS) under the RIMU. The proposed LS divides the reliability analysis under RIMU into two stages. The Markov chain simulation is used to efficiently search the design point under RIMU in the first stage, then the upper and lower bounds of failure probability are estimated by LS in the second stage. To improve the computational efficiency of the proposed LS under RIMU, the Kriging model is employed to reduce the model evaluation numbers in the two stages. For efficiently searching the design point, the Kriging model is constructed and adaptively updated in the first stage to accurately recognize the Markov chain candidate state, and then it is sequentially updated by the improved U learning function in the second stage to accurately estimate the failure probability bounds. The proposed LS under RIMU with Kriging model can not only reduce the model evaluation numbers but also decrease the candidate sample pool size for constructing the Kriging model in two stages. The presented examples demonstrate the superior computational efficiency and accuracy of the proposed method by comparison with some existing methods.

Complex carotid artery segmentation in multi-contrast MR sequences by improved optimal surface graph cuts based on flow line learning.

Carotid atherosclerosis is one of the leading causes of cardiovascular disease with high mortality. Multi-contrast MRI can identify atherosclerotic plaque components with high sensitivity and specificity. Accurate segmentation of the diseased carotid artery from MR images is very essential to quantitatively evaluate the state of atherosclerosis. However, due to the complex morphology of atherosclerosis plaques and the lack of well-annotated data, the segmentation of lumen and wall is very challenging. Different from popular deep learning methods, in this paper, we propose an integration segmentation framework by introducing a lightweight prediction model and improved optimal surface graph cuts (OSG), which adopts a simplified flow line sampling and post-reconstructing method to reduce the cost of graph construction. Moreover, a flexibly adaptive smoothing penalty is presented for maintaining the shape of diseased carotid surface. For the experiments, we have collected an MR image dataset from patients with carotid atherosclerosis and evaluated our method by cross-validation. It can reach 89.68%/80.29% of dice coefficients and 0.2480 mm/0.3396 mm of average surface distances on the lumen/wall segmentation, respectively. The experimental results show that our method can generate precise and reliable segmentation of both lumen and wall of diseased carotid artery with a quite small training cost.

A New Developed Line Sampling Method for Reliability-Based Design Optimization of Structures

A New Developed Line Sampling Method for Reliability-Based Design Optimization of Structures

Potensi dan Keragaman Tumbuhan Bawah Non-Kayu Di Lahan Bera Kampung Womnowi Distrik Sidey Manokwari Papua Barat

During successionally process the non-woody plant understory cover related to dominance of tree vegetation around successional land. Fallow land are models of secondary successional are present the land of New Guinea (Papua). The study was conducted at fallow land 15 years old Womnowi, Sidey Manokwari West Papua to determine the important value index (IVI), diversity, evenness, and describe potential species composition of vegetation non-woody plant understory cover. We used continouse line sampling method when field inventory and make purposive sampling 2x2 m each a plot 20x20 m. We had found 749 individual part of 41 species, highest IVI are Sellaginella wyldenowii (25.04%), Selaginella sp (23.44%)., and Spathoglottis plicata (14.60%), diversity index Shannon-Weiner (Hʹ) is 3.13, and evenness (E) is 0.84. We also had found orchids and some unique Arecaceae and some species can used by local wisdom like Diplazium esculentum and Pothos spp. Based the floristic composition of analysis vegetation we temporary conclude non-woody plant understory cover are shade plant.

Accurate Structural Reliability Analysis Using an Improved Line-Sampling-Method-Based Slime Mold Algorithm

Line sampling (LS) is a robust and powerful simulation technique to reduce the computational burden provided by Monte Carlo simulation (MCS) for the reliability analysis of engineering structures. However, when dealing with highly nonlinear and implicit limit-state functions, LS yields instable results as nonconvergence or divergence. In this study, a novel framework that integrates the LS method with the slime mold algorithm (LS-SMA) is proposed to solve complex structural reliability problems. SMA is a new metaheuristic population-based algorithm inspired by the behavior and morphological changes in slime molds that can well solve multivariable optimization problems. In the proposed method, the determination of the important direction of LS is formulated as an unconstrained optimization problem according to the LS theory. Then SMA is employed to solve this optimization problem to decrease the computational cost. Thus, the LS-SMA is able to overcome the drawbacks of LS such as the local convergence and divergence. Seven numerical problems were utilized to investigate the LS-SMA applicability, where its performance was compared with MCS, subset simulation (SS), importance sampling (IS), LS, first-order reliability method (FORM), and first-order control variate method (FOCM). The results demonstrate that the proposed LS-SMA can be applied with high efficiency for solving the reliability problems that involve highly nonlinear or dimensional and complex implicit limit-state functions.

Non-intrusive imprecise stochastic simulation by line sampling

The non-intrusive imprecise stochastic simulation (NISS) is a general framework for the propagation of imprecise probability models and analysis of reliability. The most appealing character of this methodology framework is that, being a pure simulation method, only one precise stochastic simulation is needed for implementing the method, and the requirement of performing optimization analysis on the response functions can be elegantly avoided. However, for rare failure events, the current NISS methods are still computationally expensive. In this paper, the classical line sampling developed for precise stochastic simulation is injected into the NISS framework, and two different imprecise line sampling (ILS) methods are developed based on two different interpretations of the classical line sampling procedure. The first strategy is devised based on the set of hyperplanes introduced by the line sampling analysis, while the second strategy is developed based on an integral along each individual line. The truncation errors of both methods are measured by sensitivity indices, and the variances of all estimators are derived for indicating the statistical errors. A test example and three engineering problems of different types are introduced for comparing and demonstrating the effectiveness of the two ILS methods.

Using the geometric wheel-rail contact algorithms for fault detection in turnout areas based on the variable section characteristics of rails

This paper presents a geometric wheel–rail contact algorithm suitable for fault detection in a railway turnout. It employs a dynamic profile sampling method based on the characteristics of the variable section rails in the turnout regions. This algorithm provides a fast and accurate method to identify the wheel–rail contact points in turnouts under different degrees of lateral shift and yaw angles. This method determines the contact point based on the minimum distance and can be applied quickly through the use of a moving window to scale the potential contact boundary within the rail width. The wheel–rail contact points and the geometric contact parameters in the internal rail that matched with the LMa and 60 N were virtually identical in both methods, which verifies the accuracy of the dynamic profile sampling model. A comparison of the different wheel–rail contact points and geometric parameters under different wheelset yaw angles in turnouts using the trace line and dynamic profile sampling methods shows that a trace method based on the assumption of equal rail sections is not applicable to turnouts, thus demonstrating the necessity of calculating the wheel–rail contact geometry in turnouts using the dynamic profile sampling method, which takes the characteristics of the variable sections into account.

The shift in the abundance of two Stipa species in response to land use change is associated with their divergent reproductive strategies

The divergent changes of plant species under land use changes are key mechanisms underlying vegetation succession. Stipa grandis steppe and Stipa krylovii steppe are two plant communities widely distributed on the Mongolian Plateau. They have been speculated to be able to succeed into each other under different land use types and intensities based on the observations on their presence and abundance at the sites with different land use history. However, no direct evidence, neither the underlying mechanisms, have been reported for this speculation. Here, we verified this speculation and explored the underlying mechanisms in the typical steppe region of Inner Mongolia. We investigated the abundance and reproductive behavior of S. krylovii and S. grandis under different land use types and intensities. We used 18 grassland paddocks to run a 6-year experiment with 6 management treatments (T0—unused, T1—grazing monthly in plant growing season, T2, T4, T6—grazing in different months in plant growing season, and T8—mowing) replicated three times. We measured the relative density and cover of S. krylovii and S. grandis using line sampling method and examined their number and biomass of vegetative and reproductive tillers using quadrat method in each paddock after treatments for 4 and 6 years. We also determined these plant attributes in 14 pairs of heavily versus lightly used grassland plots in a wide area (150 km × 200 km) of the typical steppe region. 1. Grazing largely and mowing moderately decreased the density ratio and coverage ratio of S. grandis to S. krylovii in grasslands (P < 0.05), and the differences in these ratios between grazed and unused grasslands increased with time. 2. Grazing, but not mowing, significantly enhanced the relative density (Nᵣₑₚ = reproductive tiller number/total tiller number) of, and biomass allocation (Bᵣₑₚ = reproductive tiller biomass/total biomass) to, reproductive tillers of S. krylovii (P < 0.05), but not S. grandis. This grazing enhancement to sexual reproduction of S. krylovii, and additionally inhibition to Nᵣₑₚ of S. grandis (P < 0.05), were found across the 14 pairs of heavily versus lightly used plots. 3. Seasonal pattern of grazing affected sexual reproduction of S. krylovii. The Nᵣₑₚ and Bᵣₑₚ was higher under grazing in July and September (T4) than in July and August (T6) or in May and July (T2) (P < 0.05), suggesting a relatively positive effect of grazing on sexual reproduction in July (tasseling phenophase) than in May or August. Our results provide direct evidence to the reciprocal change of S. grandis and S. krylovii in steppe communities under different management and indicate that gazing or mowing enhancement of sexual reproduction of S. krylovii relative to S. grandis is one of the mechanisms for the change.

Đa dạng hệ thực vật bậc cao tại khu đất ngập nước Hòa An thuộc huyện Phụng Hiệp, tỉnh Hậu Giang

The investigation was conducted from July 2016 to May 2017 at Hoa An wetland, Phung Hiep district, Hau Giang province. The vascular plants were collected in six biotopes through standard square and investigation line sampling method. The list of vascular plants was constructed. There were 56 species belonging to 51 genera of 38 families in 2 phyla of the vascular plants. In the term of species diversity, the genera, family and the average of genera in family index of the vascular plants system at the Hoa An wetland were 1,1, 1,47 and 1,34, respectively. Of the 7 existing groups of life forms, the grass group has the highest percentage. There were 55 useful plants found, of which medicinal plants have the highest number of species and one species was listed for conservation by Vietnam Red Book (2007). In six biotopes, each biotopes has specific plant groups.

An Adaptive Line Sampling Method for Reliability Analysis

Rare event probability estimation imposes serious difficulties to the conventional simulation methods like crude Monte Carlo. Several methods have been put forward to address this issue. Line sampling, directional simulation, importance sampling and subset simulation are more known among other methods. This paper aims at improving the line sampling method. The proposed method iteratively adapts the line sampling procedure to the limit state surface and at the end yields an estimation of the failure probability with the required coefficient of variation. The proposed method is compared to the conventional line sampling via well-known academic problems. The results show considerable improvement over the conventional line sampling method.

Tree species diversity around some Mayas in Dinder National Park, Sudan

This study was conducted in Dinder National Park, during the dry season from February to May 2016, with the aim to determine the density, relative density, frequency and abundance of trees in the five Mayas in Dinder National Park. Data was collected using the transect line sampling method in the five Mayas namely; Abdel Ghani, Musa, Ras-Amir, Ein- Elshamis and Gererrisa. Abundance of trees and densities per Kilometer2 varied but highest abundance trees were Acacia seyal, Ziziphus spp, Combertum, Balanitie aegyptiaca and Acacia polycantha. Acacia seyal covers larger area in Dinder National Park and also one of the common and dominant tree species. So control of the spread of this species could be by cutting and selling them at local markets and nearby villages to avoid the entrance of people to the park for that purpose.

Coupling the cross-entropy with the line sampling method for risk-based design optimization

An algorithm for risk-based optimization (RO) of engineering systems is proposed, which couples the Cross-entropy (CE) optimization method with the Line Sampling (LS) reliability method. The CE-LS algorithm relies on the CE method to optimize the total cost of a system that is composed of the design and operation cost (e.g., production cost) and the expected failure cost (i.e., failure risk). Guided by the random search of the CE method, the algorithm proceeds iteratively to update a set of random search distributions such that the optimal or near-optimal solution is likely to occur. The LS-based failure probability estimates are required to evaluate the failure risk. Throughout the optimization process, the coupling relies on a local weighted average approximation of the probability of failure to reduce the computational demands associated with RO. As the CE-LS algorithm proceeds to locate a region of design parameters with near-optimal solutions, the local weighted average approximation of the probability of failure is refined. The adaptive refinement procedure is repeatedly applied until convergence criteria with respect to both the optimization and the approximation of the failure probability are satisfied. The performance of the proposed optimization heuristic is examined empirically on several RO problems, including the design of a monopile foundation for offshore wind turbines.

Reliability analysis with Metamodel Line Sampling

This paper presents an approach for reliability analysis of engineering structures, referred to as Metamodel Line Sampling (MLS). The approach utilizes a metamodel of the performance function, within the framework of the Line Sampling method, to reduce computational demands associated with the reliability analysis of engineering structures. Given a metamodel of the performance function, the failure probability is estimated as a product of a metamodel-based failure probability and a correction coefficient. The correction coefficient accounts for the error in the metamodel estimate of failure probability introduced by the replacement of the performance function with a metamodel. Computational efficiency and accuracy of the MLS approach are evaluated with the Kriging metamodel on analytical reliability problems and a practical reliability problem of a monopile foundation for offshore wind turbine. The MLS approach demonstrated efficient performance in low to medium-dimensional reliability problems.

Advanced Line Sampling for efficient robust reliability analysis

A numerical strategy for the efficient estimation of set-valued failure probabilities, coupling Monte Carlo with optimization methods, is presented in this paper. The notion of uncertainty is generalized to include both aleatory and epistemic uncertainties, allowing to capture gaps of knowledge and scarcity of data. The proposed formulation of the generalized uncertainty model allows for sets of probability distribution functions, also known as credal sets, and sets of bounded variables. The developed Advanced Line Sampling method is combined with the generalized uncertainty model, in order to both speed up the reliability analysis, and provide a better estimate for the lower and upper bounds of the failure probability. The proposed strategy knocks down the computational barrier of computing interval failure probabilities, and reduces the cost of a robust reliability analysis by many orders of magnitude. The efficiency and applicability of the developed method is demonstrated via numerical examples. The solution strategy is integrated into the open-source software for uncertainty quantification and risk analysis OpenCossan, allowing its application on large-scale engineering problems as well as broadening its spectrum of applications.