Error Metrics Research Articles

Estimation of Solar Power Generation Through the Use of Effective Forecasting Algorithms

The unpredictable nature of solar power generation poses significant challenges to energy management, particularly in power grids with high solar penetration, leading to potential imbalances between supply and demand. This has increased interest in developing accurate forecasting methods for photovoltaic power generation. This study focuses on short-term forecasting of solar power generation using MATLAB, based on historical generation trends through three different hybrid models. It uses a multilayer perceptron neural network as the forecasting tool, which is optimized through various algorithms to fine-tune the network's hyperparameters, such as the weights and biases of the input and hidden layers, for optimal performance. The Root Mean Square Error is used as the objective metric to minimize the discrepancy between actual and predicted values. The models use Particle Swarm Optimization (PSO), Imperialistic Competitive Algorithm, and Genetic Algorithm for network optimization. This research analyzes PV generation data from Belgium in July and August 2022, taken at 15-minute intervals, and evaluates model performance using six different error metrics, including Mean Absolute Error. The results show the accuracy and reliability in forecasting solar power generation time series.

Vehicle Delay Model for Signalized Midblock Crosswalk Under Mixed Traffic Conditions

For signalized locations, delay is one of the key parameters in assessing the level of service and redesigning the traffic signals. Around the world, Highway Capacity Manual (HCM) and Webster delay models are commonly used in calculating the vehicle delay at signalized intersections, notwithstanding that these models assume homogeneous traffic conditions and lane discipline. Furthermore, it is worth noting that previous studies have mostly focused on developing delay models for signalized intersections, whereas signalized midblock crosswalks were overlooked by past researchers. In view of this, the current study presents a modified vehicle delay model for signalized midblock crosswalks (SMCs) under mixed traffic conditions. Mixed traffic conditions refers to diverse vehicles, complex interactions, and no lane discipline on the road—conditions which are usually noticed in developing nations. The HCM vehicle delay model is modified in the current study by incorporating factors related to mixed traffic conditions and SMCs. To test the accuracy of the proposed model, it was validated with the field delay using data collected at other SMCs in Hyderabad, India. Field delay was calculated by plotting the measured queue length against the signal cycle length. The performance metrics of root mean square error (RMSE), mean absolute percentage error, Nash–Sutcliffe efficiency, RMSE-observations standard deviation ratio, and percent bias were used to test the accuracy of the proposed model. Results revealed that the proposed model yielded the lowest error rates and the highest correlation coefficients between modeled and actual vehicle delay. The maximum error between the field delay and the modeled delay was found to be less than 5%.

Apple, Microsoft, and Amazon stock price prediction based on ARIMA and LSTM

Along with the advancement in technology and data analysis, efforts have been made to use various factors to predict the stock market to improve portfolio performance and ensure an efficient market. This study explores two stock forecasting models, Long Short-Term Memory(LSTM) and Auto Regressive Integrated Moving Average (ARIMA), and evaluates their performance on the same datasets of historical stock prices of Apple, Microsoft, and Amazon. While ARIMA exhibited superior performance in terms of Root Mean Squared Error(RMSE) and R2 metrics, the research acknowledges inherent limitations, such as the exclusion of potential external influencing factors and the simplistic approach toward LSTM optimization. Despite ARIMA's commendable forecasting ability in this context, the dynamic and non-linear nature of stock prices suggests the potential of hybrid models and broader datasets for future research. The findings underscore the significance of selecting appropriate forecasting tools in the volatile domain of stock investments and pave the way for a more holistic and informed approach to stock price prediction.

The ARIMA model approach for the biofilm-forming capacity prediction of Listeria monocytogenes recovered from carcasses

The present study aimed to predict the biofilm-formation ability of L. monocytogenes isolates obtained from cattle carcasses via the ARIMA model at different temperature parameters. The identification of L. monocytogenes obtained from carcass samples collected from slaughterhouses was determined by PCR. The biofilm-forming abilities of isolates were phenotypically determined by calculating the OD value and categorizing the ability via the microplate test. The presence of some virulence genes related to biofilm was revealed by QPCR to support the biofilm profile genotypically. Biofilm-formation of the isolates was evaluated at different temperature parameters (37 °C, 22 °C, 4 °C and − 20 °C). Estimated OD values were obtained with the ARIMA model by dividing them into eight different estimation groups. The prediction performance was determined by performance measurement metrics (ME, MAE, MSE, RMSE, MPE and MAPE). One week of incubation showed all isolates strongly formed biofilm at all controlled temperatures except − 20 °C. In terms of the metrics examined, the 3 days to 7 days forecast group has a reasonable prediction accuracy based on OD values occurring at 37 °C, 22 °C, and 4 °C. It was concluded that measurements at 22 °C had lower prediction accuracy compared to predictions from other temperatures. Overall, the best OD prediction accuracy belonged to the data obtained from biofilm formation at -20 °C. For all temperatures studied, especially after the 3 days to 7 days forecast group, there was a significant decrease in the error metrics and the forecast accuracy increased. When evaluating the best prediction group, the lowest RMSE at 37 °C (0.055), 22 °C (0.027) and 4 °C (0.024) belonged to the 15 days to 21 days group. For the OD predictions obtained at -20 °C, the 15 days to 21 days prediction group had also good performance (0.011) and the lowest RMSE belongs to the 7 days to 15 days group (0.007). In conclusion, this study will guide in using indicator parameters to evaluate biofilm forming ability to predict optimum temperature-time. The ARIMA models integrated with this study can be useful tools for industrial application and risk assessment studies using different parameters such as pH, NaCl concentration, and especially temperature applied during food processing and storage on the biofilm-formation ability of L. monocytogenes.

Advertisement design in dynamic interactive scenarios using DeepFM and long short-term memory (LSTM).

This article addresses the evolving landscape of data advertising within network-based new media, seeking to mitigate the accuracy limitations prevalent in traditional film and television advertising evaluations. To overcome these challenges, a novel data-driven nonlinear dynamic neural network planning approach is proposed. Its primary objective is to augment the real-time evaluation precision and accuracy of film and television advertising in the dynamic interactive realm of network media. The methodology primarily revolves around formulating a design model for visual advertising in film and television, customized for the dynamic interactive milieu of network media. Leveraging DeepFM+long short-term memory (LSTM) modules in deep learning neural networks, the article embarks on constructing a comprehensive information statistics and data interest model derived from two public datasets. It further engages in feature engineering for visual advertising, crafting self-learning association rules that guide the data-driven design process and system flow. The article concludes by benchmarking the proposed visual neural network model against other models, using F1 and root mean square error (RMSE) metrics for evaluation. The findings affirm that the proposed model, capable of handling dynamic interactions among images, visual text, and more, excels in capturing nonlinear and feature-mining aspects. It exhibits commendable robustness and generalization capabilities within various contexts.

Predicting Urban Happiness: A Comparative Analysis of Deep Learning Models

This study explores the efficacy of various deep learning models in predicting urban happiness scores, a critical indicator of the quality of life in urban environments. Recognizing the complex interplay of factors contributing to urban happiness, we employed a suite of models, including Dense Neural Networks (DNN), Long Short-Term Memory networks (LSTM), Convolutional Neural Networks (CNN), Autoencoders, Multi-Layer Perceptron with Dropout (MLP Dropout), and Simple Recurrent Neural Networks (RNN), to analyze a comprehensive dataset encompassing environmental quality, socio-economic factors, and urban infrastructure. Our methodology centered on rigorous data preprocessing to ensure integrity and usability, followed by a detailed comparative analysis of model performances based on Root Mean Squared Error (RMSE) metrics. The results revealed that the CNN model outperformed others in identifying spatial patterns crucial for urban happiness, indicating its superior capability in processing complex urban data. In contrast, the LSTM model showed less accuracy, suggesting a nuanced understanding of temporal data's role in predicting urban happiness. This research not only sheds light on the potential of deep learning in urban studies but also offers valuable insights for urban planners and policymakers aiming to enhance urban living conditions. Through this comparative analysis, our study contributes to the growing discourse on leveraging advanced data analytics for urban planning and opens avenues for future research into the integration of diverse data sources and model hybridization to refine urban happiness predictions.

Lithium-ion battery state of health prognostication employing multi-model fusion approach based on image coding of charging voltage and temperature data

The employment of readily obtainable parameters, including voltage and temperature, derived from the battery management system facilitates the real-time evaluation of lithium-ion batteries health status. However, the complex aging mechanisms and noise interference inherent in lithium-ion batteries present substantial challenges to accurate estimation. Hence, this research proposes a multi-model fusion approach utilizing Gramian Angular Field encoding to accurately predict the health status of lithium-ion batteries. Battery voltage and temperature data are acquired through system aging experiments. The Gramian Angular Field-based image encoding transforms these data into images, accentuating the subtle characteristics of the data and thereby enhancing its recognizability by neural networks. Subsequently, two-dimensional Convolutional Neural Networks are employed to extract features from the images, followed by one-dimensional Convolutional Neural Networks to reduce the dimensions of the feature matrix. The battery health status is then predicted utilizing Long Short-term Memory Networks. The culmination is the evaluation of the model performance through the application of quantitative error metrics. The study results show that the method can pinpoint the prediction error to within 2%, significantly improving accuracy over traditional prediction methods. It proves the great potential of direct data, such as voltage and temperature, in predicting battery health.

Point cloud denoising using a generalized error metric

Effective removal of noises from raw point clouds while preserving geometric features is the key challenge for point cloud denoising. To address this problem, we propose a novel method that jointly optimizes the point positions and normals. To preserve geometric features, our formulation uses a generalized robust error metric to enforce piecewise smoothness of the normal vector field as well as consistency between point positions and normals. By varying the parameter of the error metric, we gradually increase its non-convexity to guide the optimization towards a desirable solution. By combining alternating minimization with a majorization-minimization strategy, we develop a numerical solver for the optimization which guarantees convergence. The effectiveness of our method is demonstrated by extensive comparisons with previous works.

Artificial neural networks ensemble methodology to predict significant wave height

The forecast of wave variables are important for several applications that depend on a better description of the ocean state. Due to the chaotic behaviour of the differential equations which model this problem, a well know strategy to overcome the difficulties is basically to run several simulations, by for instance, varying the initial condition, and averaging the result of each of these, creating an ensemble. Moreover, in the last few years, considering the amount of available data and the computational power increase, machine learning algorithms have been applied as surrogate to traditional numerical models, yielding comparative or better results. In this work, we present a methodology to create an ensemble of different artificial neural networks architectures, namely, MLP, RNN, LSTM, CNN and a hybrid CNN–LSTM, which aims to predict significant wave height on six different locations in the Brazilian coast. The networks are trained using NOAA’s numerical reforecast data and target the residual between observational data and the numerical model output. A new strategy to create the training and target datasets is demonstrated. Results show that our framework is capable of producing high efficient forecast, with an average accuracy of 80%, that can achieve up to 88% in the best case scenario, which means 5% reduction in error metrics if compared to NOAA’s numerical model, and a increasingly reduction of computational cost.

Enhanced Water Quality Prediction in the Yellow River Basin: The Application of the HHO-LSTM Model

In the pivotal water resource region of the Yellow River Basin in China, precise prediction of water resources is essential for their effective and rational management. This study introduces a novel approach to water resource prediction by employing the Harris Hawks Optimization-Long Short-Term Memory (HHO-LSTM) model. This method overcomes the constraints faced by traditional techniques in processing time series data and various variable factors. It encompasses a comprehensive description of the multi-source hydrological data collection process within the Yellow River Basin, followed by meticulous data preprocessing. The data set for this study includes estimates of four critical water quality parameters, and the efficacy of the model is gauged through the mean squared error (MSE) and root mean squared error (RMSE) metrics. This facilitates the projection of future water quality trends in specific areas by leveraging historical water quality data. The HHO-LSTM model has demonstrated outstanding accuracy and robustness in predicting water quality across diverse temporal scales and water resource variables, marking a significant advancement in water resource management within the Yellow River Basin. This approach not only enhances current management strategies but also contributes valuable insights for ongoing water resource research and decision-making processes.

Assessing the impact of missing data on water quality index estimation: a machine learning approach

Despite the regulations and controls implemented worldwide by governments and institutions to ensure the availability and quality of water resources, many water sources remain susceptible to contamination. This contamination poses significant risks to human health and can lead to substantial economic losses. One of the challenges in this context is the presence of missing or incomplete data, which can arise from various factors such as the methodology used or the expertise of personnel involved in sample collection and analysis. The existence of such data gaps hampers the accurate analysis that can be conducted. To address this issue and estimate a water quality index from the available samples, it is crucial to handle missing information appropriately to avoid biased calculations. This study focuses on the application of machine learning methods for imputing missing data in water samples. Furthermore, it quantifies the performance of different models based on the distribution of the obtained data. By applying 10 distinct methods to a sample of water quality data, the most effective approaches, namely Bayesian Ridge, Gradient Boosting, Ridge, Support Vector Machine, and Theil-Sen regressors, were identified. The selection of these models was based on the evaluation of two estimation error metrics: average percent bias (PBIAS) and Kling-Gupta Efficiency statistic (KGEss). The respective metric values for the aforementioned methods are as follows: ⟨PBIAS⟩0.5=14.665,19.555,14.300,15.380,15.920\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle \\hbox {PBIAS}\\rangle _{0.5}=14.665, 19.555, 14.300, 15.380, 15.920$$\\end{document} and ⟨KGEss⟩0.5=0.670,0.585,0.655,0.620,0.595\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle \\hbox {KGEss}\\rangle _{0.5}=0.670, 0.585, 0.655, 0.620, 0.595$$\\end{document}. The results obtained from these models have been utilized to establish unbiased relationships among physical, chemical, and biological parameters based on the information retrieved through the applied imputation methods.

Comparative Analysis of ARIMA and LSTM Models for Agricultural Product Price Forecasting

The fluctuations in vegetable prices can have an impact on the economy. Machine learning can identify price trend changes. This study investigates the performance of ARIMA and LSTM models in predicting price trends for agricultural products, focusing on greens and lotus roots. The objective was to ascertain the superior model in terms of accurately reflecting market oscillations—a critical aspect for stakeholders in the agricultural sector. The investigation contrasted the ARIMA model's adeptness at detecting linear tendencies against the LSTM's capacity to decode intricate nonlinear dynamics. Empirical assessment employing metrics such as RMSE, MAE, and SMAPE disclosed a consistent supremacy of the ARIMA model over the LSTM in both datasets. This was particularly evident within the lotus root forecasts, where the discrepancy in error metrics for LSTM was remarkably pronounced. The outcomes indicate that notwithstanding the sophisticated structure of LSTM, ARIMA models maintain their status as robust and precise tools for agricultural time series forecasting. This is especially pertinent in contexts demanding computational efficiency and model interpretability. This investigation evaluates the efficacy of ARIMA and LSTM models in forecasting time-series data for agricultural commodities.

A Novel Remote Sensing-Based Modeling Approach for Maize Light Extinction Coefficient Determination

This study focused on developing a novel semi-empirical model for maize’s light extinction coefficient (kp) by integrating multiple remotely sensed vegetation features from several different remote sensing platforms. The proposed kp model’s performance was independently evaluated using Campbell’s (1986) original and simplified kp approaches. The Limited Irrigation Research Farm (LIRF) in Greeley, Colorado, and the Irrigation Innovation Consortium (IIC) in Fort Collins, Colorado, USA, served as experimental sites for developing and evaluating the novel maize kp model. Data collection involved multiple remote sensing platforms, including Landsat-8, Sentinel-2, Planet CubeSat, a Multispectral Handheld Radiometer, and an unmanned aerial system (UAS). Ground measurements of leaf area index (LAI) and fractional vegetation canopy cover (fc) were included. The study evaluated the novel kp model through a comprehensive analysis using statistical error metrics and Sobol global sensitivity indices to assess the performance and sensitivity of the models developed for predicting maize kp. Results indicated that the novel kp model showed strong statistical regression fitting results with a coefficient of determination or R2 of 0.95. Individual remote sensor analysis confirmed consistent regression calibration results among Landsat-8, Sentinel-2, Planet CubeSat, the MSR, and UAS. A comparison with Campbell’s (1986) kp models reveals a 44% improvement in accuracy. A global sensitivity analysis identified the role of the normalized difference vegetation index (NDVI) as a critical input variable to predict kp across sensors, emphasizing the model’s robustness and potential practical environmental applications. Further research should address sensor-specific variations and expand the kp model’s applicability to a diverse set of environmental and microclimate conditions.

Fusion-based approach for hydrometeorological drought modeling: a regional investigation for Iran.

The objective of this study was to model a new drought index called the Fusion-based Hydrological Meteorological Drought Index (FHMDI) to simultaneously monitor hydrological and meteorological drought. Aiming to estimate drought more accurately, local measurements were classified into various clusters using the AGNES clustering algorithm. Four single artificial intelligence (SAI) models-namely, Gaussian Process Regression (GPR), Ensemble, Feedforward Neural Networks (FNN), and Support Vector Regression (SVR)-were developed for each cluster. To promote the results of single of products and models, four fusion-based approaches, namely, Wavelet-Based (WB), Weighted Majority Voting (WMV), Extended Kalman Filter (EKF), and Entropy Weight (EW) methods, were used to estimate FHMDI in different time scales, precipitation, and runoff. The performance of single and combined products and models was assessed through statistical error metrics, such as Kling-Gupta efficiency (KGE), Mean Bias Error (MBE), and Normalized Root Mean Square Error (NRMSE). The performance of the proposed methodology was tested over 24 main river basins in Iran. The validation results of the FHMDI (the compliance of the index with the pre-existing drought index) revealed that it accurately identified drought conditions. The results indicated that individual products performed well in some river basins, while fusion-based models improved dataset accuracy more compared to local measurements. The WMV with the highest accuracy (lowest NRMSE) had a good performance in 60% of the cases compared to all other products and fusion-based models. WMV also showed higher efficiency in 100% of the cases than all other fusion-based and SAI models for simultaneous hydrological and meteorological drought estimation. In light of these findings, we recommend the use of fusion-based approach to improve drought modeling.

A neural network approach for population synthesis

This work explores techniques and metrics applied to the process of population synthesis used in activity-based modeling for traffic and transport simulation. The paper presents a novel population synthesis approach based on applying artificial neural networks (ANNs) and evaluates the approach against techniques derived from iterative proportional fitting (IPF), Bayesian networks, and data sampling methods. The documented research also investigates the appropriateness of goodness-of-fit measures and the need to consider similarity measures in assessing technique effectiveness with a focus on measures derived from Jaccard similarity coefficient. We established that IPF techniques should be preferred when datasets with the required composition are available, targeting few output variables and in relatively large zones of 5% region size. However, in smaller zones with sparser datasets, or inadequate dataset composition, the proposed ANN technique and identified sampling method are favorable. The proposed ANN method shows suitability for the population synthesis problem compared with the examined methods, but further work is required to improve model fitting speed, explore mixture models of multiple ANNs, and apply data reduction techniques to reduce the observation–decision space. The research findings also established that comparing scenarios of varying sizes and variable numbers is challenging when employing specific goodness-of-fit measures. Furthermore, the mentioned similarity measures can reveal concerns regarding inconsistent archetypes and low-quality populations that can remain concealed when using error metrics.

A new Takagi–Sugeno–Kang model for time series forecasting

A fuzzy inference system consists of a machine learning concept that combines accuracy and interpretability. They are divided into two main groups: Mamdani and Takagi–Sugeno-Kang. While Mamdani models favor interpretability, Takagi–Sugeno-Kang models provide more accurate results because of their ability to approximate a nonlinear system through a collection of linear subsystems. The evolving Takagi Sugeno model inspired a new class of Takagi–Sugeno-Kang models classified as an evolving fuzzy system, which can update their structure and functionality to adapt themselves to changes in the data. However, these models may provide several rules that reduce the interpretability. Furthermore, as they usually present many hyper-parameters, it can be challenging to obtain results that satisfy specific requirements in terms of the accuracy-interpretability trade-off. To overcome such shortcomings, this paper introduces a new model in which the only hyper-parameter is the maximum number of rules. Consequently, the user can define the number of rules considering the accuracy-interpretability trade-off. The introduced models are evaluated using benchmark time series, three well-known financial series, S&P 500, NASDAQ, and TAIEX, and renewable energy datasets. The results are compared with other state-of-the-art machine learning models, such as classical models and some rule-based evolving Fuzzy Systems. The results are evaluated regarding error metrics and the number of final rules. The proposed model obtained similar or equal performance in the simulations to the compared models with increased interpretability. The code of the proposed model is available at https://github.com/kaikerochaalves/NTSK.git.

Parametric and Nonparametric Approaches of Reid Vapor Pressure Prediction for Gasoline Containing Oxygenates: A Comparative Analysis Using Partial Least Squares, Nonlinear, and LOWESS Regression Modelling Strategies with Physical Properties

This study provides insights into the challenges involved in predicting the Reid vapor pressure (RVP) of gasoline-oxygenate blends (GOB), which is an important indicator of fuel quality and compliance with environmental and performance standards. Given the enormous variety of gasoline compositions and ratios available, there is a significant demand for a fast, straightforward, and cost-effective technique to predict RVP without relying on costly instruments or complicated spectral measurements that involve numerous input variables. A comparative performance analysis has been performed for different regression modelling strategies for predicting RVP in GOB, which is valuable for researchers and practitioners in the petroleum industry for saving time and money. Parametric and nonparametric approaches were compared using partial least squares regression (PLSR), nonlinear regression (NLR), and nonparametric regression (NPR) models. Locally weighted scatterplot smoothing (LOWESS) approach was applied to the NPR model. The gasoline’s physical characteristics (distillation curves and density) formed the basis for the analysis of these models’ performances. Acceptable error metrics have been reached for root mean square error of calibration and prediction (RMSEC and RMSEP) values, for the PLSR, NLR, and NPR models, which are 4.790, 6.235, 4.739, 6.149, 3.968, and 6.029, respectively, which are close for those reported in literature. The NPR model eliminates parametric constraints and allows for a different kind of data structure to emerge. The established models here demonstrate a sound ability to overcome barriers by omitting the use of inconvenient spectral measurements to save expense and simplify data calibration, making them a promising approach for RVP detection of GOB. This finding aids in the development of more accurate RVP prediction models and contributes to the optimization of fuel formulations.

A novel probabilistic gradient boosting model with multi-approach feature selection and iterative seasonal trend decomposition for short-term load forecasting

Existing regression, tree-based and NN models either lacks probabilistic prediction, takes longer training time, have high computational requirements or sacrifice accuracy. This paper introduces a novel framework, (MAFS+ISTD+PGBM), specifically to overcome these limitations. First three challenges are addressed by integrating gradient boosting and quantile regression model. The key idea is to combine speed and scalability of gradient boosting with probabilistic capabilities of quantile regression, forming PGBM. However, the issue of mediocre accuracy still remained. To address this, two pre-processing techniques are introduced. MAFS utilizes statistical methods and knowledge-based analysis to identify the most relevant features, while ISTD extracts and eliminates trend and seasonality components, ensuring stationarity. After rigorous evaluations, (MAFS+ISTD+PGBM) emerges as the superior performer surpassing all existing models in terms of training time and accuracy with highest R2 score of 0.997 and low values across all error metrics. The proposed model took less than one-third of training time (∼15 min) compared to CNN-LSTM+attn., (∼48 min), the only model with comparable accuracy of proposed model. Thus, proposed approach shall be used to empower grid operators with highly accurate and cost-effective probabilistic forecasts which allows them to make informed decisions about system stability and optimize resource utilization, ensuring reliability and efficiency.

Hybrid ARIMA-IIS Approach for Wheat Yield Forecasting: An Integrated Approach

This study explores the application of a hybrid approach, combining the Impulse Indicator Saturation (IIS) method with an ARIMA(x) model, to forecast wheat yield. The IIS method is employed to find potential impulse responses, which are then integrated into the ARIMA(x) framework. The IIS method captures the potential joint effects of the weather, climate and other inputs on the data generating process of the wheat yield time series. The performance of the hybrid ARIMA(x) model is compared with that of the standalone ARIMA model using various error metrics, including Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE), and Mean Absolute Deviation (MAD). Additionally, model selection criteria such as the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Schwarz Bayesian Information Criterion (SBIC), and Hannan-Quinn Criterion (HQ) are used to identify the optimal model for forecasting. The training data of wheat yield from 1948-2018 was used to fit both the ARIMA and ARIMA(x) models, while the remaining observations until 2023 are used for model validation. The results of the study reveal that the hybrid ARIMA(x) model exhibits superior forecasting ability, demonstrating lower error metrics compared to the standalone ARIMA model. Notably, the ex-ante forecasts for the 2023-24 period predict a wheat production of 29.916 million tons using the ARIMA(x) model and 29.656 million tons using the ARIMA (2,1,2) model. These findings underscore the efficacy of the hybrid approach in enhancing production forecasting accuracy, thereby serving as a valuable basis for early warning systems to address potential demand and supply gaps in wheat production.

A regularized constrained two-stream convolution augmented Transformer for aircraft engine remaining useful life prediction

Remaining Useful Life (RUL) prediction is of great significance for maintaining the reliability and safety of industrial equipment. To address the challenges faced by existing methods in simultaneously extracting local and global degradation information from monitoring data. This paper proposes a Two-Stream Convolution Augmented Transformer (TACT) model based on L2 regularization constraint. Specifically, we design the parallel multi-scale Convolution Neural Network (CNN) and Transformer module to combine the local modeling ability of CNN and the global modeling ability of Transformer to improve the overall architecture of RUL prediction model. Moreover, the two-stream network based on the parallel structure also realizes the synchronous extraction of different time steps and sensor features in the sequence. Then, in the process of model training, the prediction reliability constraint is fused, the delay prediction constraint term is introduced, and the L2 regularization loss function is constructed. Finally, extensive experiments on the commercial modular aero-propulsion system simulation (C-MAPSS) show that our model provides competitive performance in terms of Root-Mean-Square Error (RMSE) and Score metrics. Compared to the state-of-the-art method based on Recurrent Neural Network (RNN) or CNN and its variants, Score is reduced by at least 2.71% and RMSE by at least 3.13%. Compared to the Transformer-based improved method, the Score is decreased by at least 4.54% and the RMSE is decreased by at least 2.78%. The effectiveness of the proposed method is demonstrated.