Uncertainty Modeling Methods Research Articles

Robust Unit Commitment of Integrated Electric-Heat Systems With Weather Parameter Driven Uncertainties

The integrated electric-heat system (IEHS) is currently one of the most prevalent realizations of a multienergy system, however, most of the existing research merely modeled the source, network, and demand sides of IEHS independently, without further exploring the internal correlation built up by the regional weather parameters. This article proposed a two-stage weather-driven risk-constrained robust unit commitment (WRRUC) model. Compared with the existing RUC works for IEHSs, two main contributions are made in our work: 1) a unified weather-driven uncertainty modeling method is proposed for the IEHS, which could decrease the conservativeness of the robust decision-making framework; 2) the uncertainty set boundaries are set as adaptive variables and the aftermath of unmodeled uncertainties is quantified by additional operational risk term in the objective function. The proposed WRRUC model is solved by the column-and-constraint generation algorithm. Compared with other off-the-shelf UC models, the summation of operational costs and risks of the test system is remarkably lower than the RUC case, verifying the effectiveness of the proposed weather-driven unified modeling of uncertainties and adaptive robust dispatch framework.

Gaussian Mixture Model for Multivariate Wind Power Based on Kernel Density Estimation and Component Number Reduction

The Gaussian mixture model (GMM) is a powerful tool to establish the probability distributions of random variables in power system analyses. GMM can model arbitrary probability distributions by increasing the number of its Gaussian components, but the commonly used expectation-maximization (EM) algorithm fails to obtain accurate GMM for large component numbers, which limits the application of GMM to multivariate wind power modeling. In this letter, a parameter estimation method for GMM with large component numbers is proposed based on kernel density estimation (KDE) and the improved density-preserving hierarchical EM algorithm. Then, the closed-form solution to probabilistic power flow (PPF) calculation is derived based on piecewise linearization and GMM, which validates the importance of large component numbers. Finally, the proposed uncertainty modeling method is compared with EM-based GMM, Copula functions, KDE, k-nearest neighbors and block neural autoregressive flow on actual wind speed data to validate its superiority in describing the details of probability densities of wind power. PPF calculation is performed to show the efficiency and accuracy of the proposed uncertainty analysis method.

Quantifying the uncertainty of precipitation forecasting using probabilistic deep learning

Abstract. Precipitation forecasting is an important mission in weather science. In recent years, data-driven precipitation forecasting techniques could complement numerical prediction, such as precipitation nowcasting, monthly precipitation projection and extreme precipitation event identification. In data-driven precipitation forecasting, the predictive uncertainty arises mainly from data and model uncertainties. Current deep learning forecasting methods could model the parametric uncertainty by random sampling from the parameters. However, the data uncertainty is usually ignored in the forecasting process and the derivation of predictive uncertainty is incomplete. In this study, the input data uncertainty, target data uncertainty and model uncertainty are jointly modeled in a deep learning precipitation forecasting framework to estimate the predictive uncertainty. Specifically, the data uncertainty is estimated a priori and the input uncertainty is propagated forward through model weights according to the law of error propagation. The model uncertainty is considered by sampling from the parameters and is coupled with input and target data uncertainties in the objective function during the training process. Finally, the predictive uncertainty is produced by propagating the input uncertainty in the testing process. The experimental results indicate that the proposed joint uncertainty modeling framework for precipitation forecasting exhibits better forecasting accuracy (improving RMSE by 1 %–2 % and R2 by 1 %–7 % on average) relative to several existing methods, and could reduce the predictive uncertainty by ∼28 % relative to the approach of Loquercio et al. (2020). The incorporation of data uncertainty in the objective function changes the distributions of model weights of the forecasting model and the proposed method can slightly smooth the model weights, leading to the reduction of predictive uncertainty relative to the method of Loquercio et al. (2020). The predictive accuracy is improved in the proposed method by incorporating the target data uncertainty and reducing the forecasting error of extreme precipitation. The developed joint uncertainty modeling method can be regarded as a general uncertainty modeling approach to estimate predictive uncertainty from data and model in forecasting applications.

Uncertainty modeling method of weather elements based on deep learning for robust solar energy generation of building

During the actual use stage, the uncertainty of weather leads to errors between the performance of building energy and the simulated values. Usually, uncertainty of weather cannot be eliminated, and difficult to quantify accurately due to complex occurrence rules. Based on the influence of weather uncertainty on solar power generation, this research propose a highly reliable and high-efficiency uncertainty modeling method based on two neural networks: (i) dual-stage attention-based recurrent neural network(DARNN): due to the use of two-stage attention mechanism, as the method to achieve importance interpretability in this study. (ii) Bayesian recurrent neural network(Bayesian RNN): regard the weight and bias value as an unknown distribution, as the method of uncertainty modeling in this study. DARNN analyzes the weight value of each weather element at each time point as the importance through a single learning, and the results show that the importance of solar radiation and relative humidity to solar power generation ranks in the top two. Based on the above results, Bayesian RNN establishes the probability distribution models of solar radiation and relative humidity at each time point of a year by learning the potential correlation between weather elements and taking the historical data of low importance weather elements as input.

A two-point estimate approach for energy management of multi-carrier energy systems incorporating demand response programs

Gas-based power plants have attracted more attention in providing electrical energy worldwide because of their lower costs and air pollution. In addition, the use of multi-carrier energy systems has several advantages, such as sustainability benefits and improving performance in supplying the energy demand. This study aims to optimize the total operation cost of multi-carrier energy systems considering the uncertain parameters. The storage technology and consumption side assist the operator in achieving lower costs based on conceptions of demand response programs. Therefore, this study presents a comprehensive mathematical model for the coordinated operation of integrated multi-carrier energy systems while the operational constraints of both gas and power networks are considered. Furthermore, this paper utilizes a new uncertainty modeling method based on Hong's two-point estimate method for addressing the uncertainties of load consumption and wind generation. The proposed model is applied to a gas and power multi-carrier energy system through four case studies. The results affirm the high performance of the presented method and investigate the influence of demand response programs in both sides of energy carriers.

Optimal probabilistic operation of energy hub with various energy converters and electrical storage based on electricity, heat, natural gas, and biomass by proposing innovative uncertainty modeling methods

In recent years, attention to energy hubs (EHs) has increased significantly as active and intelligent elements in multi-energy systems (MESs). This article proposes a stochastic framework for the optimal operation of a new EH structure with various energy converters and electric storage based on electricity, heat, natural gas, and biomass. The proposed framework plays the role of a bidding strategy for a smart element in MESs. For modeling uncertainties in this framework, such as energy market prices, wind speed, and solar radiation, it is necessary to generate random scenarios based on recorded past behaviors or forecasting future trends. The Monte Carlo (MC) and the ARIMA methods have received significant attention in the literature to generate scenarios. Proposing uncertainty modeling methods in this paper, including the MC based on the Kolmogorov-Smirnov test, the ARIMA model based on Akaike Information Criterion, TBATS model, and the LSTM model of deep learning, as another innovation, has been such that efforts are made to make a significant improvement in the generated scenarios. Comparing various proposed uncertainty modeling methods is one of the most contributions. Based on the actual data in Finland, the simulation results demonstrate the effectiveness of the proposed operation strategy and the uncertainty modeling methods. Increasing the accuracy of uncertainty modeling has a significant impact on EH's profit and energy storage behavior and can also reduce the dependence of EHs on incoming energy carriers.

Individual pitch controller characteristics analysis and optimization under aerodynamic imbalanced loads of wind turbines

Individual pitch control technology can reduce asymmetric loads of wind turbines. The assumption of three completely symmetrical blades is the design premise of traditional individual pitch controller. However, production, assembly, and operation will inevitably lead to aerodynamic imbalanced characteristics for blades. Therefore, the failure mechanism of the traditional individual pitch controller is analyzed based on the frequency-domain decomposition method and verified by the simulation analysis. Based on the failure mechanism, the uncertainty modeling method is proposed to handle aerodynamic imbalanced loads. Then the robust individual pitch control is designed based on the product perturbation model. The D–K iterative algorithm is used to solve the H∞-optimization for the controller. The proposed robust individual pitch controller can effectively suppress imbalanced loads through simulation verification.

Uncertainty modeling of wind power frequency regulation potential considering distributed characteristics of forecast errors

Large-scale integration of wind power generation decreases the equivalent inertia of a power system, and thus makes frequency stability control challenging. However, given the irregular, nonlinear, and non-stationary characteristics of wind power, significant challenges arise in making wind power generation participate in system frequency regulation. Hence, it is important to explore wind power frequency regulation potential and its uncertainty. This paper proposes an innovative uncertainty modeling method based on mixed skew generalized error distribution for wind power frequency regulation potential. The mapping relationship between wind speed and the associated frequency regulation potential is established, and key parameters of the wind turbine model are identified to predict the wind power frequency regulation potential. Furthermore, the prediction error distribution of the frequency regulation potential is obtained from the mixed skew model. Because of the characteristics of error partition, the error distribution model and predicted values at different wind speed sections are summarized to generate the uncertainty interval of wind power frequency regulation potential. Numerical experiments demonstrate that the proposed model outperforms other state-of-the-art contrastive models in terms of the refined degree of fitting error distribution characteristics. The proposed model only requires the wind speed prediction sequence to accurately model the uncertainty interval. This should be of great significance for rationally optimizing system frequency regulation resources and reducing redundant backup.

Operation Optimization of Integrated Energy System under a Renewable Energy Dominated Future Scene Considering Both Independence and Benefit: A Review

An integrated energy system interconnects multiple energies and presents a potential for economics improvement and energy sustainability, which has attracted extensive attention. However, due to the obvious volatility of energy demands, most existing integrated energy systems cannot operate in a totally self-sufficient way but interact with the upper grid frequently. With the increasingly urgent demand for energy saving and emissions reduction, renewable resources have occupied a larger and larger proportion in energy system, and at last they may be dominant in the future. Unlike conventional fossil fuel generation, the renewable resources are less controllable and flexible. To ease the pressure and guarantee the upper grid security, a more independent integrated energy system is required. Driven by that, this paper firstly reviews the optimal strategies considering both independence and benefit from perspectives of individual efforts and union efforts. Firstly, the general optimization process is summarized in terms of energy flows modelling and optimization methods to coordinate supply–demand side and realize benefit maximization. Based on that, handling with uncertainty of high-ratio renewable energy is reviewed from uncertainty modeling methods and multi-stage operation strategy perspectives to make the strategy accurate and reduce the adverse effects on the upper grid. Then, the hybrid timescale characteristics of different energy flows are explored to enhance operation flexibility of integrated energy systems. At last, the coordination among different participants is reviewed to reduce the whole adverse effect as a union. Remarks are conducted in the end of each part and further concluded in the final part. Overall, this study summarizes the research directions in operation optimization of integrated energy systems to cater for a renewable energy dominated scene to inspire the latter research.

Method of Estimating Uncertainty as a Way to Evaluate Continuity Quality of Power Supply in Hospital Devices

The article presents issues related to the determination of the continuity quality of power supply (CQoPS) for hospital electrical devices. The model describing CQoPS takes into account power redundancy. The uncertainty modeling method based on the certainty factor (CF) of the hypothesis was used to establish the single-valued CQoPS factor. CQoPS modeling takes into account multidimensional quality models and physical stages of power. The quality models take into account seven dimensions that make up CQoPS (availability, appropriate amount, power supply reliability, power quality, assurance, responsiveness, security). The model of power stages includes five of these stages (power generation, delivery to recipient, distribution by recipient, delivery to device, power-consuming device). To date, when designing hospital power systems, the applied reliability indicators revealed limitations because they do not consider all the possible factors influencing the power continuity. Estimating the supply continuity quality with the use of the uncertainty modeling proposed in this article allows for taking into account all possible factors (not just reliability factors) that may affect supply continuity. The presented modeling offers an additional advantage, namely, it allows an expanded evaluation of the hospital supply system and a description using only one indicator. This fact renders the evaluation of the supply system possible for unqualified staff. At the end of the article, some examples of calculations and simulations are presented, thus showing that the applied methods give the expected results.

Data-Driven Adjustable Robust Unit Commitment of Integrated Electric-Heat Systems

This paper proposes a data-driven adjustable robust unit commitment (UC) model for integrated electric-heat systems (IEHSs), where the data-driven, and robustness adjustable features are endowed by the novel uncertainty modeling method. The devised uncertainty set is the intersections of a series of hyperplanes. It combines the merits of the traditional box-like uncertainty set, whose underlying computation burden is moderate, and the convex hull formed by historical data, which would lead to less conservative operation strategies. The boundaries of the bounding high-dimensional rectangle of the uncertainty set are set as decision variables to achieve the balance between the operation costs, and risk. The two-stage decision-making framework is employed in the robust UC model of IEHSs, in which the district heating networks are operated at the variable-flow-variable-temperature mode. The modified column-and-constraint generation (C, and CG) algorithm is employed to solve the proposed robust program, where an additional feasible region reduction step is embedded to decrease the computation burden of the worst case identification. Simulation results on two test systems verify the effectiveness of the proposed methods.

Data-Driven Distributionally Robust Chance-Constrained Unit Commitment With Uncertain Wind Power

The Unit commitment (UC) problem in power systems has been studied for a long time; however, many new challenges have emerged in the UC problem with the increasing penetration of renewable generation which is intermittent and uncertain. Compared with the common uncertainty modeling methods including stochastic programming and robust optimization, in this paper, we develop a data-driven distributionally robust chance-constrained (DDRC) UC model. The proposed two-stage UC model focuses on the commitment decision and dispatch plan in the first stage, and considers the worst-case expected cost for possible power imbalance or re-dispatch in the second stage. To capture the uncertainty of wind power distribution, a distance-based ambiguity set is designed which can be constructed in a data-driven manner. Based on the ambiguity set, the original complicated UC problem is reformulated to a tractable optimization problem which is then solved by the column-and-constraint generation (C&CG) algorithm. The performance of the the proposed approach is validated by case studies with different test systems including the IEEE 6-bus test system, modified IEEE 118-bus system and a practical-scale system, especially the value of data in controlling the conservativeness of the problem.

Investigation on the impact of nongeometric uncertainty in dynamic performance of serial and parallel robot manipulators

Uncertainty in robot manipulations is a fundamental source of inaccuracy. Most nongeometric uncertainties is caused by the mechanical components of robot manipulators such as gear transmission systems and joints. This study integrates existing uncertainty models for practical applications of both three-degrees-of-freedom serial robot and parallel robot (closed-loop 5R mechanism). We first review the literature on uncertainty and existing methods for improving the precision of robot manipulation. For existing methods for uncertainty modeling: (1) the mathematical model of a harmonic drive considering kinematic error and compliance is derived; (2) joint clearance analysis that includes models of contact force and friction force is presented; (3) Archard’s wear model is used to estimate the effect of joint wear, based on which the geometry of joints is updated. Computer simulation is then used to demonstrate the application of the proposed method for serial and parallel robot manipulators. Simulations are used to examine the behavior of robot manipulators operating under uncertainty, with performance-evaluated positional error and trajectory error. The proposed method can provide some insight into nongeometric uncertainty in robot manipulations. The proposed methodology can be further used to improve the accuracy of robot manipulation under uncertainty by identifying uncertainty parameters.

Novel fuzzy uncertainty modeling for land cover classification based on clustering analysis

It is well known that there is a degree of fuzzy uncertainty in land cover classification using remote sensing (RS) images. In this article, we propose a novel fuzzy uncertainty modeling algorithm for representing the features of land cover patterns, and present an adaptive interval type-2 fuzzy clustering method. The proposed fuzzy uncertainty modeling method is performed in two main phases. First, the segmentation units of the input multi-spectral RS image data are subjected to object-based interval-valued symbolic modeling. As a result, features for each land cover type are represented in the form of an interval-valued symbolic vector, which describes the intra-class uncertainty better than the source data and improves the separability between different classes. Second, interval type-2 fuzzy sets are generated for each cluster based on the distance metric of the interval-valued vectors. This step characterizes the inter-class high-order fuzzy uncertainty and improves the classification accuracy. To demonstrate the advantages and effectiveness of the proposed approach, extensive experiments are conducted on two multispectral RS image datasets from regions with complex land cover characteristics, and the results are compared with those given by well-known fuzzy and conventional clustering algorithms.

Visualization and Visual Analysis of Ensemble Data: A Survey.

Over the last decade, ensemble visualization has witnessed a significant development due to the wide availability of ensemble data, and the increasing visualization needs from a variety of disciplines. From the data analysis point of view, it can be observed that many ensemble visualization works focus on the same facet of ensemble data, use similar data aggregation or uncertainty modeling methods. However, the lack of reflections on those essential commonalities and a systematic overview of those works prevents visualization researchers from effectively identifying new or unsolved problems and planning for further developments. In this paper, we take a holistic perspective and provide a survey of ensemble visualization. Specifically, we study ensemble visualization works in the recent decade, and categorize them from two perspectives: (1) their proposed visualization techniques; and (2) their involved analytic tasks. For the first perspective, we focus on elaborating how conventional visualization techniques (e.g., surface, volume visualization techniques) have been adapted to ensemble data; for the second perspective, we emphasize how analytic tasks (e.g., comparison, clustering) have been performed differently for ensemble data. From the study of ensemble visualization literature, we have also identified several research trends, as well as some future research opportunities.

Review of Robust Aerodynamic Design Optimization for Air Vehicles

The ever-increasing demands for risk-free, resource-efficient and environment-friendly air vehicles motivate the development of advanced design methodology. As a particularly promising design methodology considering uncertainties, robust aerodynamic design optimization (RADO) is capable of providing robust and reliable aerodynamic configuration and reducing cost under probable uncertainties in the flight envelop and all life cycle of air vehicle. However, the major challenges including high computational cost with increasing dimensionality of uncertainty and complex RADO procedure hinder the wider application of RADO. In this paper, the complete RADO procedure, i.e., uncertainty modeling, establishment of uncertainty quantification approach as well as robust optimization subject to reliability constraints under uncertainty, is elaborated. Systematic reviews of RADO methodology including uncertainty modeling methods, comprehensive uncertainty quantification approaches, and robust optimization methods are provided. Further, this paper presents a brief survey of the main applications of RADO in the aerodynamic design of transonic flow and natural-laminar-flow, and discusses the application prospects of RADO methodology for air vehicles. The detailed statement of the paper indicates the intention, i.e., to present the state of the art in RADO methodology, to highlight the key techniques and primary challenges in RADO, and to provide the beneficial directions for future researches.

A universal power-law model for wind speed uncertainty

The uncertainty is a significant characteristic of wind speed in wind engineering field. Especially, it has brought much more problems to the grid in safe and efficient utilization of large scale wind power. And there is urgent need of systematic and perfect models that can describe windspeed uncertainty in grid scheduling and controlling. In this paper, a universal power-law model is proposed for properly depicting the uncertainty of both wind speed and wind power. According to the turbulence nature of wind uncertainty, the uncertainty model of wind speed is firstly obtained by using wavelet multi-scale transform algorithm for its tight supporting characteristic, which is more reasonable than the traditional algorithm of getting the mean valve and the variance valve of the time series. And the turbulent intensity model is further improved by a power-law model, which is suitable for much more kinds of turbulence on complex geographical conditions than that proposed in current international IEC standard with the sufficient actual data. In physically speaking, the model improvement with three parameters is consistent with turbulence development mechanism. Moreover, the uncertainty modeling method of wind power is developed based on the universal power-law model, which is not only suitable for the power of single wind turbine, but also suitable for the power of whole wind farm. It’s very importance that the wind speed uncertainty model is extended to model the power uncertainty of wind turbine and farm, in especial its or their power output is usually limited for human adjustment control. It has a certain significance to the real-time dispatch and optimal control of the renewable energy power system.

A Novel Optimized Fuzzy Approach Based on Monte Carlo Method for System Load, Wind Turbine and Photovoltaic Unit Uncertainty Modeling in Unit Commitment

Developing usage of renewable resources, such as wind turbine and photovoltaic units, and their output uncertainty beside the system total load forecasting imprecision leads to the uncertainty of unit commitment solution. This article presents a new fuzzy approach for modeling of these uncertainty sources behavior in a power system including wind turbine, photovoltaic, and thermal units. For the first time, based on Monte Carlo simulation, a new concept called Monte Carlo mismatch index is proposed as a criterion for uncertainty modeling precision, which is used as a fitness function for optimization of the proposed fuzzy system parameters by genetic algorithm. Then this stochastic-optimized fuzzy system is applied for uncertainty modeling. The fuzzy system output is that part of the power system total load, which should be distributed among thermal units. Then, this output is fed to a crisp unit commitment program based on particle swarm optimization. Finally, optimal thermal units generation cost and scheduling is presented and the proposed method performance is compared with other uncertainty modeling methods.

Uncertainty in reservoir modeling

Uncertainty is due to incomplete and imprecise knowledge as a result of limited sampling of the subsurface heterogeneities. Well data and seismic data have incomplete coverage and finite resolution. The interpretations are uncertain. Reservoirs are heterogeneous and difficult to predict away from wells. Ignoring uncertainty and locking in important model parameters and choices amounts to an assumption of perfect knowledge and is generally an unacceptable approach. Uncertainty must be explicitly modeled. Understanding the (1) sources of uncertainty, (2) methods to represent uncertainty, (3) the formalisms of uncertainty, and (4) uncertainty modeling methods and workflows were essential for the integration of all reservoir information sources and providing good models for decision making in the presence of uncertainty.

Effects of Product Attributes in Case-Based Reasoning Methods for Cost Estimation and Cost Uncertainty Modeling

This paper presents case-based reasoning methods for cost estimation and cost uncertainty modeling that may help designers select a new product concept at the early stage of product development. The case-based reasoning methods without cost adjustment (CBR) and with cost adjustment (CBR-A) are compared with analogy-based cost estimation (ABCE) and multivariate linear regression analysis (RA). Under the conditions studied in the illustrative example of this paper (i.e., a single knowledge base, sport utility vehicle (SUV) concepts, and up to five concept attributes), leave-one-out cross-validation results indicate that both CBR-A and RA accurately estimate cost and reliably model cost uncertainty; and optimum attribute sets for the most accurate cost estimation and the most reliable cost uncertainty modeling are different in all methods. The results of this paper indicate that designers may need to carefully select attribute sets by analyzing trade-offs between the accuracy of cost estimation and the reliability of cost uncertainty modeling when product cost is used as a criterion to select concepts.