Variational Inference Based Kernel Dynamic Bayesian Networks for Construction of Prediction Intervals for Industrial Time Series With Incomplete Input

Prediction intervals(PIs)for industrial time series can provide useful guidance for workers.Given that the failure of industrial sensors may cause the missing point in inputs,the existing kernel dynamic Bayesian networks(KDBN),serving as an effective method for PIs construction,suffer from high computational load using the stochastic algorithm for inference.This study proposes a variational inference method for the KDBN for the purpose of fast inference,which avoids the timeconsuming stochastic sampling.The proposed algorithm contains two stages.The first stage involves the inference of the missing inputs by using a local linearization based variational inference,and based on the computed posterior distributions over the missing inputs the second stage sees a Gaussian approximation for probability over the nodes in future time slices.To verify the effectiveness of the proposed method,a synthetic dataset and a practical dataset of generation flow of blast furnace gas(BFG)are employed with different ratios of missing inputs.The experimental results indicate that the proposed method can provide reliable PIs for the generation flow of BFG and it exhibits shorter computing time than the stochastic based one.

Ensemble Wind Power Prediction Interval with Optimal Reserve Requirement

Wind power prediction interval(WPPI)models in the literature have predominantly been developed for and tested on specific case studies.However,wind behavior and characteristics can vary significantly across regions.Thus,a prediction model that performs well in one case might underperform in another.To address this shortcoming,this paper proposes an ensemble WPPI framework that integrates multiple WPPI models with distinct characteristics to improve robustness.Another important and often overlooked factor is the role of probabilistic wind power prediction(WPP)in quantifying wind power uncertainty,which should be handled by operating reserve.Operating reserve in WPPI frameworks enhances the efficacy of WPP.In this regard,the proposed framework employs a novel bi-layer optimization approach that takes both WPPI quality and reserve requirements into account.Comprehensive analysis with different real-world datasets and various benchmark models validates the quality of the obtained WPPIs while resulting in more optimal reserve requirements.

Conditional Coverage Estimation for High-Quality Prediction Intervals

Deep learning has been recently studied to generate high-quality prediction intervals(PIs)for uncertainty quantification in regression tasks,including recent applications in simulation metamodeling.The high-quality criterion requires PIs to be as narrow as possible,whilst maintaining a pre-specified level of data(marginal)coverage.However,most existing works for high-quality PIs lack accurate information on conditional coverage,which may cause unreliable predictions if it is significantly smaller than the marginal coverage.To address this problem,we propose an end-to-end framework which could output high-quality PIs and simultaneously provide their conditional coverage estimation.In doing so,we design a new loss function that is both easy-to-implement and theoretically justified via an exponential concentration bound.Our evaluation on real-world benchmark datasets and synthetic examples shows that our approach not only achieves competitive results on high-quality PIs in terms of average PI width,but also accurately estimates conditional coverage information that is useful in assessing model uncertainty.

Optimal dispatching method for integrated energy system based on robust economic model predictive control considering source-load power interval prediction

Effective source-load prediction and reasonable dispatching are crucial to realize the economic and reliable operations of integrated energy systems(IESs).They can overcome the challenges introduced by the uncertainties of new energies and various types of loads in the IES.Accordingly,a robust optimal dispatching method for the IES based on a robust economic model predictive control(REMPC)strategy considering source-load power interval prediction is proposed.First,an operation model of the IES is established,and an interval prediction model based on the bidirectional long short-term memory network optimized by beetle antenna search and bootstrap is formulated and applied to predict the photovoltaic power and the cooling,heating,and electrical loads.Then,an optimal dispatching scheme based on REMPC is devised for the IES.The source-load interval prediction results are used to improve the robustness of the REPMC and reduce the influence of source-load uncertainties on dispatching.An actual IES case is selected to conduct simulations;the results show that compared with other prediction techniques,the proposed method has higher prediction interval coverage probability and prediction interval normalized averaged width.Moreover,the operational cost of the IES is decreased by the REMPC strategy.With the devised dispatching scheme,the ability of the IES to handle the dispatching risk caused by prediction errors is enhanced.Improved dispatching robustness and operational economy are also achieved.

Prediction model of interval grey number based on DGM(1,1)

In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ones.Hereby,a prediction model based on interval grey number sequences is proposed.By mining the geometric features of interval grey number sequences on a two-dimensional surface,all the interval grey numbers are converted into real numbers by means of certain algorithm,and then the prediction model is established based on those real number sequences.The entire process avoids the algebraic operations of grey number,and the prediction problem of interval grey number is usefully solved.Ultimately,through an example＇s program simulation,the validity and practicability of this novel model are verified.

Interval finite difference method for steady-state temperature field prediction with interval parameters

A new numerical technique named interval finite difference method is proposed for the steady-state temperature field prediction with uncertainties in both physical parameters and boundary conditions. Interval variables are used to quantitatively describe the uncertain parameters with limited information. Based on different Taylor and Neumann series, two kinds of parameter perturbation methods are presented to approximately yield the ranges of the uncertain temperature field. By comparing the results with traditional Monte Carlo simulation, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed method for solving steady-state heat conduction problem with uncertain-but-bounded parameters.

Ultra-short-term Interval Prediction of Wind Power Based on Graph Neural Network and Improved Bootstrap Technique

Reliable and accurate ultra-short-term prediction of wind power is vital for the operation and optimization of power systems.However,the volatility and intermittence of wind power pose uncertainties to traditional point prediction,resulting in an increased risk of power system operation.To represent the uncertainty of wind power,this paper proposes a new method for ultra-short-term interval prediction of wind power based on a graph neural network(GNN)and an improved Bootstrap technique.Specifically,adjacent wind farms and local meteorological factors are modeled as the new form of a graph from the graph-theoretic perspective.Then,the graph convolutional network(GCN)and bi-directional long short-term memory(Bi-LSTM)are proposed to capture spatiotemporal features between nodes in the graph.To obtain highquality prediction intervals(PIs),an improved Bootstrap technique is designed to increase coverage percentage and narrow PIs effectively.Numerical simulations demonstrate that the proposed method can capture the spatiotemporal correlations from the graph,and the prediction results outperform popular baselines on two real-world datasets,which implies a high potential for practical applications in power systems.

An integrated new threshold FCMs Markov chain based forecasting model for analyzing the power of stock trading trend

This paper explores the power of stock trading trend using an integrated New ThresholdFuzzy Cognitive Maps(NTFCMs)Markov chain model.This new model captures thepositive as well as the negative jumps and predicts the trend for different stocks over 4months which follow an uptrend,downtrend and a mixed trend.The mean absolute percent error(MAPE)tolerance limits,the root mean square error(RMSE)tolerance limits aredetermined for various stock indices over a multi-timeframe period and observed for theexisting methods lying within the defined limits.The results show for every‘n’number ofpredictions made,the predicted close value of the day’s stock price was within tolerancelimit with 0%error and with 100%accuracy in predicting the future trend.

Nonparametric Probabilistic Prediction of Regional PV Outputs Based on Granule-based Clustering and Direct Optimization Programming

Regional photovoltaic(PV) power prediction plays an important role in power system planning and operation. To effectively improve the performance of prediction intervals(PIs) for very short-term regional PV outputs, an efficient nonparametric probabilistic prediction method based on granulebased clustering(GC) and direct optimization programming(DOP) is proposed. First, GC is proposed to formulate and cluster the sample granules consisting of numerical weather prediction(NWP) and historical regional output data, for the enhanced hierarchical clustering performance. Then, to improve the accuracy of samples' utilization, an unbalanced extension is used to reconstruct the training samples consisting of power time series. After that, DOP is applied to quantify the output weights based on the optimal overall performance. Meanwhile, a balance coefficient is studied for the enhanced reliability of PIs. Finally, the proposed method is validated through multistep PIs based on the numerical comparison of real PV generation data.

Adaptive forgetting factor OS-ELM and bootstrap for time series prediction

Online sequential extreme learning machine(OS-ELM)for single-hidden layer feedforward networks(SLFNs)is an effective machine learning algorithm.But OS-ELM has some underlying weaknesses of neglecting time series timeliness and being incapable to provide quantitative uncertainty for prediction.To overcome these shortcomings,a time series prediction method is presented based on the combination of OS-ELM with adaptive forgetting factor(AFF-OS-ELM)and bootstrap(B-AFF-OS-ELM).Firstly,adaptive forgetting factor is added into OS-ELM for adjusting the effective window length of training data during OS-ELM sequential learning phase.Secondly,the current bootstrap is developed to fit time series prediction online.Then associated with improved bootstrap,the proposed method can compute prediction interval as uncertainty information,meanwhile the improved bootstrap enhances prediction accuracy and stability of AFF-OS-ELM.Performances of B-AFF-OS-ELM are benchmarked with other traditional and improved OS-ELM on simulation and practical time series data.Results indicate the significant performances achieved by B-AFF-OS-ELM.

Prediction of rice productivity in Kandhamal district of Orissa using simulation modeling

Simulation technique has been employed to predict rice yield of Kandhamal plateaus in Orissa(India)using the data of previous years.Preliminary simulation model has been developed The test for uniformity and independence has been conducted using Kolmogrov–smironov test and auto-correlation test,respectively.The result obtained has been subjected to testing of hypothesis by using two sided test.Data for five years(1995 to 2000)are used for model validation and the sample size is increased to 12 years i.e.,from 1995 to 2007 for prediction up to 2012.Sensitivity analysis is conducted by changing the parameters within feasible limits to find out the effect on the model.

Machine learning approach for estimating the human-related VOC emissions in a university classroom

Indoor air quality becomes increasingly important,partly because the COVID-19 pandemic increases the time people spend indoors.Research into the prediction of indoor volatile organic compounds(VOCs)is traditionally confined to building materials and furniture.Relatively little research focuses on estimation of human-related VOCs,which have been shown to contribute significantly to indoor air quality,especially in densely-occupied environments.This study applies a machine learning approach to accurately estimate the human-related VOC emissions in a university classroom.The time-resolved concentrations of two typical human-related(ozone-related)VOCs in the classroom over a five-day period were analyzed,i.e.,6-methyl-5-hepten-2-one(6-MHO),4-oxopentanal(4-OPA).By comparing the results for 6-MHO concentration predicted via five machine learning approaches including the random forest regression(RFR),adaptive boosting(Adaboost),gradient boosting regression tree(GBRT),extreme gradient boosting(XGboost),and least squares support vector machine(LSSVM),we find that the LSSVM approach achieves the best performance,by using multi-feature parameters(number of occupants,ozone concentration,temperature,relative humidity)as the input.The LSSVM approach is then used to predict the 4-OPA concentration,with mean absolute percentage error(MAPE)less than 5%,indicating high accuracy.By combining the LSSVM with a kernel density estimation(KDE)method,we further establish an interval prediction model,which can provide uncertainty information and viable option for decision-makers.The machine learning approach in this study can easily incorporate the impact of various factors on VOC emission behaviors,making it especially suitable for concentration prediction and exposure assessment in realistic indoor settings.

Statistical and environmental analyses for the definition of a regional rainfall threshold system for landslide triggering in Tuscany （Italy）

The aim of this work is the determination of regional-scale rainfall thresholds for the triggering of landslides in the Tuscany Region （Italy）. The critical rainfall events related to the occurrence of 593 past landslides were characterized in terms of duration （D） and intensity （I） I and D values were plotted in a log-log diagram and a lower boundary was clearly noticeable： it was interpreted as a threshold representing the rainfall conditions associated to landsliding. That was also confirmed by a comparison with many literature thresholds, but at the same time it was clear that a similar threshold would be affected by a too large approximation to be effectively used for a regional warning system. Therefore, further analyses were performed differentiating the events on the basis of seasonality, magnitude, location, land use and lithology. None of these criteria led to discriminate among all the events different groups to be characterized by a specific and more effective threshold. This outcome could be interpreted as the demonstration that at regional scale the best results are obtained by the simplest approach, in our case an empirical black box model which accounts only for two rainfall parameters （I and D）. So a set of thresholds could be conveniently defined using a statistical approach： four thresholds corresponding to four severity levels were defined by means of the prediction interval technique and we developed a prototype warning system based on rainfall recordings or weather forecasts.

Energy Management System Design and Testing for Smart Buildings Under Uncertain Generation (Wind/Photovoltaic) and Demand

This study provides details of the energy management architecture used in the Goldwind microgrid test bed. A complete mathematical model, including all constraints and objectives, for microgrid operational management is first described using a modified prediction interval scheme. Forecasting results are then achieved every 10 min using the modified fuzzy prediction interval model, which is trained by particle swarm optimization.A scenario set is also generated using an unserved power profile and coverage grades of forecasting to compare the feasibility of the proposed method with that of the deterministic approach. The worst case operating points are achieved by the scenario with the maximum transaction cost. In summary, selection of the maximum transaction operating point from all the scenarios provides a cushion against uncertainties in renewable generation and load demand.

Time-of-use Pricing Model Considering Wind Power Uncertainty

Large-scale new energy pressures on the grids bring challenges to power system's security and stability.In order to optimize the user's electricity consumption behavior and ease pressure,which is caused by new energy on the grid,this paper proposes a time-of-use price model that takes wind power uncertainty into account.First,the interval prediction method is used to predict wind power.Then typical wind power scenes are selected by random sampling and bisecting the K-means algorithm.On this basis,integer programming is used to divide the peak-valley period of the multi-scenes load.Finally,under the condition of many factors such as user response based on consumer psychology,user electricity charge and power consumption,this paper takes the peak-valley difference of equivalent net load and the user dissatisfaction degree as the goal,and using the NSGA-II multi-objective optimization algorithm,evaluates the Pareto solution set to obtain the optimal solution.In order to test the validity of the model proposed in this paper,we apply it to an industrial user and wind farms in Yan'an city,China.The results show that the model can effectively ensure the user's electrical comfort while achieving the role of peak shaving and valley flling.