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Traffic reliability is a crucial property of the transportation system, showing its ability to resist traffic jams or collapse. Traditional traffic reliability analysis only considers stochastic uncertainty but neglects epistemic uncertainty, which widely exists in the traffic network and leads to an underestimation of traffic failure. In this paper, we introduce uncertainty theory to model epistemic uncertainty, thereby developing a belief reliability analysis method for transportation systems based on the traffic performance margin. We established an uncertain percolation semi Markov (UPSM) model to describe the essential physical characteristics of the traffic accidents considering both stochastic and epistemic uncertainty. And the uncertain percolation model is utilized to describe the traffic performance degradation and the semi Markov process is developed to represent the influence of random emergency events. According to the traffic failure propagation process, a simulation method for calculating belief reliability is proposed. Finally, a case study was given to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

Multiple modes are ubiquitous in current industrial processes, and the amount of historical data contained in different modes may vary considerably. Insufficient data can easily lead to cold start problems when building a fault detection model for a particular mode. To solve this problem, while considering the similarity and differences between multiple modes, a deep model using domain adaptation based on feature separation is proposed for nonlinear process monitoring with few samples. The model extracts common features from modes and the data deficiency is compensated by transferring the domain knowledge from the source to the common features. On the other hand, to avoid missing useful information by focusing only on common features, the model also extracts the specific features of the target domain. Thus, monitoring performance is improved with the help of domain adaptation while taking into account the specific characteristics of the target domain. Furthermore, three detection indices are designed to monitor the common feature subspace, the specific feature subspace, and the residual subspace, respectively. The benefit of this is allowing more diagnostic information to be obtained when a fault occurs. The proposed method was tested with a numerical example and a real industrial hydrocracking process to verify the detection effectiveness. [ABSTRACT FROM AUTHOR]

Data quality is an important consideration in many engineering applications and projects. Data collection procedures do not always involve careful utilization of the most precise instruments and strictest protocols. As a consequence, data are invariably affected by imprecision and sometimes sharply varying levels of quality of the data. Different mathematical representations of imprecision have been suggested, including a classical approach to censored data which is considered optimal when the proposed error model is correct, and a weaker approach called interval statistics based on partial identification that makes fewer assumptions. Maximizing the quality of statistical results is often crucial to the success of many engineering projects, and a natural question that arises is whether data of differing qualities should be pooled together or we should include only precise measurements and disregard imprecise data. Some worry that combining precise and imprecise measurements can depreciate the overall quality of the pooled data. Some fear that excluding data of lesser precision can increase their overall uncertainty about results because lower sample size implies more sampling uncertainty. This paper explores these concerns and describes simulation results that show when it is advisable to combine fairly precise data with rather imprecise data by comparing analyses using different mathematical representations of imprecision. Pooling data sets is preferred when the low-quality data set does not exceed a certain level of uncertainty. However, so long as the data are random, it may be legitimate to reject the low-quality data if its reduction of sampling uncertainty does not counterbalance the effect of its imprecision on the overall uncertainty. [ABSTRACT FROM AUTHOR]

• Proposing an uncertainty-based knowledge distillation method for compressing Bayesian deep neural network (BDNN). • Utilizing BDNN as the teacher to exploit its ensemble nature and transfer more accurate knowledge from the teacher network to the student network. • Incorporating uncertainty into knowledge distillation to adaptively adjust the hyperparameters of the knowledge distillation method for each sample and enhancing the performance of the compression process. • Distinguishing between Epistemic and Aleatoric uncertainties to regulate the influence of the teacher network using Epistemic uncertainty and adjust temperature parameter using Aleatoric uncertainty. • Demonstrating the superior performance of the proposed method in both accuracy and robustness in comparison to standard knowledge distillation-based methods. Deep learning models have been widely employed across various fields. In real-world scenarios, especially safety-critical applications, quantifying uncertainty is as crucial as achieving high accuracy. To address this concern, Bayesian deep neural networks (BDNNs) emerged to estimate two different types of uncertainty: Aleatoric and Epistemic. Nevertheless, implementing a BDNN on resource-constrained devices poses challenges due to the substantial computational and storage costs imposed by approximation inference techniques. Thus, efficient compression methods should be utilized. We propose an uncertainty-based knowledge distillation method to compress BDNNs. Knowledge distillation is a model compression technique that involves transferring knowledge from a complex network, known as the teacher network, to a simpler one, referred to as the student network. Our method incorporates uncertainty into knowledge distillation to address situations where inappropriate teacher supervision undermines compression performance. We utilize the Epistemic uncertainty of teacher predictions to tailor supervision for each sample individually to take into account teacher's limited knowledge. Additionally, we adjust the temperature parameter of the distillation process for each sample based on the Aleatoric uncertainty of the teacher predictions, ensuring that the student receives appropriate supervision even in the presence of ambiguous data. As a result, the proposed method enables the Bayesian student network to be trained under both appropriate supervision of the Bayesian teacher network and ground truth labels. We evaluated our method on the CIFAR-10, CIFAR-100, and RAF-DB datasets, demonstrating notable improvements in accuracy over state-of-the-art knowledge distillation-based methods. Furthermore, the robustness of our approach was assessed through testing weakly trained teacher networks and the analysis of blurred and low-resolution data, which have high uncertainty. Experimental results show that the proposed method outperformed existing methods. [ABSTRACT FROM AUTHOR]

In this paper, the Tsallis entropy based novel uncertainty relations on vector signals and matrix signals in terms of sparse representation are deduced for the first time. These new uncertainty bounds are not only related with the entropy parameter, but also related with the vector length, the min non-zero correlation between standard orthogonal basis and the given signals, the max correlation between the two given orthogonal basis and even the eigenvalues along with eigenvectors. Especially, the relationship between uncertainty bounds and matrix eigenvalues is discussed as well, as discloses the new interesting interpretation on sparse representation. In addition, the theoretical analysis and numerical examples have been shown to verify these newly proposed uncertainty principles, e.g., under the case of special parameters of Tsallis entropy, the uncertainty bound reaches its peak value for the sparsest representation of matrix (i.e., only one eigenvalue is not zero). Moreover, various numerical relations between uncertainty bounds and Tsallis entropy parameters are shown in perceptual form, as maybe give us the possible enlightenment or guidance in future sparse representation analysis. [ABSTRACT FROM AUTHOR]

[Display omitted] • A scalable and direct probabilistic model, probabilistic inference neural network (PINN), is proposed for estimating aleatoric and epistemic uncertainties. • Self-consistent condition is built by empirical prior, which serves as uncertainty measurement for prediction. • The uncertainty measurement can be mapped onto diagonal covariance matrices to yield parametric distribution, which spares multiple forecasts. • PINN is able to be incorporated into the policy learning framework to improve the performance of learning policy and data efficiency. Reinforcement learning is very much democratized for autonomous control of an unknown dynamics system. However, low data efficiency is a practical concern in physical systems. The underlying reason is that, for the current state-of-the-art probabilistic models, it is required to evaluate multiple forecasts before uncertainty estimation, leading to computationally intensive, if not intractable, uncertainty inference. To this gap, probabilistic dynamics is introduced in the current study. A self-consistent condition in terms of empirical prior is formulated to measure uncertainty via inferring parametric distribution, and the resulted neural network is termed as probabilistic inference neural network (PINN). This approach is remarkably effective for data regression and policy learning frameworks. Experiments are performed on UCI datasets. The results demonstrate that PINN performance is more competitive than those of the currently prevailing methods. Finally, a PINN-based policy learning framework is proposed and applied to benchmark control tasks and physical control task of an in-house self-developed 14-DOF robot featuring high dimensional state/action spaces. The results demonstrate highly competitive data efficiency and policy performance to outperform the most prevailing policy learning framework. [ABSTRACT FROM AUTHOR]

As a typical multi-sensor fusion technology, the evidential reasoning (ER) rule has been widely used in evaluation, decision, and classification tasks. Current researches on the ER rule tend to fuse objects of the same type, such as the unquantized analog quantity. However, the fusion of unquantized analog quantity and quantized digital quantity is more common in engineering, but has received minimal attention. Given the characteristics of the ER rule, the biggest challenge imposed by this fusion is to consider the reliability of digital quantity reasonably. In this paper, a new fusion approach of digital and analog quantity based on the ER rule is proposed. In order to improve the fusion accuracy, the combination of quantization error and external noise is adopted to measure the reliability of digital quantity. On this basis, the digital and analog quantities are fused together according to the ER rule. To further explore the intrinsic mechanism of the proposed approach, a detailed performance analysis is conducted to study the variation law of evidence reliability and fusion results. Finally, a numerical example and a case study are intended to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

• A new nonlinear hybrid vehicle routing problem is developed. • An ambiguous equilibrium risk value objective function is defined. • An ambiguity set is constructed via the central limit theorem. • The proposed model is derived to a mixed integer second-order cone programming. • Experimental studies show the applicability of the proposed approach. A novel nonlinear hybrid vehicle routing problem is examined, and its nonlinear component is linearised considering the transportation costs associated with electricity and traditional fuel-based driving. Due to the fact that the transportation cost and fuel consumption involve the twofold uncertainty of randomness and fuzziness, and only partial probability distribution information may be available. Therefore, these two parameters are considered as random fuzzy variables with ambiguous probability distributions. An ambiguous equilibrium risk value objective function and an ambiguous equilibrium chance constraint are formulated. Accordingly, a distributionally robust equilibrium approach is proposed, in which the ambiguity sets are used to characterize the ambiguous probability distributions of the random fuzzy variables. Specifically, this paper first applies the central limit theorem to construct the ambiguity sets. Subsequently, the inner ambiguous probability constraint and the outer credibility constraint are derived into their equivalent counterparts, respectively. In this manner, the proposed model is successfully converted into a mixed integer second-order cone programming model, where the conventional branch-and-cut algorithm is adopted to obtain the optimal routing. Finally, the performance of the proposed model and its price of distributional robustness are verified in the numerical experiments. Overall, the main achievements of this paper are summarized as (1) the proposal of a distributionally robust equilibrium optimization model for a nonlinear hybrid vehicle routing problem, (2) the definitions of an ambiguous equilibrium risk value objective function and an ambiguous equilibrium chance constraint under twofold uncertainty, and (3) the derivation of an equivalent second-order cone programming model for computationally solvable. [ABSTRACT FROM AUTHOR]

Due to the growing complexity of multi-state deteriorating systems and the lack of data, information and knowledge, epistemic uncertainty cannot be ignored anymore. Although there already exist some reliability metrics to deal with epistemic uncertainty problems in multi-state deteriorating systems, the final results provided by these methods are always probability intervals, which will suffer from the interval extension challenge in the subsequent operation. In this paper, we propose a reliability analysis method for the multi-state deteriorating system based on belief reliability theory, which can provide more conservative estimations and avoid interval extension problems. To describe the state transition process of multi-state deteriorating systems under the effect of epistemic uncertainty, a mathematical model called uncertain state transition chain is proposed. Under the framework of uncertainty theory, a total uncertainty inequality is given to assist the calculation of belief reliability. Using the proposed model and inequality, an algorithm of belief reliability for multi-state deteriorating systems considering the uncertainty of inspection time is provided. As a numerical example, the calculating process, the evaluation result and some discussions of a specific deteriorating system are given at last. [ABSTRACT FROM AUTHOR]

A recent report from Purdue University discusses the challenges of predicting pedestrian behaviors in the development of autonomous vehicles. The study distinguishes between two types of uncertainties, intrinsic randomness and knowledge limitations, and analyzes these uncertainties in road crossing and short-term movement prediction. The findings indicate that knowledge limitations pose a greater difficulty in predicting pedestrian actions due to limited information. The research emphasizes the need for autonomous vehicle algorithms to account for different levels of behavior-related uncertainties in order to enhance safety and efficiency. [Extracted from the article]

A recent study conducted by researchers from the London School of Economics and Political Science explores how people discern between truth and untruth and engage with evidence, particularly in times of uncertainty such as the early months of the COVID-19 pandemic. The study focuses on the workings of suspicion and its relationship with evidence by analyzing conversations in a Facebook group dedicated to 'Covid truth'. The research concludes that suspicion can lead to its own forms of falsification but has a complex relationship with positive truth. By understanding the mechanisms behind the proliferation of COVID conspiracy theories, the study sheds light on why some individuals believe they have a critical edge over others. [Extracted from the article]

Uncertainty quantification of belief functions is an unsolved issue in belief function theory that is used widely to tackle epistemic uncertainty. This study provides a new definition of conditional entropy of belief functions, called conditional plausibility entropy, in terms of Dempster conditioning and plausibility entropy of mass functions. The proposed conditional plausibility entropy mainly meets two aspects of good properties, one is the semantics of independence property, the other is the compatibility with Shannon's conditional entropy for probability distributions, which are not simultaneously satisfied by existing definitions of conditional entropy of belief functions. The effectiveness of conditional plausibility entropy is validated further through comparison and analysis on the basis of different conditioning methods. [ABSTRACT FROM AUTHOR]

This article discusses a study on the impact of anxiety on adaptive learning in uncertain situations. The study found that individuals with anxiety have difficulty learning from aversive outcomes, especially as the outcomes become more uncertain. The researchers used a novel eye-tracking method to measure policy and epistemic uncertainty and found that individuals without anxiety flexibly switch between resolving these uncertainties to learn about trustworthy and untrustworthy individuals. However, individuals with anxiety do not exhibit this flexibility and instead express less uncertainty overall. The study suggests that altered learning in people with anxiety stems from insensitivity to policy uncertainty and rigid decision-making, leading to maladaptive behaviors. [Extracted from the article]

Possibility theory stands halfway between logical and probabilistic representation frameworks. Possibility theory, as a setting for handling epistemic uncertainty, may have a qualitative or a quantitative flavor depending on the way conditioning is defined. In particular, qualitative possibility theory is totally compatible with classical logic, while quantitative possibility theory is related to statistics. This feature suggests the possibility theory setting as an interesting candidate for interfacing reasoning and learning. The potential of the possibilistic representation framework for reasoning, explanation and learning tasks is particularly highlighted. [ABSTRACT FROM AUTHOR]

According to a preprint abstract, individuals with anxiety may have difficulty learning from uncertain outcomes. The study used a novel eye-tracking method to measure policy and epistemic uncertainty, and found that people without anxiety flexibly switch between resolving these uncertainties to learn about trustworthy individuals. However, those with anxiety prioritize reducing epistemic uncertainty at the expense of optimizing behavior, leading to maladaptive behaviors with untrustworthy people. This research has not yet been peer-reviewed. [Extracted from the article]

The missing data problem – attributed to malfunctioning detectors, packet loss during transmission, or data removed by quality control procedures – is unavoidable in most traffic-related datasets. However, this problem has adversely affected traffic engineering applications as they heavily rely on accurate and comprehensive data. This study aims to impute missing loop detector data in order to improve the estimation results of traffic flow analysis. This paper presents a statistically principled methodology that focuses not only on proposing a computationally efficient imputation approach, but also on assessing the uncertainty associated with imputed values. The proposed methodology quantifies the accuracy of imputation and estimation of uncertainty for a range of challenging patterns of missing loop detector data, and compares them with existing methods. The results of the analysis demonstrate that the performance of the proposed approach remains unaffected by the presence of a large number of missing patterns and reflects the true statistical properties of the principal data. The proposed approach is also comparatively less computationally complex than the existing methods. Further, the comparative analysis of the proposed estimator shows that the generated prediction intervals are reasonably accurate and conform to the desired confidence levels with relatively small interval width. [ABSTRACT FROM AUTHOR]

• Classical interval arithmetic should not be used for modeling the uncertain shape. • Modification of directed interval arithmetic reduces overestimations. • The interval parametric integral equation system method is less time-consuming. • The correctness of the interval PIES solutions are proved. This paper presents a new method for simultaneous modeling the uncertainty of measurement data (necessary to define the boundary shape and boundary conditions) in boundary problems. The interval parametric integral equation system (interval PIES) was developed for solving boundary problems with input data defined in this way. The motivation for conducting this research was that this topic (simultaneous consideration of uncertainties of all input data) has appeared sporadically in the literature (mainly with uncertainly defined boundary conditions or other parameters). In this paper, the uncertainty was defined using interval numbers and modeled using interval arithmetic. The direct application of both classical and directed interval arithmetic caused the overestimation and obtained solutions were useless in practice. Therefore, modification of the directed interval arithmetic was developed. The reliability of the interval PIES solutions obtained using such arithmetic was verified on 2D problems described by Laplace's equation. The solutions were compared with the interval analytical solutions (differently obtained), as well as with the solutions of exactly defined (without the uncertainty) numerical methods. All performed tests indicated the high potential of the method. Obtained interval solutions occurred to be less overestimated and not as time-consuming as presented alternative methods. [ABSTRACT FROM AUTHOR]

In the response analysis of uncertain structural models with limited information, probability-boxes can be effectively employed to address the aleatory and epistemic uncertainty together. This paper presents a copula-based uncertainty propagation method which can accurately perform uncertainty propagation analysis with correlated parametric probability-boxes. Firstly, the parameter estimation and Akaike information criterion analysis are utilized to select an optimal copula based on available samples, by which the joint cumulative distribution function is constructed for the correlated input variables. Then, using the obtained joint cumulative distribution function, the correlated parametric probability-boxes are transformed into independent normal variables, and an efficient method based on sparse grid numerical integration is proposed to calculate the bounds on statistical moments of a response function. Finally, numerical examples and an engineering application are provided to verify the effectiveness of the presented method. [ABSTRACT FROM AUTHOR]

Outlier detection is one of the most important issues in contemporary data analysis. At present, many methods are employed for anomaly and outlier detection, but there is still no universal tool that delivers a high degree of efficiency. In this study, we present a novel approach for outlier detection based on the skillful use of the law of large numbers. The main idea of the proposed solution consists of the random clustering of the elements of the analyzed set. Then, those elements that are sufficiently distant from the random cluster centers are marked as outliers. The proposed approach, besides being highly effective, is also very intuitive. The results of the conducted numerical experiments confirm the high degree of effectiveness of the proposed method, with the measures of accuracy and precision reaching a value of 1. The indisputable advantages of this novel approach for outlier detection are the simplicity of interpretation and the possibility of its modification by people who may lack an extensive experience in data analysis. The effectiveness of the proposed method was compared with other recognized techniques in detecting outliers within both artificially generated and empirical data sets. [ABSTRACT FROM AUTHOR]

A rule-based system is a widely used artificial intelligence system that employs a set of rules to make decisions. The belief rule-based (BRB) classification system is an extension of fuzzy rule-based (FRB) system that handles uncertainty and imprecision in classification tasks by incorporating Dempster-Shafer evidence theory and fuzzy set theory. However, the BRB classification system suffers from the combinatorial explosion and high time complexity problems. To solve these issues, the fuzzy unordered rule induction algorithm (FURIA) is introduced into the BRB classification systems to design a novel BRB classification system in this paper. FURIA is computationally less complex and has superior classification performance. The proposed system outperforms BRB classification systems in terms of classification performance and significantly reduces the number of rules and conditions. Furthermore, the proposed system offers a more effective solution than FURIA. To evaluate the validity and superiority of the proposed system, we conduct two classification experiments, comparing it with five traditional classifiers and seven rule-based systems, respectively, in terms of classification performance and interpretability. [ABSTRACT FROM AUTHOR]

How to measure the uncertainty of orderable sets is still an open issue. In this paper, a new method based on Deng entropy to measure the uncertainty of orderable sets is proposed. When orderable sets degenerate as unorderable sets, the new entropy would degenerate as Deng entropy. When orderable sets degenerate into singleton, the new entropy would degenerate into Shannon entropy. Some numerical examples are used to illustrate the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Vision-based autonomous driving through imitation learning mimics the behavior of human drivers by mapping driver view images to driving actions. This article shows that performance can be enhanced via the use of eye gaze. Previous research has shown that observing an expert’s gaze patterns can be beneficial for novice human learners. We show here that neural networks can also benefit. We trained a conditional generative adversarial network to estimate human gaze maps accurately from driver-view images. We describe two approaches to integrating gaze information into imitation networks: eye gaze as an additional input and gaze modulated dropout. Both significantly enhance generalization to unseen environments in comparison with a baseline vanilla network without gaze, but gaze-modulated dropout performs better. We evaluated performance quantitatively on both single images and in closed-loop tests, showing that gaze modulated dropout yields the lowest prediction error, the highest success rate in overtaking cars, the longest distance between infractions, lowest epistemic uncertainty, and improved data efficiency. Using Grad-CAM, we show that gaze modulated dropout enables the network to concentrate on task-relevant areas of the image. [ABSTRACT FROM AUTHOR]

Randomness and fuzziness are two fundamental kinds of uncertain phenomena, which can be handled respectively by probability theory (sigma system) and possibility theory (max system). For many practical problems of information processing, random uncertainty may often co-exist with fuzzy uncertainty, which reminds us to look for a novel mechanism called sigma-max hybrid uncertainty inference. This mechanism can cope with randomness and fuzziness jointly and achieve a direct fusion of heterogeneous information modeled by probability or possibility. Specifically, we are interested in two typical forms of uncertainty inference, i.e., uncertainty update equation combining heterogeneous information as well as composition rule of heterogeneous relations. Such an objective is achieved by the adoption of joint description of a random variable and a fuzzy variable, i.e., hybrid distribution of probability and possibility, which lays the foundation for connecting the two uncertainty systems of probability and possibility, and results in the integrated sigma-max system. The hybrid distribution, other than joint probability (or possibility) distribution, has a couple of special normalization requirements that are order-dependent with respective to "addition" operation over random variable and "max' operation over fuzzy variable. The derived sigma-max inference is applied to target recognition, an example of which is simulated to demonstrate the merit of the proposed method over the classic Bayesian classifier when randomness and fuzziness are both involved. [ABSTRACT FROM AUTHOR]

In reliability engineering, the observations of the variables of interest are always limited due to cost or schedule constraints. Consequently, the epistemic uncertainty, which derives from lack of knowledge and information, plays a vital influence on the reliability evaluation. Belief reliability is a new reliability metric that takes the impact of epistemic uncertainty into consideration and belief reliability distribution is fundamental to belief reliability application. This paper develops a new method called graduation formula to construct belief reliability distribution with limited observations. The developed method constructs the belief reliability distribution by determining the corresponding belief degrees of the observations. An algorithm is designed for the graduation formula as it is a set of transcendental equations, which is difficult to determine the analytical solution. The developed method and the proposed algorithm are illustrated by two numerical examples to show their efficiency and future application. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronization of multiple memristive neural networks (MMNNs) under cyber-physical attacks through distributed event-triggered control. In the field of multi-agent dynamics, memristive neural network (MNN) is considered as a kind of switched systems because of its state-dependent parameters which can lead to the parameters mismatch during synchronization. This will increase the uncertainty of the system and affect the theoretical analysis. Also, neural network is considered as a typical nonlinear system. Therefore, the model studied in this paper is a nonlinear system with switching characteristics. In complex environments, MMNNs may receive mixed attacks, one of which is called cyber-physical attacks that may influence both communication links and MNN nodes to cause changes in topology and physical state. To tackle this issue, we construct a novel Lyapunov functional and use properties of M -matrix to get the criteria for synchronization of MMNNs under cyber-physical attacks. It is worth mentioning that the controllers in this paper are designed to be distributed under event-triggering conditions and Zeno behavior is also excluded. In addition, the algorithm of parameter selection is given to help designing the controllers. One example is given at the end of the paper to support our results. [ABSTRACT FROM AUTHOR]

In Dempster–Shafer evidence theory (DST)-based classifier design, the newly proposed evidence reasoning (ER) rule can be used as a multi-attribute classifier to combine multiple pieces of evidence generated from quantitative samples or qualitative knowledge of many attributes. Different from the classical Dempster's combination (DC) rule and its improved forms, ER rule definitely distinguishes the reliability and importance weight of evidence. The former reflects the ability of a single attribute or the corresponding evidence to give correct classification results whereas the latter clarifies the relative importance of evidence when it is combined with other pieces of evidence. Here how to determine the reliability factor is a key problem because it is the connection between the preceding evidence acquisition and the following evidence combination with the importance weights. Therefore, the main aim of this paper is to present a universal method for obtaining the reliability factor by quantifying the uncertainties of samples and the generated evidence. Experiential results on five popular benchmark databases taken from University of California Irvine (UCI) machine learning database show the improved classifier can give higher classification accuracy than the original ER-based classifier without considering uncertainty quantification and other classical or mainstream classifiers. [ABSTRACT FROM AUTHOR]

This paper introduces a special approach for the design of complex systems in early development stages accounting for lack-of-knowledge uncertainty. As complex systems have to be broken down into their components by a decoupling methodology, the presented work regards so-called box-shaped solution spaces as subsets of the total set of permissible designs not violating any design constraints. Hereby, the design variables are decoupled and their design intervals are maximized. Then, each aspect related to the corresponding interval can be studied independently in a subsequent development step by different stakeholders (design groups or designers). Especially in early design phases, the consideration of uncertainty is crucial; this is not so much related to aleatoric uncertainty as probability functions are often unavailable. More important and more difficult to handle is epistemic uncertainty, i.e., lack-of-knowledge uncertainty. Here, uncertainties which occur later in the development and the facts that the current design stage does not include smaller design features and that the available models represent only coarsely the later designs are important. This paper complements prior work by providing a complete methodology for relevant uncertainties. This includes uncertainties in controllable design variables as well as in uncontrollable parameters all captured by interval arithmetic. Furthermore, it extends existing worst-case approaches by best-case approaches. The user can now base design decisions on (a) a deterministic solution space without consideration of lack-of-knowledge uncertainties, (b) the same with consideration of uncertainties in uncontrollable parameters only or controllable variables only, or (c) the most complete approach where uncertainties in both controllable variables and uncontrollable parameters are considered. The corresponding scenarios are exemplified via examples from automotive engineering (design for crashworthiness). [ABSTRACT FROM AUTHOR]

By achieving their purposes through interactions with the physical world, Cyber-Physical Systems (CPS) pose new challenges in terms of dependability. Indeed, the evolution of the physical systems they control with transducers can be affected by surrounding physical processes over which they have no control and which may potentially hamper the achievement of their purposes. While it is illusory to hope for a comprehensive model of the physical environment at design time to anticipate and remove faults that may occur once these systems are deployed, it becomes necessary to evaluate their degree of effectiveness in vivo. In this paper, the degree of effectiveness is formally defined and generalized in the context of the measure theory. The measure is developed in the context of the Transferable Belief Model (TBM), an elaboration on the Dempster-Shafer Theory (DST) of evidence so as to handle epistemic and aleatory uncertainties respectively pertaining the users' expectations and the natural variability of the physical environment. The TBM is used in conjunction with the Input/Output Hidden Markov Modeling framework we denote by Ev-IOHMM to specify the expected evolution of the physical system controlled by the CPS and the tolerances towards uncertainties. The measure of effectiveness is then obtained from the forward algorithm, leveraging the conflict entailed by the successive combinations of the beliefs obtained from observations of the physical system and the beliefs corresponding to its expected evolution. The proposed approach is applied to autonomous vehicles and shows how the degree of effectiveness can be used for bench-marking their controller relative to the highway code speed limitations and passengers' well-being constraints, both modeled through an Ev-IOHMM. [ABSTRACT FROM AUTHOR]

Basic Uncertain Information (BUI) was proposed as an information granule that simultaneously accounts for both the value of the input and the certainty about that value. To aggregate BUI granules using Ordered Weighted Averaging (OWA) operators with bi-polar optimism–pessimism preferences, the ordered weighted averaging (BUIOWA) operators have been proposed recently. As weighted geometric mean is an alternative aggregation operator to weighted mean, the ordered weighted geometric averaging operator (OWGA) is the alternative to the OWA operator. Therefore, this study proposes basic uncertain information ordered weighted geometric averaging (BUIOWGA) operators to serve as the alternative aggregation choice to BUIOWA operators. Unlike BUIOWA operators, BUIOWGA operators have three different types, BUIOWGA type I, BUIOWGA type II, and BUIOWGA type III, with an increasing order relation. Several monotonicities, properties, and relations are proposed for the three different BUIOWGA operators and the BUIOWA operator. Finally, we present comparative analysis, numerical examples, and applications. [ABSTRACT FROM AUTHOR]

In this paper, fuzzy fault-tolerant tracking control is investigated for high-order nonstrict feedback nonlinear systems in fixed time interval. The gain fault and bias fault in actuator are considered for high-order nonstrict feedback nonlinear systems. Contrary to the existing results, an adaptive estimation tactic is proposed to estimate the coexisting uncertainties such that no priori knowledge is needed for the adaptive parameters, in spite of unknown virtual control gains, nonlinear uncertainties, time-varying disturbances and actuator faults. Based on this tactic, the unknown virtual control gains are slackened to completely unknown, which is more practical. Unlike the general fixed time control tactics, the singularity problem has been overthrew by using the inequality transformation strategy without destroying the control performance. The growth assumptions are removed and the complex nonstrict feedback structure is overcome with the support of fuzzy logic systems (FLS). Finally, two examples demonstrate the validity of the formulated method. [ABSTRACT FROM AUTHOR]

This paper proposes a general type of discontinuous activation functions (AFs) and studies the μ -stability of multiple equilibrium points (EPs) in delayed neural networks (DNNs). By judging 4 n algebraic inequalities and the nonsingularity of an M -matrix, DNNs with the general discontinuous AFs can be shown to have 5 n EPs, therein 3 n EPs are locally μ -stable. Moreover, these 3 n EPs are located at the points of continuity of the AF. Compared with the existing general continuous AF, DNNs with the general discontinuous AF can have more total/stable EPs. Hence, DNNs with the general discontinuous AF could store a much larger number of memory patterns if they are applied to associative memory. In addition, the attraction basin (AB) of each stable EP in DNNs is estimated. Two numerical examples are shown to testify the validity of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, synchronization control of shunting inhibitory cellular neural networks with multiple proportional delays is studied. Firstly, a controller is designed to ensure L p synchronization between the response and drive shunting inhibitory cellular neural networks. Then, a method based on system solutions is proposed to obtain L p synchronization criteria. On the one hand, the synchronization criteria obtained by this method only contain some simple inequalities, and hence the calculation amount is greatly reduced. On the other hand, the method does not require the establishment of any Lyapunov–Krasovskii functional. The obtained L p synchronization criteria are simpler and can be tested by standard software tools. Finally, a numerical example is given to illustrate the superiority of the proposed L p synchronization criteria. It is worth emphasizing that the L p synchronization control problem is analyzed for the first time in this paper. [ABSTRACT FROM AUTHOR]

Complex evidence theory (CET), as a generalized D-S evidence theory, has the ability to express uncertainty in the complex field. CET has been applied in many information fields. One of the key issues in CET is uncertainty measurement of the complex basic belief assignment (CBBA). Previous research on uncertainty measures usually focused on classical probability theories such as belief function assignments, sets, and probability. However, in recent years, research on quantum information has provided a novel thinking direction for the measurement of uncertainty. In this paper, a novel quantum representation of CBBA is proposed based on the density matrix. In addition, a novel quantum belief entropy based on CBBA has been proposed to describe the discord part of uncertainty. In the quantum belief entropy, a concept of quantum interference is introduced to express the quantum effect of element interaction. Furthermore, some properties are analyzed and explained in the paper, and some numerical examples are given to help illustrate the novel measurement of uncertainty. [ABSTRACT FROM AUTHOR]

Various software reliability growth models (SRGMs) have been developed to evaluate software reliability. Since software faults are caused by bugs in the logic of the code, which are introduced due to human errors, software faults embody lots of epistemic uncertainties. Under the framework of uncertainty theory, a software belief reliability growth model (SBRGM) was proposed. Actually, during software testing fault detection rate function may show multiple phases due to changes of testing strategies and resources allocation. Thus, fault detection rate function may be discontinuous at some time known as the change point. Noting that the previous SBRGM did not consider the change point, this paper construct a new SBRGM incorporating change point, named CPSBRGM. Based on the new proposed model, reliability for software is evaluated under the framework of belief reliability theory. Method to estimate unknown parameters in the proposed model is also provided. The new proposed model is validated on three datasets and compared with the previous SBRGM. Results show that the new proposed model can clearly distinguish the change point during software testing, and is more in line with the actual software test situation than previous model without considering change points. • This paper construct a new SBRGM incorporating change point. • Reliability for software is evaluated based on belief reliability theory. • The new proposed model is validated on three datasets. [ABSTRACT FROM AUTHOR]

Among Bayesian methods, Monte Carlo dropout provides principled tools for evaluating the epistemic uncertainty of neural networks. Its popularity recently led to seminal works that proposed activating the dropout layers only during inference for evaluating epistemic uncertainty. This approach, which we call dropout injection , provides clear benefits over its traditional counterpart (which we call embedded dropout) since it allows one to obtain a post hoc uncertainty measure for any existing network previously trained without dropout, avoiding an additional, time-consuming training process. Unfortunately, no previous work thoroughly analyzed injected dropout and compared it with embedded dropout; therefore, we provide a first comprehensive investigation, focusing on regression problems. We show that the effectiveness of dropout injection strongly relies on a suitable scaling of the corresponding uncertainty measure, and propose an alternative method to implement it. We also considered the trade-off between negative log-likelihood and calibration error as a function of the scale factor. Experimental results on benchmark data sets from several regression tasks, including crowd counting, support our claim that dropout injection can effectively behave as a competitive post hoc alternative to embedded dropout. • We analyze "injected" Monte Carlo dropout for post hoc uncertainty quantification. • Injected dropout requires a suitable rescaling of the uncertainty measure. • We show that acting on the scaling factor can also improve calibration. • Experiments on UCI data sets and crowd counting benchmarks support our findings. [ABSTRACT FROM AUTHOR]

Target area search in the standard Bayesian information-theoretic formulation consists of a repetitive cycle of sensing, recursive Bayesian estimation and motion control. The paper formulates the problem of target area search in the framework of imprecise probability theory using probability sets. The rationale is that the measurement model parameters, such as the probability of detection or the probability of false alarm, are rarely known as precise values. Instead, we adopt probability intervals to express beliefs. The paper formulates the Bayes-like state estimation equations as well as the reward function for motion control. The reward function is based on an uncertainty measure which takes into account both randomness and epistemic uncertainty. [ABSTRACT FROM AUTHOR]

This study proposes a methodology for developing deterioration models to estimate the remaining lifetime of a system using physics-informed learning. The approach consists of combining physical knowledge about the system with a set of data obtained from similar systems that have failed in the past to build a set of constraints on the evolution over time of the state of health of the system. The data consists of partial measurements of the system variables, taken from its commissioning to the present. The physical knowledge used comprises a set of differential equations that approximate the dynamics and aging of the system. In contrast to other studies, the physical model is not assumed to be accurate, but is considered to be an approximation of reality. Constraints on the temporal evolution of the state of health derived from this physical knowledge take into account its imprecision and consist of possibility distributions. In this study, the max-max, max-min and min-max regret principles are applied to extract the time evolution of the deterioration rate that best fits the constraints. The effectiveness of the proposed algorithm is evaluated by means of a comparative empirical analysis in different use cases, and the situations in which informed learning improves on purely data-driven algorithms are analyzed. [ABSTRACT FROM AUTHOR]

Distributional reinforcement learning (RL) differs from conventional RL, which only estimates the expectation of the return. Distributional RL considers the return as a random variable and estimates its distribution. The return distribution can provide more information than its expectation in conventional RL. Thus, distributional RL has been widely studied. However, very few previous works take full advantage of the learned distribution to improve distributional RL. This paper improves distributional RL by introducing epistemic and aleatoric uncertainty estimation. First, an epistemic and aleatoric uncertainty estimation method is introduced using deep ensembles and the learned value distribution. Next, we improve the exploration efficiency of fully parametrized quantile function (FQF) for distributional RL and obtain a FQF-U (uncertainty) algorithm. Then, to overcome the problem that distributional RL cannot operate over continuous control tasks, we propose an epistemic-uncertainty-based distributional soft actor-critic algorithm with an adaptive risk-averse and risk-seeking policy. Finally, experimental results show that our algorithms outperform the baselines in Atari games and Multi-joint dynamics with contact (MuJoCo) environments. [ABSTRACT FROM AUTHOR]

Handling the uncertainty of information sources is a key issue in parameter identification. In this work, we address this issue using the theory of belief functions. First, measurement information is described through likelihood-based belief functions, and prior information is represented by an arbitrary belief function. Second, both belief functions are combined by Dempster's rule using point-cloud representation of focal sets and Monte Carlo simulation. Lastly, to summarize the combined belief function, we propose to find the minimal-area region in the parameter space, whose belief and plausibility values exceed given thresholds. As compared to Bayesian inference, this approach is more flexible, as it allows us to specify weak prior information. Experimental results show that it is also more robust than Bayesian inference to unreliable prior information. [ABSTRACT FROM AUTHOR]

Prior research on the resilience of critical infrastructure usually utilizes the network model to characterize the structure of the components so that a quantitative representation of resilience can be obtained. Particularly, network component importance is addressed to express its significance in shaping the resilience performance of the whole system. Due to the intrinsic complexity of the problem, some idealized assumptions are exerted on the resilience-optimization problem to find partial solutions. This paper seeks to exploit the dynamic aspect of system resilience, i.e., the scheduling problem of link recovery in the post-disruption phase. The aim is to analyze the recovery strategy of the system with more practical assumptions, especially inhomogeneous time cost among links. In view of this, the presented work translates the resilience-maximization recovery plan into the dynamic decisionmaking of runtime recovery option. A heuristic scheme is devised to treat the core problem of link selection in an ongoing style. Through Monte Carlo simulation, the link recovery order rendered by the proposed scheme demonstrates excellent resilience performance as well as accommodation with uncertainty caused by epistemic knowledge. [ABSTRACT FROM AUTHOR]

Belief reliability is a newly developed, model-based reliability metric which considers both what we know (expressed as reliability models) and what we don’t know (expressed as epistemic uncertainty in the reliability models) about the reliability. In this paper, we show that due to the explicit representation of epistemic uncertainty, belief reliability should not be regarded as a probability measure; rather, it should be treated as an uncertain measure in uncertainty theory. A minimal cut set-based method is developed to calculate the belief reliability of coherent systems. A numerical algorithm is, then, presented for belief reliability analysis based on fault tree models. The results of application show that the developed methods require less computations than the structure function-based method of classical reliability theory. [ABSTRACT FROM AUTHOR]

An uncertainty compiler is a tool that automatically translates original computer source code lacking explicit uncertainty quantification into code containing appropriate uncertainty representations and uncertainty propagation algorithms. It handles the specifications of input uncertainties, and inserts calls to intrusive uncertainty quantification algorithms. In theory, one could create an uncertainty compiler for any scientific programming language. The uncertainty compiler can apply intrusive uncertainty propagation methods to codes or parts of codes and, therefore, more comprehensively and flexibly address epistemic and aleatory uncertainties. This paper explores the concept and the practicalities of creating such a compiler. [ABSTRACT FROM AUTHOR]

We consider a wide range of measures of uncertainty that have been proposed within the Dempster–Shafer evidence theory. All these measures aim to quantify the uncertainty associated with a given basic probability assignment. As a preliminary step, we offer a study of the literature, which shows a recent resurgence of interest in the quantification of uncertainty in the evidence theory. Then, we compare a number of uncertainty measures by means of numerical simulations and analyze their similarities and differences using rank correlation coefficients, hierarchical clustering, and centrality analysis. The results show that uncertainty measures with similar formulations do not necessarily have similar numerical properties, and some original results are obtained. In particular, we demonstrate that numerical studies on uncertainty measures are necessary to obtain more insight and to enhance the interpretability of the values returned by the measures. [ABSTRACT FROM AUTHOR]

Sydney, Australia, Australia and New Zealand, Health and Medicine, Mental Health, Psychological, Psychopathology Keywords: Sydney; Australia; Australia and New Zealand; Health and Medicine; Mental Health; Psychological; Psychopathology EN Sydney Australia Australia and New Zealand Health and Medicine Mental Health Psychological Psychopathology 680 680 1 04/03/23 20230407 NES 230407 2023 APR 3 (NewsRx) -- By a News Reporter-Staff News Editor at Mental Health Weekly Digest -- Researchers detail new data in Health and Medicine. [Extracted from the article]

Modeling complex dynamical systems from heterogeneous pieces of knowledge varying in precision and reliability is a challenging task. We propose the combination of dynamical Bayesian networks and of imprecise probabilities to solve it. In order to limit the computational burden and to make interpretation easier, we also propose to encode pieces of (numerical) knowledge as probability intervals, which are then used in an imprecise Dirichlet model to update our knowledge. The idea is to obtain a model flexible enough so that it can easily cope with different uncertainties (i.e., stochastic and epistemic), integrate new pieces of knowledge as they arrive and be of limited computational complexity. [ABSTRACT FROM AUTHOR]

Bayesian inference under a set of priors, called robust Bayesian analysis, allows for estimation of parameters within a model and quantification of epistemic uncertainty in quantities of interest by bounded (or imprecise) probability. Iterative importance sampling can be used to estimate bounds on the quantity of interest by optimizing over the set of priors. A method for iterative importance sampling when the robust Bayesian inference relies on Markov chain Monte Carlo (MCMC) sampling is proposed. To accommodate the MCMC sampling in iterative importance sampling, a new expression for the effective sample size of the importance sampling is derived, which accounts for the correlation in the MCMC samples. To illustrate the proposed method for robust Bayesian analysis, iterative importance sampling with MCMC sampling is applied to estimate the lower bound of the overall effect in a previously published meta-analysis with a random effects model. The performance of the method compared to a grid search method and under different degrees of prior-data conflict is also explored. [ABSTRACT FROM AUTHOR]

This paper proposes algorithms to construct fuzzy probabilities to represent or model the mixed aleatory and epistemic uncertainty in a limited-size ensemble. Specifically, we discuss the possible requirements for the fuzzy probabilities in order to model the mixed types of uncertainty, and propose algorithms to construct fuzzy probabilities for both independent and dependent datasets. The effectiveness of the proposed algorithms is demonstrated using one-dimensional and high-dimensional examples. After that, we apply the proposed uncertainty representation technique to isocontour extraction, and demonstrate its applicability using examples with both structured and unstructured meshes. [ABSTRACT FROM AUTHOR]

Evidence theory has a strong ability to handle the epistemic uncertainty, based on which the uncertain parameters with limited information can be conveniently treated. In this paper, a numerical method is developed to predict the exterior acoustic field with epistemic uncertainties based on evidence theory. In order to alleviate the computational cost, the interval analysis technique is adopted to acquire the approximate frequency response amplitude bounds for each focal element, and the corresponding formulations of interval perturbation analysis for exterior acoustic field prediction are deduced. Inspired by the probability theory, the mean value, standard deviation and cumulative distribution are used to describe the distribution characteristics of evidence variables. Two numerical examples are given to illustrate the feasibility and effectiveness of the present method. [ABSTRACT FROM AUTHOR]

The epistemic uncertainty in the free coefficients of two popular Reynolds-averaged Navier–Stokes (RANS) eddy-viscosity turbulence models is quantified. In particular, the Launder–Sharma low-Reynolds K - ε and the Menter K - ω SST models are considered. The free coefficients present in turbulence models are retrieved from some properties of benchmark turbulent flows, viz. the energy power law exponent for decaying homogeneous isotropic turbulence, the value of the Von Karman constant, the turbulence production over dissipation rate estimated in the asymptotic regime of a homogeneous shear flow and the dimensionless turbulent kinetic energy in the logarithmic layer. The values presented in literature for these quantities, obtained from experiments or direct numerical simulations (DNS), show a significant dispersion, indicating the presence of an epistemic uncertainty. Starting from the data collected in literature, realistic continuous probability density functions of the basic flow properties, and hence of the RANS model coefficients, are obtained through generalized Polynomial Chaos (gPC). The impact of this uncertainty on the results of RANS simulations of the turbulent channel flow is then investigated for different Reynolds numbers through comparison with DNS data. The solution over the continuous multi-dimensional uncertainty space of the considered random variables is reconstructed through the application of a surrogate model (response surface) obtained by means of gPC. In general, the predictions of the K - ω SST model are less sensitive to the uncertainty in the model parameters than those of the low-Reynolds K - ε model. For both models and for any combination of the coefficients, the predictions of the turbulent kinetic energy profile are not satisfactory, while low errors can be obtained for friction and mean velocity. Evaluation of optimal values of free parameters is a Data Assimilation (DA) problem. An example of the use of the gPC response surface for an efficient calibration of the model coefficients in order to minimize the error in the prediction of these two last variables is provided. The result accuracy estimated through the gPC surrogate model well agrees with that obtained in deterministic simulations carried out with the calibrated values of the model constants. [ABSTRACT FROM AUTHOR]