Uncertainty Distribution Research Articles

Some Properties of Lognormal Uncertain Variables

Uncertainty theory, as a mathematical tool to rationally handle degrees of belief of human beings, has been widely applied in science and engineering. As a basic component of uncertainty theory, uncertainty distribution is a carrier to describe the characterization of an uncertain variable. Moreover, inverse uncertainty distribution provides an easy way to calculate the functions of uncertain variables as well as their expected value. This paper mainly provides the formulas to calculate the expected value, variance, moments and entropy of lognormal uncertain variable. Besides, some operational laws of lognormal uncertain variables are proved.

Quantifying aquifer heterogeneity using superparamagnetic DNA particles

Identifying and determining hydraulic parameters of physically heterogeneous aquifers is pivotal for flow field analysis, contaminant migration and risk assessment. In this research, we applied a novel uniquely sequenced DNA tagged superparamagnetic silica microparticles (SiDNAmag) to quantify hydraulic parameters and associated uncertainties of a heterogeneous sand tank. In the sand tank with lens shaped heterogeneity, we conducted three sets of multi – point injection experiments in unconsolidated (1) homogeneous (zone 0), (2) heterogeneous with a no-conductivity-zone (zone 1), and (3) heterogeneous with a high-conductive-zone (zone 2). From the breakthrough curves (BTC), we estimated the parameters distributions of hydraulic conductivity (k), effective porosity (ne), longitudinal dispersivity (αL), transverse vertical (αTV), and transverse horizontal dispersivities (αTH) applying Monte Carlo simulation approach for BTC fitting. The estimated parameters and associated uncertainties for each of the heterogeneous sections were further statistically compared (distribution non-specific Mann Whitney U test) these parameter distributions with parameter distributions estimated from the conservative salt tracer. While the time of arrival and time to peak concentration of SiDNAmag and salt in effluent were comparable, peak concentration of SiDNAmag was 1–3 log reduced as compared to the salt tracer due to first order kinetic attachment. Nonetheless, the parameters and associated uncertainty distributions (5 %–95 %) of K, ne, αL, αTV, and αTH, determined from SiDNAmag BTCs were statistically equivalent to the salt tracer in all three experiment systems. Through our experimental and modelling approach, our work demonstrated that in a coarse to very coarse grain sand medium, with lens shaped heterogeneity, the uniquely sequenced SiDNAmag were a promising tool to identify heterogeneity and determine hydraulic parameters and associated uncertainty distributions.

Derivation of Uncertainty Distributions for Channel Flow Rate and Fuel Critical Heat Flux Predictions for Best-Estimate Plus Uncertainty Analysis of Slow Loss-of–Reactor Power Regulation Accidents in CANDU Stations

Derivation of Uncertainty Distributions for Channel Flow Rate and Fuel Critical Heat Flux Predictions for Best-Estimate Plus Uncertainty Analysis of Slow Loss-of–Reactor Power Regulation Accidents in CANDU Stations

Selection of aerodynamic characteristics and engine parameters of a maneuverable aircraft under epistemic uncertainty

At the preliminary stage of aircraft design, it is usually required to solve the problem of insufficient initial data for applying traditional algoristic-type mathematical programming models. In many cases, numerous input parameters cannot be accurately specified at the time of making design decisions. If the inaccuracy of parameters is not taken into account, the actual values of target functions may differ significantly from the calculated ones when solving optimization problems. In this regard, the issue of current interest is the development of algorithms to improve the reliability of design decisions under conditions of epistemological uncertainty when experts engage in the formation of initial data. The paper considers the problem of selecting aerodynamic characteristics and engine parameters of maneuverable aircraft under conditions of uncertainty associated with inaccuracy of expert data. The applied problem under consideration is further complicated by the necessity to include “black box” models in the algorithms being developed. The paper proposes algorithms that apply the uncertainty theory together with “black box” models that implement optimization calculation techniques derived from previous engineering practice of aircraft design. Using these algorithms, experts are able to set uncertain parameters whereby the lack of data is factored in using uncertainty distribution functions. In cases of monotonicity of uncertain parameters in target functions, application of the uncertainty theory provides a significant reduction in computational costs compared to the method of statistical modeling in optimization calculations. The paper presents the results of computational studies of the developed algorithms. A genetic algorithm (mathematical optimization solver) is used to optimize the search for design solutions. Pareto frontiers are obtained for different confidence levels enabling to make design decisions including values of aerodynamic characteristics and engine parameters of maneuverable aircraft.

Assessment of earthquake location uncertainties for the design of local seismic networks

The ability to estimate earthquake source locations, along with the appraisal of relevant uncertainties, is paramount in monitoring both natural and human-induced micro-seismicity. For this purpose, a monitoring network must be designed to minimize the location errors introduced by geometrically unbalanced networks. In this study, we first review different sources of errors relevant to the localization of seismic events, how they propagate through localization algorithms, and their impact on outcomes. We then propose a quantitative method, based on a Monte Carlo approach, to estimate the uncertainty in earthquake locations that is suited to the design, optimization, and assessment of the performance of a local seismic monitoring network. To illustrate the performance of the proposed approach, we analyzed the distribution of the localization uncertainties and their related dispersion for a highly dense grid of theoretical hypocenters in both the horizontal and vertical directions using an actual monitoring network layout. The results expand, quantitatively, the qualitative indications derived from purely geometrical parameters (azimuthal gap (AG)) and classical detectability maps. The proposed method enables the systematic design, optimization, and evaluation of local seismic monitoring networks, enhancing monitoring accuracy in areas proximal to hydrocarbon production, geothermal fields, underground natural gas storage, and other subsurface activities. This approach aids in the accurate estimation of earthquake source locations and their associated uncertainties, which are crucial for assessing and mitigating seismic risks, thereby enabling the implementation of proactive measures to minimize potential hazards. From an operational perspective, reliably estimating location accuracy is crucial for evaluating the position of seismogenic sources and assessing possible links between well activities and the onset of seismicity.

Time series prediction method for multi-source observation data

Traditional time series analysis focuses on modeling and predicting time series data obtained from a single observation source. However, in a confrontational environment, one party often creates biased data to interfere with the other party's predictions. To mitigate the observation error inherent in single-source data, there is a growing emphasis on the importance of utilizing and studying multi-source observation data, which motivates this paper to propose methods for analyzing and predicting this kind of data. First, this paper proves that the accuracy of the estimation can be improved by introducing multiple sets of time-invariant data with bias. Subsequently, when this approach is extended to include time-varying data, these findings continue to hold. For time-varying data with bias, this paper proposes a comprehensive prediction procedure to provide the uncertainty distribution for the forthcoming moment. Finally, three examples are proposed to illustrate the effectiveness and efficiency of the methods.

Estimating Unknown Parameters and Disturbance Term in Uncertain Regression Models by the Principle of Least Squares

In the field of statistics, uncertain regression analysis occupies an important position. It can thoroughly analyze data sets contained in complex uncertainties, aiming to quantify and reveal the intricate relationships between variables. It is worth noting that the traditional least squares method only takes into account the reduction in the deviations between predictions and observations, and fails to fully consider the inherent characteristics of the correlation uncertainty distributions under the uncertain regression framework. In light of this, this paper constructs a statistical invariant with symmetric uncertainty distribution based on the observations and the disturbance term. It also proposes the least squares estimation of unknown parameters and disturbance term in the uncertain regression model based on the least squares principle and, combined with the mathematical properties of the normal uncertainty distribution, gives a numerical algorithm for solving specific estimates. Finally, in order to verify the effectiveness of the least squares estimation method proposed in this paper, we also design two numerical examples and an empirical study of forecasting of electrical power output.

Review on Location of Fresh Cold Chain Logistics Distribution Center

This paper reviews the research status, existing problems and challenges, and future research directions of the location of fresh cold chain logistics distribution centers. The research background is based on factors such as the development of the fresh product market, the technological progress of cold chain logistics, the requirements of environmental protection and sustainable development, and the intensification of market competition. The significance of site selection includes improving transportation efficiency, reducing costs, improving customer satisfaction, optimizing supply chain networks, and achieving environmental sustainability.The former focuses on low-carbon, demand uncertainty, and competitive distribution center location, while the latter focuses on the new retail environment and cold chain distribution. The review of relevant literature points out that some progress has been made in the research, but there are challenges such as market demand uncertainty, incomplete data and limited model applicability.Future research directions include the location model of cold chain logistics distribution center based on big data, the location model considering sustainable development factors, and the location method of cold chain logistics distribution center integrating multi-index evaluation.In the conclusion, it is pointed out that in the past, the time window and the overall logistics network were rarely used as research evaluation indicators in the site selection problems, and the cost of reverse logistics and closed-loop supply chain was rarely considered. In the prospect part, it is proposed that in the future, we should pay attention to the problems of reverse logistics and closed-loop supply chain in the distribution of fresh agricultural products, consider the multi-objective optimization of low-carbon cold chain logistics network in different policies and fields, and combine full simulation technology and optimization technology to realize the system optimization research.

Average Waiting Time of Customers in Single-Server Uncertain Queueing System

Uncertain queueing system is an important research object in the field of operations research, and widely exists in logistics, production, insurance and other fields. In order to further analyze the performance of the single-service uncertain queueing system, this paper derives the generalized inverse uncertainty distributions of the waiting times of customers, and provides the calculation formulas for the average waiting times of customers on this basis. Finally, this paper also provides two examples to illustrate the generalized inverse uncertainty distributions of waiting times and the calculation formulas of the average waiting times under specific uncertainty distributions.

Negative cumulative extropy of uncertain variables with applications

Recently, a measure of uncertainty termed by negative cumulative extropy (NCEX) is proposed by Tahmasebi and Toomaj (2022). It is a flexible extension of extropy measure which was proposed by Lad, Sanfilippo, and Agro (2015). To measure the uncertainty of uncertain variables, in this article, we propose the concept of NCEX through uncertainty distributions. Some properties of NCEX are derived, and some practical examples of uncertain variables are given. Several basic theorems are proposed. A formula of cross-extropy is defined via inverse uncertainty distributions. We also delve into a pattern recognition problem to highlight the importance of cross-extropy. Finally, applications to portfolio selection and signal processing are presented.

Energy-related uncertainty shocks and inflation dynamics in the U.S: A multivariate quantile-on-quantile regression approach

Existing literature suggests that uncertainty shocks can propagate like aggregate demand shocks or aggregate supply shocks. By way of extension, this study investigates the effect of energy-related uncertainty shocks on U.S. inflation while incorporating the effect of industrial production and interest rate uncertainty shocks. Using a multivariate quantile-on-quantile regression for the period 2000:M6 to 2019:M7, the findings reveal that energy-related uncertainty shocks amplify inflation by manifesting as cost-push shocks with a stronger connection emerging in quantiles slightly above the median quantile distribution of energy-related uncertainty. Although industrial production positively drives inflation, its effect is observed less around median quantiles of inflation than in the lower and upper quantiles. Furthermore, the effect of interest rate uncertainty is negative and stronger in quantiles around the median of inflation, suggesting that interest rate uncertainty behaves like aggregate demand shocks. Based on these findings, policy implications are offered.

Collaborative scheduling and benefit allocation for waste-to-energy, hydrogen storage, and power-to-gas under uncertainties with temporal relevance

Waste-to-energy (WTE) is a technology that converts inexhaustible waste into electricity, thus significantly alleviating energy crisis. Integrating hydrogen storage into WTE provides an effective way to store and utilize surplus electricity from WTE on-site (by producing hydrogen). Additionally, integrating power-to-gas (P2G) into WTE provides an effective way to reduce CO2 emission from WTE on-site (by producing natural gas). To this end, a novel waste-driven renewable energy system (WRES), which is consisted of WTE, hydrogen storage, and P2G, has been proposed. However, the uncertain waste supply and electrical load markedly interfere with WRES operation. Meanwhile, when WTE, hydrogen storage, and P2G belong to different agents, the collaborative benefit from WRES operation should be rationally allocated among agents for system sustainability. This paper endeavors to achieve WRES scheduling and collaborative benefit allocation for WTE, hydrogen storage, and P2G under uncertainties. Firstly, a temporal relevance based distributionally robust optimization model is proposed for WRES scheduling under uncertainties, in which the possible range of the joint distribution for uncertainties is depicted by data covariance matrices involved ambiguity set. Secondly, collaborative benefit is allocated according to WTE, hydrogen storage, and P2G contributions, in which Gauss-Legendre quadrature formula is integrated with Aumann-Shapley value method to reduce calculation complexity. Finally, simulation results show that 1) the proposed scheduling model guarantees the economic and stable operation of WRES under uncertainties. 2) after considering the temporal relevance, WRES operation benefit is 8.35 % higher, which indicates that the proposed scheduling model has superiority in decision conservatism by introducing temporal relevance to remove impractical distributions in ambiguity set. 3) the proposed allocation model rationally distributes the collaborative benefit according to contributions, and presents lower calculation complexity, e.g., the calculation time is 95.52 % lower than the Shapely value method. This paper provides policy insights to promote widespread application and sustainable operation of WRES.

Stochastic Optimization of Onboard Photovoltaic Hybrid Power System Considering Environmental Uncertainties

Environmental uncertainties present a significant challenge in the design of onboard photovoltaic hybrid power systems (PV-HPS), a pivotal decarbonization technology garnering widespread attention in the shipping industry. Neglecting environmental uncertainties associated with photovoltaic (PV) output and hull resistance can lead to suboptimal solutions. To address this issue, this paper proposes a stochastic optimization method for PV-HPS, aiming to minimize greenhouse gas (GHG) emissions and lifecycle costs. Copula functions are employed to establish joint distributions of uncertainties in solar irradiance, ambient temperature, significant wave height, and wave period. Monte Carlo simulation, the bi-bin method, and the multi-objective particle swarm optimization (MOPSO) algorithm are utilized for scenario generation, scenario reduction, and design space exploration. The efficacy of the proposed method is demonstrated through a case study involving an unmanned ship. Additionally, deterministic optimization and two partial stochastic optimizations are conducted to underscore the importance of simultaneously considering environmental uncertainties related to power sources and hull resistance. The results affirm the proposed approach’s capability to reduce GHG emissions and lifecycle costs. A sensitivity analysis of bin number is performed to investigate the tradeoff between optimality and computation time.

Projecting Future Tropical Cyclone Frequencies by Combining Uncertain Empirical Estimates of Baseline Frequencies with Climate Model Estimates of Change

Various studies have given projections for how frequencies of tropical cyclones (TCs) might change under climate change. In this study, we combine a set of such projections with uncertain estimates of frequencies of tropical cyclones in a baseline climate to produce probabilistic projections of tropical cyclone frequencies for the next 50 years. The novel aspect of our projections is the inclusion of baseline uncertainty. We consider frequencies of Saffir-Simpson Hurricane Wind Scale category 0-5 and category 4-5 storms for the six major tropical cyclone basins. We find that in several cases the means and medians of the frequency of category 0-5 storms are projected to decrease, but that increasing uncertainty nevertheless leads to increases in the likelihood of high rates of TC activity in the future. We then show how the variance of the distributions of uncertainty can be decomposed into terms due to baseline uncertainty and climate change uncertainty. We use this decomposition to determine the year in which climate change uncertainty overtakes baseline uncertainty. Over the next 20 years we find that in some basins baseline uncertainty dominates and in other basins climate change uncertainty dominates. We are able to relate these variations between basins to the coefficients of variation of the baseline and climate change inputs. Finally, we quantify how climate change affects estimates of near-term TC frequency, including the extent to which it increases the uncertainty. These results help us understand two of the major sources of uncertainty in estimates of tropical cyclone behaviour now and in the future, and the role climate change is playing in changing that behaviour. They also demonstrate how estimates of TC change can be combined with observations to create projections of future TC climate.

Hiddenly degrading performance prognosis based on recursive model incorporating double-layer rolling optimization strategy

An integrated and adaptive prognostic framework is proposed for hiddenly degrading actuator in the closed-loop system. Furthermore, the dual influence of degradation progress and operation time is considered in the established augmented model. It is important to obtain accurate and real-time distribution of degradation information under different degradation progress. Firstly, the expectation and variance of hidden index, unknown operation time parameter and degradation progress parameter are evaluated by designing a double-layer rolling optimization strategy. Then, the uncertainty distribution of degradation model is iteratively derived by employing Bayesian theorem. Finally, the distribution of remaining useful life (RUL) is calculated based on available distribution of degradation model and states. The effectiveness of proposed algorithm is demonstrated by a mold model of continuous casting driven by servo motor.

Least Squares Estimation of Multifactor Uncertain Differential Equations with Applications to the Stock Market

Multifactor uncertain differential equations are powerful tools for studying dynamic systems under multi-source noise. A key challenge in this study is how to accurately estimate unknown parameters based on the framework of uncertainty theory in multi-source noise environments. To address this core problem, this paper innovatively proposes a least-squares estimation method. The essence of this method lies in constructing statistical invariants with a symmetric uncertainty distribution based on observational data and determining specific parameters by minimizing the distance between the population distribution and the empirical distribution of the statistical invariant. Additionally, two numerical examples are provided to help readers better understand the practical operation and effectiveness of this method. In addition, we also provide a case study of JD.com’s stock prices to illustrate the advantages of the method proposed in this paper, which not only provides a new idea and method for addressing the problem of dynamic system parameter estimation but also provides a new perspective and tool for research and application in related fields.

Influences of Space Weather Forecasting Uncertainty on Satellite Conjunction Assessment

AbstractA significant increase in the number of anthropogenic objects in Earth orbit has necessitated the development of satellite conjunction assessment and collision avoidance capabilities for new spacecraft. Neutral mass density variability in the thermosphere, driven by enhanced geomagnetic activity and solar EUV absorption, is a major source of satellite propagation error. This work investigates the impacts of space weather driver forecasting uncertainty on satellite drag and collision avoidance maneuver decision‐making. Since most operational space weather driver forecasts do not offer an uncertainty assessment, the satellite operator community is left to make dangerous assumptions about the trustworthiness of the forecast models they use to perform satellite state propagation. Climatological persistence‐based forecast models are developed for F10.7 and Kp. These models accurately capture the heteroscedastic and, at times, highly non‐Gaussian uncertainty distribution on forecasts of the drivers of interest. A set of realistic satellite conjunction scenarios is simulated to demonstrate the contributions of space weather driver forecast uncertainty on the probability of collision and maneuver decisions. Improved driver forecasts, especially forecasts of F10.7, are demonstrated to be very useful for enabling durable maneuver decisions with additional lead time (up to 24 hr for the period examined), though the improvement depends on the specific conjunction scenario of interest.

What Can Measured Beliefs Tell Us About Monetary Non-Neutrality?

This paper studies how measured beliefs can be used to identify monetary non-neutrality. In a general equilibrium model with both nominal rigidities and endogenous information acquisition, we analytically characterize firms’ optimal dynamic information policies and how their beliefs affect monetary non-neutrality. We then show that data on the cross-sectional distributions of uncertainty and pricing durations are both necessary and sufficient to identify monetary non-neutrality. Finally, implementing our approach in New Zealand survey data, we find that informational frictions approximately double monetary non-neutrality and endogeneity of information is important: models with exogenous information would overstate monetary non-neutrality by approximately 50%.

The impact of the proposed revised Australia's microbiological monitoring programme for beef and sheep meat exported to the EU.

The European Commission asks scientific and technical assistance from EFSA to determine the impact of the revision of the Australian monitoring programme on its ability to detect microbiological contamination. Considering that, in 2010, the European Commission determined the current Australian monitoring programme to be equivalent to the EU requirements for microbiological monitoring further to an EFSA scientific assessment, the current and proposed programmes were described and the total number of alerts was compared using a probabilistic modelling approach. In the current programme, only beef and sheep carcasses are monitored using three-class moving window sampling plans, while in the proposed programme, carcass, bulk meat, primal and offal are monitored using four two-class sampling plans and Salmonella testing is excluded. The models revealed that the current programme provides a higher number of alerts for APC, while the proposed monitoring programme provides a higher number of alerts for E. coli. For APC and E. coli combined, the mean, 5th and 95th centiles of the uncertainty distribution of the total number of alerts in the current and the proposed monitoring programme are 201 [179, 227] and 172 [149, 194] for beef, and 199 [175, 222] and 2897 [2795, 3008] for sheep, respectively. For Salmonella, there are no alerts for the proposed programme since sampling is excluded while for the current programme, the estimated mean, 5th and 95th centiles of the uncertainty distribution of the number of alerts for a 5-year period were 143 [126, 144] for heifer/steer, 1.6 [0, 4] for cow/bull and 0 [0, 0] for lamb/sheep. Overall, for APC and E. coli, the estimated total number of alerts was similar (beef) or higher (sheep) for the proposed compared to the current programme. In contrast, Salmonella sampling is excluded from the proposed programme and thus cannot detect the number of current alerts.

Robust Bayesian target vector optimization for multi-stage manufacturing processes

This research focuses on optimizing multi-stage manufacturing processes using Bayesian optimization (BO) with a robust Expected Improvement (EI) acquisition function. The aim is to optimize towards pre-selected target vectors, not to just minimize or maximize a function. To achieve this, we minimize the Euclidean distance between the actual and target output vectors, which requires transforming the Gaussian surrogate model posterior distribution into a non-central χ2(NCχ2) distribution. Furthermore, the distance measure additionally uses aleatoric uncertainty estimates of the actual output vectors to achieve robustness. We use a cascaded method that also considers the optimization results of intermediate stages, whereby optimization results are propagated from the last stage towards the first stage in each optimization iteration. By considering intermediate process outputs and aleatoric effects, our approach provides a robust optimization method for multi-stage manufacturing processes. To validate our method and to evaluate its properties, we use two artificial use cases. Moreover, we evaluate our approach in an industrial multi-stage forging process for the manufacturing of a nickel basis superalloy turbine disk, where involved stages are represented by corresponding 2D finite element method (FEM) DEFORM simulations. Evaluation suggests that our approach is superior in optimizing multi-stage manufacturing processes by considering all stage outcomes, robust distance measures, and the use of appropriate uncertainty distributions.