Mean Square Error Percentage Research Articles

Machine Learning Approaches for Battery Durability Prediction: Leveraging Diverse Datasets and Advanced Feature Engineering Techniques

Lithium-ion batteries play a pivotal role in various applications due to their high energy density and longevity. However, accurately predicting their lifespan remains a significant challenge due to the complex and varied degradation patterns inherent in battery chemistry. This study employs advanced machine learning (ML) techniques to forecast the State of Health (SOH) of lithium-ion batteries, focusing on a diverse range of chemistries.The study encompasses a comprehensive analysis of battery datasets, combining in-house data and publicly available datasets featuring varied chemistries. By incorporating data from multiple sources, including chemistries such as NMC 811, NMC 532, LFP, etc the model's robustness is enhanced, enabling it to better handle the variability in battery chemistry.Feature engineering is a critical component of the model development process. Various battery characteristics, including anode-cathode balance, resistance metrics, and charge/discharge behavior, are extracted and integrated. Advanced techniques such as Minimum Redundancy Maximum Relevance (MRMR) feature selection and Box-Cox transformation are employed to optimize feature relevance, reduce data dimensionality, and enhance model interpretability.Model performance is rigorously evaluated using established metrics such as Mean Absolute Percentage Error (MAPE) and Mean Squared Percentage Error (MSPE). Initial predictions using the first 10 cycles reveal a trend of increasing prediction errors as SOH values rise. However, when focusing on SOH values above 0.75, prediction accuracy significantly improves, highlighting the effectiveness of this approach for batteries in good condition.The study also explores the evolving importance of different feature sets across battery lifetimes. Capacity-based features prove crucial for early-cycle SOH prediction, reflecting the initial health status and degradation patterns of the battery. As the battery undergoes more cycles, the predictive power of CC/CV curve-based features becomes increasingly significant, capturing nuanced charging and discharging behaviors.MRMR feature selection further refines the model, identifying the top 40 influential features that are most relevant to SOH prediction. This process enhances model interpretability and focuses on features that capture the complex relationships between battery characteristics and degradation dynamics.Optimized Random Forest regression models demonstrate robust performance across various prediction scenarios. For SOH at 250 cycle predictions, the model achieves an MSPE of 0.13% and MAPE of 2.54%, underscoring its accuracy and reliability for batteries in good condition.In conclusion, this research demonstrates the potential of ML techniques in enhancing lithium-ion battery durability prediction. By leveraging diverse datasets, advanced feature engineering techniques, and rigorous model evaluation, we can significantly improve prediction accuracy. This advancement holds promise for proactive battery management, optimization of battery performance, and acceleration of battery technology development. Figure 1

A Coupled Model for Forecasting Spatiotemporal Variability of Regional Drought in the Mu Us Sandy Land Using a Meta-Heuristic Algorithm

Vegetation plays a vital role in terrestrial ecosystems, and droughts driven by rising temperatures pose significant threats to vegetation health. This study investigates the evolution of vegetation drought from 2010 to 2024 and introduces a deep-learning-based forecasting model for analyzing regional spatial and temporal variations in drought. Extensive time-series remote-sensing data were utilized, and we integrated the Temperature–Vegetation Dryness Index (TVDI), Drought Severity Index (DSI), Evaporation Stress Index (ESI), and the Temperature–Vegetation–Precipitation Dryness Index (TVPDI) to develop a comprehensive methodology for extracting regional vegetation drought characteristics. To mitigate the effects of regional drought non-stationarity on predictive accuracy, we propose a coupling-enhancement strategy that combines the Whale Optimization Algorithm (WOA) with the Informer model, enabling more precise forecasting of long-term regional drought variations. Unlike conventional deep-learning models, this approach introduces rapid convergence and global search capabilities, utilizing a sparse self-attention mechanism that improves performance while reducing model complexity. The results demonstrate that: (1) compared to the traditional Transformer model, test accuracy is improved by 43%; (2) the WOA–Informer model efficiently handles multi-objective forecasting for extended time series, achieving MAE (Mean Absolute Error) ≤ 0.05, MSE (Mean Squared Error) ≤ 0.001, MSPE (Mean Squared Percentage Error) ≤ 0.01, and MAPE (Mean Absolute Percentage Error) ≤ 5%. This research provides advanced predictive tools and precise model support for long-term vegetation restoration efforts.

Supraharmonics Reconstruction Method Based on Blackman Window and Compressed Sensing

This paper proposes a method that combines window functions with compressed sensing for the detection of ultra-high harmonics in the frequency range of 2–150 kHz. By analyzing the sparsity of the signal, the Bruckmann window function, which is most suitable for the compressed sensing reconstruction process and the characteristics of ultra-high harmonics, is selected. Simulations indicate that, compared to existing methods, the proposed algorithm based on the fusion of the Bruckmann window and compressed sensing achieves a sparser post-observation signal with reduced fluctuations. The robustness and anti-interference capabilities are enhanced, while the harmonic detection accuracy and signal reconstruction performance are significantly improved. The reconstruction error reaches 4.15 × 10−6, the mean squared error percentage (MSE) reaches 4.13 × 10−6, and the signal-to-noise ratio (SNR) is as high as 97.69 dB, marking an increase of 54.11%. This study provides a new theoretical and methodological approach for the analysis and processing of ultra-high harmonics caused by a high proportion of power electronic devices.

Development of objective function-based ensemble model for streamflow forecasts

The objective function plays an important role in hydrological model calibrations/training, since it largely determines the values of the model parameters and consequently influences the model performance. In this study, we establish two application-orientated objective functions, namely high flow balance error (HFBE) and mean squared percentage error (MSPE), for the forecasts of high flows and low flows, respectively. We examine the strengths and weaknesses of these streamflow forecast models trained with HFBE, MSPE and mean square error (MSE). Furthermore, we develop an objective function-based ensemble model (OEM) framework that can integrate the models trained with different objective functions. Our results in 273 catchments over USA show that the models trained on MSE have obvious underestimation in high-flow prediction. The models trained on HFBE can alleviate this underestimation and thus perform remarkably better for high-flow forecast. In addition, the models trained on MSPE outperform the other two models in low-flow forecast, but with an expense of the deterioration in the forecasting performance for high-flow. By incorporating the models trained on HFBE, MSPE and MSE, our proposed OEM performs well under all streamflow levels, with a median KGE of 0.96 and a median logNSE of 0.95. OEM realistically captures the mean and the variability of the observational streamflow under different scenarios with a variety of hydrometeorological conditions. This study highlights the necessity of applying objective functions that are appropriate for the modeling goal and the potential of ensemble learning methods for multi-objective optimization in hydrological modeling.

Improving Lettuce Fresh Weight Estimation Accuracy through RGB-D Fusion

Computer vision provides a real-time, non-destructive, and indirect way of horticultural crop yield estimation. Deep learning helps improve horticultural crop yield estimation accuracy. However, the accuracy of current estimation models based on RGB (red, green, blue) images does not meet the standard of a soft sensor. Through enriching more data and improving the RGB estimation model structure of convolutional neural networks (CNNs), this paper increased the coefficient of determination (R2) by 0.0284 and decreased the normalized root mean squared error (NRMSE) by 0.0575. After introducing a novel loss function mean squared percentage error (MSPE) that emphasizes the mean absolute percentage error (MAPE), the MAPE decreased by 7.58%. This paper develops a lettuce fresh weight estimation method through the multi-modal fusion of RGB and depth (RGB-D) images. With the multimodal fusion based on calibrated RGB and depth images, R2 increased by 0.0221, NRMSE decreased by 0.0427, and MAPE decreased by 3.99%. With the novel loss function, MAPE further decreased by 1.27%. A MAPE of 8.47% helps to develop a soft sensor for lettuce fresh weight estimation.

Day-Ahead Electricity Market Price Forecasting Considering the Components of the Electricity Market Price; Using Demand Decomposition, Fuel Cost, and the Kernel Density Estimation

This paper aims to improve the forecasting of electricity market prices by incorporating the characteristics of electricity market prices that are discretely affected by the fuel cost per unit, the unit generation cost of the large-scale generators, and the demand. In this paper, two new techniques are introduced. The first technique applies feature generation to the label and forecasts the transformed new variables, which are then post-processed by inverse transformation, considering the characteristic of the fuel types of marginal generators or prices through two variables: fuel cost per unit by the representative fuel type and argument of the maximum of Probability Density Function (PDF) calculated by Kernel Density Estimation (KDE) from the previous price. The second technique applies decomposition to the demand, followed by a feature selection process to apply the major decomposed feature. It is verified using gain or SHapley Additive exPlanations (SHAP) value in the feature selection process. In the case study, both showed improvement in all indicators. In the Korean Electricity Market, the unit generation cost for each generator is calculated monthly, resulting in a step-wise change in the electricity market price depending on the monthly fuel cost. Feature generation using the fuel cost per unit improved the forecasting by eliminating monthly volatility caused by the fuel costs and reducing the error that occurs at the beginning of the month. It improved the Mean Squared Percentage Error (MAPE) of 3.83[%]. Using the argument of the maximum PDF calculated by KDE improved the forecasting during the test period, where discrete monthly variations were not included. The resulting MAPE was 3.82[%]. Combining these two techniques resulted in the most accurate performance compared to the other techniques used, which had a MAPE of 3.49[%]. The MAPE of the forecasting with the decomposed data of the original price was 4.41[%].

WoX+: A Meta-Model-Driven Approach to Mine User Habits and Provide Continuous Authentication in the Smart City.

The literature is rich in techniques and methods to perform Continuous Authentication (CA) using biometric data, both physiological and behavioral. As a recent trend, less invasive methods such as the ones based on context-aware recognition allows the continuous identification of the user by retrieving device and app usage patterns. However, a still uncovered research topic is to extend the concepts of behavioral and context-aware biometric to take into account all the sensing data provided by the Internet of Things (IoT) and the smart city, in the shape of user habits. In this paper, we propose a meta-model-driven approach to mine user habits, by means of a combination of IoT data incoming from several sources such as smart mobility, smart metering, smart home, wearables and so on. Then, we use those habits to seamlessly authenticate users in real time all along the smart city when the same behavior occurs in different context and with different sensing technologies. Our model, which we called WoX+, allows the automatic extraction of user habits using a novel Artificial Intelligence (AI) technique focused on high-level concepts. The aim is to continuously authenticate the users using their habits as behavioral biometric, independently from the involved sensing hardware. To prove the effectiveness of WoX+ we organized a quantitative and qualitative evaluation in which 10 participants told us a spending habit they have involving the use of IoT. We chose the financial domain because it is ubiquitous, it is inherently multi-device, it is rich in time patterns, and most of all it requires a secure authentication. With the aim of extracting the requirement of such a system, we also asked the cohort how they expect WoX+ will use such habits to securely automatize payments and identify them in the smart city. We discovered that WoX+ satisfies most of the expected requirements, particularly in terms of unobtrusiveness of the solution, in contrast with the limitations observed in the existing studies. Finally, we used the responses given by the cohorts to generate synthetic data and train our novel AI block. Results show that the error in reconstructing the habits is acceptable: Mean Squared Error Percentage (MSEP) 0.04%.

Spatiotemporal Deep Learning Model for Prediction of Taif Rose Phenotyping

Despite being an important economic component of Taif region and the Kingdom of Saudi Arabia (KSA) as a whole, Taif rose experiences challenges because of uncontrolled conditions. In this study, we developed a phenotyping prediction model using deep learning (DL) that used simple and accurate methods to obtain and analyze data collected from ten rose farms. To maintain broad applicability and minimize computational complexity, our model utilizes a complementary learning approach in which both spatial and temporal instances of each dataset are processed simultaneously using three state-of-the-art deep neural networks: (1) convolutional neural network (CNN) to treat the image, (2) long short-term memory (LSTM) to treat the timeseries and (3) fully connected multilayer perceptions (MLPs)to obtain the phenotypes. As a result, this approach not only consolidates the knowledge gained from processing the same data from different perspectives, but it also leverages on the predictability of the model under incomplete or noisy datasets. An extensive evaluation of the validity of the proposed model has been conducted by comparing its outcomes with comprehensive phenotyping measurements taken from real farms. This evaluation demonstrates the ability of the proposed model to achieve zero mean absolute percentage error (MAPE) and mean square percentage error (MSPE) within a small number of epochs and under different training to testing schemes.

Deep Learning Based Purchase Forecasting for Food Producer-Retailer Team Merchandising

Expired foods turning into waste has always been an important issue. In Taiwan, more than 36,000 metric tons of unopened expired food, worth more than $130 million, are thrown away from retail stores as waste each year. Insufficient inventory results in the loss of business prospects for retailers, whilst excessive inventory results in abandoned merchandise. Foods with a short shelf life are particularly vulnerable. Typically, food producer and retailer would form team merchandising (MD). The team MD mechanism is responsible for ensuring safety and quality, not for forecasting demand. This study uses artificial neural networks (ANNs) to analyze sales data to forecasting purchase volume in response to changes in store environment, weather, events, and consumer attributes. The study object is a sort of cream puff with a short shelf life cobranded by a retailer. According to the experimental results, the adopted proposed model in this study effectively reduces the error in purchasing; the mean-square percentage error (MSPE) of the forecast values is less than 6%. The importance of this study is on promoting the team MD’s green energy management capabilities in food production and verifiably achieving the goal of environmental sustainability.

Quantitative Assessment of Stress Through EEG During a Virtual Reality Stress-Relax Session.

Recent studies have addressed stress level classification via electroencephalography (EEG) and machine learning. These works typically use EEG-based features, like power spectral density (PSD), to develop stress classifiers. Nonetheless, these classifiers are usually limited to the discrimination of two (stress and no stress) or three (low, medium, and high) stress levels. In this study we propose an alternative for quantitative stress assessment based on EEG and regression algorithms. To this aim, we conducted a group of 23 participants (mean age 22.65 ± 5.48) over a stress-relax experience while monitoring their EEG. First, we stressed the participants via the Montreal imaging stress task (MIST), and then we led them through a 360-degree virtual reality (VR) relaxation experience. Throughout the session, the participants reported their self-perceived stress level (SPSL) via surveys. Subsequently, we extracted spectral features from the EEG of the participants and we developed individual models based on regression algorithms to predict their SPSL. We evaluated stress regression performance in terms of the mean squared percentage error (MSPE) and the correlation coefficient (R2). The results yielded from this evaluation (MSPE = 10.62 ± 2.12, R2 = 0.92 ± 0.02) suggest that our approach predicted the stress level of the participants with remarkable performance. These results may have a positive impact in diverse areas that could benefit from stress level quantitative prediction. These areas include research fields like neuromarketing, and training of professionals such as surgeons, industrial workers, or firefighters, that often face stressful situations.

Forecasting based on an ensemble Autoregressive Moving Average - Adaptive neuro - Fuzzy inference system – Neural network - Genetic Algorithm Framework

This paper proposes a novel ensemble methodology comprising an auto regressive integrated moving average, artificial neural network, fuzzy inference system model, adaptive neuro fuzzy inference system, support vector regression, extreme machine learning, and genetic algorithm to forecast aggregated, long-term energy demand. After comparing the framework with several benchmark methods by the loss functions mean squared error and mean absolute percentage error, and applying a model confidence set this work suggests that the proposed method improves forecasting accuracy over previous approaches. The proposed approach resulted in a mean squared error decrease of 22.3% and mean absolute percentage error by 33.1% with respect to the best artificial intelligence and econometric models in a sample study. Post-processing optimization of the forecasting ensemble in this methodology improves prediction accuracy. The approach developed herein provides an addition to the field for how hybridized models and augmented forecasting accuracy can be improved. Continued improvements to forecasting techniques are extremely important especially in areas where there are upper bound constraints on supply and lower bound on minimum operation levels.

Development of a generalized proportional integral control strategy for level control in a coupled tank system

This work presents the analysis and design of a generalized proportional integral control strategy for a level control in a coupled tank system, such analysis is made under the active disturbance rejection. The principle objective is to show the advantages of the control strategy generalized proportional integral as to signals tracking and disturbance rejection, compared to conventional control techniques such as the proportional integral derivative control. To validate the process, the modeling of the system was carried out and with this model simulations were carried out under nominal conditions, applying the two control strategies. It was found that the generalized proportional integral control presented a better performance since it achieves a lower mean squared error percentage than the proportional integral derivative control, even in the presence of disturbances.

Improved support vector regression models for predicting rock mass parameters using tunnel boring machine driving data

The sensitivity of tunnel boring machines (TBMs) to complex rock mass parameters makes the accurate and reliable prediction of these parameters crucial for the selection of reasonable operational parameters and the reduction of construction project risks. We introduce and verify a TBM driving data–based method for predicting rock mass parameters including the uniaxial compressive strength (UCS), brittleness index (BI), distance between planes of weakness (DPW), and orientation of discontinuities (α). For this purpose, an artificial intelligence (AI) algorithm, namely support vector regression (SVR), is improved by the stacked single-target (SST) technique and used to establish rock mass parameter prediction models. A dataset of 180 samples is established based on parameters from the 4th section of the Water Supply Project from Songhua River, with 150 randomly selected samples used for training. The constructed models are applied to the remaining 30 samples, and the mean squared percentage error (MSPE) of prediction results for UCS, BI, DPW, and α are determined as 3.0%, 4.6%, 3.0%, and 2.5%, respectively, while the respective determination coefficients (R2) are obtained as 0.83, 0.75, 0.63, and 0.63. The above results are better than the results of common SVR method, and show that the developed models can effectively simulate rock mass parameters and their sudden changes, i.e., the prediction of these parameters based on TBM driving data is both feasible and practical. Moreover, the initial models are used on the dataset, the comparison between their results and the results of proposed models verify the positive effect of the SST on SVR method.

Comparison of exponential smoothing and neural network method to forecast rice production in Indonesia

Rice is the most important food commodity in Indonesia. In order to achieve affordability, and the fulfillment of the national food consumption according to the Indonesia law no. 18 of 2012, Indonesia needs information to support the government's policy regarding the collection, processing, analyzing, storing, presenting and disseminating. One manifestation of the Information availability to support the government’s policy is forecasting. Exponential smoothing and neural network methods are commonly used to forecasting because it provides a satisfactory result. Our study are comparing the variants of exponential and backpropagation model as a neural network to forecast rice production. The evaluation is summarized by utilizing Mean Square Percentage Error (MAPE), Mean Square Error (MSE). The results show that neural network method is preferable than the statistics method since it has lower MSE and MAPE values than statistics method.

Assessing the influence of weather parameters on rainfall to forecast river discharge based on short-term

Rain serves as one of the key components in water cycle and it comes in the form of water droplets that are condensed from atmosphere and then fall on earth surface as rainfall. It has much importance. However, excessive rainfall can cause environmental hazards. This work developed an adaptive neuro – fuzzy inference system (ANFIS) to relate certain weather parameters (temperature and relative humidity) with rainfall in order to forecast the amount of rainfall capable of causing River Yazaram in Mubi town to discharge. It is predicted that, Mubi will experience high rainfall on 7th, 27th and 30th August 2016 as 56mm, 28.8mm and 28.8mm respectively. Furthermore, on 7th August 2016 River Yazaram is likely to discharge. The model developed is validated with mean square percentage error (MAPE) of 4.64% and correlation coefficient of 0.1277 and 0.075 of rainfall with temperature and relative humidity respectively.

MSPE를 이용한 임금총액 소지역 추정

국내외적으로 지역통계에 관한 관심이 높아지고 있으며 이와 관련하여 소지역 추정에 관한 많은 연구가 진행되고 있다. 소지역 추정에 사용되는 추정량의 대부분은 MSE(moan squared error)를 최소화하여 얻어진다 (Rao, 2003). 최근 황희진과 신기일 (2008)은 MSPE(mean squared percentage error)를 최소화하는 추정량을 사용한 소지역 추정법을 제안하였다. 본 논문에서는 노동통계 중 지청별 일인당 평균 임금총액 추정에 황희진과 신기일 (2008)이 제안한 방법을 적용하여 보았으며 2007년 매월 노동통계 자료를 이용하여 기존의 MSE를 최소화 하여 얻어진 여러 추정량과 우수성을 비교해 보았다. 또한 노동통계를 위 한 소지역 추정의 실제 사용 가능성을 살펴보았다. Many researches have been devoted to the small area estimation related with the area level statistics. Almost all of the small area estimation methods are derived based on minimization of mean squared error(MSE). Recently Hwang and Shin (2008) suggested an alternative small area estimation method by minimizing mean squared percentage error. In this paper we apply this small area estimation method to the labor statistics, especially monthly wages by a branch area of labor department. The Monthly Labor Survey data (2007) is used for analysis and comparison of these methods.

Modeling of electricity consumption in the Asian gaming and tourism center—Macao SAR, People's Republic of China

The use of electricity is indispensable to modern life. As Macao Special Administrative Region becomes a gaming and tourism center in Asia, modeling the consumption of electricity is critical to Macao's economic development. The purposes of this paper are to conduct an extensive literature review on modeling of electricity consumption, and to identify key climatic, demographic, economic and/or industrial factors that may affect the electricity consumption of a country/city. It was identified that the five factors, namely temperature, population, the number of tourists, hotel room occupancy and days per month, could be used to characterize Macao's monthly electricity consumption. Three selected approaches including multiple regression, artificial neural network (ANN) and wavelet ANN were used to derive mathematical models of the electricity consumption. The accuracy of these models was assessed by using the mean squared error (MSE), the mean squared percentage error (MSPE) and the mean absolute percentage error (MAPE). The error analysis shows that wavelet ANN has a very promising forecasting capability and can reveal the periodicity of electricity consumption.

축소예측을 이용한 소지역 추정

Many small area estimation methods have been suggested. Also for the comparison of the estimation methods, model diagnostic checking techniques have been studied. Almost all of the small area estimators were developed by minimizing MSE(Mean square error) and so the MSE is the well-known comparison criterion for superiority. In this paper we suggested a new small area estimator based on minimizing MSPE(Mean square percentage error) which is recently re-highlighted. Also we compared the new suggested estimator with the estimators explained in Shin et al. (2007) using MSE, MSPE and other diagnostic checking criteria.

A Shrinked Forecast in Stationary Processes Favouring Percentage Error

Abstract. In stationary time‐series forecasting, the commonly used criterion for selecting a proper forecast is the mean square error (MSE), which is minimized by the conditional expectation of future observation given the entire past known as a minimum MSE forecast. In this paper, mean square percentage error (MSPE) instead of is used to forecast autoregressive moving average (ARMA)(p,q) series. The suggested forecast takes the form of or (CVt+1 is the coefficient of variation for one step ahead) times the minimum MSE forecast, which performs better not only in MSPE, but also in mean absolute percentage error (MAPE) than the ordinary MSE forecast in simulation studies. A real data example also supported this result. We conclude that, if percentage error is a prime concern, this shrinked version of MSE forecast performs better than the ordinary forecast in the stationary ARMA(p,q) model.

DATA-DRIVEN NONPARAMETRIC SPECTRAL DENSITY ESTIMATORS FOR ECONOMIC TIME SERIES: A MONTE CARLO STUDY

ABSTRACT Spectral analysis at frequencies other than zero plays an increasingly important role in econometrics. A number of alternative automated data-driven procedures for nonparametric spectral density estimation have been suggested in the literature, but little is known about their finite-sample accuracy. We compare five such procedures in terms of their mean-squared percentage error across frequencies. Our data generating processes (DGP) include autoregressive-moving average (ARMA) models, fractionally integrated ARMA models and nonparametric models based on 16 commonly used macroeconomic time series. We find that for both quarterly and monthly data the autoregressive sieve estimator is the most reliable method overall.