Grey Relational Degree Research Articles

Intuitionistic Fuzzy SVM based on Kernel Gray Relational Analysis

Fuzzy Support Vector Machine (FSVM) is a machine learning algorithm that combines fuzzy logic with Support Vector Machine (SVM) to deal with the uncertainty and fuzziness in classification and regression problems. This algorithm improves the performance of traditional SVM by introducing fuzzy membership degrees, making it more robust when handling datasets with noise or uncertainty. Although the existing FSVM algorithms can overcome the influence of noise to a certain extent, they cannot effectively distinguish outliers or abnormal values from boundary support vectors. To solve this problem, this study proposes an Intuitionistic Fuzzy Support Vector Machine algorithm (KGRA-IFSVM) based on Kernel Grey Relational Analysis (KGRA). This approach utilizes gray relational analysis in the kernel space to calculate the gray relational degree between each sample and its K isomorphic neighboring points, and takes the average value as the membership degree of the sample. Then, the same approach is used to compute the gray relational degree between each sample and its K heterogeneous neighboring points, and the average value is taken as the non-membership degree of the sample. Finally, each sample is assigned with an appropriate fuzzy value based on intuitionistic fuzzy sets using a specific scoring function. Test results on UCI datasets show that KGRA-IFSVM has better classification performance and stronger noise resistance.

Multi-Objective Optimization of the Forming Process Parameters of Disc Forgings Based on Grey Correlation Analysis and the Response Surface Method

This paper introduces a multi-objective optimization problem (MPO) for the forming process parameters of disc forgings using grey relational analysis (GRA) and the response surface methodology (RSM). Firstly, an experimental design based on the Box–Behnken design (BBD) principle was established, and simulations were performed in Deform to obtain response data. Secondly, GRA was used to transform the MPO into a grey relational degree (GRD) problem, and the entropic weight method was integrated to ascertain the influence weights of each variable on GRD. Then, a quadratic polynomial prediction model based on the RSM was constructed, and its accuracy was ensured through model validation. Finally, the optimal process parameter combination was determined through the particle swarm optimization algorithm, which included a friction coefficient of 0.3, an initial temperature of 1250 °C, and a downward pressing speed of 7.5 mm/s. The results of the experimental investigation indicate that optimized process parameters significantly reduce the forming load, equivalent stress, and damage value, effectively enhancing the overall quality of forged parts.

Multivariate Analysis of Grain Yield and Main Agronomic Traits in Different Maize Hybrids Grown in Mountainous Areas

Inconsistent reports exist on the relationships between key agronomic traits and maize yield. We performed a multivariate analysis of yield and 10 agronomic traits in 59 hybrids to explore maize yields in mountainous areas. The yield per plant (YP) was significantly and positively correlated with kernel weight (KW), growth period (GP), and kernel row number (KRN). KW and KRN had positive effects on YP, whereas kernel rows per ear (KRE) had a negative effect. GP indirectly affected YP. GP, KW, KRN, and ear length (EL) showed the highest grey relational degree with YP. The first four principal components cumulatively accounted for 73.36% of variation. EL, KW, plant height (PH), ear height (EH), GP, KRN, and YP contributed positively to the variation, whereas KRE, shelling percentage (SP), bald-tip length (BTL), and ear girth (EG) contributed negatively. Based on trait similarity, the 59 maize hybrids were classified into two clusters, Clusters I and II. A total of 11 traits were grouped into four clusters, Clusters A–D. Cluster D included KW, GP, KRN, EL, EH, PH, and YP, and the 22 maize hybrids in Cluster I performed better in these traits. These results provide a theoretical basis for the breeding of high-yield maize varieties in mountainous areas.

Application of multi index comprehensive evaluation method in the selection of wastewater treatment processes

The study comprehensively evaluates various wastewater treatment processes by using Grey Relational Analysis (GRA) and Analytic Hierarchy Process (AHP) to identify the optimal method for wastewater treatment. To conduct this evaluation, six key indicators were identified and used for assessment: five-day biochemical oxygen demand (BOD5) removal rate, chemical oxygen demand (COD) removal rate, ammonia nitrogen removal rate, total nitrogen removal rate, total phosphorus removal rate, and suspended solid removal rate. Initially, GRA was employed to calculate the grey relational degree of each treatment process based on the weights of the indicators, and the treatment processes were then ranked and analyzed according to these degrees. Subsequently, AHP was applied to construct a judgment matrix, determine the weights of each indicator, and ensure the matrix's rationality through consistency testing. The study reveals significant differences in the performance of various wastewater treatment processes among the indicators, with the Modified A2/O+AO process showing the highest comprehensive performance in the evaluation. The findings provide a scientific basis for improving efficiency, reducing pollution, and guiding policy and technological development.

Coupling Coordination Degree of Land, Ecology, and Food and Its Influencing Factors in Henan Province

Studying the spatiotemporal evolution characteristics of the coupling coordination of the land–ecology–food system (LEF) aids in promoting green agricultural development and regional resource management. This study enriches food indicators under the dietary structure and uses the coupling coordination degree model to analyze the coupling coordination relationship among the LEF of 18 cities in Henan Province from 2011 to 2020. The gray relational degree model is used to investigate the main influencing factors determining the synergistic development of the system. The results show that the comprehensive development index of the LEF in Henan Province ranges between 0.4 and 0.6. The overall comprehensive evaluation index of various cities is ranked as Southern Henan > Eastern Henan > Central Henan > Northern Henan > Western Henan, with the greatest fluctuation observed in the food subsystem. During the study period, the coupling degree of Henan’s LEF ranged from 0.277 to 0.996, indicating stages from low- to high-level coupling. The coupling coordination degree ranged from 0.338 to 0.775, generally bordering on imbalance and barely coordinated. The impact of each subsystem evaluation index on the system’s coupling coordination degree can be ranked as food subsystem > ecology subsystem > land subsystem, with the correlation degree of internal indicators of the food and ecology subsystems with the system’s coupling coordination degree being over 85%, emphasizing the importance of strict management. In summary, the coupling coordination of the LEF system in Henan Province urgently needs to be improved; especially, the coordination of the agricultural system is particularly important. Clarifying the spatiotemporal pattern of the LEF coupling and its coordination can provide a scientific basis for the coordinated development of land use, agricultural ecology, and grain production in Henan Province.

New insights into the cation exchange resin-driven carbon migration and recovery from waste activated sludge: Mass transfer environment and cation exchange force

Innovative cation exchange resin (CER)-driven anaerobic fermentation showed significant promise for enhancing carbon recovery from waste activated sludge. However comprehensive microscopic studies on the responses of cation exchange environments have been scarcely reported. This study clarified the transport mechanism of divalent cations within the “sludge→CER→cation exchange groups” pathway, along with comprehensive evaluations of carbon migration and recovery. It demonstrated that the sludge suspension solid (SS) and cation exchange groups dominantly determined the CER treatment performance, instead of CER pore structure. The –COOH exhibited the strongest electrostatic-adsorption capacity among various cation exchange groups. Such mass transfer environment modification and cation exchange groups regulation could improve ionic charge removal to 4.91 mmol e−/g VSS. By macroporous-COOH CER treatment at sludge SS of 20 g/L, the overall carbon migration reached 192.66 mg C/g VSS (44.98 %). As such, the ultimate carbon recovery elevated to 120.34 mg C/g VSS (28.10 %), against the lower performances of 13.91–32.97 mg C/g VSS without cation exchange environment regulations. The cation exchange groups showed correlations with carbon migration, biotransformation, and recovery, as indicated by grey relational analysis degrees of 0.48–0.66. Simultaneously, by adopting the optimized regulation strategy of CER-driven anaerobic fermentation, the equivalent economic income raised to 410.93 CNY/ton sludge SS.

Decision Analysis and Practical Pathways for Innovative Teaching Methods in Information Technology Education

With the rapid advancement of information technology, its integration into modern education has become essential, with a focus on enhancing teaching outcomes and the student learning experiences through innovative teaching methods. However, existing studies predominantly suffer from a lack of systematic evaluation indicators and scientific decision models. The selection of evaluation indicators is often subjective, incomplete, and primarily qualitative, lacking quantitative data support. A systematic decision analysis method was proposed in this study to address these issues. This study comprises three components: the construction of an evaluation indicator system for innovative teaching methods in information technology education, a scale analysis based on gray relational degree, and the computational steps for the decision model concerning innovative teaching methods. This study provides scientific bases and practical pathways for the selection of innovative teaching methods in information technology education, aiming to enhance teaching effectiveness and educational quality.

Multifactor Mathematical Modeling and Analysis of the Impact of Extreme Climate on Geological Disasters

Objective: To investigate the impact of extreme climate on geological disasters in Shanxi and propose effective disaster prevention and mitigation strategies. Methods: Using daily temperature and precipitation data from 27 meteorological stations in Shanxi Province from 1975 to 2020, 32 extreme climate indices were calculated. Combined with geological disaster site data, the distribution characteristics of extreme climates and their relationship with geological disasters were analyzed, and a regression model for geological disaster risk zones was constructed. Results: Sixteen extreme climate indices in Shanxi Province showed significant changes, especially TMAXmean (100% significant). Indices related to negative precipitation effects showed a declining trend, with 77.78% being significant, while 96.3% of positive temperature effect indices showed an increasing trend, with 73.6% being significant. Geological disaster hotspots were concentrated in the mid-altitude (500–1500 m) hilly and low mountain areas along the central north–south axis and on Q and Pz strata. Extreme high-temperature indices were significantly positively correlated with geological disaster hotspots, while extreme low-temperature indices were negatively correlated. Indices related to extreme heavy precipitation (e.g., R99p.Slope, RX5day.Slope) were associated with an increase in geological disaster hotspots, whereas higher total precipitation and frequent heavy precipitation events were associated with a decrease in disaster hotspots. The grey relational degree between the Z-score and TXn.Slope, TXx.Slope, GSL.Slope, and TX90P.Slope was greater than 0.8. The random forest model performed best in evaluation metrics such as MAE, RMSE, and R2. Conclusions: Shanxi is likely to experience more extreme high-temperature and precipitation events in the future. The low-altitude hilly and terraced areas in Zones III and VII are key regions for geological disaster prevention and control. High temperatures and extreme rainfall events generally increase the disaster risk, while higher total precipitation reduces it. The random forest model is the optimal tool for predicting geological disaster risks in Shanxi Province.

Performance comparison of two ORC-VCR system configurations using pure/mixture working fluids based on multi-objective optimization

The organic Rankine cycle-vapor compression refrigeration combined system is an effective way to sufficiently utilize low-grade heat energy and achieve refrigeration without electricity consumption. The combined system typically includes single-fluid configuration with a common condenser and double-fluid configuration with two condensers. In order to determine the optimal configuration of the combined system, the performance comparison of two system configurations using pure/mixture working fluids is carried out. The main innovations of this paper different from the previous literature are as follows: the performance comparison is based on the results of multi-objective optimization. Moreover, the working fluids are selected as the decision variables of multi-objective optimization. In order to provide theoretical guidance for the determination of the optimal system under different performance preferences, single-objective optimization is also conducted. The optimal system is determined under comprehensive performance and different performance preferences. The results indicate that the double-fluid system configuration has better thermodynamic performance than the single-fluid system configuration. Moreover, the performance of the systems using mixture working fluids is greatly improved compared with that of the system using pure working fluids. When users’ performance preference is coefficient of performance, system exergy efficiency or comprehensive performance, the optimal system is the double-fluid system using mixture working fluids with system coefficient of performance of 0.23, system exergy efficiency of 43%, and grey relational degree of 0.96, respectively. When users’ performance preference is levelized cost of cooling, the optimal system is the single-fluid system using mixture working fluids with levelized cost of cooling of 0.027$/kWh.

Research on the operational capital management performance of real estate enterprises under the background of high-quality developmen

Taking Vanke Real Estate as the research object, this study uses entropy weight method and grey relational analysis to quantitatively evaluate its working capital management performance from three dimensions: profitability, riskiness, and liquidity. The results show that during the period from 2021 to 2023, Vanke ranks behind Poly in terms of comprehensive grey relational degree ranking, indicating inferior working capital management performance compared to Poly. Based on the above analysis results, this study provides insightful suggestions for optimizing the working capital management strategies of real estate companies. It serves as a theoretical reference for improving the working capital management performance of real estate enterprises and promoting their high-quality development.

Evaluating the Websites of Academic Departments Using the GRA Method

The academic world heavily relies on search engine referrals, making SEO particularly relevant in this sector. To effectively improve page rankings, SEO encompasses two primary categories of factors: 'on-page' and 'off-page. ‘The on-page' factors are elements directly controlled on the website itself. These include strategic keyword usage, content quality, meta tags, URL structure, and internal linking. Conversely, 'off-page' factors involve external elements that influence a website's ranking. Examples include acquiring quality backlinks, maintaining a strong social media presence, and managing online reputation. To attain the maximum benefits from SEO, it is essential to consider relevant factors and criteria. Employing MCDM techniques allows website owners to evaluate and prioritize various SEO elements effectively, enabling a strategic and data-driven approach to improve their web content's search engine rankings. Today, with the advancement and widespread adoption of information systems, the quantity of websites has risen significantly. According to World Wide Web estimates based on the page index by search engines like Google and Bing, the total number of web pages has reached an impressive 4.48 billion. However, this sheer volume of websites makes it challenging for visitors to promptly find the information they are looking for. Thankfully, search engines play a crucial role in helping users access the relevant information they seek quickly and efficiently. The purpose of this study is to explore the challenges of multiple attribute decision-making when dealing with intuitionistic fuzzy information. In this scenario, the attribute weights are not entirely known, and the attribute values are represented by intuitionistic fuzzy numbers. To determine the attribute weights, an optimization model is constructed based on the traditional Grey Relational Analysis (GRA) method's fundamental principles. The proposed method involves calculating the Grey Relational degree between each alternative and the positive-ideal solution and negative-ideal solution. This degree is then used to define a relative relational degree, which enables the ranking of all alternatives simultaneously with respect to both the positive-ideal solution (PIS) and negative-ideal solution (NIS). Alternative taken as Performance criteria(C1), Design criteria (C2), Content criteria (C3), Meta tags criteria (C4), Backlink criteria (C5). Evaluation preference taken as Abdullah Gul University, Turkey (A1); Adana Science and Technology University, Turkey (A2); Aksaray University, Turkey (A3); Alanya Alaaddin Keykubat University, Turkey (A4); Anadolu University, Turkey (A5).

Human Behavior Analysis Using Machine Learning

The study and analysis of human behavior have been longstanding challenges in various fields such as psychology, sociology, and anthropology. With the advent of advanced technologies and the proliferation of data, machine learning has emerged as a powerful tool for deciphering and understanding complex human behaviors. This research aims to explore the application of machine learning techniques in the analysis of human behavior, leveraging diverse datasets and cutting-edge algorithms to gain insights into individual and collective actions. The research methodology involves the collection of multidimensional data sources, including but not limited to social media interactions, physiological measurements, and environmental factors. These datasets are preprocessed and integrated to create a comprehensive representation of human behavior. Machine learning models, ranging from traditional statistical methods to deep learning architectures, are then applied to uncover patterns, correlations, and predictive insights from the data. Machine learning algorithms can analyze patterns in behavior to identify potential signs of mental health issues, enabling early intervention and treatment. Tracking behavioral data can help in managing chronic conditions by providing insights into lifestyle choices, adherence to treatment plans, and overall well-being. Machine learning models can identify unusual patterns of behavior, which is crucial for security purposes. This can include recognizing suspicious activities in public spaces or flagging unusual behavior in online environments. The purpose of this study is to explore the challenges of multiple attribute decision-making when dealing with intuitionist fuzzy information. In this scenario, the attribute weights are not entirely known, and the attribute values are represented by intuitionist fuzzy numbers. To determine the attribute weights, an optimization model is constructed based on the traditional grey relational analysis (GRA) fundamental principles. The proposed method involves calculating the grey relation degree between each alternative and the positive-ideal solution and negative-ideal solution. This degree is then used to define a relative relational degree, which enables the ranking of all alternatives simultaneously with respect to both the positive-ideal solution (PIS) and negative-ideal solution (NIS). From the result 22 is ranked at first position and 45 is ranked at fifth position

Evaluation of mine ecological environment based on fuzzy hierarchical analysis and grey relational degree

In order to improve the level of mine ecological environment management and restoration, and to improve and enhance the overall environmental quality of mines. This study takes coal mine as the perspective, and constructs evaluation indexes in two steps, i.e., social network analysis method and relevant policy documents are combined to construct evaluation indexes. The indicator system contains 5 first-level indicators and 23 s-level indicators, and the triangular fuzzy number hierarchical analysis method is introduced to determine the comprehensive weight of each evaluation indicator, which overcomes the inadequacy of the objective empowerment method or the subjective empowerment method of single empowerment. The grey correlation analysis theory is used to establish a grey correlation evaluation model of mine ecological environment, which is applied to the evaluation of ecological environmental protection level of four coal mines in a province of China, making full use of the information of each index for quantitative evaluation, and finally obtaining the evaluated value of ecological environmental protection level of each coal mine. It is demonstrated that the evaluation model can make scientific and effective evaluation of the level of ecological environmental protection in mines. The study concludes that coal mines should pay attention to improving the comprehensive utilization rate of coal gangue in the next mine ecological environment management and restoration, and at the same time, reduce the ton of coal power consumption, ton of coal water consumption, and Increase in vegetation cover. This study provides a useful evaluation method for ecological environment management in mining areas, which is helpful to improve the quality of ecological management in mining areas.

Multi-attribute quantum group interference decision model considering minimum constraint and information entropy

About multi-attribute group decision making process, the opinions of different decisions will interfere with each other, or be affected by the decision-making environment, resulting in an unobserved interference effect, which is regarded as quantum entanglement in quantum theory. In this paper, an interference effect model based on minimum constraint and information entropy is proposed to measure the interference value in quantum decision models. Firstly, considering the interference effects of decision makers’ opinions, the evaluation opinions of decision makers are aggregated using Quantum-like Bayesian Network (QLBN), which are regarded as wave functions superimposed in the quantum model. Secondly, due to the uncertainty of decision process, information entropy and minimum constraint are combined to solve the interference effect. The minimum constraint is used to limit the range of interference values and the information entropy represents the uncertainty in the decision process. The grey relational degree represents the conditional probability of the decision maker about the alternatives. Thirdly, the weights of attributes and the probabilities of the alternatives are aggregated about decision makers by the proposed interference effect model, and then the alternatives are ranked by the aggregated probabilities. Subsequently, a numerical example is used to verify the validity and rationality of the model. Comparative analyses and sensitivity analyses are also implemented to demonstrate the stability and reliability of our method.

Hyperspectral estimation model of soil organic matter content based on principal gradient grey information

PurposeIn order to explore a new estimation approach of hyperspectral estimation, this paper aims to establish a hyperspectral estimation model of soil organic matter content with the principal gradient grey information based on the grey information theory.Design/methodology/approachFirstly, the estimation factors are selected by transforming the spectral data. The eigenvalue matrix of the modelling samples is converted into grey information matrix by using the method of increasing information and taking large, and the principal gradient grey information of modelling samples is calculated by using the method of pro-information interpolation and straight-line interpolation, respectively, and the hyperspectral estimation model of soil organic matter content is established. Then, the positive and inverse grey relational degree are used to identify the principal gradient information quantity of the test samples corresponding to the known patterns, and the cubic polynomial method is used to optimize the principal gradient information quantity for improving estimation accuracy. Finally, the established model is used to estimate the soil organic matter content of Zhangqiu and Jiyang District of Jinan City, Shandong Province.FindingsThe results show that the model has the higher estimation accuracy, among the average relative error of 23 test samples is 5.7524%, and the determination coefficient is 0.9002. Compared with the commonly used methods such as multiple linear regression, support vector machine and BP neural network, the hyperspectral estimation accuracy of soil organic matter content is significantly improved. The application example shows that the estimation model proposed in this paper is feasible and effective.Practical implicationsThe estimation model in this paper not only fully excavates and utilizes the internal grey information of known samples with “insufficient and incomplete information”, but also effectively overcomes the randomness and grey uncertainty in the spectral estimation. The research results not only enrich the grey system theory and methods, but also provide a new approach for hyperspectral estimation of soil properties such as soil organic matter content, water content and so on.Originality/valueThe paper succeeds in realizing both a new hyperspectral estimation model of soil organic matter content based on the principal gradient grey information and effectively dealing with the randomness and grey uncertainty in spectral estimation.

A novel additive manufacturing strategy with high hydrogen production for ordered-porous stainless steel catalyst support

This paper proposes to improve hydrogen production performance of ordered-porous stainless steel by increasing its forming structure parameters. Firstly, selective laser melting additive manufacturing of ordered-porous stainless steel is carried out through designed orthogonal experiment table, to obtain its forming structure parameters under different manufacturing process parameters. Then, different forming structure parameters of ordered-porous stainless steel are converted into a comprehensive index by grey relation theory, which is grey relational degree (GRD). When powder thickness, scanning speed, scanning space and laser power are 30 μm, 800 mm/s, 90 μm and 60 W, respectively, the highest GRD of 0.930 is obtained, when those are 40 μm, 1200 mm/s, 70 μm and 60 W, respectively, the lowest GRD of 0.410 is gained. Finally, catalyst bonding strength and hydrogen production performance of the ordered-porous stainless steels with the above GRDs are verified. It is found that the ordered-porous stainless steel with the highest GRD has higher catalyst bonding strength and higher hydrogen production performance. When 12 mL/h injection rate of methanol–water solution and 250 ℃ reaction temperature are used, CH3OH conversion, H2 flowing rate and CO selectivity of the above ordered-porous stainless steel are 64.3%, 0.396 mol/h and 6.75%, respectively.

Evaluation of Goalkeepers’ Performance via Grey Relational Analysis Method: Example of Africa Cup of Nations

Aim: The aim of the study is to evaluate the technical performance of goalkeepers via the gray relational analysis method. Materials and Method: The sample of the study consisted of 21 goalkeepers competing in the African Cup of Nations 2023. Data was obtained from the official website of the Confederation of African Football and Transfermarkt. Technical performance indicators were determined as “save percentage”, “claimed crosses” and “passing accuracy”. The data were evaluated by the grey relational analysis method among the quantitative research methods. In this context, six steps of the grey relational analysis method were applied respectively. These are "preparation of the data set and generation of the decision matrix", "normalization of the data", "generation of the reference series", "generation of the absolute value table", "generation of the grey relational coefficient matrix", "calculation and ranking of the grey relational degrees". Results: According to the analysis results, the highest technical performance value was calculated as 0.7654, while the lowest technical performance value was calculated as 0.3949. Thus, the top 3 goalkeepers were determined as Ronwen Williams (South Africa), Edouard Mendy (Senegal), and Babacar Niass (Mauritania). The last 3 goalkeepers were determined as Richard Ofori (Ghana), Ibrahim Koné (Guinea), and Baboucarr Gaye (Gambia). Conclusion: According to the results of the research, Ronwen Williams (South Africa), who won the Golden Glove Award and was selected for the team of the tournament at the Africa Cup of Nations, was determined as the goalkeeper with the highest performance. His national team South Africa completed the tournament in 3rd place, despite being ranked 19th among 24 teams in terms of market value. Similar conclusions were obtained for the remained goalkeepers. It is expected that this conclusion will provide significant contributions for stakeholders such as researchers, goalkeepers, coaches, scouts, and trainers.

Research on tribological performance of textured thrust bearing using gray relational degree and improved multi-objective water circulation algorithm

To enhance the loading capacity of the oil film, reduce the lubricating oil temperature, and minimize the deformation of the friction pairs, three types of concave textures were proposed. The tribological properties of the thrust bearing underwent multi-objective optimization analysis using the two different methods. By comparing the two methods, it was found that the improved algorithm (MOWCA) demonstrated better optimization performance. Under this algorithm, when the texture shape was triangular, the number of textures was 18n, the size was approximately 0.135 mm, and the spacing between textures was approximately 4.6 mm, the loading capacity of the oil film increased by approximately 26.8%, and the temperature decreased by approximately 0.46%.

A combined framework for carbon emissions prediction integrating online search attention

As CO2 emissions continue to rise, the problem of global warming is becoming increasingly serious. It is important to provide a robust management decision-making basis for the reductions of carbon emissions worldwide by predicting carbon emissions accurately. However, affected by various factors, the prediction of carbon emissions is challenging due to its nonlinear and nonstationary characteristics. Thus, we propose a combination forecast model, named CEEMDAN-GWO-SVR, which incorporates multiple features to predict trends in China’s carbon emissions. First, the impact of online search attention and public health emergencies are considered in carbon emissions prediction. Since the impact of different variables on carbon emissions is lagged, the grey relational degree is used to identify the appropriate lag series. Second, irrelevant features are eliminated through RFECV. To address the issue of feature redundancy of online search attention, we propose a dimensionality reduction method based on keyword classification. Finally, to evaluate the features of the proposed framework, four evaluation indicators are tested in multiple machine learning models. The best-performed model (SVR) is optimized by CEEMDAN and GWO to enhance prediction accuracy. The empirical results indicate that the proposed framework maintains good performance in both multi-scenario and multi-step prediction.

Method for wind power forecasting based on support vector machines optimized and weighted composite gray relational analysis

This study proposes a weighted composite approach for grey relational analysis (GRA) that utilizes a numerical weather prediction (NWP) and support vector machine (SVM). The approach is optimized using an improved grey wolf optimization (IGWO) algorithm. Initially, the dimension of NWP data is decreased by t-distributed stochastic neighbor embedding (t-SNE), then the weight of sample coefficients is calculated by entropy-weight method (EWM), and the weighted grey relational of data points is calculated for different weather numerical time series data. At the same time, a new weighted composite grey relational degree is formed by combining the weighted cosine similarity of NWP values of the historical day and to be measured day. The SVM’s regression power prediction model is constructed by the time series data. To improve the accuracy of the system’s predictions, the grey relational time series data is chosen as the input variable for the SVM, and the influence parameters of the ideal SVM are discovered using the IGWO technique. According to the simulated prediction and analysis based on NWP, it can be observed that the proposed method in this study significantly improves the prediction accuracy of the data. Specifically, evaluation metrics such as root mean squared error (RMSE), regression correlation coefficient (r2), mean absolute error (MAE) and mean absolute percent error (MAPE) all show corresponding enhancements, while the computational burden remains relatively low.