Uncertainty Model Research Articles

The effect of correlated color temperature (CCT) variation on spectral mismatch factor (SMF) for incandescent luminous flux lamps

In this research, a setup including NIS Spectroradiometer Ocean Optics HR 2000 with an uncertainty of 4.7%, a photometric bench, and a group of NIS total luminous flux standard lamps calibrated at the National Physical Laboratory (NPL) in England with an uncertainty of 0.8%, was used to measure the correlated color temperature (CCT) and spectral power distribution (SPD) of six incandescent lamps. The correlated color temperature (CCT) curves and their equations are crucial for determining the uncertainty and variations in the spectral mismatch correction factor (SMF) for each lamp. Uncertainty calculations and analyses were conducted, revealing that the correlated color temperature (CCT) of the standard lamps ranged from 2400 K and 2750 K, and the correlated color temperature (CCT) of the tested lamps ranged from 2043 K to 2095 K influencing the uncertainty. Additionally, data analysis was performed, and an uncertainty model was developed in conjunction with the measurements. The uncertainty estimation for spectral mismatch correction factors varied from 0.0011 to 0.0084 depending on the correlated color temperature.

Research on Vehicle Path Planning Method with Time Windows in Uncertain Environments

With the growing complexity of logistics and the demand for sustainability, the vehicle routing problem (VRP) has become a key research area. Classical VRPs now incorporate practical challenges such as time window constraints and carbon emissions. In uncertain environments, where many factors are stochastic or fuzzy, optimization models based on uncertainty theory have gained increasing attention. A single-objective optimization model is proposed in this paper to minimize the total cost of VRP in uncertain environments, including fixed costs, transportation costs, and carbon emission costs. Practical constraints like time windows and load capacity are incorporated, and uncertain variables, such as carbon emission factors, are modeled using normal distributions. Two uncertainty models, based on the expected value and chance-constrained criteria, are developed, and their deterministic forms are derived using the inverse distribution method. To solve the problem effectively, a hybrid ant colony–zebra optimization algorithm is proposed, integrating ant colony optimization, zebra optimization, and the 3-opt algorithm to enhance global search and local optimization. Numerical experiments demonstrate the superior performance of the hybrid algorithm, achieving lower total costs compared to standalone ant colony, zebra optimization, genetic algorithm, and particle swarm optimization algorithms. The results highlight its robustness and efficiency in addressing complex constraints.

Role of Statistics in Artificial Intelligence Technology

Artificial intelligence (AI) research and applications have sparked a broad scientific, economic, social, and political debate. Statistical approaches and techniques are fundamental to AI because they allow robots to learn from data and make intelligent decisions. It's possible even to view statistics as a fundamental component of AI. Statistics is an ideal partner for other disciplines in teaching, research, and practice because of its specialized knowledge of data evaluation, which begins with the correct phrasing of the research question and continues through a study design stage to analysis and interpretation of the results. This work aims to demonstrate how statistical methodology is relevant to the development of AI. In terms of methodological development, planning, research design, evaluation of data quality and collection, distinction of causation and relationships, and evaluation of result uncertainty, we talk about the contributions of statistics to the field of artificial intelligence. This study thoroughly analyzes the crucial role statistics play in AI, demonstrating the numerous applications of statistical ideas like probability, regression, classification, and clustering. The essay highlights the value of statistical analysis in handling uncertainty, making predictions, and training AI models all of which improve the efficiency and precision of AI systems.

Info-gap robustness analysis of linear regression: an epidemiological example

Policy formulation and planning in many disciplines depends on mathematical modelling of empirical data. Linear regressions are common. However, data may vary substantially from one situation to another. This paper does not focus on statistical fluctuation. Rather, data at one time (e.g. prior to the 2019 Covid outbreak) may differ in important ways from data at a later time (e.g. post-Covid). Likewise, data from one location may differ substantively from data elsewhere with a different population, culture, milieu, etc. This challenge introduces data-uncertainty for which probabilistic models are unavailable or require assumptions that may be unjustified. This paper uses non-probabilistic info-gap models of uncertainty to represent data-uncertainty, and the info-gap concept of robustness to uncertainty as the basis for choosing between alternative realizations of a linear regression of empirical data. We demonstrate three properties of info-gap robustness functions when predicting an outcome variable of interest: zeroing, trade off and preference reversal. We also demonstrate the potential utility of excluding selected dependent variables. This analysis supports the use of linear regressions for policy analysis, planning, and decision making. We illustrate the analysis with an epidemiological example.

Uncertainty Modeling and Stability Assessment of Minimum Spanning Trees in Network Design

The Minimum Spanning Tree (MST) problem in networks focuses on finding efficient routes, with applications in transportation, logistics, telecommunications, and more. However, catastrophes can make these networks uncertain, requiring robust computational models for decision-making. This paper introduces an uncertainty theory-based model to analyze the stability of MSTs in uncertain networks. By incorporating reliability and risk variables, we assess the robustness of uncertain MSTs (UMSTs) and address the challenge of computing link tolerances, which define the range within which network links can vary without compromising MST optimality. This study proposes computational formulations to systematically calculate these tolerances, offering a more efficient alternative to traditional re-optimization methods.

Uncertainty-Boosted Robust Video Activity Anticipation.

Video activity anticipation aims to predict what will happen in the future, embracing a broad application prospect ranging from robot vision and autonomous driving. Despite the recent progress, the data uncertainty issue, reflected as the content evolution process and dynamic correlation in event labels, has been somehow ignored. This reduces the model generalization ability and deep understanding on video content, leading to serious error accumulation and degraded performance. In this paper, we address the uncertainty learning problem and propose an uncertainty-boosted robust video activity anticipation framework, which generates uncertainty values to indicate the credibility of the anticipation results. The uncertainty value is used to derive a temperature parameter in the softmax function to modulate the predicted target activity distribution. To guarantee the distribution adjustment, we construct a reasonable target activity label representation by incorporating the activity evolution from the temporal class correlation and the semantic relationship. Moreover, we quantify the uncertainty into relative values by comparing the uncertainty among sample pairs and their temporal-lengths. This relative strategy provides a more accessible way in uncertainty modeling than quantifying the absolute uncertainty values on the whole dataset. Experiments on multiple backbones and benchmarks show our framework achieves promising performance and better robustness/interpretability.

Feature selection for label distribution learning based on neighborhood fuzzy rough sets

In recent years, label distribution learning (LDL) has gained extensive application in actual classification endeavors. Nevertheless, most LDL datasets contain superfluous features that significantly impede the efficacy of classification algorithms and prolong their execution time. In addition, existing feature selection algorithms are usually limited to a specific label assignment paradigm or ignore the overall distribution information of the label significance in LDL. To address the aforementioned issues, this study constructs a novel uncertainty model known as neighborhood fuzzy rough sets, and proposes a LDL feature selection algorithm (LDNF) for better utilization of the overall distribution information of label significance. Specifically, the fuzzy equivalence relation for samples is defined using the correlation of label distributions, and the probabilities of classifying the same category are evaluated. To exploit the overall distribution information, the definitions of the upper and lower approximations are provided with the fuzzy equivalence relation of the label distribution. The experimental results indicate that the performance of the LDNF algorithm is superior to that of five leading-edge comparative algorithms on 10 publicly available real-world datasets. Neighborhood fuzzy rough sets and their applications will be further investigated in the future.

The influence of cardiac substructure dose on survival in a large lung cancer stereotactic radiotherapy cohort using a robust personalized contour analysis

Background/Purpose: Radiation-induced cardiac toxicity in lung cancer patients has received increased attention since RTOG 0617. However, large cohort studies with accurate cardiac substructure (CS) contours are lacking, limiting our understanding of the potential influence of individual CSs. Here, we analyse the correlation between CS dose and overall survival (OS) while accounting for deep learning (DL) contouring uncertainty, a/b uncertainty and different modelling approaches. Materials/Methods: This single institution, retrospective cohort study includes 730 patients (early-stage tumours (I or II). All treated: 2009–2019), who received stereotactic body radiotherapy (≥5 Gy per fraction). A DL model was trained on 70 manually contoured patients to create 12 cardio-vascular structures. Structures with median dice score above 0.8 and mean surface distance (MSD) <2 mm during testing, were further analysed. Patientspecific CS dose was used to find the correlation between CS dose and OS with elastic net and random survival forest models (with and without confounding clinical factors). The influence of delineation-induced dose uncertainty on OS was investigated by expanding/contracting the DL-created contours using the MSD ± 2 standard deviations. Results: Eight CS contours met the required performance level. The left atrium (LA) mean dose was significant for OS and an LA mean dose of 3.3 Gy (in EQD2) was found as a significant dose stratum. Conclusion: Explicitly accounting for input parameter uncertainty in lung cancer survival modelling was crucial in robustly identifying critical CS dose parameters. Using this robust methodology, LA mean dose was revealed as the most influential CS dose parameter.

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.

Deep Reinforcement Learning-Enhanced Multi-Stage Stochastic Programming for Real-Time Decision-Making in Centralized Seed Packaging Systems

The centralized seed packaging system faces significant challenges in dynamic decision-making due to stochastic demand fluctuations and operational constraints. This paper presents a novel hybrid approach integrating deep reinforcement learning (DRL) with multi-stage stochastic programming (MSP) to optimize decision-making processes. Our method leverages DRL for adaptive learning and MSP for uncertainty modeling, enabling real-time adjustments. Results from case studies demonstrate improved efficiency, reduced costs, and enhanced robustness compared to traditional approaches.

A comprehensive survey of recent advances in facility location problems: Models, solution methods, and applications

Logistics management research has significantly benefited from the increased prominence of warehouse management challenges in recent years, which are now extensively utilized in analyzing logistics distribution and transportation networks. Concerning Facility Location Problems and their variations, this work attempts to perform an extensive literature assessment of current model advances and improvements. This study also aims to ascertain the influence and developments in Facility Location Problems, which are classic optimization problems with numerous applications in manufacturing, distribution, transportation, and supply chain management decisions. This study thoroughly analyzes current developments in facility location problems, a category of optimization issues frequently used in network architecture, logistics, and supply chain management. The review analyzes literature from the past decade, categorizing works based on problem variants, mathematical formulations, solution methods, and exact approaches. Key findings highlight significant progress in solving complex facility location problems through advances in mathematical programming, scalable exact methods, and hybrid metaheuristics. Emerging trends such as uncertainty modeling, multi-objective optimization, and sustainability are also discussed. Sustainable Development Goals (SDGs): SDG 9: Industry, Innovation and Infrastructure; SDG 11: Sustainable Cities and Communities; SDG 12: Responsible Consumption and Production; SDG 13: Climate Action

Two-stage optimization strategy for the active distribution network considering source-load uncertainty

This study aims to advance the development of the active distribution network (ADN) by optimizing resource allocation across different stages to enhance overall system performance and economic benefits. First, an ADN optimization model is constructed based on a two-stage robust optimization approach. The first stage focuses on determining optimal decision variables within the uncertainty set, while the second stage adjusts control variables based on the initial stage decisions. This model effectively addresses source-load uncertainties while preserving the flexibility and adaptability of decision-making solutions. Additionally, this study explores uncertainty models that incorporate correlation factors. The IEEE33-node model is employed to validate the effectiveness and superiority of the proposed optimization strategy through numerical simulations. Simulation results demonstrate that Model 3 comprehensively accounts for photovoltaic and wind turbine generator planning by optimizing their capacity configurations, leading to a 23% increase in distributed generation (DG) penetration. During high-load periods (e.g., 13:00 and 16:00), DG output reaches 47% and 50% of the demand load, underscoring the critical role of DG in supporting the power grid during peak hours. Overall, the proposed two-stage optimization strategy considers source-load uncertainties, significantly reducing economic costs, enhancing DG output, and improving overall system performance. In scenarios with correlated uncertainties, the optimized results exhibit greater accuracy and reliability, providing robust support for the planning and operation of practical distribution networks.

An Imprecise Hybrid Reliability Methodology for Rock Structures Considering Spatial Variations of Inputs with Mixed Uncertainties: Theory and Application

Rock properties often contain epistemic uncertainties due to their subjective estimation or insufficient objective data, inhibiting their traditional uncertainty modelling via probability models. This paper proposes a hybrid reliability framework to consider the spatial variations of inputs, modelled via non-stochastic (fuzzy, intervals, p-boxes) and stochastic models based on their information levels. The proposed methodology assigns appropriate uncertainty models for inputs, subsequently generates their interval and random fields in FLAC-2D via a developed MATLAB-FLAC interface code. The random and interval field of inputs are generated via an advanced Karhunen–Loève method, based on their spatial dependency and correlation functions. The methodology is demonstrated for a mining rock slope, with inputs modelled via different uncertainty models to manifest its generalised nature. A comparative analysis is also performed with the traditional random field analysis. Present methodology propagates the input uncertainties invoked by insufficient information faithfully to estimate the intervals/fuzzy/p-boxes of probability of failure (Pf). In contrast, the traditional method estimates a constant Pf by assigning the probability models to the inputs with limited data (based on subjective judgements). Further, the estimated bound of Pf was bounding its point estimate verifying the accuracy of the methodology and enabling the users for more informed decision-making.

Data-driven dynamic state estimation in power systems via sparse regression unscented Kalman filter

This paper proposes a novel data-driven modeling and dynamic state-estimation approach for nonlinear power and energy systems, highlighting the critical role of a known dynamic model for accurate state estimation in the face of uncertainty and complex models. The proposed framework consists of a two-phase approach: data-driven model identification and state-estimation. During the model identification phase, which spans a relatively short time interval, state feedback is collected to identify the dynamics of the nonlinear systems in the power grid using a novel density-guided sparse identification algorithm. Unlike conventional sparse regression, which relies on a large library of linear and nonlinear functions to fit data, our proposed algorithm iteratively updates a relatively small initial library by adding higher-order nonlinear functions if the coefficients of the current functions are dense. Following the identification of the model’s dynamics, the estimation phase addresses the challenge of incomplete state measurements. By implementing an unscented Kalman filter, the state variables of the system are dynamically estimated by measuring the noisy output. Finally, simulation results on an IEEE 30-bus system are presented to illustrate the effectiveness of the density-guided sparse regression unscented Kalman filter compared to a physics-based unscented Kalman filter with model uncertainty. This study contributes to the fields of data-driven modeling techniques, machine learning for power systems, and computational intelligence in smart grids. It emphasizes the use of advanced sparse regression and unscented Kalman filter methods for state estimation, enhancing the robustness and accuracy of monitoring and control in electrical and energy systems.

A monocular three-dimensional object detection model based on uncertainty-guided depth combination for autonomous driving

Three-Dimensional (3D) object detection is a crucial task for enhancing safety and efficiency in autonomous driving. However, estimating depth from monocular images remains a challenging task. Most existing monocular 3D object detection methods rely on additional auxiliary data sources to compensate for the lack of spatial information in monocular images. Nevertheless, these methods bring substantial computational overhead and time-consuming preprocessing steps. To address this issue, we propose a novel depth estimation method for monocular images that does not rely on any auxiliary information. Leveraging both the texture and geometric cues of detected objects, our method generates two depth estimates for each object based on the extracted Region of Interest (RoI) features: a direct depth estimate and a height-based depth estimate with uncertainty modeling. Our model dynamically assigns weights to these depth estimates based on their respective uncertainties and combines them to obtain the final depth. During the training process, the model assigns higher weights to depth branches with higher uncertainties, as these estimates exhibit greater tolerance to errors. As the combined depth network introduces increased complexity, we utilize Group Normalization (GN) to better capture spatial information in the prediction branch outputs. Furthermore, we leverage the Two-Dimensional (2D) information of objects to predict the residual in the 2D center after downsampling, aiding in the regression of 3D center. On the KITTI benchmark, our model achieves an average precision (AP) of 16.65 % and 23.19 % on 3D and bird's-eye view (BEV) detection for the moderate category, surpassing the state-of-the-art (SOTA) models in each category.

Electricity demand uncertainty modeling with Temporal Convolution Neural Network models

This work presents a Temporal Convolution Network (TCN) model for half-hourly, three-hourly and daily-time step to predict electricity demand (G) with associated uncertainties for sites in Southeast Queensland Australia. In addition to multi-step predictions, the TCN model is applied for probabilistic predictions of G where the aleatoric and epistemic uncertainties are quantified using maximum likelihood and Monte Carlo Dropout methodologies. The benchmarks of TCN model include an attention-based, bi-directional, gated recurrent unit, seq2seq, encoder–decoder, recurrent neural networks and natural gradient boosting models. The testing results show that the proposed TCN model attains the lowest relative root mean square error of 5.336-7.547% compared with significantly larger errors for all benchmark models. In respect to the 95% confidence interval using the Diebold–Mariano test statistic and key performance metrics, the proposed TCN model is better than benchmark models, capturing a lower value of total uncertainty, as well as the aleatoric and epistemic uncertainty. The root mean square error and total uncertainty registered for all of the forecast horizons shows that the benchmark models registered relatively larger errors arising from the epistemic uncertainty in predicted electricity demand. The results obtained for TCN, measured by the quality of prediction intervals representing an interval with upper and lower bound errors, registered a greater reliability factor as this model was likely to produce prediction interval that were higher than benchmark models at all prediction intervals. These results demonstrate the effectiveness of TCN approach in electricity demand modelling, and therefore advocates its usefulness in now-casting and forecasting systems.

Stochastic economic sizing and placement of renewable integrated energy system with combined hydrogen and power technology in the active distribution network

The current study concentrates on the planning (sitting and sizing) of a renewable integrated energy system that incorporates power-to-hydrogen (P2H) and hydrogen-to-power (H2P) technologies within an active distribution network. This is expressed in the form of an optimization model, in which the objective function is to reduce the annual costs of construction and maintenance of integrated energy systems. The model takes into account the planning and operation model of wind, solar, and bio-waste resources, as well as hydrogen storage (a combination of P2H, H2P, and hydrogen tank), and the optimal power flow constraints of the distribution network. Electrical and hydrogen energy are administered in an integrated energy system. The modeling of the uncertainties regarding the quantity of load and renewable resources is achieved through stochastic optimization using the Unscented Transformation method. The novelties of the scheme include the sizing and placement of a combined hydrogen and power-based renewable integrated energy system, the consideration of the impacts of bio-waste units, P2H, and H2P systems on the planning of the integrated energy system and the operation of the active distribution network, and the modeling of uncertainties using the Unscented Transformation method to reduce the calculation time. The study’s results demonstrate the scheme’s ability to improve the technical conditions of the distribution network by considering the optimal planning of integrated energy systems. In comparison to the network power flow, the operation status of the network has been improved by approximately 23-45% through the optimal siting, sizing, and energy management of hydrogen storage equipment, as well as renewable resources in the form of integrated energy systems. In other words, optimal energy management and planning of the integrated energy systems in the distribution network has been able to reduce energy losses and voltage drop by 44.5% and 42.4% compared to the load flow studies. In this situation, peak load carrying capability has increased by about 23.7%. In addition, compared to the case of the network with renewable resources, the overvoltage has decreased by about 43.5%. Also, Unscented Transformation method has a lower calculation time than scenario-based stochastic optimization.

Modelling of wind and solar power output uncertainty in power systems based on historical data: A characterisation through deterministic parameters

The inherent uncertainty associated with wind and solar energy poses challenges in ensuring the reliability of the power system with a high penetration of renewable energy. Therefore, incorporating uncertainty is vital during the planning of power systems. Traditional analytical methods often necessitate transforming the uncertainty of large-scale power systems into deterministic optimisation planning, while those approaches tend to be overly conservative, yielding unsolvable solutions, or rely on assumptions and data fitting, creating a significant gap with real-world scenarios. To address this, this study employs upper α-quantiles originating from abundant historical data to replace power output expectations to consider uncertainty during the planning. Additionally, random sampling based on historical data generates potential wind and solar output scenarios, and Monte Carlo simulations are used to validate the proposed method's reliability and assess system investment distribution. Using China's power system as a case study, 64 quantile choices are evaluated. Compared to planning through output expectations, using quantiles can reduce the load loss rate from 10−1 to 10−5, and both the cost expectations and the extreme cost risk decrease. The use of fossil fuels has also decreased by 10%. Results underscore the necessity of choosing upper α-quantiles with higher α, such as 85, to account for the long-tailed wind power distribution. However, even overly conservative wind power output α is still challenging to mitigate residual load loss. The combination of photovoltaics and intraday energy storage ensures that the α selection of photovoltaics should not be too low, due to the reason that there is a need to balance the gradual decrease of load loss rates and the steep ascent of expected investment costs in the power system.

Low-carbon economic optimization strategy for industrial loads in parks considering source-load-price multivariate uncertainty

A low-carbon economic optimization method is proposed for industrial loads in parks considering multivariate uncertainty. Model of dynamic load node carbon intensity is proposed considering the uncertainty of clean energy and dynamic conventional units carbon intensity based on system currents. The robustness is improved based on multi-interval uncertainty set. The gap is filled by hybrid copula model with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) prices in the uncertainty model. The GARCH is used to built the marginal distribution function of prices, and a hybrid copula model is proposed to obtain the joint probability density function based on the weights calculated by Euclidean distance. The LNCI probability distributions of the regulation potential of loads are proposed with the virtual energy storage and the virtual power model to improve the descriptive ability of uncertainty based on the expansion and contraction functions. Finally, the typical scenarios are extracted based on Monte Carlo and Wasserstein measures. The Column sum Constraint Generation algorithm and strong duality theory are used to get the robust-stochastic optimization. The method proposed in the paper has a positive effect on enterprises to rationalize their production schedules, reduce electricity and carbon emissions costs and increase the revenue from participating in grid regulation.

Linear parameter varying μ synthesis robust control of CDC semi‐active suspension system for nonlinearity and uncertainty

AbstractBecause the continuous damping control (CDC) semi‐active suspension system has complex nonlinear and uncertain characteristics that can significantly affect the performance of the system. And in the controller design process, achieving a balance of multiple performance objectives is often difficult. Therefore, this paper designs a linear parameter varying (LPV) μ synthesis robust controller for the vibration suppression and multi‐objective control of a 7‐degree‐of‐freedom (7‐DOF) vehicle suspension system equipped with CDC dampers. Firstly, the nonlinear force model of the solenoid valve CDC damper is developed based on the actual damping variation. Considering the nonlinear forces of the coil springs, the nonlinear model of the 7‐DOF suspension system is expressed as LPV form. Further, the linear fractional transformation (LFT) method is used to analyze and reconstruct the system model for multiple parameter uncertainties of the suspension. The actuator time delays are also simulated through a frequency domain transfer function, which is considered to be an unmodeled dynamic at the input of the system. Finally, an LPV‐μ synthesis robust controller based on nonlinearity and mixed uncertainty is designed to improve car ride comfort and achieve the best relationship between comfort and handling stability. Simulation and experimental results under random disturbance conditions show that the LPV‐μ synthesis controller has better anti‐jamming performance and controllability compared to the H∞ controller and μ synthesis controller.