Quantification Of Margins And Uncertainties Research Articles

QMU Analysis of Flexoelectric Timoshenko Beam by Evidence Theory

In recent years, with the rapid development of nanotechnology, a new type of electromechanical coupling effect similar to the piezoelectric effect, the flexoelectric effect, has gradually come into the public’s view. The flexoelectric beam that is the main structural unit of the flexoelectric signal output has broad application prospects in the next generation of micro- and nanoelectromechanical systems. Therefore, the investigation of flexoelectric materials and structures has important scientific and engineering application significances for the design of flexoelectric devices. In this paper, a model of flexoelectric Timoshenko beam is established, the deflection, rotation angle, and dynamic electrical signal output of the forced vibration are taken as the system response, and the density ρ , shear correction factor κ , and frequency ratio λ are selected as the key performance parameters of the system. The combination of available data and engineers’ experience suggests that there are random and cognitive uncertainties in the parameters. Therefore, the probability distribution of the system performance response is expressed by the likelihood function and belief function through the quantification of margins and uncertainties (QMUs) analysis methodology under the framework of evidence theory, and the system reliability or performance evaluation is measured by the calculated confidence factors. These results provide a theoretical basis for accurate analysis of flexoelectric components and provide guidance for the design of flexoelectric components with excellent performance.

Quantitative structural uncertainty analysis of composite honeycomb sandwich using a feedback neural network

The quantification of margins and uncertainty (QMU) method was applied using a neural network to inversely determine the strength boundary of a composite honeycomb sandwich structure considering the random uncertainty of its elastic modulus, shear modulus, tensile strength, compressive strength, and shear strength in the warp and fill directions, and panel thickness. An application framework for the deterministic quantitative analysis of strength was proposed based on margin design theory, combining the strength problem with the quantitative analysis of uncertainty. First, the failure criterion of the structure was modeled based on the progressive damage principle using ABAQUS. Next, Latin hypercube sampling was applied to simulate the stochastic uncertainty of the structural parameters, and the resulting sample sets were input into ABAQUS to calculate the corresponding structure lateral bearing capacities. These results were considered to collectively represent the actual strength boundary of the composite structure. A feedback neural network was subsequently trained on these ABAQUS data to obtain the functional mapping relationship between the parameters and capacity. The capacity obtained using this relationship was multiplied by an empirical safety factor to serve as the theoretical strength boundary. Finally, the QMU method was applied using cumulative distribution functions of the theoretical and actual strength boundaries to calculate the confidence factor and thereby evaluate the reliability of the composite honeycomb sandwich structure.

Risk assessment method of gas explosion based on quantification of margins and uncertainties (QMU):a case study on beam structures in buildings

Combustible gas explosions are common accidents in residential areas. Key building structural components, such as beams, slabs and columns, can be quickly damaged and destroyed by explosive overpressure loads, which may also result in continual collapse. Risk of interior gas explosions in buildings should be assessed to analyze the ability of structures to withstand disasters, which can also offer a theoretical basis for improving the structural design and construction of buildings. In this study, reinforced concrete beams in buildings were selected as the research object, and the risks to beam structures under mixed methane and air explosions were assessed using the quantification of margins and uncertainties (QMU) method. First, the uncertainty of the existing methods to calculate gas explosion and beam bending loads was analyzed. Through an influence regularity analysis, the expansion factor of combustible gas combustion products in enclosed explosion chamber, the initial density of the gas mixture in the explosion chamber before deflagration, the compressive strength of concrete, and the tensile strength of reinforcement were selected as the key uncertainty parameters. Furthermore, the Monte Carlo method was used to create 5000 samples of the selected uncertainty parameters, and statistical analysis was conducted to obtain the probability distribution of the gas explosion overpressure load and reinforced concrete beam bending load. Based on the sampling results, the beam structure’s safety margin and uncertainty analysis were analyzed to determine the probability of structural failure at the 90% confidence level. Finally, this paper provides guidelines for determining structural failure under different boundary value conditions of combustion explosion overpressure loads and reveals the sensitivity of different uncertainty parameters to structural safety margins using stepwise regression analysis. Compared to previous methods, this work includes the uncertainty features of disasters and disaster-bearing items when analyzing combustible gas explosion accidents; we anticipate it offers a fresh perspective on the quantitative assessment of gas explosion risks in buildings.

Vulnerability Assessment of Equipment Excited by Transient Electromagnetic Disturbances Based on Distribution-Free QMU Method

Based on the framework of quantification of margins and uncertainties (QMU) method, a distribution-free QMU method is proposed for the vulnerability evaluation of electrical and electronic equipment excited by transient electromagnetic disturbances. The proposed method can provide a comprehensive evaluation of the equipment considering the stress and the strength with uncertainties. The stress is represented by the induced responses on the equipment conductors, the strength is quantified by the occurrence probability of failure obtained from the experiment. The quantile-based QMU metric can take account of the inherent probability characteristics of stress and strength, as well as the aleatory uncertainties caused by sampling variability. The quantiles and their tolerance bounds are estimated by a nonparametric estimation method based on order statistics, which is a data-driven method without being constrained by the type of probability distribution. A case study of an electronic equipment in the power plant is carried out to illustrate the evaluation procedures of the proposed method.

Rigorous uncertainty quantification with correlated random variables from multiple sources

A method of quantification of margins and uncertainties (QMU) is developed for structures with correlated random variables originated from multiple sources. The QMU analysis aims to certify the concerned structure with a prescribed confidence factor (CF), and further determine an adequate design margin. After partitioning correlated random variables into different groups based on their uncertain sources, the multidimensional parallelepiped model is established to describe the uncertainty domain of these correlated random variables. Based on the grouped independent random vectors, McDiarmid’s inequality is applied to realize rigorous uncertainty quantification of the structural performance. The computation of structural uncertainty is formulated as an optimization problem of variables within the multidimensional parallelepiped uncertainty domain. The QMU framework is then established and applied to low cycle fatigue life assessment of aero-engine turbine disc made of GH720Li superalloy. Stochastic parameters involving loads, geometries, and material properties, are chosen as input random variables. It is demonstrated that the turbine disc can be rigorously certified under the given design specification. By contrast, it will provide a wrong certification decision when the correlation of variables is not considered. The assessment provides an effective basis for the design with enough confidence in engineering applications from the perspective of QMU analysis.

Rigorous uncertainty quantification and design with uncertain material models

We assess a method of quantification of margins and uncertainties (QMU) in applications where the main source of uncertainty is an imperfect knowledge or characterization of the material behavior. The aim of QMU is to determine adequate design margins given quantified uncertainties and a desired level of confidence in the design. We quantify uncertainties through rigorous probability bounds computed by exercising an existing deterministic code in order to sample the mean response and identify worst-case combinations of parameters. The resulting methodology is non-intrusive and can be wrapped around existing solvers. The use of rigorous probability bounds ensures that the resulting designs are conservative to within a desired level of confidence. We assess the QMU framework by means of an application concerned with sub-ballistic impact of AZ31B Mg alloy plates. We assume the design specification to be a maximum allowable backface deflection of the plate. As a simple scenario, we specifically assume that, under the conditions of interest, the plate is well-characterized by the Johnson-Cook model, but the parameters of the model are uncertain. In calculations, we use the commercial finite-element package LS-Dyna and DAKOTA Version 6.7. The assessment demonstrates the feasibility of the approach and how it results in high-confidence designs that are well-within the practical range of engineering application.

Reliability assessment for traction power supply system based on Quantification of Margins and Uncertainties

The traction power supply is a crucial part of high-speed rail network. A failure of the traction power supply system may lead to delay or outage of high-speed trains that will not only have direct impact on the entire operation schedule but will also cause tremendous losses. Therefore, the reliability assessment of the traction power supply system is extremely important to ensure the transportation quality of high-speed trains and improve the economy. This paper presents a reliability evaluation method for the traction power supply system based on Quantification of Margins and Uncertainties (QMU). Firstly, the characteristics of the traction power supply equipment and system are combined to establish the observation list and then the performance channel for the equipment and system is determined. Finally, the confidence factor is calculated and the reliability of the equipment and system quantified by the quantification of the performance margin and uncertainty. In order to validate the effectiveness of the proposed method, simulations are conducted using practical operation data from a China traction power supply system. The simulation results demonstrate that the proposed reliability assessment method can account for the uncertainty and quantify the system reliability index. The proposed method has good applicability and can be used to effectively evaluate the reliability of the traction power supply system.

An integrated QMU approach to structural reliability assessment based on evidence theory and kriging model with adaptive sampling

The objective of this paper is to propose an implementation framework of the quantification of margins and uncertainties (QMU) calculation for reliability and safety assessment of high-consequence systems in the presence of mixed (aleatory and epistemic) uncertainties. The aleatory and epistemic uncertainties are represented by a probability distribution and the Dempster–Shafer theory of evidence (DSTE), respectively. This study focuses on the need to alleviate the computational cost in terms of mixed uncertainties propagation, which is the core of the QMU process. The kriging model together with an adaptive sampling method is tailored to predict the responses of a system simulation model. The confidence factor (CF) for the QMU calculation is then evaluated by integrating the surrogate model and the DSTE analysis. The proposed approach is demonstrated by a numerical example to examine the computational efficiency. Finally, the proposed QMU framework is demonstrated via a simulation-based structural analysis of a pressure vessel with corrosion damage.

Quantification of Margins and Uncertainties for the Risk of Water Inrush in a Karst Tunnel: Representations of Epistemic Uncertainty with Probability

Accidents involving water inrush in karst tunnels often occur in China, resulting in serious social impact and huge economic loss. So, it is important that engineers provide a method with which to evaluate the risk of water inrush in karst tunnels. There are some problems regarding water inrush such as nonlinearity, and nominal, uncertain variables. Based on the mathematical model of water inrush, this paper proposes a methodology including a mechanical model dependent on geology and a mathematical model with quantification of margins and uncertainties (QMU), to evaluate the risk of water inrush. The following subjects are considered: (1) the risk assessment model is combined with mechanical analysis of water inrush in the karst tunnel in a perfect, dynamic way, (2) the analysis of uncertainty in QMU in the risk of water inrush, (3) the representations of uncertainty with probability theory, (4) the QMU analyses containing only epistemic uncertainty are represented, (5) the sensitivity analysis of parameters was performed through a step-wise regression analysis. This synthetic risk evaluation system provides a powerful and novel tool for systematically evaluating water inrush risk in karst tunnels.

On the Application of McDiarmid's Inequality to Complex Systems

McDiarmid's inequality has recently been proposed as a tool for setting margin requirements for complex systems. If $F$ is the bounded output of a complex system, depending on a vector of $n$ bounded inputs, this inequality provides a bound $B_F(\epsilon)$, such that the probability of a deviation exceeding $B_F(\epsilon)$ is less than $\epsilon$. I compare this bound with the absolute bound, based on the range of $F$. I show that when $n_{eff}$, the effective number of independent variates, is small, and when $\epsilon$ is small, the absolute bound is smaller than $B_F(\epsilon)$, while also providing a smaller probability of exceeding the bound, i.e., zero instead of $\epsilon$. Thus, for $B_F(\epsilon)$ to be useful, the number of inputs must be large, with a small dependence on any single input, which is consistent with the usual guidance for application of concentration-of-measure results. When the number of inputs is small, or when a small number of inputs account for much of the uncertainty, the absolute bounds will provide better results. The use of absolute bounds is equivalent to the original formulation of the method of quantification of margins and uncertainties (QMU).

Quantification of Margins and Uncertainties Approach for Structure Analysis Based on Evidence Theory

Quantification of Margins and Uncertainties (QMU) is a decision-support methodology for complex technical decisions centering on performance thresholds and associated margins for engineering systems. Uncertainty propagation is a key element in QMU process for structure reliability analysis at the presence of both aleatory uncertainty and epistemic uncertainty. In order to reduce the computational cost of Monte Carlo method, a mixed uncertainty propagation approach is proposed by integrated Kriging surrogate model under the framework of evidence theory for QMU analysis in this paper. The approach is demonstrated by a numerical example to show the effectiveness of the mixed uncertainty propagation method.

Quantification of margins and mixed uncertainties using evidence theory and stochastic expansions

The objective of this paper is to implement Dempster–Shafer Theory of Evidence (DSTE) in the presence of mixed (aleatory and multiple sources of epistemic) uncertainty to the reliability and performance assessment of complex engineering systems through the use of quantification of margins and uncertainties (QMU) methodology. This study focuses on quantifying the simulation uncertainties, both in the design condition and the performance boundaries along with the determination of margins. To address the possibility of multiple sources and intervals for epistemic uncertainty characterization, DSTE is used for uncertainty quantification. An approach to incorporate aleatory uncertainty in Dempster–Shafer structures is presented by discretizing the aleatory variable distributions into sets of intervals. In view of excessive computational costs for large scale applications and repetitive simulations needed for DSTE analysis, a stochastic response surface based on point-collocation non-intrusive polynomial chaos (NIPC) has been implemented as the surrogate for the model response. The technique is demonstrated on a model problem with non-linear analytical functions representing the outputs and performance boundaries of two coupled systems. Finally, the QMU approach is demonstrated on a multi-disciplinary analysis of a high speed civil transport (HSCT).

Quantification of margins and uncertainties using multiple gates and conditional probabilities

A methodology to perform the Quantification of Margins and Uncertainties (QMU) is introduced to enable the assessment of the safety associated with the operating conditions of complex engineering devices consisting of multiple subcomponents or coupled multi-physics processes. One of the key components of the approach is the possibility of decomposing the system into subcomponents characterized by critical metrics—gates—that collectively describe the reliability of the whole system. In the present study we formalize the process of constructing conditional probabilities for system performance and illustrate it with two applications: the evaluation of the test-time in a shock-tube experimental facility and the assessment of the unstart limit in the combustion chamber of a supersonic propulsion engine. In both cases, multiple uncertainties are considered and the gates are used as a mechanism to reduce the complexity of the resulting stochastic problem.

New developments in uncertainty assessment and uncertainty management

The paper presents a general method for doing predictions and test planning which can also be used as a tool for managing uncertainty. Uncertainty is generally defined as “that which is not precisely known”. This definition permits the identification of different kinds of uncertainty arising from different sources and activities, most of which go unnoticed in analysis. In this paper, the description of uncertainty begins from a historical perspective and concludes with a new perspective based upon making inferences; fuzzy logic can be most helpful in quantifying some inferences. Our assessment of uncertainty begins the identification of the various forms of uncertainty (ambiguity, fuzziness, randomness, non-specificity, ignorance, etc.) and concludes with models and methods for assessing the ‘total uncertainty’ within an application. The material contained herein is described in the context of physical science and engineering applications; however, nothing presented precludes application to other fields, e.g. economics, social sciences, medicine and business. Uncertainty assessment involves how to identify, classify, characterize, quantify, and combine uncertainties within an application, with the expressed goal of understanding how to manage uncertainties. Uncertainty management presumes that we have a process to quantify uncertainties and to be able to aggregate them in such a way that they can be compared in terms of their individual contributions to the ‘total uncertainty’. Managing uncertainties is important, because uncertainties directly affect decision and policy making. An example, using a concept called Quantification of Margins and Uncertainty (QMU), is provided to illustrate our ideas.

Quantification of margins and uncertainties: Example analyses from reactor safety and radioactive waste disposal involving the separation of aleatory and epistemic uncertainty

In 2001, the National Nuclear Security Administration (NNSA) of the U.S. Department of Energy (DOE) in conjunction with the national security laboratories (i.e., Los Alamos National Laboratory, Lawrence Livermore National Laboratory, and Sandia National Laboratories) initiated development of a process designated quantification of margins and uncertainties (QMU) for the use of risk assessment methodologies in the certification of the reliability and safety of the nation's nuclear weapons stockpile. A previous presentation, “Quantification of Margins and Uncertainties: Conceptual and Computational Basis,” describes the basic ideas that underlie QMU and illustrates these ideas with two notional examples. The basic ideas and challenges that underlie NNSA's mandate for QMU are present, and have been successfully addressed, in a number of past analyses for complex systems. To provide perspective on the implementation of a requirement for QMU in the analysis of a complex system, three past analyses are presented as examples: (i) the probabilistic risk assessment carried out for the Surry Nuclear Power Station as part of the U.S. Nuclear Regulatory Commission's (NRC's) reassessment of the risk from commercial nuclear power in the United States (i.e., the NUREG-1150 study), (ii) the performance assessment for the Waste Isolation Pilot Plant carried out by the DOE in support of a successful compliance certification application to the U.S. Environmental Agency, and (iii) the performance assessment for the proposed high-level radioactive waste repository at Yucca Mountain, Nevada, carried out by the DOE in support of a license application to the NRC. Each of the preceding analyses involved a detailed treatment of uncertainty and produced results used to establish compliance with specific numerical requirements on the performance of the system under study. As a result, these studies illustrate the determination of both margins and the uncertainty in margins in real analyses.

Quantification of margins and uncertainties: Conceptual and computational basis

In 2001, the National Nuclear Security Administration of the U.S. Department of Energy in conjunction with the national security laboratories (i.e., Los Alamos National Laboratory, Lawrence Livermore National Laboratory and Sandia National Laboratories) initiated development of a process designated Quantification of Margins and Uncertainties (QMU) for the use of risk assessment methodologies in the certification of the reliability and safety of the nation's nuclear weapons stockpile. This presentation discusses and illustrates the conceptual and computational basis of QMU in analyses that use computational models to predict the behavior of complex systems. The following topics are considered: (i) the role of aleatory and epistemic uncertainty in QMU, (ii) the representation of uncertainty with probability, (iii) the probabilistic representation of uncertainty in QMU analyses involving only epistemic uncertainty, and (iv) the probabilistic representation of uncertainty in QMU analyses involving aleatory and epistemic uncertainty.

A QMU approach for characterizing the operability limits of air-breathing hypersonic vehicles

The operability limits of a supersonic combustion engine for an air-breathing hypersonic vehicle are characterized using numerical simulations and an uncertainty quantification methodology. The time-dependent compressible flow equations with heat release are solved in a simplified configuration. Verification, calibration and validation are carried out to assess the ability of the model to reproduce the flow/thermal interactions that occur when the engine unstarts due to thermal choking. quantification of margins and uncertainty (QMU) is used to determine the safe operation region for a range of fuel flow rates and combustor geometries.

Probabilistic bounding analysis in the Quantification of Margins and Uncertainties

The current challenge of nuclear weapon stockpile certification is to assess the reliability of complex, high-consequent, and aging systems without the benefit of full-system test data. In the absence of full-system testing, disparate kinds of information are used to inform certification assessments such as archival data, experimental data on partial systems, data on related or similar systems, computer models and simulations, and expert knowledge. In some instances, data can be scarce and information incomplete. The challenge of Quantification of Margins and Uncertainties (QMU) is to develop a methodology to support decision-making in this informational context. Given the difficulty presented by mixed and incomplete information, we contend that the uncertainty representation for the QMU methodology should be expanded to include more general characterizations that reflect imperfect information. One type of generalized uncertainty representation, known as probability bounds analysis, constitutes the union of probability theory and interval analysis where a class of distributions is defined by two bounding distributions. This has the advantage of rigorously bounding the uncertainty when inputs are imperfectly known. We argue for the inclusion of probability bounds analysis as one of many tools that are relevant for QMU and demonstrate its usefulness as compared to other methods in a reliability example with imperfect input information.

Quantification of margins and uncertainties of complex systems in the presence of aleatoric and epistemic uncertainty

Performance assessment of complex systems is ideally done through full system-level testing which is seldom available for high consequence systems. Further, a reality of engineering practice is that some features of system behavior are not known from experimental data, but from expert assessment, only. On the other hand, individual component data, which are part of the full system are more readily available. The lack of system level data and the complexity of the system lead to a need to build computational models of a system in a hierarchical or building block approach (from simple components to the full system). The models are then used for performance prediction in lieu of experiments, to estimate the confidence in the performance of these systems. Central to this are the need to quantify the uncertainties present in the system and to compare the system response to an expected performance measure. This is the basic idea behind Quantification of Margins and Uncertainties (QMU). QMU is applied in decision making—there are many uncertainties caused by inherent variability (aleatoric) in materials, configurations, environments, etc., and lack of information (epistemic) in models for deterministic and random variables that influence system behavior and performance. This paper proposes a methodology to quantify margins and uncertainty in the presence of both aleatoric and epistemic uncertainty. It presents a framework based on Bayes networks to use available data at multiple levels of complexity (i.e. components, subsystem, etc.) and demonstrates a method to incorporate epistemic uncertainty given in terms of intervals on a model parameter.

Quantification of margins and uncertainties: A probabilistic framework

Quantification of margins and uncertainties (QMU) was originally introduced as a framework for assessing confidence in nuclear weapons, and has since been extended to more general complex systems. We show that when uncertainties are strictly bounded, QMU is equivalent to a graphical model, provided confidence is identified with reliability one. In the more realistic case that uncertainties have long tails, we find that QMU confidence is not always a good proxy for reliability, as computed from the graphical model. We explore the possibility of defining QMU in terms of the graphical model, rather than through the original procedures. The new formalism, which we call probabilistic QMU, or pQMU, is fully probabilistic and mathematically consistent, and shows how QMU may be interpreted within the framework of system reliability theory.