Revisiting Akaike’s Final Prediction Error and the Generalized Cross Validation Criteria in Regression from the Same Perspective: From Least Squares to Ridge Regression and Smoothing Splines

In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.

Prediction and driving factors of forest fire occurrence in Jilin Province,China

Forest fires are natural disasters that can occur suddenly and can be very damaging,burning thousands of square kilometers.Prevention is better than suppression and prediction models of forest fire occurrence have developed from the logistic regression model,the geographical weighted logistic regression model,the Lasso regression model,the random forest model,and the support vector machine model based on historical forest fire data from 2000 to 2019 in Jilin Province.The models,along with a distribution map are presented in this paper to provide a theoretical basis for forest fire management in this area.Existing studies show that the prediction accuracies of the two machine learning models are higher than those of the three generalized linear regression models.The accuracies of the random forest model,the support vector machine model,geographical weighted logistic regression model,the Lasso regression model,and logistic model were 88.7%,87.7%,86.0%,85.0%and 84.6%,respectively.Weather is the main factor affecting forest fires,while the impacts of topography factors,human and social-economic factors on fire occurrence were similar.

Cross-Band Spectrum Prediction Algorithm Based on Data Conversion Using Generative Adversarial Networks

Spectrum prediction is one of the new techniques in cognitive radio that predicts changes in the spectrum state and plays a crucial role in improving spectrum sensing performance.Prediction models previously trained in the source band tend to perform poorly in the new target band because of changes in the channel.In addition,cognitive radio devices require dynamic spectrum access,which means that the time to retrain the model in the new band is minimal.To increase the amount of data in the target band,we use the GAN to convert the data of source band into target band.First,we analyze the data differences between bands and calculate FID scores to identify the available bands with the slightest difference from the target predicted band.The original GAN structure is unsuitable for converting spectrum data,and we propose the spectrum data conversion GAN(SDC-GAN).The generator module consists of a convolutional network and an LSTM module that can integrate multiple features of the data and can convert data from the source band to the target band.Finally,we use the generated target band data to train the prediction model.The experimental results validate the effectiveness of the proposed algorithm.

Generating Time-Series Data Using Generative Adversarial Networks for Mobility Demand Prediction

The increasing penetration rate of electric kickboard vehicles has been popularized and promoted primarily because of its clean and efficient features.Electric kickboards are gradually growing in popularity in tourist and education-centric localities.In the upcoming arrival of electric kickboard vehicles,deploying a customer rental service is essential.Due to its freefloating nature,the shared electric kickboard is a common and practical means of transportation.Relocation plans for shared electric kickboards are required to increase the quality of service,and forecasting demand for their use in a specific region is crucial.Predicting demand accurately with small data is troublesome.Extensive data is necessary for training machine learning algorithms for effective prediction.Data generation is a method for expanding the amount of data that will be further accessible for training.In this work,we proposed a model that takes time-series customers’electric kickboard demand data as input,pre-processes it,and generates synthetic data according to the original data distribution using generative adversarial networks(GAN).The electric kickboard mobility demand prediction error was reduced when we combined synthetic data with the original data.We proposed Tabular-GAN-Modified-WGAN-GP for generating synthetic data for better prediction results.We modified The Wasserstein GAN-gradient penalty(GP)with the RMSprop optimizer and then employed Spectral Normalization(SN)to improve training stability and faster convergence.Finally,we applied a regression-based blending ensemble technique that can help us to improve performance of demand prediction.We used various evaluation criteria and visual representations to compare our proposed model’s performance.Synthetic data generated by our suggested GAN model is also evaluated.The TGAN-Modified-WGAN-GP model mitigates the overfitting and mode collapse problem,and it also converges faster than previous GAN models for synthetic data creation.The presented model’s performance is compared to existing ensemble and baseline models.The experimental findings imply that combining synthetic and actual data can significantly reduce prediction error rates in the mean absolute percentage error(MAPE)of 4.476 and increase prediction accuracy.

Introducing atmospheric angular momentum into prediction of length of day change by generalized regression neural network model

The general regression neural network(GRNN) model was proposed to model and predict the length of day(LOD) change, which has very complicated time-varying characteristics. Meanwhile, considering that the axial atmospheric angular momentum(AAM) function is tightly correlated with the LOD changes, it was introduced into the GRNN prediction model to further improve the accuracy of prediction. Experiments with the observational data of LOD changes show that the prediction accuracy of the GRNN model is 6.1% higher than that of BP network, and after introducing AAM function, the improvement of prediction accuracy further increases to 14.7%. The results show that the GRNN with AAM function is an effective prediction method for LOD changes.

An Approach to Carbon Emissions Prediction Using Generalized Regression Neural Network Improved by Genetic Algorithm

The study on scientific analysis and prediction of China’s future carbon emissions is conducive to balancing the relationship between economic development and carbon emissions in the new era,and actively responding to climate change policy.Through the analysis of the application of the generalized regression neural network(GRNN)in prediction,this paper improved the prediction method of GRNN.Genetic algorithm(GA)was adopted to search the optimal smooth factor as the only factor of GRNN,which was then used for prediction in GRNN.During the prediction of carbon dioxide emissions using the improved method,the increments of data were taken into account.The target values were obtained after the calculation of the predicted results.Finally,compared with the results of GRNN,the improved method realized higher prediction accuracy.It thus offers a new way of predicting total carbon dioxide emissions,and the prediction results can provide macroscopic guidance and decision-making reference for China’s environmental protection and trading of carbon emissions.

Bayesian Prediction of Future Generalized Order Statistics from a Class of Finite Mixture Distributions

This article is concerned with the problem of prediction for the future generalized order statistics from a mixture of two general components based on doubly?type II censored sample. We consider the one sample prediction and two sample prediction techniques. Bayesian prediction intervals for the median of future sample of generalized order statistics having odd and even sizes are obtained. Our results are specialized to ordinary order statistics and ordinary upper record values. A mixture of two Gompertz components model is given as an application. Numerical computations are given to illustrate the procedures.

Generalized Nonlinear Irreducible Auto-Correlation and Its Applications in Nonlinear Prediction Models Identification

There is still an obstacle to prevent neural network from wider and more effective applications, i.e., the lack of effective theories of models identification. Based on information theory and its generalization, this paper introduces a universal method to achieve nonlinear models identification. Two key quantities, which are called nonlinear irreducible auto-correlation (NIAC) and generalized nonlinear irreducible auto-correlation (GNIAC), are defined and discussed. NIAC and GNIAC correspond with intrinstic irreducible auto-(dependency) (IAD) and generalized irreducible auto-(dependency) (GIAD) of time series respectively. By investigating the evolving trend of NIAC and GNIAC, the optimal auto-regressive order of nonlinear auto-regressive models could be determined naturally. Subsequently, an efficient algorithm computing NIAC and GNIAC is discussed. Experiments on simulating data sets and typical nonlinear prediction models indicate remarkable correlation between optimal auto-regressive order and the highest order that NIAC-GNIAC have a remarkable non-zero value, therefore demonstrate the validity of the proposal in this paper.

Adversarial Training-Aided Time-Varying Channel Prediction for TDD/FDD Systems

In this paper, a time-varying channel prediction method based on conditional generative adversarial network(CPcGAN) is proposed for time division duplexing/frequency division duplexing(TDD/FDD) systems. CPc GAN utilizes a discriminator to calculate the divergence between the predicted downlink channel state information(CSI) and the real sample distributions under a conditional constraint that is previous uplink CSI. The generator of CPcGAN learns the function relationship between the conditional constraint and the predicted downlink CSI and reduces the divergence between predicted CSI and real CSI.The capability of CPcGAN fitting data distribution can capture the time-varying and multipath characteristics of the channel well. Considering the propagation characteristics of real channel, we further develop a channel prediction error indicator to determine whether the generator reaches the best state. Simulations show that the CPcGAN can obtain higher prediction accuracy and lower system bit error rate than the existing methods under the same user speeds.

Statistical Downscaling for Multi-Model Ensemble Prediction of Summer Monsoon Rainfall in the Asia-Pacific Region Using Geopotential Height Field

The 21-yr ensemble predictions of model precipitation and circulation in the East Asian and western North Pacific （Asia-Pacific） summer monsoon region （0°-50°N, 100° 150°E） were evaluated in nine different AGCM, used in the Asia-Pacific Economic Cooperation Climate Center （APCC） multi-model ensemble seasonal prediction system. The analysis indicates that the precipitation anomaly patterns of model ensemble predictions are substantially different from the observed counterparts in this region, but the summer monsoon circulations are reasonably predicted. For example, all models can well produce the interannual variability of the western North Pacific monsoon index （WNPMI） defined by 850 hPa winds, but they failed to predict the relationship between WNPMI and precipitation anomalies. The interannual variability of the 500 hPa geopotential height （GPH） can be well predicted by the models in contrast to precipitation anomalies. On the basis of such model performances and the relationship between the interannual variations of 500 hPa GPH and precipitation anomalies, we developed a statistical scheme used to downscale the summer monsoon precipitation anomaly on the basis of EOF and singular value decomposition （SVD）. In this scheme, the three leading EOF modes of 500 hPa GPH anomaly fields predicted by the models are firstly corrected by the linear regression between the principal components in each model and observation, respectively. Then, the corrected model GPH is chosen as the predictor to downscale the precipitation anomaly field, which is assembled by the forecasted expansion coefficients of model 500 hPa GPH and the three leading SVD modes of observed precipitation anomaly corresponding to the prediction of model 500 hPa GPH during a 19-year training period. The cross-validated forecasts suggest that this downscaling scheme may have a potential to improve the forecast skill of the precipitation anomaly in the South China Sea, western North Pacific and the East Asia Pacific regions, where the anomaly correlation coefficient （ACC） has been improved by 0.14, corresponding to the reduced RMSE of 10.4% in the conventional multi-model ensemble （MME） forecast.

Neuro-fuzzy generalized predictive control of boiler steam temperature

Power plants are nonlinear and uncertain complex systems. Reliable control of superheated steam temperature is necessary to ensure high efficiency and high load-following capability in the operation of modem power plant. A nonlinear generalized predictive controller based on neuro-fuzzy network （NFGPC） is proposed in this paper. The proposed nonlinear controller is applied to control the superheated steam temperature of a 200MW power plant. From the experiments on the plant and the simulation of the plant, much better performance than the traditional controller is obtained,

THE PRINCIPLE OF ROBUSTNESS IN GENERALIZED PREDICTIVE CONTROL

This paper deeply analyzes the closed-loop nature ofGPCin the fram ework ofinter- nalm odelcontrol(IMC) theory. A new sort ofrelation lies in the feedback structure so that robustreason can be satisfactorily explained. The resultissignificantbecause the previous con- clusions are only applied to open-loop stable plant(orm odel).

A Long-Range Generalized Predictive Control Algorithm for a DFIG Based Wind Energy System

This paper presents a new Long-range generalized predictive controller in the synchronous reference frame for a wind energy system doubly-fed induction generator based. This controller uses the state space equations that consider the rotor current and voltage as state and control variables, to execute the predictive control action. Therefore, the model of the plant must be transformed into two discrete transference functions, by means of an auto-regressive moving average model, in order to attain a discrete and decoupled controller, which makes it possible to treat it as two independent single-input single-output systems instead of a magnetic coupled multiple-input multiple-output system. For achieving that, a direct power control strategy is used, based on the past and future rotor currents and voltages estimation. The algorithm evaluates the rotor current predictors for a defined prediction horizon and computes the new rotor voltages that must be injected to controlling the stator active and reactive powers. To evaluate the controller performance, some simulations were made using Matlab/Simulink. Experimental tests were carried out with a small-scale prototype assuming normal operating conditions with constant and variable wind speed profiles. Finally, some conclusions respect to the dynamic performance of this new controller are summarized.

ON THE ROBUSTNESS OF A GENERALIZED PREDICTIVE CONTROLLER

In this paper, we present a quantitative analysis of the robustness of a generalized predictive controller. The result of stability analysis shows that, under a specific bounded modelling error, the closed-loop system is BIBO stable in the presence of unmodelled dynamics.

Adaptive Cascade Generalized Predictive Control

Cascade control is one of the most popular structures for process control as it is a special architecture for dealing with disturbances. However, the drawbacks of cascade control are obvious that primary controller and secondary controller should be tuned together, which influences each other. In this paper, a new Adaptive Cascade Generalized Predictive Controller (ACGPC) is introduced. ACGPC is a method issued from GPC and the inner and outer controllers of a cascade system are replaced by one cascade generalized predictive controller, where both loops model are updated by Recursive Least Squares method. Compared with existing methods, the new method is simpler and yet more effective. It can be directly integrated into commercially available industrial auto-tuning systems. Some examples are given to illustrate the effectiveness and robustness of the proposed method.

Proportion integral-type active disturbance rejection generalized predictive control for distillation process based on grey wolf optimization parameter tuning

The high-purity distillation column system is strongly nonlinear and coupled,which makes it difficult to control.Active disturbance rejection control(ADRC)has been widely used in distillation systems,but it has limitations in controlling distillation systems with large time delays since ADRC employs ESO and feedback control law to estimate the total disturbance of the system without considering the large time delays.This paper designs a proportion integral-type active disturbance rejection generalized predictive control(PI-ADRGPC)algorithm to control the distillation column system with large time delay.It replaces the PD controller in ADRC with a proportion integral-type generalized predictive control(PI-GPC),thereby improving the performance of control systems with large time delays.Since the proposed controller has many parameters and is difficult to tune,this paper proposes to use the grey wolf optimization(GWO)to tune these parameters,whose structure can also be used by other intelligent optimization algorithms.The performance of GWO tuned PI-ADRGPC is compared with the control performance of GWO tuned ADRC method,multi-verse optimizer(MVO)tuned PI-ADRGPC and MVO tuned ADRC.The simulation results show that the proposed strategy can track reference well and has a good disturbance rejection performance.

Improving Multi-model Ensemble Probabilistic Prediction of Yangtze River Valley Summer Rainfall

Seasonal prediction of summer rainfall over the Yangtze River valley（YRV） is valuable for agricultural and industrial production and freshwater resource management in China, but remains a major challenge. Earlier multi-model ensemble（MME） prediction schemes for summer rainfall over China focus on single-value prediction, which cannot provide the necessary uncertainty information, while commonly-used ensemble schemes for probability density function（PDF） prediction are not adapted to YRV summer rainfall prediction. In the present study, an MME PDF prediction scheme is proposed based on the ENSEMBLES hindcasts. It is similar to the earlier Bayesian ensemble prediction scheme, but with optimization of ensemble members and a revision of the variance modeling of the likelihood function. The optimized ensemble members are regressed YRV summer rainfall with factors selected from model outputs of synchronous 500-h Pa geopotential height as predictors. The revised variance modeling of the likelihood function is a simple linear regression with ensemble spread as the predictor. The cross-validation skill of 1960–2002 YRV summer rainfall prediction shows that the new scheme produces a skillful PDF prediction, and is much better-calibrated, sharper, and more accurate than the earlier Bayesian ensemble and raw ensemble.

Study on Generation Cost Prediction Based on Coal Quality and Generating Unit Performance

燃料变化条件下发电成本的预测是火电厂普遍关心的重要课题。分析了影响机组性能及发电电量成本的各种煤质指标，重点研究了基于结构参数及燃烧传热机理的锅炉稳态热力性能分析计算方法，讨论了制粉系统、风机、脱硫和脱硝装置性能随燃料等运行条件的变化关系，最终提出了基于煤质和机组性能分析计算的发电电量成本预测模型并研发了“煤炭选配与机组发电成本预测系统”。该系统在我国某600MW火电厂的实际应用经验表明：提出的电量成本分析预测模型合理，研发的软件系统有助于辅助火电厂的选煤和购煤决策，优化动力配煤方案，从而提高火电厂的运行经济性。

A Bayesian Scheme for Probabilistic Multi-Model Ensemble Prediction of Summer Rainfall over the Yangtze River Valley

A Bayesian probabilistic prediction scheme of the Yangtze River Valley (YRV) summer rainfall is proposed to combine forecast information from multi-model ensemble dataset provided by ENSEMBLES project.Due to the low forecast skill of rainfall in dynamic models,the time series of regressed YRV summer rainfall are selected as ensemble members in the new scheme,instead of commonly-used YRV summer rainfall simulated by models.Each time series of regressed YRV summer rainfall is derived from a simple linear regression.The predictor in each simple linear regression is the skillfully simulated circulation or surface temperature factor which is highly linear with the observed YRV summer rainfall in the training set.The high correlation between the ensemble mean of these regressed YRV summer rainfall and observation benefit extracting more sample information from the ensemble system.The results show that the cross-validated skill of the new scheme over the period of 1960 to 2002 is much higher than equally-weighted ensemble,multiple linear regression,and Bayesian ensemble with simulated YRV summer rainfall as ensemble members.In addition,the new scheme is also more skillful than reference forecasts (random forecast at a 0.01 significance level for ensemble mean and climatology forecast for probability density function).

Improved Generalized Predictive Control Algorithm with Offline and Online Identification and Its Application to Fixed Bed Reactor

An improved generalized predictive control algorithm is presented in this paper by incorporating offline identification into onlie identification.Unlike the existing generalized predictive control algorithms.the proposed approach divides parameters of a predictive model into the time invariant and time-varying ones,which are treated respectively by offline and onlie identification algorithms.Therefore,both the reliability and accuracy of the predictive model are improved,Two simulation examples of control of a fixed bed reactor show that this new algorithm is not only reliable and stable in the case of uncertainties and abnormal distrubances,but also adaptable to slow time varying processes.