Non-probabilistic Reliability Model Research Articles

A non-probabilistic reliability analysis method with the fuzzy failure criterion

In engineering practice, the failure boundary of structures is not usually distinct due to some ambiguous information, which brings a tricky challenge to reliability assessment. The fuzzy theory is introduced to solve it with the traditional probability assessment method. For the non-probabilistic reliability system, however, this problem tends to be at a dead end because it lacks some necessary probability information. In this study, the non-probabilistic reliability model with fuzzy failure criterion is established, which involves two different evaluation indices in terms of the limit state surface. Based on this, a corresponding calculation method is proposed to deal with it, and the interval model and the ellipsoid model are shown for instance. In addition, the HRHL-RF method owning strong robustness is utilized to calculate the index of the ellipsoid model. Eventually, an established algorithm frame can achieve the calculation of the unified fuzzy reliability index, and three examples with the classical fuzzy membership functions are computed to show its feasibility and efficiency.

Importance measure analysis of design variables and uncertain parameters in multidisciplinary systems

The traditional reliability-based multidisciplinary design optimization consumes large computation resources due to a large number of design variables and uncertain parameters in multidisciplinary systems. Therefore, the screening of important design variables and uncertain parameters contributes to reducing the difficulty of optimization. However, the current methods ignore the interaction between design variables and uncertain parameters. Via a probabilistic and nonprobabilistic reliability model, the work in this paper establishes the concept of a comprehensive reliability-based importance measure that considers both design variables and uncertain parameters. An efficient method based on the Bayesian theorem is applied to calculate the above-mentioned indices of the proposed importance measure, which can estimate importance measure accurately adopting the same samples with reliability analysis. Therefore, the probabilistic method has faster convergence speed than traditional methods. The nonprobabilitic analysis method can promote the computation efficiency but ensure accuracy when the system performance functions are monotonic. Furthermore, the developed approach contributes to decreasing the time cost of reliability-based optimization in multidisciplinary systems. Additionally, the developed approach can also be applicable to single-disciplinary systems. Moreover, two practical engineering examples and the multidisciplinary design of a hypersonic wing are employed to demonstrate the validity and applicability of the proposed method.

Interval uncertainty‐based multidisciplinary reliability analysis method for information‐poor complex system

AbstractDue to integrated structures and multiple functions, complex systems, such as large‐scale equipment and aerospace vehicle, faced prominent reliability problems. However, in real‐world applications, collecting sufficient reliability data is costly and time‐consuming. To overcome this difficulty, the information‐poor variables are modeled with interval models and the corresponding reliability analysis method for complex system is studied in this paper. First, we establish a multidisciplinary nonprobabilistic reliability model based on interval analysis, which is an optimization framework with an objective of nonprobabilistic reliability index and two constraints of interdisciplinary consistency equation and limit state equation. Second, two types of algorithms for the above model are studied. Based on typical methods of multidisciplinary design optimization (MDO), the direct algorithms including RA‐MDF and RA‐IDF are developed. Then, a decoupled reliability analysis algorithm is proposed to realize parallel multidisciplinary reliability analysis, in which two methods of multidisciplinary interval uncertainty analysis are formulated to decouple the coupling relationship between disciplines. Finally, three examples are employed to illustrate the validity and efficiency of the proposed methods.

A Comprehensive Reliability Evaluation Model of Turbine Runner Blades under Complex Conditions

In this paper, a comprehensive method to evaluate the reliability of turbine runner blades under complex conditions has been proposed. The method takes into consideration the flow excitation parameters acting on the blades under different conditions, which present different uncertain information characteristics. The structural performance function of both vibration failure and fatigue failure of runner blades has been established, according to their vibration and fatigue characteristics. A probabilistic reliability model of the multi-failure modes of runner blades under their rated conditions has been established through application of random reliability theory, and a probabilistic non-probabilistic reliability model of the multi-failure modes of runner blades under non-rated conditions has been established by applying random reliability theory and non-probabilistic reliability theory, based on the structural performance function of both vibration failure and fatigue failure, taking into consideration the uncertain information characteristics of the flow excitation parameters that act on the runner blades under different conditions. On the basis of the two reliability models, a comprehensive model to evaluate the reliability of runner blades under complex conditions has been constructed. The reliability of the turbine runner blades under complex conditions has been analyzed through the use of examples, and the accuracy of the models has been proved using the Monte Carlo simulation (MCS).

Non-Probabilistic Time-Varying Reliability-Based Analysis of Corroded Pipelines Considering the Interaction of Multiple Uncertainty Variables

Reliability analysis of corroded pipelines is critical to the integrity and safe working of pipeline infrastructure. Aiming at less probability information is obtained for corrosion pipeline engineering, and the mechanical properties of pipeline with corrosion defects deteriorate caused by the accumulative effect of corrosion growth. Based on the quasi-static analysis method and non-probability theory, this paper presents a reliability model for assessing corroded pipelines with corrosion growth. In fact, reliability analysis of corroded pipelines needs to consider the interaction of multiple uncertainty variables. By introducing interaction theory, a mathematical model of corrosion defects considering the interaction of variables is put forward. Moreover, this paper develops a non-probabilistic time-varying reliability method for pipeline systems with multiple defects. Thus, several numerical examples are investigated to discuss the effectiveness of the proposed methodology. The results show that a two-dimensional or even three-dimensional ellipsoid model with correlation has more accurate results to evaluate corroded pipelines under the interaction of multiple corroded defects with poor information. Furthermore, a non-probabilistic time-varying reliability model is established according to the time-varying characteristics of the corroded pipeline under the influence of multiple factors. An effective complement to the theory of non-probabilistic reliability analysis of system is investigated. The analysis of the results suggests that interaction of corroded pipeline has a negligible impact on reliability. It also provides a theoretical basis for maintenance and is of great significance for risk- and reliability-informed decisions regarding buried oil and gas pipelines.

A direct-integration-based structural reliability analysis method using non-probabilistic convex model

In practical structural reliability analysis, there is not only random uncertainty but also fuzzy uncertainty. Aiming at the fuzzy reliability of structure, a novel fuzzy reliability method is proposed based on direct integration method and ellipsoidal convex model. Firstly, the decomposition of fuzzy mathematics principle is used to convert fuzzy reliability model into non-probabilistic reliability model, in which fuzzy variables are converted into interval variables. The upper and lower bounds of interval variables are determined by the possibility distribution function on the membership value. Secondly, multidimensional ellipsoid convex models are constructed to quantify the uncertainty because of the complexity of non-probabilistic reliability. Finally, sigmoid function with adjustable parameter is introduced to direct integration method for approximating the step function, and then direct integration method is used to solve the fuzzy reliability. Numerical examples are investigated to demonstrate the effectiveness of the present method, which provides a feasible way for the structural fuzzy reliability analysis.

Interval non-probabilistic reliability of surrounding jointed rockmass considering microseismic loads in mining tunnels

The frequent microseismicity affects the stability and reliability of surrounding rock and the safety of supporting structures in deep mining tunnels. The limit state equations of rock blocks under microseismic loads were developed to indicate the stability conditions and sliding characteristics. The scarce field data result in the uncertainty of the physico-mechanical parameters of tunnel surrounding rock. According to the insufficient statistical information for the rockmass, a method of the interval non-probabilistic reliability was proposed to analyze the stability of surrounding jointed rockmass. The method considered both microseismic loads and the uncertainty of rockmass parameters. The solving approach of interval non-probabilistic reliability was optimized, and it can be available when the field data is scarce. To verify the proposed method, the interval non-probabilistic reliability was used to evaluate the stability of the mining tunnel rockmass in the Yongshaba mine (China). The calculated interval non-probabilistic reliability was compared with the safety factor and random reliability. Results show that the interval non-probabilistic reliability model is in agreement with practical situations. It is proved that the proposed method of interval non-probabilistic reliability, considering both the uncertainty of the rockmass parameters and the microseismic loads, is a beneficial complement to the traditional analysis methods of safety factor and random reliability.

Theoretical and Case Studies of Interval Nonprobabilistic Reliability for Tailing Dam Stability

The stability of the operation of a tailing dam is affected by reservoir water level, phreatic line, and mechanical parameters of tailings. The values of these factors are not a definite value in different situations. Meanwhile, the existence of the phreatic line makes it a more complex issue to analyze the stability of the tailing dam. Additionally, it is very hard to give a definite limit to the state of tailing dam from security to failure. To consider the uncertainty when calculating the stability of the tailing dams, interval values are used to indicate the physical and mechanical parameters of tailings. An interval nonprobabilistic reliability model of the tailing dam, which can be used when the data is scarce, is developed to evaluate the stability of the tailing dam. The interval nonprobabilistic reliability analysis model of tailing dam is established in two cases, including with and without considering phreatic line conditions. The proposed model was applied to analyze the stability of two tailing dams in China and the calculation results of the interval nonprobabilistic reliability are found to be in agreement with actual situations. Thus, the interval nonprobabilistic reliability is a beneficial complement to the traditional analysis method of random reliability.

Interval Non-Probabilistic Reliability of a Surrounding Jointed Rockmass in Underground Engineering: A Case Study

To consider the uncertainty when determining the values of geo-mechanical parameters, interval values are used to indicate the physical and mechanical parameters of the rockmass. An interval non-probabilistic reliability model of the surrounding jointed rockmass of an underground opening, which can be used when the data are scarce, is developed to evaluate the stability of the rockmass in the Jiaojia gold mine. The calculation results of the interval non-probabilistic reliability are in agreement with the actual situation. Thus, the interval non-probabilistic reliability is a beneficial complement to the traditional analysis methods of the random reliability and the safety factor.

Structural hybrid reliability index and its convergent solving method based on random–fuzzy–interval reliability model

Aiming to resolve the problems of a variety of uncertainty variables that coexist in the engineering structure reliability analysis, a new hybrid reliability index to evaluate structural hybrid reliability, based on the random–fuzzy–interval model, is proposed in this article. The convergent solving method is also presented. First, the truncated probability reliability model, the fuzzy random reliability model, and the non-probabilistic interval reliability model are introduced. Then, the new hybrid reliability index definition is presented based on the random–fuzzy–interval model. Furthermore, the calculation flowchart of the hybrid reliability index is presented and it is solved using the modified limit-step length iterative algorithm, which ensures convergence. And the validity of convergent algorithm for the hybrid reliability model is verified through the calculation examples in literature. In the end, a numerical example is demonstrated to show that the hybrid reliability index is applicable for the wear reliability assessment of mechanisms, where truncated random variables, fuzzy random variables, and interval variables coexist. The demonstration also shows the good convergence of the iterative algorithm proposed in this article.

Non-probabilistic reliability analysis of active control system for structural vibration

To solve the reliability problem of active control system of structural vibration,considering the uncertainties in controlled structure,reliability analysis of the active control system for structural vibration based on non-probabilistic reliability model was studied. The uncertain parameters were expressed in the form of interval number or vector. Calculation method of responses of the closed-loop system with interval parameters was proposed based on interval mathematics. Combined with the non-probabilistic reliability model,nonprobabilistic reliability analysis method,which requires the bounds of the uncertainties rather than the probability density function,was established for active vibration control systems. This reliability analysis approach had certain theoretical significance for reliability analysis of open-loop system,closed-loop control system and reliability-based controller design. The results of numerical examples demonstrate the effectiveness of the proposed method and the applicability for complex structures compared with the Monte Carlo method that can be taken as the benchmark of accuracy for judgment.

Non-probabilistic robust reliability method and reliability-based performance optimization for active vibration control of structures and dynamic systems with bounded uncertain parameters

Active vibration control of uncertain structures is an attractive issue and essentially a complicated multidisciplinary problem. In this research, the author focuses on dealing with parametric uncertainties of actively controlled structures and dynamic systems from the viewpoint of reliability. An efficient non-probabilistic robust reliability methodology for mixed H2/H∞ robust vibration control of uncertain structures and dynamic systems is presented systematically by describing the uncertain parameters as interval variables. The static output robust controller design is carried out by solving a reliability-based multiobjective optimization problem, by which the H2 and H∞ performances and robustness against uncertainties of the closed-loop system can be taken into account simultaneously in an integrated framework. By this method, a non-probabilistic robust reliability measure of an uncertain controlled dynamic system satisfying required H2/H∞ performance and desired decay rate can be obtained, and the robustness bounds of uncertain parameters such that the H2 and H∞ performances of the closed-loop system are guaranteed can be provided. The controller obtained may possess an optimal performance satisfying the condition that the system is robustly reliable to all admissible uncertainties. The non-probabilistic reliability model constructed in this paper is an integrated one and can be used directly for vibration control design of parametric uncertain structures and dynamic systems. Three numerical examples are investigated to demonstrate the effectiveness and feasibility of the presented method.

A Non-Probabilistic Measure of Structural Reliability Based on Convex Model

The problem of the non-probabilistic reliability is investigated in this paper, in which the convex model is used to deal with uncertainties in structural analysis and design. The limitation on the current non-probabilistic reliability is discussed. Then a novel non-probabilistic reliability model is proposed, and its computational procedure is given. Two numerical examples are conducted to illustrate the feasibility and validity of the proposed non-probabilistic reliability model.

A Non-Probabilistic Model for Structural Reliability Analysis

By representing uncertain parameters as interval variables, a novel structural non-probabilistic reliability model is proposed, which can deal with the case that the domain constructed by the basic interval variables locates in the safe domain. Two numerical examples are conducted to illustrate the validity and feasibility of the proposed non-probabilistic model.

Structural damage measure index based on non-probabilistic reliability model

Abstract Uncertainties in the structural model and measurement data affect structural condition assessment in practice. As the probabilistic information of these uncertainties lacks, the non-probabilistic interval analysis framework is developed to quantify the interval of the structural element stiffness parameters. According to the interval intersection of the element stiffness parameters in the undamaged and damaged states, the possibility of damage existence is defined based on the reliability theory. A damage measure index is then proposed as the product of the nominal stiffness reduction and the defined possibility of damage existence. This new index simultaneously reflects the damage severity and possibility of damage at each structural component. Numerical and experimental examples are presented to illustrate the validity and applicability of the method. The results show that the proposed method can improve the accuracy of damage diagnosis compared with the deterministic damage identification method.

Solving Robust Reliability Index Based on the Mutative Scale Chaos Optimization Algorithm

A novel method based on the mutative scale chaos optimization algorithm is proposed to solve the robust reliability index of non-probabilistic reliability model. Compared with the basic chaos optimization method, this novel method can minimize searching area of optimization variable and change the adjustable parameters of next search stage for improving the optimization performance. The proposed optimization algorithm is more efficient and has smaller computational complexity in solving robust reliability index. The feasibility and efficiency of the proposed method are demonstrated by two examples.

An Imprecise Probability Model for Structural Reliability Based on Evidence and Gray Theory

To avoid the shortages and limitations of probabilistic and non-probabilistic reliability model for structural reliability analysis in the case of limited samples for basic variables, a new imprecise probability model is proposed. Confidence interval with a given confidence is calculated on the basis of small samples by gray theory, which is not depending on the distribution pattern of variable. Then basic probability assignments and focal elements are constructed and approximation methods of structural reliability based on belief and plausibility functions are proposed in the situation that structure limit state function is monotonic and non-monotonic, respectively. The numerical examples show that the new reliability model utilizes all the information included in small samples and considers both aleatory and epistemic uncertainties in them, thus it can rationally measure the safety of the structure and the measurement can be more and more accurate with the increasing of sample size.

Structural reliability analysis using non-probabilistic convex model

By using the convex model approach, the bounds of the uncertain parameters are only required rather than their precise probability distributions, based on which it can be made possible to conduct the reliability analysis for many complex engineering problems with limited information. In this paper, a non-probabilistic reliability model is given for structures with convex model uncertainty, which is defined as a ratio of the multidimensional volume falling into the reliability domain to the one of the whole convex model. A Monte Carlo simulation is then formulated for the reliability model to obtain a reference solution. A first order approximation method (FOAM) is proposed to solve the reliability model based on a linear approximation of the failure surface. A second order approximation method (SOAM) is further formulated to improve the reliability analysis precision for limit-state functions with relatively strong nonlinearity. By introducing the suggested reliability model, a convex-model-based system reliability method is also formulated. Eight numerical examples are provided to demonstrate the effectiveness of the present methods.

Non-probabilistic wear reliability analysis of swash-plate/slipper of water hydraulic piston motor based on convex model

Water hydraulic piston motor is one of the important transmission components in a water hydraulic system. For lack of enough experimental information to analyze the reliability in water hydraulic motor design, the convex model is chosen as wear reliability model for hydraulic friction pairs, which is more economical and reasonable than the interval model. The non-probabilistic reliability index based on the convex model is established using first-order Taylor series expansion, and the non-probabilistic reliability model of wear reliability analysis for the friction pair of swash-plate/slipper in water hydraulic piston motor is introduced based on the convex model. For the non-probabilistic reliability model, only the bounds on uncertain parameters are needed, instead of probabilistic density distribution or statistical quantities. Numerical examples are used to illustrate the validity and feasibility of the presented method.

Non-Probabilistic Structural Reliability Model Based on Ellipsoidal-Bound Model with Nonlinear Expansion

Info-gap model is the foundation of the non-probabilistic reliability model. In this paper, ellipsoidal-bound model which is the most common Info-gap model has been updated by acquiring restriction information about uncertain quantities. The initial ellipsoidal-bound model can be degenerated from the updated model. A non-probabilistic structural reliability model based on the updated ellipsoidal-bound model was established. A non-probabilistic reliability index was proposed and the calculation method was also given. The example shows that the introduction of restriction information is valid, and the new non-probabilistic reliability model can reveal the influence of the span restriction of uncertain quantities on structural reliability.