Probabilistic Interval Research Articles

Similarity Measures of Probabilistic Interval Preference Ordering Sets and Their Applications in Decision-Making

The concept of probabilistic interval preference ordering sets (PIPOSs) provides a scientific and intuitive framework for solving real-life multi-criteria group decision-making problems. In some areas such as investment decision-making and supplier selection, PIPOSs have a wider application space, and the development of similarity and distance measures based on PIPOSs holds great significance. Similarity measure is a basic and prominent tool for dealing with imperfect and ambiguous information in fuzzy sets, but it can also be used to deal with uncertain information in preference ordering. These metrics play an important role in the actual decision-making process, as they effectively quantify the degree of similarity between two PIPOSs, and further allow for the prioritization of different scenarios. In this article, we sort out the definitions and arithmetic rules of PIPOSs, and creatively propose several new similarity measures based on PIPOSs. Then, we propose a group decision-making method based on similarity measures and conduct a comparative study with three existing similarity measures to illustrate its advantages over existing metrics. Finally, we confirm its validity through numerical illustrations in the case study, and also conduct a comparative assessment to verify the scientific validity and effectiveness of the newly introduced measure against the existing metrics.

Probabilistic interval prediction method based on shape‐adaptive quantile regression

AbstractThis article introduces customized screening ensemble with shape‐adaptive quantile regression (CseAQR), a novel probabilistic interval forecasting method built upon the quantile regression model. CseAQR utilizes ensemble learning to perform adaptive quantile regression prediction, which can handle the heteroscedasticity feature in time series data by using a weighted adaptive allocation loss function to enhance the adaptability of the basic quantile regression model on the dataset. The model performance predictor is used to select the optimal ensemble learner combination, assign reasonable adaptive weights to it, and obtain a preliminary prediction interval through weighted aggregation. Combining ensemble learners not only improves the accuracy and robustness of prediction intervals but also ensures the commutativity required for conformal prediction. Finally, the conformal prediction method is applied to locally adjust the prediction interval, constructing a more consistently aligned prediction interval with the actual data on a narrower basis.

A novel dynamic spatio-temporal graph convolutional network for wind speed interval prediction

It is crucial to predict the wind speed for the utilization of renewable wind energy and the operation of transmission lines with increased capacity. The intermittency and stochastic fluctuations of wind speed pose a significant challenge for the high-quality wind speed prediction, and a novel wind speed interval prediction (WSIP) model is constructed in this study by employing the residual estimation (RE)-oriented dynamic spatio-temporal graph convolutional network (DSTGCN) approach. Firstly, a dynamic adjacency matrix is designed to obtain time-varying global spatial weight allocations among each wind speed node. Then, the spatio-temporal features are extracted by using gated recurrent units (GRUs) and GCNs to construct the wind speed graph networks. Moreover, the RE-oriented strategy incorporating the pinball loss is designed to provide a guidance the parameter training of the constructed model, thus eliminating the quantile crossings problem. As a result, the deterministic point prediction of the wind speed is expanded to the quantile-based probabilistic interval prediction. Finally, the experimental results are presented to demonstrate the validity and superiority of proposed scheme in both qualitative and quantitative performance.

Disturbance observer‐based PID synchronization control of complex networks with probabilistic interval time‐varying delays and multiple disturbances

AbstractIn this article, the disturbance observer‐based proportional–integral–derivative (PID) control protocol is investigated for synchronization of complex networks with probabilistic interval time‐varying delays and multiple disturbances. For the sake of reducing conservatism, a method of probabilistic interval time‐varying delay is proposed by introducing two certain intervals with known probability distributions. Moreover, two different disturbances are taken into account. One of the disturbances is produced by an exogenous system which acts through the input channel, while the other is usual norm‐bounded disturbance. Simultaneously, a disturbance observer is designed to estimate and compensate the disturbance generated by the exogenous system. By constructing an appropriate Lyapunov–Krasovskii function, a sufficient criterion is obtained to ensure both the exponential synchronization and prescribed performance index. Finally, the simulation examples are employed to demonstrate the validity of the theoretical results.

Probabilistic Interval Ordering Prioritized Averaging Operator and Its Application in Bank Investment Decision Making

Probabilistic interval ordering, as a helpful tool for expressing positive and negative information, can effectively address multi-attribute decision-making (MADM) problems in reality. However, when dealing with a significant number of decision-makers and decision attributes, the priority relationships between different attributes and their relative importance are often neglected, resulting in deviations in decision outcomes. Therefore, this paper combines probability interval ordering, the prioritized aggregation (PA) operator, and the Gauss–Legendre algorithm to address the MADM problem with prioritized attributes. First, considering the significance of interval priority ordering and the distribution characteristics of attribute priority, the paper introduces probability interval ordering elements that incorporate attribute priority, and it proposes the probabilistic interval ordering prioritized averaging (PIOPA) operator. Then, the probabilistic interval ordering Gauss–Legendre prioritized averaging operator (PIOGPA) is defined based on the Gauss–Legendre algorithm, and various excellent properties of this operator are explored. This operator considers the priority relationships between attributes and their importance level, making it more capable of handling uncertainty. Finally, a new MADM method is constructed based on the PIOGPA operator using probability intervals and employs the arithmetic–geometric mean (AGM) algorithm to compute the weight of each attribute. The feasibility and soundness of the proposed method are confirmed through a numerical example and comparative analysis. The MADM method introduced in this paper assigns higher weights to higher-priority attributes to establish fixed attribute weights, and it reduces the impact of other attributes on decision-making results. It also utilizes the Gauss AGM algorithm to streamline the computational complexity and enhance the decision-making effectiveness.

Combined wind speed forecasting model based on secondary decomposition and quantile regression closed-form continuous-time neural network

ABSTRACT Reliable interval forecasts can quantify the potential risk of wind speeds, which can help people make better use of wind energy. In this study, a new probabilistic prediction model, called Quantile Regression Closed-Form Continuous-time Neural Network (QRCfC), is proposed by combining quantile regression and closed-form continuous-time neural network. A new combined model combining QRCfC, secondary decomposition, multi-objective optimization, and dynamic weight combination strategy is proposed, which makes full use of the advantages of each single model to obtain accurate deterministic prediction and reliable probabilistic interval prediction of wind speed. First, the original wind speed series is divided into several subseries using a secondary decomposition technique built on variational mode decomposition and singular spectrum analysis. Then, four base models are used to predict these subseries separately. After that, the predicted values of the four base models are input into QRCfC for training, where the hyperparameters of QRCfC are dynamically adjusted by a multi-objective ant lion optimization algorithm. Finally, to verify the effectiveness of the proposed models, experiments are conducted using data sets from three wind farms in Gansu, China. Simulation results show that the proposed model achieves excellent prediction performance in both deterministic and probabilistic prediction. For example, compared with the unoptimized quantile regression time convolution network, quantile regression long-short time memory, quantile regression gated recurrent unit, and quantile regression neural network, the proposed model reduces the MAPE by 21.89% and the CRPS by 11.14% for 1-step prediction at site 1.

An automatic and personalized recommendation modelling in activity eCoaching with deep learning and ontology

Electronic coaching (eCoach) facilitates goal-focused development for individuals to optimize certain human behavior. However, the automatic generation of personalized recommendations in eCoaching remains a challenging task. This research paper introduces a novel approach that combines deep learning and semantic ontologies to generate hybrid and personalized recommendations by considering “Physical Activity” as a case study. To achieve this, we employ three methods: time-series forecasting, time-series physical activity level classification, and statistical metrics for data processing. Additionally, we utilize a naïve-based probabilistic interval prediction technique with the residual standard deviation used to make point predictions meaningful in the recommendation presentation. The processed results are integrated into activity datasets using an ontology called OntoeCoach, which facilitates semantic representation and reasoning. To generate personalized recommendations in an understandable format, we implement the SPARQL Protocol and RDF Query Language (SPARQL). We evaluate the performance of standard time-series forecasting algorithms [such as 1D Convolutional Neural Network Model (CNN1D), autoregression, Long Short-Term Memory (LSTM), and Gated Recurrent Units (GRU)] and classifiers [including Multilayer Perceptron (MLP), Rocket, MiniRocket, and MiniRocketVoting] using state-of-the-art metrics. We conduct evaluations on both public datasets (e.g., PMData) and private datasets (e.g., MOX2-5 activity). Our CNN1D model achieves the highest prediction accuracy of 97%, while the MLP model outperforms other classifiers with an accuracy of 74%. Furthermore, we evaluate the performance of our proposed OntoeCoach ontology model by assessing reasoning and query execution time metrics. The results demonstrate that our approach effectively plans and generates recommendations on both datasets. The rule set of OntoeCoach can also be generalized to enhance interpretability.

An innovative short-term multihorizon photovoltaic power output forecasting method based on variational mode decomposition and a capsule convolutional neural network

Due to its importance regarding the integration, economic dispatch, and operation of PV smart grid systems, infrastructure planning, and budgeting, the accurate forecasting of photovoltaic (PV) power generation has drawn increasing research and industry attention. However, the instability, intermittence, and randomness of solar irradiance impose difficulties on the short-term economic dispatch of a smart integrated power, grid and significantly increase the risks arising from PV generation in a power system, exposing PV generators to potential additional costs. A deep convolutional neural network (CNN)-based method can effectively improve the performance of PV generation point prediction and probabilistic interval prediction by efficiently extracting nonlinear features at each frequency. Nevertheless, existing deep learning (DL) studies have mostly focused on more complex network topologies and data decomposition algorithms, ignoring the importance of simultaneously forecasting the PV power produced over multiple temporal periods. To solve the described challenge, we propose a novel two-stage DL approach for PV generation prediction. The end-to-end trained model used in the proposed PV generation forecasting method is an effort to combine the existing methods and avoid the separation of entire task, such as single time-scale PV generation forecasting, independent point forecasting, and probabilistic interval forecasting. A temporal signal decomposition technique called variational mode decomposition (VMD) is employed in the first stage to construct association mappings from fine-grained features to images. In the second stage, an innovative capsule CNN (ACCNet) is proposed to obtain very short-term multihorizon ahead output power predictions for seven different PV systems based on polycrystalline, monocrystalline, cadmium telluride (CdTe) thin-film, amorphous, copper indium gallium diselenide (CIGS) thin-film, heterojunction with intrinsic thin layer (HIT) hybrid, and concentrated photovoltaic (CPV) technologies. The input parameters for each system include solar radiation (diffuse/global horizontal radiation (DHR/GHR) and radiation diffuse/global tilted (RDT/RGT)) and ambient temperature, while the output parameter is the power output of each PV system. The proposed model is validated with the historical datasets of a PV system downloaded from the Desert Knowledge Precinct in Central Australia (DKASC) homepage. The performance of the developed method is proven in detail based on seven different PV systems over multiple data periods, and the experimental results reveal that the proposed approach displays significant improvements and robustness in point forecasting and probabilistic forecasting tasks. We will release the source code to ensure reproducibility and facilitate future work. Our model is open-sourced at https://github.com/YunDuanFei/ACCNet.

Efficient Influential Community Search in Large Uncertain Graphs

Influential community search aims to find cohesive subgraphs (communities) with considerable influence. It is a fundamental graph management operator that can play a crucial role in biological network analysis, activity organization, and other real-life applications. Existing research on influential community search is mainly focused on deterministic graphs with the assumption that influences between entities are certain. This assumption is invalid in many cases because it ignores the uncertainty which is an inherent property of influence. Against this backdrop, in this paper, we introduce an uncertain influential community model, namely <inline-formula><tex-math notation="LaTeX">$(k, \eta)$</tex-math></inline-formula> -influential community, based on which the influential community search problem over uncertain graphs is formulated. Furthermore, we propose an online approach by integrating a peeling-pruning strategy that can progressively refine the given uncertain graph to find the <inline-formula><tex-math notation="LaTeX">$(k, \eta)$</tex-math></inline-formula> -influential communities. To further improve the search performance, two novel indexes, ICU-Index and FICU-Index, are developed to organize the <inline-formula><tex-math notation="LaTeX">$(k, \eta)$</tex-math></inline-formula> -influential communities at different probabilistic intervals. The indexes decompose the probabilistic interval into multiple subintervals and based on this, the <inline-formula><tex-math notation="LaTeX">$(k, \eta)$</tex-math></inline-formula> -influential communities are divided into different groups in turn. Compared with ICU-Index, FICU-Index requires considerably less space with the introduction of two optimization strategies. These indexes help obtain results of an influential community search problem more efficiently. Extensive experiments on large real and synthetic datasets demonstrate the efficiency and effectiveness of our proposed algorithms.

Finite‐time fault detection for nonlinear delayed system with dynamic quantization and multiple packet dropouts

AbstractThe attention of this article is mainly paid to the finite‐time fault detection (FD) problem for nonlinear delayed system with dynamic quantization and multiple packet dropouts. The probabilistic interval time‐varying delay is addressed, which might fall into two intervals with known probability. The measurement signals are quantized by a dynamic quantizer and then transmitted over communication network, where the multiple packet dropouts might occur. The main objective of the considered problem is to design a finite‐time FD filter such that the FD system is stochastically finite‐time stable (SFTS) with guaranteed performance in the presence of probabilistic interval time‐varying delay, dynamic quantization and multiple packet dropouts. Based on Lyapunov stability theory, sufficient criteria for the presence of the desired finite‐time FD filter are presented. Afterwards, the desired filter gain matrices are given via solving certain linear matrix inequalities (LMIs). Finally, a simulation example is used to show the applicability of the obtained finite‐time FD algorithm.

Probabilistic Interval Predictor Based on Dissimilarity Functions

This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use of dissimilarity functions to estimate the conditional probability density function of the outputs. A family of empirical probability density functions, parameterized by means of two scalars, is introduced. It is shown that the proposed family encompasses the multivariable normal probability density function as a particular case. We show that the presented approach constitutes a generalization of classical estimation methods. A validation scheme is used to tune the two parameters on which the methodology relies. In order to prove the effectiveness of the presented methodology, some numerical examples and comparisons are provided.

Attack-resilient Fusion of Sensor Data with Uncertain Delays

Malicious attackers may disrupt the safety of autonomous systems through compromising sensors to feed wrong measurements to the controller. This article proposes attack-resilient sensor fusion that combines local sensor readings and shared sensing information from multiple sources. The method results in higher resilience against sensor attacks through jointly considering sensing noise and uncertain communication delay. To be specific, we first identify the considerable impact of the delay on determining attacked sensors. Second, we present a novel two-dimensional abstract sensor model, where each measurement is augmented as a probabilistic interval based on the convolution of the noise and delay. Third, we propose a fusion algorithm that admits the fused value with highest joint probability distribution of the intervals to tolerate corrupted measurements. Finally, we demonstrate the effectiveness of our method in a vehicle-platoon case study using extensive simulations and testbed experiments.

Annulus-Event-Based Finite-Time Fault Detection for Discrete-Time Nonlinear Systems with Probabilistic Interval Delay and Randomly Occurring Faults

Annulus-Event-Based Finite-Time Fault Detection for Discrete-Time Nonlinear Systems with Probabilistic Interval Delay and Randomly Occurring Faults

Short-term power load probabilistic interval multi-step forecasting based on ForecastNet

Many uncertain factors to the planning and distribution of the power grid have been brought by connecting to the distributed power grid and increasing active loads. To obtain more accurate and comprehensive information of power load forecasting value, a short-term power load-interval multi-step forecasting method based on ForecastNet is proposed in this paper. Firstly, single variable historical load data is used as input. Secondly, ForecastNet’s deep feedforward architecture is proposed to exactly capture the time-varying characteristics of load. Finally, the Gaussian distribution output is used to realize the uncertainty evaluation of the model. Deterministic point forecasting combines probabilistic forecasting to quantify the uncertainty of forecast results. Output power load forecasts in the form of probability intervals. The experimental results show that the ForecastNet forecasting model proposed in this paper outperforms the other three models in the four seasons. In the autumn when the load curve volatility and random components are large, MASE=0.357, SMAPE=4.869%, NRMSE=11.804%. It has the advantages of the high predictive range quality, high predictive accuracy, and great practical engineering value.

Multi‐objective expansion planning of park‐level integrated energy system considering the volatility trend of CETP

With the rapid development of carbon trading market, the volatility trend of carbon emission trading price (CETP) becomes one of the factors that cannot be ignored in energy system planning. Based on this, this paper proposes a multi-objective expansion planning model for park-level integrated energy system (PIES) that takes into account the volatility trend of CETP. First, the influencing factors of CETP prediction are filtered and downscaled, and a kernel extreme learning machine (KELM) model based on the improved multi-objective grey wolf algorithm optimizer (IMOGWO) is used for probabilistic interval prediction of CETP. Next, the operational characteristics of each carbon emission device are analysed and a model for calculating the cost of carbon trading is proposed. Then, a two-layer PIES planning model is developed with the objective of minimizing the annualized system cost and carbon emissions during the expansion planning cycle, the upper-layer model is a planning model for solving equipment expansion scenarios, and the lower-layer model is an operation model for calculating typical operation schemes. Finally, the simulation effect of the prediction model is verified by the European carbon trading data, and the planning schemes are compared and analysed to prove the effectiveness of the proposed method.

Probabilistic interval estimation of design floods under non-stationary conditions by an integrated approach

Abstract Quantifying the uncertainty of non-stationary flood frequency analysis is very crucial and beneficial for planning and design of water engineering projects, which is fundamentally challenging especially in the presence of high climate variability and reservoir regulation. This study proposed an integrated approach that combined the Generalized Additive Model for Location, Scale and Shape parameters (GAMLSS) method, the Copula function and the Bayesian Uncertainty Processor (BUP) technique to make reliable probabilistic interval estimations of design floods. The reliability and applicability of the proposed approach were assessed by flood datasets collected from two hydrological monitoring stations located in the Hanjiang River of China. The precipitation and the reservoir index were selected as the explanatory variables for modeling the time-varying parameters of marginal and joint distributions using long-term (1954–2018) observed datasets. First, the GAMLSS method was employed to model and fit the time-varying characteristics of parameters in marginal and joint distributions. Second, the Copula function was employed to execute the point estimations of non-stationary design floods. Finally, the BUP technique was employed to perform the interval estimations of design floods based on the point estimations obtained from the Copula function. The results demonstrated that the proposed approach can provide reliable probabilistic interval estimations of design floods meanwhile reducing the uncertainty of non-stationary flood frequency analysis. Consequently, the integrated approach is a promising way to offer an indication on how design values can be estimated in a high-dimensional problem.

Sampled-data non-fragile state estimation for delayed genetic regulatory networks under stochastically switching sampling periods

This paper is concerned with the non-fragile state estimation (NFSE) problem for a class of delayed genetic regulatory networks (GRNs) under stochastic sampling mechanisms. The measurement output is sampled before being transmitted to the estimator where the sampling period switches between two different values in a random way. By transforming the sampling periods into bounded time-delays, the issue of designing a non-fragile state estimator based on stochastically sampled measurements is converted into the NFSE problem for GRNs with multiple probabilistic interval delays. Then, by constructing a Lyapunov–Krasovskii functional and employing the Gronwall’s inequality together with Jensen’s inequality, a sufficient criterion is obtained to ensure the exponential mean-square stability of the corresponding estimation error dynamics. Furthermore, the desired non-fragile estimator gain is obtained via solving a convex optimization problem. Finally, the validity of the developed stochastic sampled-data NFSE scheme is verified via a numerical example.

Wind speed deterministic forecasting and probabilistic interval forecasting approach based on deep learning, modified tunicate swarm algorithm, and quantile regression

As a renewable, clean and economical energy source, wind energy has rapidly infiltrated into the modern power grid system. Wind speed forecasting, the crucial technology of wind power grid connection, has attracted large amounts of scholars for research and modeling. However, a large number of models only focus on the point forecasts, which are far from meeting the requirements of risk control and evaluation of power system. To fill the gap, a novel forecasting model which combined the modified multi-objective tunicate algorithm, benchmark models, and Quantile regression is proposed for deterministic and probabilistic interval forecasts. Theoretical proof demonstrates that the proposed modified algorithm can combine the merits of all benchmark models and better solve the nonlinear characteristics of wind speed. Comparative experiments which include sixteen relevant models are performed on three datasets to validate the performance of the proposed model. Simulation results show that the proposed model is the most accurate in all datasets, and can also get the interval forecast results with relatively high coverage and the narrowest width. Therefore, this model can provide accurate point forecasting results and uncertainty information, which is beneficial to the real-time control of wind turbine and power grid dispatching.

Research on solving strategy of structural reliability index based on probabilistic interval hybrid model

In this paper, a hybrid model is established in which the randomness of probabilistic parameters coexists with the uncertainty of interval parameters. Based on the reliability theory, the evaluation criteria of structural reliability under the hybrid model were proposed, and the two-layer cycle method and direct iterative algorithm were derived to calculate the structural reliability index. The correctness and effectiveness of the model and algorithm are verified by examples of a cantilever beam and a three-story frame structure. The hybrid model combines the probabilistic model with the interval model effectively and has practical significance for the engineering application of reliability theory.

Investment Probabilistic Interval Estimation for Construction Project Using the Hybrid Model of SVR and GWO

AbstractInvestment estimation is a key component of early decision-making for a construction project, which is crucial to the project cost control. Currently, most investment estimation researches ...