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Given the regional heterogeneity of economic development, electricity consumption in various regions exhibits a discrepant growth pattern. The purpose of this study is to construct a grey system forecasting model with intelligent parameters for predicting provincial electricity consumption in China.

First, parameter optimization and structural expansion are simultaneously integrated into a unified grey system prediction framework, enhancing its adaptive capabilities. Second, by setting the minimum simulation percentage error as the optimization goal, the authors apply the particle swarm optimization (PSO) algorithm to search for the optimal grey generation order and background value coefficient. Third, to assess the performance across diverse power consumption systems, the authors use two electricity consumption cases and select eight other benchmark models to analyze the simulation and prediction errors. Further, the authors conduct simulations and trend predictions using data from all 31 provinces in China, analyzing and predicting the development trends in electricity consumption for each province from 2021 to 2026.

The study identifies significant heterogeneity in the development trends of electricity consumption systems among diverse provinces in China. The grey prediction model, optimized with multiple intelligent parameters, demonstrates superior adaptability and dynamic adjustment capabilities compared to traditional fixed-parameter models. Outperforming benchmark models across various evaluation indicators such as root mean square error (RMSE), average percentage error and Theil’s index, the new model establishes its robustness in predicting electricity system behavior.

Acknowledging the limitations of traditional grey prediction models in capturing diverse growth patterns under fixed-generation orders, single structures and unadjustable background values, this study proposes a fractional grey intelligent prediction model with multiple parameter optimization. By incorporating multiple parameter optimizations and structure expansion, it substantiates the model’s superiority in forecasting provincial electricity consumption.

Traditional multivariable grey prediction models define the background-value coefficients of the dependent and independent variables uniformly, ignoring the differences between their physical properties, which in turn affects the stability and reliability of the model performance.

A novel multivariable grey prediction model is constructed with different background-value coefficients of the dependent and independent variables, and a one-to-one correspondence between the variables and the background-value coefficients to improve the smoothing effect of the background-value coefficients on the sequences. Furthermore, the fractional order accumulating operator is introduced to the new model weaken the randomness of the raw sequence. The particle swarm optimization (PSO) algorithm is used to optimize the background-value coefficients and the order of the model to improve model performance.

The new model structure has good variability and compatibility, which can achieve compatibility with current mainstream grey prediction models. The performance of the new model is compared and analyzed with three typical cases, and the results show that the new model outperforms the other two similar grey prediction models.

This study has positive implications for enriching the method system of multivariable grey prediction model.

The Grey System Theory (GST) is an emerging area of research within artificial intelligence. Since its founding in 1982, it has seen a lot of multidisciplinary applications. In just a short period, it has garnered some considerable strengths. Based on the 1987–2021 data collected from the Web of Science (WoS), the current study reports the advancement of the GST.

Research papers utilizing the GST in the fields of economics and education were retrieved from the Web of Science (WoS) platform using a set of predetermined keywords. In the final stage of the process, the papers that underwent analysis were manually chosen, with selection criteria based on the information presented in the titles and abstracts.

The study identifies prominent authors, institutions, publications and journals closely associated with the subject. In terms of authors, two major clusters are identified around Liu SF and Wang ZX, while the institution with the highest number of publications is Nanjing University of Aeronautics and Astronautics. Moreover, significant keywords, trends and research directions have been extracted and analyzed. Additionally, the study highlights the regions where the theory holds substantial influence.

The study is subject to certain limitations stemming from factors such as the language employed in the chosen literature, the papers included within the Web of Science (WoS) database, the designation of works categorized as “articles” in the database, the specific selection of keywords and keyword combinations, and the meticulous manual process employed for paper selection. While the manual selection process itself is not inherently limiting, it demands a greater investment of time and meticulous attention, contributing to the overall limitations of the study.

The significance of the study extends not only to scholars and practitioners but also to readers who observe the development of emerging scientific disciplines.

The analysis of trends revealed a growing emphasis on the application of GST in diverse domains, including supply chain management, manufacturing and economic development. Notably, the emergence of COVID-19 as a new research focal point among GST scholars is evident. The heightened interest in COVID-19 can be attributed to its global impact across various academic disciplines. However, it is improbable that this interest will persist in the long term, as the pandemic is gradually brought under control.

Software defect prediction (SDP) is a critical aspect of software quality assurance, aiming to identify and manage potential defects in software systems. In this paper, we have proposed a novel hybrid approach that combines Gray Wolf Optimization with Feature Selection (GWOFS) and multilayer perceptron (MLP) for SDP. The GWOFS-MLP hybrid model is designed to optimize feature selection, ultimately enhancing the accuracy and efficiency of SDP. Gray Wolf Optimization, inspired by the social hierarchy and hunting behavior of gray wolves, is employed to select a subset of relevant features from an extensive pool of potential predictors. This study investigates the key challenges that traditional SDP approaches encounter and proposes promising solutions to overcome time complexity and the curse of the dimensionality reduction problem.

The integration of GWOFS and MLP results in a robust hybrid model that can adapt to diverse software datasets. This feature selection process harnesses the cooperative hunting behavior of wolves, allowing for the exploration of critical feature combinations. The selected features are then fed into an MLP, a powerful artificial neural network (ANN) known for its capability to learn intricate patterns within software metrics. MLP serves as the predictive engine, utilizing the curated feature set to model and classify software defects accurately.

The performance evaluation of the GWOFS-MLP hybrid model on a real-world software defect dataset demonstrates its effectiveness. The model achieves a remarkable training accuracy of 97.69% and a testing accuracy of 97.99%. Additionally, the receiver operating characteristic area under the curve (ROC-AUC) score of 0.89 highlights the model’s ability to discriminate between defective and defect-free software components.

Experimental implementations using machine learning-based techniques with feature reduction are conducted to validate the proposed solutions. The goal is to enhance SDP’s accuracy, relevance and efficiency, ultimately improving software quality assurance processes. The confusion matrix further illustrates the model’s performance, with only a small number of false positives and false negatives.

The author aims to study and predict the sustainability governance performances of firms using an advanced grey prediction model. The case implication of the prediction model is also studied considering select firms in the Indian context.

The author has proposed an advanced grey prediction model, the first-entry grey prediction model (FGM (1, 1)) for forecasting the sustainability governance performances of firms. The proposed model is tested using the periodic data of sustainability governance performances of 10 Indian firms.

The author observes that the majority of firms (6 out of 10) show dipping performances for sustainability governance for the future predicted period. This throws insights into the direction of improving good governance practices for Indian firms.

The idea and motivation for sustainability-focussed governance need a bi-directional focus from the side of managers that act as the agents and from the side of shareholders that act as the principals, as seen from an agency theory perspective for sustainability governance.

Sustainability governance culture can be inculcated to a firm at the strategic level by having a bi-directional focus from managers and shareholders, so as to enhance the social and environmental sustainability performances.

The governance performance evaluations for firms particularly in developing countries were not dated back more than a decade or two. Hence, the author implements a prediction model that can be best suited, when there are small periodic data sets available for prediction.

The energy efficiency of buildings has been emphasized along with the continual development in the building and construction sector that consumes a significant amount of energy. To this end, the purpose of this research paper is to forecast energy consumption to improve energy resource planning and management.

This study proposes the application of the convolutional neural network (CNN) for estimating the electricity consumption in the Grey Nuns building in Canada. The performance of the proposed model is compared against that of long short-term memory (LSTM) and multilayer perceptron (MLP) neural networks. The models are trained and tested using monthly electricity consumption records (i.e. from May 2009 to December 2021) available from Concordia’s facility department. Statistical measures (e.g. determination coefficient [R²], root mean squared error [RMSE], mean absolute error [MAE] and mean absolute percentage error [MAPE]) are used to evaluate the outcomes of models.

The results reveal that the CNN model outperforms the other model predictions for 6 and 12 months ahead. It enhances the performance metrics reported by the LSTM and MLP models concerning the R², RMSE, MAE and MAPE by more than 4%, 6%, 42% and 46%, respectively. Therefore, the proposed model uses the available data to predict the electricity consumption for 6 and 12 months ahead. In June and December 2022, the overall electricity consumption is estimated to be 195,312 kWh and 254,737 kWh, respectively.

This study discusses the development of an effective time-series model that can forecast future electricity consumption in a Canadian heritage building. Deep learning techniques are being used for the first time to anticipate the electricity consumption of the Grey Nuns building in Canada. Additionally, it evaluates the effectiveness of deep learning and machine learning methods for predicting electricity consumption using established performance indicators. Recognizing electricity consumption in buildings is beneficial for utility providers, facility managers and end users by improving energy and environmental efficiency.

A time-varying grey Fourier model (TVGFM(1,1,N)) is proposed for the simulation of variable amplitude seasonal fluctuation time series, as the performance of traditional grey models can't catch the time-varying trend well.

The proposed model couples Fourier series and linear time-varying terms as the grey action, to describe the characteristics of variable amplitude and seasonality. The truncated Fourier order N is preselected from the alternative order set by Nyquist-Shannon sampling theorem and the principle of simplicity, then the optimal Fourier order is determined by hold-out method to improve the robustness of the proposed model. Initial value correction and the multiple transformation are also studied to improve the precision.

The new model has a broader applicability range as a result of the new grey action, attaining higher fitting and forecasting accuracy. The numerical experiment of a generated monthly time series indicates the proposed model can accurately fit the variable amplitude seasonal sequence, in which the mean absolute percentage error (MAPE) is only 0.01%, and the complex simulations based on Monte-Carlo method testify the validity of the proposed model. The results of monthly electricity consumption in China's primary industry, demonstrate the proposed model catches the time-varying trend and has good performances, where MAPE_F and MAPE_T are below 5%. Moreover, the proposed TVGFM(1,1,N) model is superior to the benchmark models, grey polynomial model (GMP(1,1,N)), grey Fourier model (GFM(1,1,N)), seasonal grey model (SGM(1,1)), seasonal ARIMA model seasonal autoregressive integrated moving average model (SARIMA) and support vector regression (SVR).

The parameter estimates and forecasting of the new proposed TVGFM are studied, and the good fitting and forecasting accuracy of time-varying amplitude seasonal fluctuation series are testified by numerical simulations and a case study.

This research paper aims to analyze the scientific and grey literature on Quality 4.0 and zero-defect manufacturing (ZDM) frameworks to develop an integrated quality 4.0 framework (IQ4.0F) for quality improvement (QI) based on Six Sigma and machine learning (ML) techniques towards ZDM. The IQ4.0F aims to contribute to the advancement of defect prediction approaches in diverse manufacturing processes. Furthermore, the work enables a comprehensive analysis of process variables influencing product quality with emphasis on the use of supervised and unsupervised ML techniques in Six Sigma’s DMAIC (Define, Measure, Analyze, Improve and Control) cycle stage of “Analyze.”

The research methodology employed a systematic literature review (SLR) based on PRISMA guidelines to develop the integrated framework, followed by a real industrial case study set in the automotive industry to fulfill the objectives of verifying and validating the proposed IQ4.0F with primary data.

This research work demonstrates the value of a “stepwise framework” to facilitate a shift from conventional quality management systems (QMSs) to QMSs 4.0. It uses the IDEF0 modeling methodology and Six Sigma’s DMAIC cycle to structure the steps to be followed to adopt the Quality 4.0 paradigm for QI. It also proves the worth of integrating Six Sigma and ML techniques into the “Analyze” stage of the DMAIC cycle for improving defect prediction in manufacturing processes and supporting problem-solving activities for quality managers.

This research paper introduces a first-of-its-kind Quality 4.0 framework – the IQ4.0F. Each step of the IQ4.0F was verified and validated in an original industrial case study set in the automotive industry. It is the first Quality 4.0 framework, according to the SLR conducted, to utilize the principal component analysis technique as a substitute for “Screening Design” in the Design of Experiments phase and K-means clustering technique for multivariable analysis, identifying process parameters that significantly impact product quality. The proposed IQ4.0F not only empowers decision-makers with the knowledge to launch a Quality 4.0 initiative but also provides quality managers with a systematic problem-solving methodology for quality improvement.

We attempt to construct a grey three-way conflict analysis model with constraints to deal with correlated conflict problems with uncertain information.

In order to address these correlated conflict problems with uncertain information, considering the interactive influence and mutual restraints among agents and portraying their attitudes toward the conflict issues, we utilize grey numbers and three-way decisions to propose a grey three-way conflict analysis model with constraints. Firstly, based on the collected information, we introduced grey theory, calculated the degree of conflict between agents and then analyzed the conflict alliance based on the three-way decision theory. Finally, we designed a feedback mechanism to identify key agents and key conflict issues. A case verifies the effectiveness and practicability of the proposed model.

The results show that the proposed model can portray their attitudes toward conflict issues and effectively extract conflict-related information.

By employing this approach, we can provide the answers to Deja’s fundamental questions regarding Pawlak’s conflict analysis: “what are the underlying causes of conflict?” and “how can a viable consensus strategy be identified?”

As data centres grow in size and complexity, traditional air-cooling methods are becoming less effective and more expensive. Immersion cooling, where servers are submerged in a dielectric fluid, has emerged as a promising alternative. Ensuring reliable operations in data centre applications requires the development of an effective control framework for immersion cooling systems, which necessitates the prediction of server temperature. While deep learning-based temperature prediction models have shown effectiveness, further enhancement is needed to improve their prediction accuracy. This study aims to develop a temperature prediction model using Long Short-Term Memory (LSTM) Networks based on recursive encoder-decoder architecture.

This paper explores the use of deep learning algorithms to predict the temperature of a heater in a two-phase immersion-cooled system using NOVEC 7100. The performance of recursive-long short-term memory-encoder-decoder (R-LSTM-ED), recursive-convolutional neural network-LSTM (R-CNN-LSTM) and R-LSTM approaches are compared using mean absolute error, root mean square error, mean absolute percentage error and coefficient of determination (R²) as performance metrics. The impact of window size, sampling period and noise within training data on the performance of the model is investigated.

The R-LSTM-ED consistently outperforms the R-LSTM model by 6%, 15.8% and 12.5%, and R-CNN-LSTM model by 4%, 11% and 12.3% in all forecast ranges of 10, 30 and 60 s, respectively, averaged across all the workloads considered in the study. The optimum sampling period based on the study is found to be 2 s and the window size to be 60 s. The performance of the model deteriorates significantly as the noise level reaches 10%.

The proposed models are currently trained on data collected from an experimental setup simulating data centre loads. Future research should seek to extend the applicability of the models by incorporating time series data from immersion-cooled servers.

The proposed multivariate-recursive-prediction models are trained and tested by using real Data Centre workload traces applied to the immersion-cooled system developed in the laboratory.