Uncertainty Modeling Techniques Research Articles

A novel approach for multi-objective linear programming model under spherical fuzzy environment and its application

Every decision-making process particularly those involving real-life issues is disproportionately plagued by uncertainty. It is also unavoidable and obvious. Since its conception are several ways for representing uncertainty have been proposed by numerous academics to cope with uncertainty. Fuzzy sets and hierarchical such as picture fuzzy sets stand out among them as excellent representation techniques for modeling uncertainty. However, there are several significant drawbacks to the current uncertainty modeling techniques. Due to its vast versatility and benefits we here embrace the idea of the spherical fuzzy set, an extension of the picture fuzzy set. On the other hand amid uncertainty in real life the multi-objective plays a critical role. In this research paper determining a Multi-Objective Linear Programming Problem of Spherical fuzzy sets serves to stimulate nous. The score function corresponding to the degree positive, negative and neutral is the foundation upon which the suggested approach is developed. Additionally we apply the suggested strategy to the solution of the multi-objective linear programming problem to demonstrate its superiority through certain numerical examples. Maximization or Minimizing of the cost is the primary goal of the multi-objective linear programming problem. Using an explicitly defined score function the suggested solution transformed the Spherical Fuzzy Multi-Objective Linear Programming Problem into a Crisp Multi-Objective Linear Programming Problem (CMOLPP). We establish some theorems to show that the efficient solution of CMOLPP is likewise an efficient solution of SFMOLPP. The CMOLPP is then further simplified into a single-objective Linear Programming Problem (LPP) thus we revamp the modified Zimmermann’s approach in the environment of a nonlinear membership function with the aid of the suggested technique. It is possible to simply solve this single-objective LPP using any software or standard LPP algorithm. The suggested approach achieves the fuzzy optimum result without altering the nature of the issue. An application of the suggested approach has been used to illustrate it and its results have been distinguished from those of other preexisting methods found in the literature. To determine the importance of the suggested technique which adjudicate thorough theorem and result analysis is conducted.

DebSDF: Delving into the Details and Bias of Neural Indoor Scene Reconstruction.

In recent years, the neural implicit surface has emerged as a powerful representation for multi-view surface reconstruction due to its simplicity and state-of-the-art performance. However, reconstructing smooth and detailed surfaces in indoor scenes from multi-view images presents unique challenges. Indoor scenes typically contain large texture-less regions, making the photometric loss unreliable for optimizing the implicit surface. Previous work utilizes monocular geometry priors to improve the reconstruction in indoor scenes. However, monocular priors often contain substantial errors in thin structure regions due to domain gaps and the inherent inconsistencies when derived independently from different views. This paper presents DebSDF to address these challenges, focusing on the utilization of uncertainty in monocular priors and the bias in SDF-based volume rendering. We propose an uncertainty modeling technique that associates larger uncertainties with larger errors in the monocular priors. High-uncertainty priors are then excluded from optimization to prevent bias. This uncertainty measure also informs an importance-guided ray sampling and adaptive smoothness regularization, enhancing the learning of fine structures. We further introduce a bias-aware signed distance function to density transformation that takes into account the curvature and the angle between the view direction and the SDF normals to reconstruct fine details better. Our approach has been validated through extensive experiments on several challenging datasets, demonstrating improved qualitative and quantitative results in reconstructing thin structures in indoor scenes, thereby outperforming previous work.

Probabilistic load flow in distribution networks: An updated and comprehensive review with a new classification proposal

Due to the increased penetration of distributed energy resources and the presence of uncertainties in power networks, it is essential to evaluate the uncertainty of system performance. As a result, effective technologies for load flow analysis are required. The stochastic properties of power systems can be discovered via probabilistic load flow analysis. To model the uncertainties and construct the parametric tools of probabilistic power flow, several works recently utilize ensembles of probability density functions. Nevertheless, the uncertainties may not fit into any of the conventional classes of probability density functions. Thus, nonparametric tools are required. Various studies on uncertainty modeling techniques in probabilistic load flow have recently been undertaken, although there is no single best uncertainty modeling methodology to date. The load flow problem and the type of uncertain input variables determine the best strategy. There have been positive evaluations in this area, but the main focus of this research is firstly to present an overview and classification of the available load flow strategies in distribution networks from various perspectives and also, investigate the stochastic correlation or dependency of a random variable's variation relative to others. Then, based on a fresh perspective, we present a review, taxonomy, and discussion of the strengths and shortcomings of existing uncertainty modeling techniques in stochastic load flow as probability methods (parametric, semi- and non-parametric approaches) and non-probability methods. Moreover, for first time, a comprehensive comparison and assessment between these uncertainty methods based on accuracy, complexity, and simulation time presents in the uncertainties handling of the power system. The authors suggest this review to engineers, scientists and researchers who are doing their research work in this field.

Sequential Gaussian co-simulation of tectono-geochemical anomaly for concealed ore deposit prediction

Tectono-geochemical data measured from tectonites host a wealth of information that is closely related to the accumulation and dispersion of ore-forming materials, while structure system is the only pathway to connect the deep orebody with the surficial tectono-geochemical anomaly, and both have correspondence and consistency. Based on the geological precondition that structure system and ore-forming process are closely associated with each other, the study proposed a method of sequential Gaussian co-simulation of tectono-geochemical anomaly, which integrates the tectono-geochemical anomaly with the ore-controlling structure system to solve two basic geological prospecting problems that are closely associated with ore-forming space and ore-forming material migration. A case study for concealed Pb–Zn prospecting based on tectono-geochemical data in the Huangzhuguang ore cluster (China) was employed to examine the potential applications of the proposed method. Firstly, centered logratio transformation was employed to remove the closure effect of tectono-geochemical data and to make the data conform to an approximate normal distribution. Secondly, sequential Gaussian co-simulation was applied to improve the simulation results of the tectono-geochemical anomaly by introducing the ore-controlling structure system. Thirdly, the probability distribution of tectono-geochemical anomalies was quantified by uncertainty modeling technique. The case study demonstrated that the proposed method can significantly improve the performance of the primary variable in predicting concealed ore deposits.

Predictive uncertainty assessment in flood forecasting using quantile regression

Abstract Floods and their associated impacts are topics of concern in land development planning and management, which call for efficient flood forecasting and warning systems. The performance of flood warning systems is affected by uncertainty in water level forecasts, which is due to their inability to measure or calculate a modeled value accurately. Predictive uncertainty is an emerging type of uncertainty modeling technique that emphasizes total uncertainty quantified as a probability distribution conditioned on all available knowledge. Predictive uncertainty analysis was done using quantile regression (QR) for machine learning-based flood models – Hybrid Wavelet Artificial Neural Network model (WANN) and Hybrid Wavelet Support Vector Machine model (WSVM) for different lead times. Comparing QR models of WANN and WSVM revealed that the slope, intercept, spread of forecast, and width of confidence band of the WANN model are more for each quantile indicating more uncertainty as compared to the WSVM model. In both models, with an increase in lead time, uncertainty has shown an increasing trend as well. The performance evaluation of inference obtained from QR models was evaluated using uncertainty statistics such as prediction interval coverage probability, average relative interval length (ARIL), and mean prediction interval (MPI).

Assessing safety functionalities in the design and validation of driving automation

This paper aims to contribute to the comprehensive and systematic safety assessment of Automated Driving Systems (ADSs) by identifying unknown hazardous areas of operation. The current methodologies employed in this domain typically involve estimating the distributions of situational variables based on human-centered field test, crash databases, or expert knowledge of critical values. However, due to the lack of a-priori knowledge regarding the influential factors, their critical ranges, and their distributions, these approaches may not be entirely suitable for the assessment of emerging automated driving technologies. To deal with this challenging problem, here we propose a testing methodology incorporating realistic yet unobserved driving conditions, distinguished by numerous situational variables, so to encompass unknown unsafe conditions comprehensively. Our methodology utilizes stochastic simulation and uncertainty modeling techniques to account for the variability of realistic driving conditions and their impact on ADSs' performances. By doing so, we aim to identify unsafe operational regions and triggering conditions that can lead to hazardous behaviors, thus improving the development and safety of automated driving functions. For our purposes, the Latin Hypercube Sampling technique and the recently proposed PAWN density-based sensitivity analysis method are employed. We apply this methodology for the first time in the specific field of ADSs design and validation, using an exemplificative use case. We discuss and compare the results obtained from our approach with those obtained from a traditional approach.

A Review of Uncertainty Modelling Techniques for Probabilistic Stability Analysis of Renewable-Rich Power Systems

In pursuit of identifying the most accurate and efficient uncertainty modelling (UM) techniques, this paper provides an extensive review and classification of the available UM techniques for probabilistic power system stability analysis. The increased penetration of system uncertainties related to renewable energy sources, new types of loads and their fluctuations, and deregulation of the electricity markets necessitates probabilistic power system analysis. The abovementioned factors significantly affect the power system stability, which requires computationally intensive simulation, including frequency, voltage, transient, and small disturbance stability. Altogether 40 UM techniques are collated with their characteristics, advantages, disadvantages, and application areas, particularly highlighting their accuracy and efficiency (as both are crucial for power system stability applications). This review recommends the most accurate and efficient UM techniques that could be used for probabilistic stability analysis of renewable-rich power systems.

A Robust Second-Order Conic Programming Model with Effective Budget of Uncertainty in the Optimal Power Flow Problem

Integrating large-scale wind energy in modern power systems necessitates high-efficiency mathematical models to address classical assumptions in power systems. In particular, two main assumptions for wind energy integration in power systems have not been adequately studied. First, nonlinear AC power flow equations have been linearized in most of the literature. Such simplifications can lead to inaccurate power flow calculations and result in technical issues. Second, wind power uncertainties are inevitable and have been mostly modeled using traditional uncertainty modeling techniques, which may not be suitable for large-scale wind power integration. In this study, we addressed both challenges: we developed a tight second-order conic relaxation model for the optimal power flow problem and implemented the novel effective budget of uncertainty approach for uncertainty modeling to determine the maximum wind power admissibility and address the uncertainty in the model. To the best of our knowledge, this is the first study that proposes an effective, robust second-order conic programming model that simultaneously addresses the issues of power flow linearization and wind power uncertainty with the new paradigm on the budget of uncertainty approach. The numerical results revealed the advantages of the proposed model over traditional linearized power flow equations and traditional uncertainty modeling techniques.

Overview and applications of Robust optimization in the avant-garde energy grid infrastructure: A systematic review

Over the past decade, escalating trends toward renewable energy resources, electrified transportation, magnifying load demand, erratic energy reserve capacities, dynamic demand response programs, and fast ubiquitous connectivity models have amplified the complexity of energy predicaments owing to the acute intensification of operational and technical uncertainties in the energy grid’s evolutionary phases, one of the pressing challenges that need to be properly addressed. For risk hedging and circumventing the impact of ambiguous parameters, several experts and decision-makers have developed uncertainty modeling approaches for optimization problems under uncertainty. This article first offers a generic overview of traditional uncertainty modeling techniques (such as probabilistic techniques, possibilistic techniques, hybrid probabilistic–possibilistic methods, information gap decision theory, and interval-based analysis) to highlight the significance of robust optimization (RO) method, a state-of-the-art deterministic set-based uncertainty methodology used to optimize a system having uncertain inputs. For this reason – a most popular and pertinent uncertainty modeling technique, the RO approach is precisely introduced to study and recapitulate its remarkable features, decisive modules, and shortcomings. Next, the preceding research on the RO’s contributions in the domain of the power grid is reviewed over three key enablers: Decentralization, Decarbonization, and Digitalization. More specifically, the literature on microgrid, virtual power plant, co/trigeneration, renewable energy with storage units, electric mobility, demand response, and security threats are covered in this survey. Finally, a rigorous discussion on foremost prospects, research gaps, and future directions is quantified. This strategic study can be utilized by researchers, engineers, and power industrialists to anticipate open research areas and unprecedented opportunities related to the application of the RO uncertainty handling method in the futuristic power grid.

A conservative framework for obtaining uncertain bands of multiple wind farms in electric power networks by proposed IGDT-based approach considering decision-maker's preferences

Exploiting clean energy resources (CERs) is an applicable way to enhance sustainable development and have the cleaner production of electricity. On the other hand, variability and intermittency of these clean resources are the important disadvantages for determining the reliable operation of electrical grids. Thus, using the uncertainty modeling techniques seems necessary to have more practical values for the decision-making variables. The current paper demonstrates a novel architecture based on Information Gap Decision Theory (IGDT) to model the randomness of multiple Wind Farms (WFs) existing in electric power networks. Note that employing only the IGDT technique cannot consider the preferences defined by the decision-maker. In contrast, the proposed method tackles this issue by considering different values for radii of uncertainty related to the uncertain parameters. It has been proven that the presented approach is time-saving if compared with Monte Carlo Simulation (MCS) and the Epsilon-constraint-based-IGDT. Moreover, the execution time of the presented methodology does not considerably depend on the number of WFs for a power system. It means that if the number of WFs increases in a particular case study, consequently, the execution time does not noticeably rise if compared with the MCS and the Epsilon-constraint-based-IGDT. Furthermore, the equivalent Mixed Integer Linear Programming (MILP) of the original model is employed to guarantee the optimum solution. The performances of the presented methodology have been demonstrated by utilizing IEEE 30 BUS and IEEE 62 BUS systems.

Review of Uncertainty Modeling for Optimal Operation of Integrated Energy System

The operation of the integrated energy system will be affected by uncertainties, leading to sub-optimal design decisions. Accurate and effective modeling of these uncertainties is essential to ensure the optimal integration of renewable energy in the integrated energy system. This article first gives the basic optimal operation model of the integrated energy system, and analyzes various uncertain factors in the optimal operation of the integrated energy system. The source side mainly considers the intermittent and volatility of renewable energy output. The load side mainly considers the uncertainty of load forecast errors. The network side mainly considers the characteristics of equipment under variable conditions, equipment failures, and the uncertainty of the coupling of multi-energy flow systems. The energy storage side mainly considers the uncertainty of mobile energy storage grid connection and virtual energy storage participation in demand response. The multi-energy trading market mainly considers the uncertainty of market trading methods and market operation mechanisms. Then, various integrated energy system uncertainty modeling techniques and solving methods are summarized. Finally, it looks forward to the future research directions and challenges faced by the optimal operation of the integrated energy system under the influence of uncertainty.

Bi-level multi-objective programming approach for carbon emission quota allocation towards co-combustion of coal and sewage sludge

As coal-fired power generation is responsible for more than 30% of total global emissions, co-combustion of coal and sewage sludge is widely used to reduce both carbon emissions and coal consumption. This paper proposes a bi-level multi-objective model for carbon emission quota allocation towards co-combustion of coal and sewage sludge under an uncertain environment. It considers the interactions between the authority and the coal-fired power plants in a leader-follower decision process, and seeks the trade-off among economic development, environmental protection and renewable energy utilization. Besides, fuzzy theory has been employed as an uncertainty modeling technique to characterize the vague and inaccurate decision-making environment. To solve the proposed complicated model, weighted sum method and KKT optimality conditions are applied to convert the model into a single-level single-objective model. A real case from Zhejiang Province, China is given to demonstrate the practicality and efficiency of the optimization model. Based on the analyses and discussion, this model provides reasonable and practical carbon emission quota allocation strategies for the authority. It is indicated that allocating greater quotas to lower carbon intensity coal-fired power plants could effectively achieve reduction targets. To verify the reasonableness, the results are compared with those of using single-level model.

Source fingerprinting loess deposits in Central Asia using elemental geochemistry with Bayesian and GLUE models

The provenance of loess deposits in Central Asia is largely unexplored. Accordingly, the goals of this research were to test and compare the performance of two different models (generalized likelihood uncertainty estimation - GLUE and a Bayesian model) for quantifying the uncertainty in source apportionment estimated for 46 target loess samples collected in the Ili basin, in eastern Central Asia. Model performance was evaluated using goodness-of-fit (GOF), mean absolute fit (MAF) and virtual mixtures (VM) in combination with root mean square error (RMSE) and mean absolute error (MAE). Our dataset comprised 132 surficial samples collected from three potential sources comprising river alluvium (n = 29), sand dunes (n = 35) and topsoils (n = 68). All samples were analysed for elemental geochemistry. Six geochemical properties (Co, Er, Y, Ga, Dy and Pb) were selected in a composite fingerprint which classified 83% of the samples from the three source categories correctly. Based on both models, source contributions to the loess samples were in the following order: topsoils > river alluvium > sand dunes. Based on the GOF and MAF tests, both models were accurate in predicting measured tracer concentrations in the loess samples. The Bayesian model was slightly more accurate (mean RMSE 1.6%, mean MAE 1.8%) than the GLUE (mean RMSE 5.0%, mean MAE 4.7%) model in predicting known source contributions. Overall, our results provide confirmation that application of source fingerprinting with elemental geochemistry and uncertainty modelling techniques is useful for identifying the provenance of loess sediments in arid and desert environments.

A Survey on Microgrid Energy Management Considering Flexible Energy Sources

Aggregation of distributed generations (DGs) along with energy storage systems (ESSs) and controllable loads near power consumers has led to the concept of microgrids. However, the uncertain nature of renewable energy sources such as wind and photovoltaic generations, market prices and loads has led to difficulties in ensuring power quality and in balancing generation and consumption. To tackle these problems, microgrids should be managed by an energy management system (EMS) that facilitates the minimization of operational costs, emissions and peak loads while satisfying the microgrid technical constraints. Over the past years, microgrids’ EMS have been studied from different perspectives and have recently attracted considerable attention of researchers. To this end, in this paper a classification and a survey of EMSs has been carried out from a new point of view. EMSs have been classified into four categories based on the kind of the reserve system being used, including non-renewable, ESS, demand-side management (DSM) and hybrid systems. Moreover, using recent literature, EMSs have been reviewed in terms of uncertainty modeling techniques, objective functions (OFs) and constraints, optimization techniques, and simulation and experimental results presented in the literature.

A copula-based method to consider uncertainties for multi-objective energy management of microgrid in presence of demand response

Utilization of renewable energy sources (RESs) has been increased due to economic-environmental aspects. However, uncertain nature of wind, solar power, market clearing price (MCP), and load complicates the energy management (EM) process of microgrids. This paper studies the EM problem of a grid-connected microgrid from the generating side's perspective. Firstly, the mathematical formulation of microgrid components including wind turbine (WT), photovoltaic (PV), micro turbine (MT), fuel cell (FC) and energy storage system (ESS) has been presented. An improved incentive-based demand response program (DRP) is applied to provide generation-consumption balance by modifying the load pattern. Considering the intra-day market in the formulation of EM is the first contribution of this paper. Furthermore, a new hybrid copula-scenario based uncertainty modeling technique has been presented in this paper. Formulating operational cost and environmental pollution as the objective functions, the proposed EM problem will be solved by multi-objective group search optimization (MOGSO) algorithm. Simulation results demonstrate the good performance of the proposed method in solving microgrid EM problem.

A New Approach to Studying Net Present Value and the Internal Rate of Return of Engineering Projects under Uncertainty with Three-Dimensional Graphs

Cost-benefit analysis (CBA) is very useful when appraising engineering projects and examining their long-term financial and social sustainability. However, the inherent uncertainty in the estimation of completion time, final costs, and the realization of benefits often act as an impediment to its application. Since the emergence of fuzzy set theory, there have been significant developments in uncertainty modelling in project evaluation and investment analysis, primarily in the area of formulating a fuzzy version of CBA. In this context, in studying the key indicators of CBA, whereas fuzzy net present value (fNPV) has been investigated quite extensively, there are significant issues in the calculation of fuzzy internal rate of return (fIRR) that have not been addressed. Hence, this paper presents a new conceptual model for studying and calculating fNPV and fIRR. Three-dimensional fNPV and fIRR graphs are introduced as a means of visualizing uncertainty. A new approach is presented for the precise calculation of fIRR. To facilitate practical application, a computerization process is also presented. Additionally, the proposed methodology is exemplified in a sample motorway project whereby its advantages over traditional stochastic uncertainty modelling techniques such as Monte Carlo analysis are discussed. Overall, it is concluded that the new approach is very promising for modelling uncertainty during project evaluation for both project managers and project stakeholders.

A Review of Uncertainty Handling Techniques in Smart Grid

This paper is a review of uncertainty modeling techniques used in smart grid studies. The literature dealing with uncertainty from various sources in smart grid is analyzed and presented. In a modern power grid, the risk may arise due to different reasons; in-termittent renewable energy sources, uncertain consumer reactions on demand response, driving patterns of electric vehicles, etc. The paper has two objectives. First is to bring out the trends in uncertainty handling techniques used in electrical power system problems, and second to introduce the scope of new risk processing techniques with the perspective of recent smart grid issues.

A Solution of Optimal Power Flow Incorporating Wind Generation and Power Grid Uncertainties

This paper proposes a novel approach for the solution of optimal power flow with consideration of uncertainties caused by wind generation and various factors in the power grid. Regarding the uncertainties studied here, multiple types of uncertainty modeling techniques are applied during research. Evidence theory and extended affine arithmetic are employed and mixed as the framework of uncertainty propagation to fuse probability distributions, possibility distributions, and intervals so as to obtain the best possible probability bounds, and the dependence among variables is handled by copula theory and affine arithmetic. Moreover, the uncertainty of wind farm active power and the characteristic of wind farm reactive power are modeled and integrated into the power flow calculation. An enhanced particle swarm optimization algorithm with introduction of fitness comparison and constraint handling techniques under the evidence theory framework is applied to the solution of this problem. The proposed model and method are tested on the IEEE 30-bus standard test system and a real-sized 183-bus power system to demonstrate the validity and effectiveness.

Uncertainty in the modelling of spatial and temporal patterns of shallow groundwater flow paths: The role of geological and hydrological site information

Understanding the hydrological and hydrogeochemical responses of hillslopes and other small scale groundwater systems requires mapping the velocity and direction of groundwater flow relative to the controlling subsurface material features. Since point observations of subsurface materials and groundwater head are often the basis for modelling these complex, dynamic, three-dimensional systems, considerable uncertainties are inevitable, but are rarely assessed. This study explored whether piezometric head data measured at high spatial and temporal resolution over six years at a hillslope research site provided sufficient information to determine the flow paths that transfer nitrate leached from the soil zone through the shallow saturated zone into a nearby wetland and stream. Transient groundwater flow paths were modelled using MODFLOW and MODPATH, with spatial patterns of hydraulic conductivity in the three material layers at the site being estimated by regularised pilot point calibration using PEST, constrained by slug test estimates of saturated hydraulic conductivity at several locations. Subsequent Null Space Monte Carlo uncertainty analysis showed that this data was not sufficient to definitively determine the spatial pattern of hydraulic conductivity at the site, although modelled water table dynamics matched the measured heads with acceptable accuracy in space and time. Particle tracking analysis predicted that the saturated flow direction was similar throughout the year as the water table rose and fell, but was not aligned with either the ground surface or subsurface material contours; indeed the subsurface material layers, having relatively similar hydraulic properties, appeared to have little effect on saturated water flow at the site. Flow path uncertainty analysis showed that, while accurate flow path direction or velocity could not be determined on the basis of the available head and slug test data alone, the origin of well water samples relative to the material layers and site contour could still be broadly deduced. This study highlights both the challenge of collecting suitably informative field data with which to characterise subsurface hydrology, and the power of modern calibration and uncertainty modelling techniques to assess flow path uncertainty in hillslopes and other small scale systems.

A robust undervoltage load shedding scheme against voltage instability

Undervoltage load shedding (UVLS) is an effective measure for restoring voltage stability as a last resort in emergency conditions. In this paper, a UVLS scheme is proposed considering the uncertainties of load and line parameters. The loading margin is considered as the voltage stability index. The proposed scheme determines the optimal load shedding pattern subject to technical constraints. The info-gap decision theory uncertainty modeling technique is utilized to find a robust and cost-effective pattern of load shedding. The proposed scheme is formulated as a nonlinear programming problem, which is solved using the sequential quadratic programming technique. The performance of the proposed scheme is verified for the IEEE-14 bus and IEEE-118 bus test systems.