Probabilistic Prediction Method Research Articles

Probabilistic Forecasting of Residential Energy Consumption Based on SWT-QRTCN-ADSC-NLSTM Model

Residential electricity consumption forecasting plays a crucial role in the rational allocation of resources reducing energy waste and enhancing the grid-connected operation of power systems. Probabilistic forecasting can provide more comprehensive information for the decision-making and dispatching process by quantifying the uncertainty of electricity load. In this study, we propose a method based on stationary wavelet transform (SWT), quantile regression (QR), Bidirectional nested long short-term memory (BiNLSTM), and Depthwise separable convolution (DSC) combined with attention mechanism for electricity consumption probability prediction methods. First, the data sequence is decomposed using SWT to reduce the complexity of the sequence; then, the combined neural network model with attention is used to obtain the prediction values under different quantile conditions. Finally, the probability density curve of electricity consumption is obtained by combining kernel density estimation (KDE). The model was tested using historical demand-side data from five UK households to achieve energy consumption predictions 5 min in advance. It is demonstrated that the model can achieve both reliable probabilistic prediction and accurate deterministic prediction.

A parallel GRU with dual-stage attention mechanism model integrating uncertainty quantification for probabilistic RUL prediction of wind turbine bearings

The accurate probabilistic prediction of remaining useful life (RUL) of bearings plays an important role in ensuring the safe operation of wind turbine maintenance decision making. However, it is still a challenge to improve prediction accuracy and quantify prediction uncertainty, leading to the inability of precision and reliable prediction results. Accordingly, this paper proposed a novel probabilistic RUL prediction method combined the parallel GRUs with dual-stage attention mechanism (PDAGRU) prediction model with the non-parametric uncertainty quantification approach to overcome the limitations. In the PDAGRU model, the dual-stage attention mechanism is developed to improve the capability of degradation information extraction. Meanwhile, the parallel structure can enhance prediction accuracy and help quantify model uncertainty. The proposed uncertainty quantification approach with less prior knowledge can provide probabilistic RUL prediction results based on the kernel density estimation (KDE) and Monte Carlo (MC) dropout. Moreover, a first prediction time (FPT) determination method based on the isotonic regression is developed to more accurately reflect the degradation trajectory of bearings’ RUL. Two cases including simulated data and real-world data are deployed to verify the effectiveness of the proposed method. Compared with other methods, the superiority of the proposed method is verified. The RUL prediction accuracy and interval coverage probability for wind turbine bearings are high to 90.4% and 99.7% respectively.

Wind Power Probability Density Prediction Based on Quantile Regression Model of Dilated Causal Convolutional Neural Network

Aiming at the wind power prediction problem, a wind power probability prediction method based on the quantile regression of a dilated causal convolutional neural network is proposed. With the developed model, the Adam stochastic gradient descent technique is utilized to solve the cavity parameters of the causal convolutional neural network under different quantile conditions and obtain the probability density distribution of wind power at various times within the following 200 hours. The presented method can obtain more useful information than conventional point and interval predictions. Moreover, a prediction of the future complete probability distribution of wind power can be realized. According to the actual data forecast of wind power in the PJM network in the United States, the proposed probability density prediction approach can not only obtain more accurate point prediction results, it also obtains the complete probability density curve prediction results for wind power. Compared with two other quantile regression methods, the developed technique can achieve a higher accuracy and smaller prediction interval range under the same confidence level.

Vehicle Trajectory Prediction Considering Driver Uncertainty and Vehicle Dynamics Based on Dynamic Bayesian Network

Vehicle trajectory prediction is a crucial but intricate problem for lateral driving assistance systems because of driver uncertainty. This article presents a probabilistic vehicle-trajectory prediction method based on a dynamic Bayesian network (DBN) model integrating the driver’s intention, maneuvering behavior, and vehicle dynamics. By selecting a most-relevant-feature vector using joint mutual information, we design a Gaussian mixture model- hidden Markov model and employ the model as a node in the DBN to identify the driver’s intention. Then, a reference path is generated using the road information. The uncertainties of drivers are captured in steering- and longitudinal-control using a stochastic driver model and a Markov chain, respectively. A vehicle dynamic model ensures that the predicted vehicle trajectory adheres to the vehicle dynamics, which improves the prediction accuracy. A particle filter is used to recursively estimate the vehicle trajectory, including position coordinates and the lateral distance from the vehicle center of gravity to the road edge. We evaluate the proposed DBN trajectory prediction method in both lane-keeping and lane-changing scenarios based on a dataset collected from a real-time dynamic driving simulator. Results show that the proposed method can achieve accurate long-term trajectory prediction.

Probabilistic Prediction Method of Erosion Volume and Deposition Area from Rainfall Observation Data

We propose a methodology to estimate the spatial distribution of the probability of sediment deposition due to debris flow from rainfall data by combining the probability prediction of erosion volume based on an ordinal logistic regression and a sediment transport simulation. By using the Receiver Operating Characteristic (ROC) curve and Area Under Curve (AUC) we have selected the best combination of shortand long-term rainfall indices used as explanatory variables in the ordinal logistic model. The results showed that the regression model using 60-minute and 48-hour rainfall indices performed well and that the regression model using three events improved the predictability of local disasters in 2014. Furthermore, we performed Monte Carlo debris-flow simulations using rainfall data from 2014 using the model. We confirmed that the spatial distribution of disaster probability is consistent with the actual damage.

Probability forecasting method of Three Gorges Reservoir inflow flood based on error distribution estimation

准确、及时的入库洪水预报,对三峡水库综合效益的发挥和长江流域水旱灾害防御、水资源利用、流域综合管理等具有重要作用。基于预报误差的最优分布估计和分布函数动态参数假定,提出了一种三峡水库入库洪水概率预报方法,并进行了洪水概率预报业务试验。结果表明:本文所提方法科学可行,计算快捷,使用方便,便于在实时作业预报中应用推广;概率预报结果较确定性预报结果,在水量预报、预警效果等方面均有所改善,1~5 d预见期预报的确定性系数提高0.1%~3.4%,水量误差减少0.1%~4.8%,可为三峡水库实时调度提供更可靠的预报信息;所提出的三峡水库入库洪水概率预报业务化产品,可提供更多风险信息,为三峡水库的科学调度,尤其是洪水资源化利用提供更好的优化决策支撑。;Accurate and timely inflow flood forecasting plays an important role in the comprehensive benefit of the Three Gorges Reservoir, and the prevention of floods and droughts, the utilization of water resources, the comprehensive management for the Yangtze River basin. Based on the optimal distribution estimation of the prediction error and the assumption of the dynamic parameters for the distribution function, a probability prediction method for the inflow flood of the Three Gorges Reservoir is proposed, and the operational test of the probability prediction of the flood is carried out. The results show that the physical rational of the presented method is clear, and it is easy to be applied and popularized in real-time operation forecast. Compared with the deterministic prediction results, the probability forecast has improved in water volume prediction and early warning effect. For example, the certainty coefficient of forecast in 1-5 d is increased by 0.1%-3.4%, and the water volume error is reduced by 0.1%-4.8%, which can provide more reliable forecast information for the real-time operation of the Three Gorges Reservoir. The proposed operational product of probability forecast of inflow flood process can provide more risk information, and provide better support for scientific and fine operation of the Three Gorges Reservoir, especially for optimal decision-making of flood resource utilization.

A probabilistic inverse prediction method for predicting plutonium processing conditions

In the past decade, nuclear chemists and physicists have been conducting studies to investigate the signatures associated with the production of special nuclear material (SNM). In particular, these studies aim to determine how various processing parameters impact the physical, chemical, and morphological properties of the resulting special nuclear material. By better understanding how these properties relate to the processing parameters, scientists can better contribute to nuclear forensics investigations by quantifying their results and ultimately shortening the forensic timeline. This paper aims to statistically analyze and quantify the relationships that exist between the processing conditions used in these experiments and the various properties of the nuclear end-product by invoking inverse methods. In particular, these methods make use of Bayesian Adaptive Spline Surface models in conjunction with Bayesian model calibration techniques to probabilistically determine processing conditions as an inverse function of morphological characteristics. Not only does the model presented in this paper allow for providing point estimates of a sample of special nuclear material, but it also incorporates uncertainty into these predictions. This model proves sufficient for predicting processing conditions within a standard deviation of the observed processing conditions, on average, provides a solid foundation for future work in predicting processing conditions of particles of special nuclear material using only their observed morphological characteristics, and is generalizable to the field of chemometrics for applicability across different materials.

Probabilistic prediction of ground-motion intensity for regions lacking strong ground-motion records

Probabilistic prediction of ground-motion intensity in regions lacking strong ground-motion records is a vital issue for seismic structural design. Several approaches have been suggested for this purpose, and nearly all of them directly import and adjust the ground-motion prediction equation (GMPE) of ground-motion measures such as the peak ground acceleration (PGA) or spectral acceleration (SA) from data-rich regions. However, as the transmissions of PGA and SA from the source to the site correspond to nonlinear processes, this import and adjustment may lead to an unrealistic evaluation of ground motion. In this study, a novel probabilistic prediction method of ground-motion intensity for such regions is proposed. In contrast to the current approach wherein the GMPE of ground-motion measures such as PGA or SA is directly used, a Fourier amplitude spectral (FAS) model is suggested to express the seismic transmission process from the source to the site. The ground-motion intensities of PGA or SA are obtained from the FAS model using the random vibration theory. The exceedance probability of ground-motion intensity is calculated based on Monte Carlo simulations. As the FAS conforms to the linear system theory and the determination of FAS model does not require too many ground-motion records, the proposed method should be convenient for the probabilistic prediction of ground-motion intensity in regions lacking strong ground-motion records.

A probability prediction method for the classification of surrounding rock quality of tunnels with incomplete data using Bayesian networks

The classification of surrounding rock quality is critical for the dynamic construction and design of tunnels. However, obtaining complete parameters for predicting the surrounding rock grades is always challenging in complex tunnel geological environment. In this study, a new method based on Bayesian networks is proposed to predict the probability for the classification of surrounding rock quality of tunnel with incomplete data. A database is collected with 286 cases in 10 tunnels, involving nine parameters: rock hardness, weathering degree, rock mass integrity, rock mass structure, structural plane integrity, in-situ stress, groundwater, rock basic quality, and surrounding rock level. Moreover, the Bayesian network structure is built using the collected database and quantitatively verified by strength analysis. Then, the accuracy, precision, recall, F-measure and receiver operating characteristic (ROC) curves are utilized for model evaluation. The average values of accuracy, precision, recall, F-measure, and area under the curve (AUC) are approximately 89.2%, 91%, 92%, 91%, and 0.98, respectively. These results indicate that the established classification model has high accuracy, even with small sample size and imbalanced samples. Ten additional sets of tunnel cases (incomplete data) are also used for verification. The results reveal that compared with the traditional Q-system (Q) and rock mass rating (RMR) classification methods, the proposed classification model has the lowest error rate and is capable of using incomplete data to predict sample results. Finally, sensitivity analysis suggests that the rock hardness and rock mass integrity have the strongest impact on the quality of tunnel surrounding rock. Overall, the findings of this study can serve as a useful reference for future rock mass quality evaluation in tunnels, underground powerhouses, slopes, etc.

Dealing with multi-criteria decision analysis in time-evolving approach using a probabilistic prediction method

Multi-criteria Decision Analysis (MCDA) is a methodology that has been classically used to rank alternatives according to a set of decision criteria. The MCDA techniques have been shown to be an efficient tool in a number of real-life engineering problems. Nevertheless, most of the proposed approaches in the field do not consider the temporal characteristic of the criteria values, which can be an interesting information to be explored in order to predict future rankings. The present work proposes a novel MCDA methodology in which the past data of the criteria are considered to predict their future values. Our approach is based on a tensorial formulation, together with the use of the recursive least mean squares method in the prediction step. In addition, we consider a probabilistic prediction and use the Stochastic Multi-criteria Acceptability Analysis, which allows the decision maker to observe the degree of uncertainty in the ranking. Numerical experiments with synthetic and actual data attest to the proposal’s relevance in scenarios in which the criteria values change over time.

A new framework for short-term wind power probability forecasting considering spatial and temporal dependence of forecast errors

Since deterministic prediction errors of wind power cannot be avoided, probabilistic prediction can adequately describe the uncertainty of wind power and, thus, provide further guidance to dispatching authorities for decision making. Current probabilistic prediction methods for wind power are still incomplete in mining its physical variation process. Therefore, this study constructs a new framework for short-term wind power probabilistic forecasting considering the spatio-temporal dependence of errors by mining the spatio-temporal characteristics of historical wind power data and numerical weather forecasts at numerical weather prediction (NWP). First, the deterministic prediction results are obtained by an improved deep belief network (DBN); then, a multi-location NWP is introduced to propose a multi-level error scenario partitioning method considering the spatio-temporal dependence property. Finally, a new error sample set is formed by reconstructing the kernel density estimation method to adapt the model, and the short-term wind power probability prediction at different confidence levels is carried out. It is, thus, concluded that the effectiveness of the overall framework under the probabilistic prediction considering spatio-temporal dependence is verified in a wind farm in Jilin, China, and the prediction accuracy is effectively and significantly improved compared with the same confidence level, and the coverage of the evaluation index prediction interval is improved by 1.23, 0.72, and 0.80%, and the average bandwidth of the prediction interval is reduced by 2.14, 1.40, and 0.63%, which confirms the proposed effectiveness and feasibility of the method.

The attention-assisted ordinary differential equation networks for short-term probabilistic wind power predictions

To improve the practicality, data-driven techniques of predicting the wind power generation and its uncertainty still need to address three technical challenges, uplifting the prediction accuracy via inventing an emerging data analytics mechanism, flexibly scaling up the prediction resolution from the data sampling resolution, and preventing invalid probabilistic prediction results. This study is thus motivated to investigate an advanced prediction method enabling highly accurate and valid probabilistic wind power predictions as well as the capability of a resolution scale-up. The long short term memory (LSTM) network combined with an attention-assisted ordinary differential equation network (AODEN), LSTM-AODEN, is developed for the first time in the literature to produce a novel deep network architecture for probabilistic wind power predictions via leveraging advantages of deep learning and ordinary differential equations. In the LSTM-AODEN, a two-stage training scheme, which sequentially develops one median prediction model and one multi-interval length prediction model, is proposed to fully eliminate quantile crossings and guarantee the validity of prediction results. Six evaluation metrics in computational experiments verify that the proposed LSTM-AODEN method leads to overall highly accurate and fully valid results of the point prediction, interval prediction, and quantile prediction compared to several classes of state-of-the-art probabilistic prediction methods. Meanwhile, the proposed method is proved to offer a unique capability of generating higher-resolution probabilistic wind power prediction results, which is gained from the AODEN, indicated by the lowest prediction errors.

A dimension-reduction based maximum entropy method for probabilistic ultimate load prediction in composite corrugated sandwich panels

Composite sandwich structures with excellent properties are extensively applied in aerospace. However, the mechanical properties of composite sandwich structures are variable and uncertain due to materials, processes, and processing technologies. In this study, a probability prediction method of ultimate load value in composite corrugated sandwich panels (CCSP) is proposed by combining the dimension reduction method (DRM) and the maximum entropy method (MEM). This new method is used to study the influence of fiber parameter uncertainty on the ultimate load value of CCSP. First, an n-dimensional response function about the ultimate load of CCSP is reduced in dimension. Then the first four statistical moments of this function are obtained by Taylor expansion. Finally, through fitting with MEM, the probability density function about the ultimate load of CCSP is obtained. To verify the correctness of the new method, a comparative analysis is carried out with the Monte Carlo simulation (MCS). The errors of the results are all less than 6.4%, indicating the new method can effectively predict the ultimate load value of CCSP with probability and greatly reduce finite element calculation time. The sensitivity of the ultimate load value of CCSP to basic input variables is also studied.

Probability prediction method of transmission line icing fault based on adaptive relevance vector machine

To precisely forecast the operation status of transmission line during an ice storm and achieve early warning, a method based on adaptive relevance vector machine (ARVM) is proposed for fault probability prediction of transmission line icing. According to the basic theory of RVM, this paper establishes a forecasting model, which consists of selection and preprocessing of data, initial parameter optimization, icing prediction with adaptive optimization and fault probability prediction of transmission line. The quantum particle swarm algorithm, together with K-fold Cross-validation is applied to optimize model parameters. The weight vector of the icing prediction model is corrected by repeating training to get the precise prediction result of ice thickness with its probability distribution. The case study with practical data from Zhejiang province shows that the proposed method can effectively improve the accuracy of icing prediction and further realize fault probability prediction of transmission line, which can provide early warning for the anti-icing and mitigation work of the electric power department.

Probabilistic method for fatigue crack growth prediction with hybrid prior

In practical engineering, there is usually multi-source prior knowledge which can be integrated for fatigue crack growth (FCG) prediction. This paper proposes a new probabilistic prediction method which enables the input of hybrid prior. This method comprises two inference steps. In the first inference step, a set of candidate priors are input. Then, the Monte Carlo integration is adopted in the calculation of posterior belief of each candidate prior. In the second inference step, the particle filter is extended to conduct Bayesian inference with hybrid prior. Numerical studies show integrating multiple priors can increase the robustness of FCG prediction.

Performance Improvement of Very Short-term Prediction Intervals for Regional Wind Power Based on Composite Conditional Nonlinear Quantile Regression

Accurate regional wind power prediction plays an important role in the security and reliability of power systems. For the performance improvement of very short-term prediction intervals (PIs), a novel probabilistic prediction method based on composite conditional nonlinear quantile regression (CCNQR) is proposed. First, the hierarchical clustering method based on weighted multivariate time series motifs (WMTSM) is studied to consider the static difference, dynamic difference, and meteorological difference of wind power time series. Then, the correlations are used as sample weights for the conditional linear programming (CLP) of CCNQR. To optimize the performance of PIs, a composite evaluation including the accuracy of PI coverage probability (PICP), the average width (AW), and the offsets of points outside PIs (OPOPI) is used to quantify the appropriate upper and lower bounds. Moreover, the adaptive boundary quantiles (ABQs) are quantified for the optimal performance of PIs. Finally, based on the real wind farm data, the superiority of the proposed method is verified by adequate comparisons with the conventional methods.

Thermal rating probability prediction considering the temporal correlation among the thermal ratings

The thermal rating of the overhead transmission line is an important parameter for the operation and control of the power system. In order to further integrate it into the system dispatch decisions, it is necessary to conduct the prediction for the thermal ratings in the lookahead time horizon of dispatch decisions. At present, the researches on the thermal rating prediction focus on the independent prediction for the thermal rating in each prediction period, without considering the temporal correlation among the thermal ratings. In this paper, a joint probability prediction method for multiperiod thermal ratings considering the temporal correlation among the thermal ratings is proposed. Specifically, based on the temporal correlation among the thermal ratings and the independent probability prediction of thermal rating in each period, the multivariate normal probability density function of multiperiod thermal ratings is generated. The prediction simulation shows that considering the temporal correlation among the thermal ratings in the thermal rating prediction process can improve the prediction results and make full use of the currentcarrying capability of overhead lines, which will promote the accommodation of renewable energy and energy saving and emission reduction.

Probabilistic prediction and calibration for residual shear strength of corroded reinforced concrete columns

Degradation of shear strength for reinforced concrete (RC) columns caused by steel corrosion is one of the prominent factors for shortening the entire service life of RC structures. In this work, probabilistic prediction and calibration methods for residual shear strength of corroded RC columns were developed by combining theoretical analysis with available experimental data. Deterministic shear strength degradation model accounting for the cross-sectional area reduction and mechanical properties degradation of steel reinforcement and concrete was derived first based on the truss and arch mechanisms. Then probabilistic prediction model was proposed by introducing probabilistic model parameters and systematic error. Meanwhile, probabilistic model parameters regarding the influences of prior variation coefficients and update times were investigated using the Bayesian theory. Moreover, probabilistic method was implemented to calibrate seven available deterministic shear strength models based on probability density function and confidence interval. Results indict that the proposed model can not only quantify the probabilistic characteristics of shear strength and predict the residual shear strength for any given corrosion level and guarantee rate, but also provide a suitable approach for calibrating the applicability of conventional deterministic shear strength models.

Two-Stage Energy Management for Energy Storage System by Using Stochastic Model Predictive Control Approach

There is a growing tendency for industrial consumers to invest in both photovoltaic (PV) and energy storage systems (ESSs) to meet their electricity requirements. However, the uncertainty of load demand and PV output brings great challenges for ESS operation. In this paper, a stochastic model predictive control (MPC) approach-based energy management strategy for ESSs is proposed. A non-parametric probabilistic prediction method embedded in time series correlation is adopted to describe the uncertainty of load demand and PV output. Then, a two-stage energy management model is proposed aiming at minimizing the total operation cost. The upper stage can generate an hourly operation strategy for ESSs, while the lower stage focuses on a more detailed minute-level operation strategy. The hourly operation strategy is also used as a basis to guide the ESS operation in the lower stage. Besides, a chance constraint was introduced to achieve a win–win solution between PV power consumption and electricity tariff, while the terminal value constraint of the capacity of ESSs to better cope with the uncertainty beyond the prediction time window. Finally, the numerical results showed that the proposed method can achieve an effective ESS energy management strategy.

“Targets-Plans-Decision”: A framework to identify the size of protected areas based on the balance of ecological protection and economic development

A framework called “Targets-Plans-Decision” (TPD) was established for identifying the size of adequate protected areas (PAs) based on the combination of species distribution probability prediction method, systematic conservation planning (SCP) theory, and protection efficiency analysis, to achieve a balance between ecological protection and economic development. The first step of the framework is to determine the protection targets. In this study, the protection targets were defined as important habitats and important ecosystems. The second step is to identify the PAs plans of different sizes. We adopted a SCP method, which takes into account cost-effectiveness while delineating the PAs. The third step is to determine the optimal size of the PAs through ecological protection efficiency analysis. We constructed the protection efficiency index (PEI), which is the protection cost per unit area. Then we used Kaya identity (a structural decomposition method) to decompose PEI. The decomposed PEI included value density (ecological value per unit area) and value cost (cost to realize unit ecological value). By analyzing the changes of the two, the optimal size of the PAs can be determined. We took Nanchang as an example to conduct an empirical study to verify the usability of the TPD framework. The result shows the TPD framework proposed in this study can effectively identify the optimal size of PAs and contribute to forming a cost-effective ecological protection plan. When the size of PAs was set to 70% of the important habitats and important ecosystems, it was most beneficial for ecological protection. Furthermore, the optimal protection efficiency plan recommended by the TPD framework improved the efficiency of ecological protection. The TPD framework can serve as a basis for the size identification of PAs and also support the delineation of PAs worldwide.