Distribution Of Prediction Errors Research Articles

Statistical inference for innovation distribution in ARMA and multi-step-ahead prediction via empirical process

The kernel distribution estimator (KDE) is proposed based on residuals of the innovation distribution in the autoregressive moving-average (ARMA) time series. The deviation between KDE and the innovation distribution function is shown to converge to the Brownian bridge, leading to the construction of a Kolmogorov–Smirnov smooth simultaneous confidence band for the innovation distribution function. Additionally, an empirical cumulative distribution function (CDF) based on prediction residuals is introduced for the multi-step-ahead prediction error distribution function. This empirical process weakly converges to a Gaussian process with a specific covariance function. Furthermore, a quantile estimator is derived from the empirical CDF of prediction residuals, and multi-step-ahead prediction intervals (PIs) for future observations are established using these estimated quantiles. The PIs achieve the nominal prediction level asymptotically for the finite variance ARMA model. Simulation studies and analysis of crude oil price data confirm the validity of the asymptotic theory.

Study of Urban Unmanned Aerial Vehicle Separation in Free Flight Based on Track Prediction

In recent years, the application prospect of urban logistics unmanned aerial vehicles has attracted extensive attention. The high-density operation of UAVs requires autonomous separation maintenance capability. To achieve autonomous separation maintenance, it is necessary to conduct autonomous track prediction and formulate the required separation accordingly. Based on the target level of safety requirements for UAV operation, aiming at the autonomous separation maintenance ability of UAVs and considering the accuracy of track prediction, a method to calculate the required separation between UAVs is proposed. This study consists of two parts. Firstly, based on historical data, the position prediction error of the flight track is investigated. Using a machine learning model, a two-stage track prediction method, which involves classification followed by prediction, is proposed for urban logistics UAV track data. Subsequently, based on the track prediction error distribution, by designing a gas model and a position error probability model, a separation-formulating model for urban logistics UAVs in free flight is proposed in which UAV maneuverability is considered. By applying this model, the required separation is formulated for UAVs. When the required separation is set to 48.5 m, the overall collision risk meets the TLS requirements. The research provides a feasible method for establishing autonomous separation for urban logistics UAVs.

Comparative Study of ANN and SVM Model Network Performance for Predicting Brake Power in SI Engines Using E15 Fuel

Currently, artificial neural networks (ANNs) and support vector machines (SVMs) are the most common applications of machine learning approaches. In this study, a comparative study of ANN and SVM is presented to evaluate the performance of each model in predicting the brake power (BP) of GX35-OHC 4-stroke, air-cooled, single cylinder gasoline engine with E15 (15% ethanol + 85% gasoline) fuel. Two models are compared based on experimental dataset that has single output (BP) and five inputs, engine speed (S), engine torque (T), intake air temperature (Tair), intake air flow (Qair), and fuel consumption (ṁ). The samples were split into three sets: Training set (70%), Validation set (15%), and the Test set (15%) based on 60 samples. The results are compared through different graphs such as target vs actual values, regression plots, histograms of prediction errors, residual plots, learning curves, and error distributions. The results showed that SVM model is indicated to have lower RMSE (0.0044) and higher EVS (0.9953), while ANN is shown to have lower value of MAPE (1.51%). These results have significant implications for the use of ANN and SVM models in real-world applications that need gradual comprehensibility and model generalization. In addition, work done with the models outlined above should try and test them in other engines and operating conditions to demonstrate the model’s and performance.

Refined offshore wind speed prediction: Leveraging a two-layer decomposition technique, gated recurrent unit, and kernel density estimation for precise point and interval forecasts

Precise forecasting of offshore wind speeds is paramount for various applications, including offshore wind energy production, disaster prevention and mitigation, and maritime navigation. This study introduces a novel model for point and interval prediction of offshore wind speed, incorporating an innovative two-layer decomposition technique, gated recurrent unit (GRU), and kernel density estimation (KDE). Initially, the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is utilized to decompose the raw series into multiple subsequences, thus alleviating the inherent data nonstationarity. Subsequently, we employ the refined composite multiscale fuzzy entropy (RCMFE) to reconstruct the subsequences into multiple components, thereby reducing the computational complexity. Variational mode decomposition (VMD) is utilized to enhance the modeling accuracy to decompose the high-frequency component, thereby generating a set of submodels. The GRU, a specialized recurrent neural network architecture, is leveraged to forecast the remaining components and submodels, producing a series of subresults. The subresults are linearly summed to obtain the final point prediction result. Finally, based on point prediction, employing KDE to gauge the probability density distribution of prediction errors culminates in the derivation of the offshore wind speed prediction interval. The experimental results substantiate the superior predictive performance of the proposed prediction model.

Predicting Social Inequality in Poland Using Price Dispersion on the Real Estate Market

Measuring and predicting price dispersion on the real estate market is an important issue for both investors and policymakers. Price dispersion in the housing market can be seen as an additional dimension for measuring social inequality and one of the main goals of public policies that focus on life satisfaction and the accumulation of permanent wealth. The article considers the Polish real estate market and proposes the prediction methods of four measures of dispersion. They are based on quantiles and allow overall measurement of dispersion. In the prediction of dispersion measures the plug-in predictors utylizing longitudinal mixed models are proposed. Furthermore, the ex ante prediction accuracy measure called the quantile of absolute prediction errors (QAPE) is assessed using the residual bootstrap estimators. QAPE allows for a comprehensive description of the distribution of prediction errors, thus fostering discussion of possible various market scenarios.

Study on the effect of stress path on the deformation and non-coaxial characteristics of modified iron tailings

In order to study the deformation and non-coaxial characteristics of fiber cement modified iron tailing sand (FCIT) under different stress paths. The evolution law of the dynamic stress ratio (η) on the cumulative deformation and non-coaxial angle of FCIT under different tension-compression amplitude ratios (α) was explored through hollow torsional shear tests. The deformation behavior of FCIT is analyzed by using the stability theory. The research results show that: 1) The increase of dynamic stress level will deepen the cumulative deformation of FCIT, while the increase of α will make the deformation mode of FCIT develop into bulging failure-shear failure-tensile failure. 2) According to the development trend of cumulative strain and cumulative strain rate of FCIT, it can be divided into three stages: plastic stability, plastic creep and incremental collapse, and the cumulative strain rate development prediction model is established, and the prediction error distribution is within ±20%. 3) The stress path determines the non-coaxiality of FCIT to a certain extent, and the non-coaxial angle fluctuates and decreases with the increase of the principal stress direction angle. When α=0.125, the maximum and minimum values of the non-coaxial angle of FCIT are 1.5 rad and 0.4 rad respectively. 4) Cement hydration reaction generates calcium alumina and hydrated calcium silicate (C-S-H) to make FCIT structure more compact, fiber-matrix interfacial connections more dense, and play a role in filling the pores.

Research on a Deep Ensemble Learning Model for the Ultra-Short-Term Probabilistic Prediction of Wind Power

An accurate method for predicting wind power is crucial in effectively mitigating wind energy fluctuations and ensuring a stable power supply. Nevertheless, the inadequacy of the stability of wind energy severely hampers the consistent functioning of the power grid and the reliable provision of electricity. To enhance the accuracy of wind power forecasting, this paper proposes an ensemble model named the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and convolutional bidirectional long short-term memory (CNN-BiLSTM), which incorporates a data preprocessing technique, feature selection method, deep ensemble model, and adaptive control. Initially, CEEMDAN is utilized to decompose wind speed and power sequences and hence obtain decomposed subsequences for further analysis. Subsequently, the CNN is used to extract features from each subsequence, whereas each subsequence is processed by BiLSTM to obtain an ultra-short-term deterministic prediction model. Additionally, the adaptive kernel density estimation (AKDE) method is employed to estimate the probabilistic distribution of prediction error, enabling ultra-short-term probabilistic wind power prediction. Finally, based on real datasets, the reliability of the model in probabilistic prediction is verified through the evaluation metrics of multi-step prediction intervals (PIs).

Flow Prediction of a Measurement and Control Gate Based on an Optimized Back Propagation Neural Network

The measurement and control gate, as a new type of measurement and control equipment, has been widely used for water quantity control in irrigation areas. However, there is a lack of methods for calibrating the flow inside the measurement box at present. This paper establishes a flow prediction model based on a back propagation (BP) neural network and its optimization algorithm by using 450 sets of sample data obtained from the indoor gate overflow test and verified the effectiveness and accuracy of the prediction model by using another 205 sets of sample data. The results show that the gate flow prediction model based on a BP neural network and its optimization algorithm has self-adaptability to different flow patterns, and its prediction accuracy is significantly higher than that of the traditional water measurement method. Compared to the unoptimized BP model, the BP model optimized by the genetic algorithm (GA) or particle swarm optimization (PSO) has higher prediction accuracy and better error distribution. Both GA and PSO algorithms can be used to optimize the initial weights and thresholds of the BP flow prediction model. However, by comprehensively analyzing the prediction accuracy, error distribution, and running time, the PSO algorithm has better optimization performance compared to the GA algorithm. The prediction model can provide a reference for flow rate calibration and the anomaly rejection of measurement and control gates in the irrigation area.

Studying the evolutions, differences, and water security impacts of water demands under shared socioeconomic pathways: A SEMs-bootstrap-ANN approach applied to Sichuan Province

In this study, a SEMs-bootstrap-ANN method was presented for constructing prediction intervals (PIs) of water demand under shared socioeconomic pathways (SSPs). The primary objective was to examine the evolution, disparities, and impacts on water security. Initially, a bootstrap algorithm and an artificial neural network (ANN) were combined to form a bootstrap-ANN model, which determined the centres and widths of the PIs at a specified significance level by estimating the distributions of prediction values and errors. The water demand factors in SSPs were projected using socioeconomic models like Cobb-Douglas, based on the narratives of the International Institute for Applied Systems Analysis (IIASA). By incorporating these factors into the bootstrap-ANN model, the study obtained the temporal changes of water demand PIs in SSPs, while quantifying the differences and water security implications using the interval difference index (IDI) and surface water exploration index (SWEI). The case study focused on Sichuan province, and the model performance was evaluated via the evaluation indices and cross-validation. The results demonstrated five key findings.Firstly, the proposed method showed a greater PICP of 0.985, slightly larger PIRAW of 9.83%, and higher MAIS than other methods in the historical dataset, indicating a small disadvantage in width in return for better accuracy and overall performance.Secondly, the reliability of the results in the SSP period was supported by the PIRAWs (mostly within 15%), the cross errors (approximately 5%), and their performance in 2021 (the PIs in SSP2 almost covered all true values).Thirdly, the total water demands in all SSPs within Sichuan Province exhibited a consistent upward trajectory, with SSP5 displaying the highest increase of 44–63% compared to current water usage.Fourthly, among the four SSPs, the most substantial disparities were observed between SSP5 and SSP3, reaching a maximum difference of 32%. Conversely, the disparities between SSP2 and SSP1 fluctuated around zero, transitioning from negative to positive trends. Notably, from an environmental perspective, SSP1 was considered preferable to SSP2.Lastly, the SWEIs, which reflected water security conditions in Sichuan Province under the four SSPs, ranked in the following order: SSP3, SSP1, SSP2, and SSP5, indicating a progressively worsening situation. Despite not reaching stress thresholds even during dry years until 2100, the water security conditions could deteriorate by 28–46% compared to historical extremes and by 3–16% compared to extended extremes in dry years.

Inherent spatiotemporal uncertainty of renewable power in China

Solar and wind resources are vital for the sustainable energy transition. Although renewable potentials have been widely assessed in existing literature, few studies have examined the statistical characteristics of the inherent renewable uncertainties arising from natural randomness, which is inevitable in stochastic-aware research and applications. Here we develop a rule-of-thumb statistical learning model for wind and solar power prediction and generate a year-long dataset of hourly prediction errors of 30 provinces in China. We reveal diversified spatiotemporal distribution patterns of prediction errors, indicating that over 60% of wind prediction errors and 50% of solar prediction errors arise from scenarios with high utilization rates. The first-order difference and peak ratio of generation series are two primary indicators explaining the uncertainty distribution. Additionally, we analyze the seasonal distributions of the provincial prediction errors that reveal a consistent law in China. Finally, policies including incentive improvements and interprovincial scheduling are suggested.

Population Pharmacokinetic Analysis of Follicle-Stimulating Hormone During Ovarian Stimulation: Relation with Weight, Prolactin and Gene Polymorphism in THADA and ADIPOQ.

Personalisation strategies of ovarian stimulation for in vitro fertilisation (IVF)/ intracytoplasmic sperm injection (ICSI) treatments using exogenous follicle-stimulating hormone (FSH) have been extensively studied over the past 20 years. This research aimed to develop a FSH population pharmacokinetic (PPK) model taking into account the contribution of gene polymorphisms in Chinese reproductive-age women. Data from 173 patients undergoing GnRH agonist down-regulation long protocols of IVF/ICSI treatment were collected. PPK analysis was subsequently conducted using the nonlinear mixed-effect model (NONMEM) software. Several covariates, including 18 single nucleotide polymorphisms, demographic factors and biological characteristics, were evaluated. The final PPK model was extensively validated using bootstrapping and normalised prediction error distribution, as well as external validation on an independent group of 35 patients. FSH PPK was accurately described by a one-compartment model with first-order absorption. The typical population value of apparent clearance was estimated to be 0.81 L/h [relative standard errors (RSE) 5.3%] with an inter-individual variability (IIV) of 16.0%. The typical apparent distribution volume was 8.36 L (RSE 9.7%, 59.7% IIV), and the absorption rate constant was estimated to be 0.0444 h-1 (RSE 9.1%). Body weight, basal prolactin concentration and the gene ADIPOQ (rs1501299) showed a significant covariate effect on the FSH clearance rate and exposure concentration. Genotypes of THADA (rs12478601) significantly influenced the distribution volume. Simulation results indicated that patients with the TT genotype of THADA (rs12478601) required a longer time to reach steady state and had less fluctuation in FSH levels. Model evaluations showed that the final model accurately and precisely described the observed data and demonstrated effective prediction performance. PPK models of FSH have been developed, which could potentially be used for FSH dosage individualisation in the clinical setting. This study has been registered with the Chinese Clinical Trials Registry (ChiCTR2100049142).

Multi-correntropy fusion based fuzzy system for predicting DNA N4-methylcytosine sites

The identification of DNA N4-methylcytosine (4mC) sites is an important field of bioinformatics. Statistical learning methods and deep learning have been applied in this direction. The previous methods focused on feature representation and feature selection, and did not take into account the deviation of noise samples for recognition. Moreover, these models were not established from the perspective of prediction error distribution. To solve the problem of complex error distribution, we propose a maximum multi-correntropy criterion based kernelized higher-order fuzzy inference system (MMC-KHFIS), which is constructed with multi-correntropy fusion. There are 6 4mC and 8 UCI data sets are employed to evaluate our model. The MMC-KHFIS achieves better performance in the experiment.

The role of strength distributions for premature creep failure

Premature and unexpected creep damage is a significant concern in high-temperature engineering. Identifying outliers in creep rupture data is essential for assessing the risk of premature creep failure. This study proposes a new method to evaluate premature creep failure using log-logistic distribution fit of prediction errors and outlier positions. Fitting results for seven different alloys were obtained from extrapolation procedures using soft-constrained machine learning algorithms (SCMLAs) and constrained time-temperature parameters (TTPs) based on prior research. A comprehensive statistical analysis was conducted for all materials. The log-logistic distribution was validated as a suitable method for fitting prediction error distributions. Regression plots demonstrate effective residual balance and accurate outlier capture. The best fitting methods were identified based on the width of the distributions. Outlier positions were used to evaluate the probability of premature creep failure quantitatively. For example, a 0.5% probability of observing creep rupture strengths that are approximately 50% lower than the standardized creep stress was found for TP316H, T321H, and high Cr steels SUH616B. These findings offer valuable insights for estimating premature creep failure in materials.

Energy Conservation and Loss Reduction Strategy of Active Distribution System with Distributed Photovoltaic Resources Considering Conservation Voltage Reduction

With the massive distributed photovoltaic resources and multi-load connected to the distribution network, network loss and energy consumption have become two of the most important issues. To solve this problem, an energy conservation and loss reduction optimization strategy for active distribution network (ADN) considering conservation voltage reduction (CVR) is proposed. First, the probability density distribution of photovoltaic resources output prediction error is fitted by the Gaussian mixture model (GMM) to simulate the random characteristics of distributed photovoltaics. Second, according to the multiple load types, the load controlled by CVR is modeled, cooperating with the on-load tap changer (OLTC) to achieve energy reduction. Finally, the controllable resources are co-optimized to maintain the voltage level while saving energy. Case studies on the modified IEEE-33 node distribution network verify the applicability of the strategy.

Graph Spatiotemporal Pattern Learning Network for Real-Time Road Network Traffic Abnormal Incident Detection

To improve the efficiency of detecting abnormal traffic incidents on the road network and reduce the false alarm rate, a real-time traffic anomaly detection framework based on a graph spatiotemporal pattern learning (GSTPL) network is proposed. In this framework, a traffic pattern search algorithm based on a fluctuation similarity measure is designed to screen traffic flow data with the same traffic pattern, and a traffic pattern graph tuple is constructed as the input of the network model to avoid the sample imbalance problem and the effect of single-sample randomness for traffic pattern learning. Then the GSTPL network is designed to extract, unsupervised, the traffic spatiotemporal pattern features and make a reasonable prediction of future traffic parameters as the basis for anomaly evaluation. To further restrain the effect of random fluctuations in traffic flow parameters, an abnormal state evaluation method is designed to calculate the anomaly state likelihood by prediction error distribution learning. The overall detection framework realizes stable prediction of network key node traffic parameters by using spatiotemporal pattern features to construct the traffic pattern graph tuple, and gives incident evaluation results in real time by combination with the detection data. The experiment uses I90 and I405 highway traffic data in Seattle, WA, from 2015. Through comparative analysis, the proposed incident detection method based on GSTPL has a higher detection rate and lower false alarm rate, can adaptively learn dynamic changes of the traffic pattern, and has strong adaptability and stability to different traffic environments.

A non-ferrous metal price ensemble prediction system based on innovative combined kernel extreme learning machine and chaos theory

Non-ferrous metal futures, as a significant component of the financial market, are complementary and coordinated with other financial elements, which has been a key area of research in recent years. However, given the apparent volatility and chaotic nature of the non-ferrous metal price sequence, forecasting it remains a difficult challenge. While prior research employed a variety of methodologies to forecast metal prices, they overlooked the critical role of chaos feature analysis and the necessity of error analysis, severely limiting prediction accuracy. This paper designs a novel non-ferrous metal price ensemble prediction system that incorporates data decomposition, phase space reconstruction, multi-objective optimization, point prediction, and interval prediction. A combined kernel extreme learning machine based on the improved multi-objective lion swarm optimization algorithm is developed and theoretically explained to improve prediction accuracy and reliability. Additionally, the appropriate creation of the prediction interval based on the best-fit distribution of the point prediction error enabled the examination of various levels of uncertainty. In an empirical experiment using copper and aluminum prices from the London Metal Exchange, the proposed system demonstrated benefits in point and interval prediction, providing decision makers with useful prediction references.

Horizontal Data Augmentation Strategy for Industrial Quality Prediction.

In recent years, neural network-based soft sensor technology has been widely used in industrial production processes and has excellent optimization, monitoring, and quality prediction performance. This paper proposes a horizontal data augmentation strategy to provide highly available data for subsequent prediction models, called the combined autoencoder data augmentation (CADA) strategy. This paper has developed a CADA-based convolutional neural network (CADA-CNN) soft sensor model and applied it to the process of industrial debutanizer and industrial steam volume. In terms of method validation, this paper compares the output data of the proposed CADA by the Spearman correlation coefficient to verify the strategy’s feasibility. Then, the output data of the CADA strategy is fed into the artificial neural network (NN), support vector regression (SVR), and convolutional neural network (CNN) for comparison experiments. The final experimental results show that our proposed CADA-CNN model has lower prediction error and better prediction error distribution.

Active power control strategy for wind farms based on power prediction errors distribution considering regional data.

One of the renewable energy resources, wind energy is widely used due to its wide distribution, large reserves, green and clean energy, and it is also an important part of large-scale grid integration. However, wind power has strong randomness, volatility, anti-peaking characteristics, and the problem of low wind power prediction accuracy, which brings serious challenges to the power system. Based on the difference of power prediction error and confidence interval between different new energy power stations, an optimal control strategy for active power of wind farms was proposed. Therefore, we focus on solving the problem of wind power forecasting and improving the accuracy of wind power prediction. Due to the prediction error of wind power generation, the power control cannot meet the control target. An optimal control strategy for active power of wind farms is proposed based on the difference in power prediction error and confidence interval between different new energy power stations. The strategy used historical data to evaluate the prediction error distribution and confidence interval of wind power. We use confidence interval constraints to create a wind power active optimization model that realize active power distribution and complementary prediction errors among wind farms with asymmetric error distribution. Combined with the actual data of a domestic (Cox’s Bazar, Bangladesh) wind power base, a simulation example is designed to verify the rationality and effectiveness of the proposed strategy.

Short-Term Forecasting and Uncertainty Analysis of Photovoltaic Power Based on the FCM-WOA-BILSTM Model

Aiming to solve the problem that photovoltaic power generation is always accompanied by uncertainty and the short-term prediction accuracy of photovoltaic power (PV) is not high, this paper proposes a method for short-term photovoltaic power forecasting (PPF) and uncertainty analysis using the fuzzy-c-means (FCM), whale optimization algorithm (WOA), bi-directional long short-term memory (BILSTM), and no-parametric kernel density estimation (NPKDE). First, the principal component analysis (PCA) is used to reduce the dimensionality of the daily feature vector, and then the FCM is used to divide the weather into four categories: sunny, cloudy, rainy, and extreme weather. Second, the WOA algorithm is used to train the hyperparameters of BILSTM, and finally, the optimized hyperparameters were used to construct a WOA-BILSTM prediction model to train the four types of weather samples after FCM clustering. The NPKDE method was used to calculate the probability density distribution of PV prediction errors and confidence intervals for PPF. The RMSEs of the FCM-WOA-BILSTM model are 2.46%, 4.89%, and 1.14% for sunny, cloudy, and rainy weather types, respectively. The simulation results of the calculation example show that compared with the BP, LSTM, GRU, PSO-BILSTM, and FCM-PSO-BP models, the proposed FCM-WOA-BILSTM model has higher prediction accuracy under various weather types, which verifies the effectiveness of the method. Moreover, the NPKDE method can accurately describe the probability density distribution of forecast errors.

Electricity Price Prediction for Energy Storage System Arbitrage: A Decision-Focused Approach

Electricity price prediction plays a vital role in energy storage system (ESS) management. Current prediction models focus on reducing prediction errors but overlook their impact on downstream decision-making. So this paper proposes a decision-focused electricity price prediction approach for ESS arbitrage to bridge the gap from the downstream optimization model to the prediction model. The decision-focused approach aims at utilizing the downstream arbitrage model for training prediction models. It measures the difference between actual decisions under the predicted price and oracle decisions under the true price, i.e., decision error, by regret, transforms it into the tractable surrogate regret, and then derives the gradients to predicted price for training prediction models. Based on the prediction and decision errors, this paper proposes the hybrid loss and corresponding stochastic gradient descent learning method to learn prediction models for prediction and decision accuracy. The case study verifies that the proposed approach can efficiently bring more economic benefits and reduce decision errors by flattening the time distribution of prediction errors, compared to prediction models for only minimizing prediction errors.