Uncertain Random System Research Articles

Dynamic risk assessment of Uncertain Random System considering operator's simple emergency-stop action in short time window

Human-machine systems can be considered as typical Uncertain Random Systems (URS). In human-machine systems, operator's simple emergency-stop actions act as a vital soft barrier. Conventional Human Reliability Analyses face challenges in evaluating operator's simple emergency-stop action due to their static characteristics, incompatibility with short time windows, and problems posed by small samples. This paper provides a novel solution to risk assessment of human-machine systems involving operator's simple emergency-stop mechanism. Specifically, an evaluation method of operator's simple emergency-stop action is established, where human cognition is decomposed according to its temporal and logical dimensions, key indicators of human sub-cognition are evaluated, and uncertainty theory is used to integrate these indicators. The output of proposed method is uncertainty of operator's behavior (UOB), which can offer more information than traditional Human Error Probability (HEP) and can be readily converted into uncertainty of human error. Further, a precise simulation method for dynamic risk assessment of Uncertain Random Systems is developed, in which the integration of the UOB is achieved. A case study demonstrates the effectiveness of the proposed methods, and its results show that the proposed methods can clearly reflect the differences in system risk under short time window conditions that have minor distinctions.

Optimal control and zero-sum game subject to multifactor uncertain random systems with jump

A differential equation incorporating random matrices, multiple Liu processes, and multiple V jump processes is employed to portray a multifactor uncertain random system with jump. The existence and uniqueness theorem for such an equation is proved. Based on the theorem, problems of optimal control and two-person zero-sum game subject to multifactor uncertain random systems with jump are considered. An equation of optimality is provided for solving a problem of optimal control. Equilibrium equations are proposed to identify the saddle-point of a two-person zero-sum game problem. As an extension, we generalize the obtained results to the problems subject to differential equations including random matrices, multiple Liu processes, and multiple V-n jumps processes. Finally, a portfolio selection game problem is analysed utilizing the acquired theoretical results.

Optimal Control for a Multistage Uncertain Random System

Chance theory is a mathematical methodology for modelling complex systems including both uncertainty and randomness. Based on chance theory, this paper introduces the optimal control model for a multistage uncertain random system. For solving such a model, recurrence equations are presented via Bellman’s principle. With the aid of recurrence equations, the bang-bang problem of optimal control model and indefinite linear quadratic (LQ) problem of optimal control model are studied. Meanwhile, the exact solutions of such problems are presented. Furthermore, numerical examples are provided on the proposed theorems to show the effectiveness of our results.

Optimal control for uncertain random singular systems with multiple time-delays

Chance theory provides us a useful tool to solve an optimal control problem with indeterminacy composing of both uncertainty and randomness. Based on chance theory, this paper studies an optimal control for uncertain random singular systems with multiple time-delays. First, an uncertain random singular system with multiple time-delays is introduced, and then the corresponding optimal control problem is established. The equivalent relationship between this problem and the optimal control problem for standard uncertain random systems is derived. Then the appropriate recurrence equations are proposed according to the dynamic programming method. Furthermore, two kinds of optimal control problems are discussed. The optimal control inputs and respective optimal values of the problems are provided via the solvability of the obtained equations. Finally, a numerical example is presented to show the effectiveness of our theoretical results.

Uncertainty Expression and Propagation in the Risk Assessment of Uncertain Random System

Expressions and propagations of uncertainties have been the core topics in the development of risk science in last decades, whose purpose is to provide decision-makers with clear information about the uncertainty of system's risk. Uncertainty theory is an emerging theory that has great advantages in the expression of epistemic uncertainty, compared to the theories such as subjective probability, evidence theory, and possibility theory. A new framework of uncertainty expression is proposed in this article to properly express different uncertainty sources that exist in the system, where the uncertainty theory is used to express epistemic uncertainties and frequentist probability is used to express aleatory uncertainties. A general propagation method is further developed to address the joint calculations of proposed uncertainty expressions, which can be degenerated into pure probabilistic approach and pure uncertainty-based approach. A case study is conducted to show the effectiveness of proposed method, whose results indicate that the application of proposed method will lead to a result which is easier to be understood than results of theories such as evidence theory and possibility theory, and is more robust than results of Bayesian approach.

Risk assessment of uncertain random system—Level-1 and level-2 joint propagation of uncertainty and probability in fault tree analysis

Uncertainty analysis plays a significant role in risk assessment, which consists of two tasks: uncertainty expressions of input variables in the model and their propagations through the model built. We aim to provide, in fault tree analysis context, suitable methods of expression and propagation of uncertainty corresponding to different stages of knowledge that the risk analyst own, where frequentist probability is used to express the aleatory uncertainty and uncertainty theory is used to represent the epistemic uncertainty. To do so, we divide the analyst's knowledge state into five different stages, and develop the correct expression of uncertainty corresponding to each stage, where different combinations of probability and uncertainty are considered. Methods of propagation of these uncertainties through fault trees are further developed, where we introduce probability distributions, uncertainty distributions, newly-developed level-2 distributions, and the varying time t into the operational law for Boolean uncertain random system to better address the needs of practical risk assessments. A case study is conducted to show the differences in the propagation methods corresponding to various knowledge stages, and the results highlight that the proposed methods are effective and could deliver clear messages to decision makers.

A linear quadratic model based on multistage uncertain random systems

In this paper, a linear quadratic (LQ) optimal control model is studied for a multistage uncertain random system. First, recurrence equations are presented for this model based on Bellman’s Principle. Second, analytical expressions are derived for solving both the optimal objective function and the optimal control strategy of the model. Finally, an example is given to illustrate our results.

Expected loss of uncertain random system

Uncertain random variable is a main tool to deal with phenomena in which uncertainty and randomness are present simultaneously. This paper proposes a concept of expected loss to quantify the risk of an uncertain random system. In addition, an expected loss theorem is proved and applied to series system, parallel system, k-out-of-n system, standby system and structural system.

Value-at-risk in uncertain random risk analysis

Uncertain random variables provide a tool to deal with phenomena in which uncertainty and randomness simultaneously exist. This paper proposes a concept of value-at-risk to quantify the risk of an uncertain random system. In addition, a value-at-risk theorem is proved in order to calculate the value-at-risk, and is applied to series systems, parallel system, k-out-of-n system, standby system, and structural system.

Importance index of components in uncertain random systems

Importance measure is an index to describe the importance of an individual component or a group of components within a reliability system. Up to now, importance measures for components in stochastic reliability systems have been investigated. And importance index for a component and a group of components in an uncertain reliability system has also been studied. In the real world, components with samples and components without samples always coexist in a complex system which is actually an uncertain random reliability system. For describing the importance extent of an individual component and a group of components in an uncertain random reliability system, this paper aims at introducing a new concept of importance index and presenting some formulas to calculate the importance index. Furthermore, this paper takes several examples including uncertain random series, uncertain random parallel, uncertain random parallel-series, uncertain random series-parallel and uncertain random bridge systems to illustrate how to calculate an importance index.

Reliability analysis in uncertain random system

Reliability analysis of a system based on probability theory has been widely studied and used. Nevertheless, it sometimes meets with one problem that the components of a system may have only few or even no samples, so that we cannot estimate their probability distributions via statistics. Then reliability analysis of a system based on uncertainty theory has been proposed. However, in a general system, some components of the system may have enough samples while some others may have no samples, so the reliability of the system cannot be analyzed simply based on probability theory or uncertainty theory. In order to deal with this type systems, this paper proposes a method of reliability analysis based on chance theory which is a generalization of both probability theory and uncertainty theory. In order to illustrate the method, some common systems are considered such as series system, parallel system, k-out-of-n system and bridge system.

Risk Index in Uncertain Random Risk Analysis

In many systems, randomness and uncertainty are present simultaneously. Uncertain random variables provide a tool to deal with these inexact phenomena. This paper proposes a concept of risk index to quantify the risk of an uncertain random system. In addition, a risk index theorem is proved in order to calculate the risk index, and is applied to series systems, parallel systems and standby systems. Finally, a concept of expected loss is suggested for an uncertain random system.