Grey Relational Degree Research Articles

A novel study on a micromixer with Cantor fractal obstacle through grey relational analysis

This paper proposes a multi-objective optimization method for a micromixer with Cantor fractal baffles through grey relational analysis, and evaluates the comprehensive performance of the micromixer through two aspects. The height of the baffle (h), the distance of the baffle (p), the width of the microchannel (L) and the height of the microchannel (H) are selected as design variables, and the orthogonal experiment table L16(44) is obtained. The optimized performance characteristics take into account the mixing index and Poiseuille number. Numerical simulations are used to obtain the results of each experimental design group. We use the grey relational degree as an index to evaluate the comprehensive performance of the multi-objective of the micromixer, and optimize to find a set of optimal design variables. Finally, we judge the influence of the four design variables on the two performance characteristics respectively, so as to obtain the importance of different design variables. The results show that the optimized micromixer, namely CFM-11, has a maximum increase of 23.75% in mixing index and a maximum decrease in Poiseuille number of 34.40%. Among all the parameters, the h and the L have a greater impact on the performance characteristics. This work can provide a good analysis method for multi-objective research and structural optimization related to micromixers.

Stability sensitivity for a cable-based coal–gangue picking robot based on grey relational analysis

This article aims to establish the relationship between the position and cable tension influencing factors and the stability, and propose a method for quantitative stability sensitivity assessment for a cable-based coal–gangue picking robot. Firstly, a structural stability measure approach is proposed for the cable-based coal–gangue picking robot. Secondly, a stability sensitivity analysis model is developed to investigate the stability sensitivity on the selected influencing factors based on the grey relational degree, where the influencing degree of each factor on the stability for the cable-based coal–gangue picking robot is explored with grey relational analysis. At last, a numerical study is carried out to demonstrate the stability measure approach and stability sensitivity analysis model for the cable-based coal–gangue picking robot was scientific and reasonable, where the end-grab position set which the robot can meet the predetermined stability requirements is obtained. And meanwhile, the correlation of each influencing factor on the stability for the robot is calculated. And the stability sensitivity simulation results show that (1) the correlation of the seven influencing factors on the stability are, in a descending order, cable tension T 2 > cable tension T 4 > cable tension T 3 > cable tension T 1 > z-direction displacement of the end-grab > x-direction displacement > y-direction displacement; (2) among the influencing factors, the cable tensions have greater influence on the stability of coal–gangue picking robot, and it is followed by the z-direction displacement of the end-grab, while y-direction displacement is found to have the minimal influence. This article provides a guiding direction for robust design of the sorting trajectory planning and control of the coal–gangue picking robots.

Multi-quality Index Optimization of Injectionof injection Compression Process Parameters Based on Grey Robustness

Aiming at the balance optimization of multiple mass indexes, such as sink marks, warpage and residual stress in the injection compression molding process of optical products, from the perspective of robust design, the experiment of injection compression processing of wedge-shaped light guide plate with five factors and four levels was designed by orthogonal experiment method. The optimal combination of process parameters, the order of influence and the trend of change were obtained by S/N analysis. Finally, the grey relational theory was used to transform the multi-quality index optimization problem into the single objective optimization of grey relational degree, and the optimal process parameter combination considering multiple quality indexes were obtained. Compared with before optimization, each quality index decreased by 23.89%, 8.87% and 24.68% respectively. The research shows that the optimization technology based on grey robustness can effectively solve the problem of balance optimization among multiple mass indexes, and can realize the overall optimization of injection compression process parameters.

Research on Operation Reliability Evaluation of Power-generating Unit

Objective and reasonable evaluation is the basis of power-generating unit optimal operation, but evaluation method based on single weight can’t adapt to the high accuracy requirement of comprehensive evaluation. In order to achieve the accurate evaluation of power-generating unit operating reliability, this paper firstly calculates subjective weight and objective weight of target attribute by analytic hierarchy process method and entropy weight method. It calculates the associated weight of target attribute by grey relational degree method, and it obtains the linear combined weight by relaxation factor. Then, the power-generating unit operating reliability is evaluated by improved TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution), and the evaluation result is obtained. Finally, the relaxation factor is continuously evaluated from 0 to 1 to perform sensitivity analysis. This paper evaluates the operation reliability of nine wind turbines in a wind farm, and the evaluation result is closer to actual operation state of wind turbines. This method has high reliability and practical value, and it provides a new technical means for making a reasonable maintenance plan of wind turbines.

Comprehensive evaluation of surface integrity and parameter optimization of 45 steel subjected to ultrasonic surface rolling process

In order to explore the influence of ultrasonic surface rolling process (USRP) parameters on 45 steel surface integrity, the significance of static pressure, amplitude, feed rate and rolling times on rolling effect was analyzed. The grey relational degree of the comprehensive index of surface integrity after USRP was obtained by orthogonal test and grey relational analysis, and the optimal combination of process parameters was obtained. The feasibility of process parameter optimization was verified by experiments. The results show that the significant influence of USRP parameters on 45 steel workpiece surface integrity was as follows: rolling times> feed speed> static pressure> amplitude. The optimal process parameters are rotational rolling times 9 times, feed speed 3200 mm⋅min-1, static pressure 300 N and amplitude 6 μm. Under the optimum combination of process parameters, the surface roughness decreases by 70.8 %. The surface hardness and the surface residual compressive stress increase by 16.5 % and 134 % respectively compared with the surface performance parameters of the material before rolling.

Effect of different boron levels on yield and nutrient content of wheat based on grey relational degree analysis

Effect of different boron levels on yield and nutrient content of wheat based on grey relational degree analysis

Taguchi Tabanlı Gri İlişkisel Analiz Kullanılarak Sürtünme Karıştırma Nokta Kaynak İşleminin Çoklu Yanıt Optimizasyonu

Friction stir spot welding (FSSW) is a solid state welding method mainly used to join non-ferrous metals and their alloys. When opposed to other welding processes, FSSW has the benefits of being pollution-free and having no filler material. In this study an attempt was made for multi response optimization of friction stir spot welded EN AW 5005 aluminum alloy using Taguchi method and Grey relational analysis (GRA). Pin height (h, mm), tool rotation (S, rpm), and welding time (t, s) were used as input parameters while tensile shear strength (TSS, MPa) and joint efficiency (JE, %) were used as multi response parameters. Therefore, Taguchi’s L8 orthogonal design matrix was used in order to plan the experiments. GRA was then applied to determine the optimum condition which gives the higher grey relational degree. Analysis of Variance method (ANOVA) was also carried out in order to show the most significant parameter. Finally, confirmation test was applied to confirm the results and determine the improvement in grey relational grade throughout this method. The best results were obtained with parameters such as
 2.6 mm pin height, 1500 rpm tool rotation and 10 s welding time with 122.16 MPa TSS and 111.05 JE. A significant improvement of 0.310 was obtained in the optimal parameter in grey relation grade.

Optimization of milling process parameters and prediction of abrasive wear rate increment based on cutting force experiment

Tuning the parameters of Computerized Numerical Control (CNC) is essential for practical manufacturers. Well configured parameters ensure the efficiency of production and the accuracy of the products. However, with the abrasive wear on the flank of the milling cutter, the milling processing parameters should re-configure to adapt to the increment of the abrasive wear. This paper aims to propose a method to predict the abrasive wear rate increment on the flank of the milling cutter and optimize the processing parameters of CNC milling. Firstly, we set a cutting data acquisition system to sample the processing time and cutting force among X, Y coordinates based on the five-factor and four-level orthogonal experiments. Then, the sampled cutting force data increment is transformed into the abrasive wear rate increment by applying the incremental model. Next, five processing parameters for CNC milling are optimized by the gray relational method, which takes the limited abrasive wear rate increment of the flank face and the non-increasing processing time as the constrained conditions. We obtain the relationship between five processing parameters and abrasive wear rate increment. We also find the basic principle of selecting process parameters is to reduce the abrasive wear rate without increasing the processing time. The experimental results verify that the optimized process parameters make the gray relational degree increase by 0.02, and the abrasive wear rate increment decreases by 0.42432 × 10−10 mm3/s without affecting the production efficiency. In the prediction section, by applying the Back Propagation (BP) neural network, we obtain an accurate prediction model from measurable five factors to the abrasive wear increment on the flank of the milling cutter. The maximum error between the predicted value and the actual value is 0.0003, and the predicted value curve fits well with the actual value curve. From the perspective of abrasive wear rate increment prediction, it provides a new idea for online tool wear monitoring.

Comparative Analysis for Grey Relation Estimation Models of Soil Organic Matter based on Hyperspectral Data

Rapid and accurate acquisition of farmland soil organic matter content is of great significance for the rapid monitoring soil fertility and the development of precision agriculture. Based on the hyperspectral data and organic matter content data of 74 soil samples in Zhangqiu District, Jinan City, Shandong Province, first transform soil spectral reflectance by the logarithm of the first-order differential, square, reciprocal, logarithm and square root, the estimation factors were selected according to the principle of maximum relation. Second, the hyperspectral estimation of soil organic matter was carried out by using six models such as grey close relation degree, and the estimation results of different methods were combined and analyzed. The results show that the combined grey relation model can effectively improve the estimation accuracy, and the average relative error of 16 test samples is 8.931%. Studies have shown that using the combined model of grey relation degree to estimate soil organic matter content with hyperspectral data is valid.

Optimization and measurement of flank wear and surface roughness via Taguchi based grey relational analysis

ABSTRACT This study examined experimentally and statistically the machinability of AISI 430 stainless steel on a lathe using two type different coated tool inserts, three various cutting speeds (80, 140, 200 m/min) and three various feed rates (0.75, 1.5, 2.25 mm/rev). Experimental studies were carried out using a coolant and cutting depth of 1.5 mm was used constant under all experiment conditions. In the machinability tests, the impact of turning parameters and levels on Ra and the amount of wear on the cutting tool were examined. The impact of machinability parameters on VB and Ra were calculated using analysis of variance, which determined that feed rate was the most powerful machining parameter for the VB and Ra. Taguchi-based gray relational analysis was performed to find out the ideal machining orders for Ra and VB. According GRA, the percentage of improvement in the gray relational degree was calculated as 69.1%. As a result of this work, multiple performance outputs (surface roughness-flank wear) were improved considerably in machining of difficult-to-machine AISI 430 stainless steel.

Improved angle data fusion method for multimode compound seeker

Multimode compound guidance is the important research direction of the future intelligent ammunition development. For the fusion of seeker’s pitch and azimuth deviations in laser, millimeter wave, and infrared three-mode compound guidance, a grey relational belief degree least squares method is proposed in this study. Angle measurement models are firstly constructed for the three guidance modes. Grey relational degrees among the data of different modes are calculated to construct the grey relational matrix. And then, the grey relational matrix is used as the probability distribution between different modes. The belief degree of each mode is calculated in real time according to evidence theory in the fusion process. Finally, the least squares fusion result based on the grey relational belief degree is obtained. In simulation experiments, compared with weighted least square method, the fusion approach in this study achieves a lower root mean square error.

Correlations between content of linarin in Chrysanthemum indicum and climatic factors in habitats

Chrysanthemi Indici Flos(CIF), the capitulum of Chrysanthemum indicum, is widely used in proprietary Chinese medicine and daily chemical products. At present, CIF is mainly produced from wild resources and rarely cultivated. This study aims to reveal the correlations between linarin content in CIF and climatic factors in different habitats, and provide a theoretical basis for suitable zoning and rational production of medicinal materials. The content of linarin in CIF was determined by HPLC. Grey relational analysis and Pearson correlation analysis were carried out for linarin content with climatic factors. The results showed that the content of linarin in CIF was significantly different among different habitats. The grey relational degrees of climatic factors with linarin content was in an order of average annual precipitation>annual average sunshine hours>annual average temperature>longitude>annual frost-free period>latitude>altitude. Longitude, annual average temperature and average annual precipitation had significantly positive correlations with the content of linarin in CIF, whereas latitude and altitude showed negative correlations with it. The annual frost-free period and annual average sunshine hours had no significant correlation with the content of linarin in CIF. The content of linarin in CIF varied significantly in different habitats. High longitude, low latitude, low altitude, high annual average temperature and high annual average precipitation could be used as indicators for the habitats of high-quality Ch. indicum. This study provides a reference for selecting suitable producing areas of Ch. indicum and establishing artificial cultivation system.

In-situ tool wear area evaluation in micro milling with considering the influence of cutting force

In order to realize the tool wear in-situ monitoring in micro milling, a novel two-dimensional tool wear estimation approach is developed in this work. The novelty and strong point of the approach is that it can achieve both high estimation accuracy and computational efficiency for fast tool condition monitoring. For this purpose, an empirical statistical model including both process parameters and force features is firstly proposed for in-situ tool wear area estimation. Then the model is improved to enhance its practicability. By comparing the experimental measurements against the results predicted by the improved model and neural network model, it is shown that the improved model has better prediction effect, which illustrates that this approach can realize tool wear estimation in micro milling. Finally, the influence of each variable in improved model on tool wear is analyzed by grey relational degree. The results of this study indicate that this approach can be used to optimize cutting parameters and predict tool wear online.

Soil Chemical Properties under Various Land-Use Types in the Karst Area with a Case Study in Shibing County of China

The effects of different land-use types on the pH, organic carbon, total nutrient, and available nutrients of soil in the 0–30 cm and 30–60 cm layers were studied using the gray relational analysis method. The research area is located in Baiduo village in the dolomite karst region and Shiqiao village in the limestone karst region of Shibing County, Guizhou Province, China. The land-use types investigated included shrubland, forest, grass slope, dryland, paddy field, pear orchard, and flue-cured tobacco field. The contents of organic carbon, total nitrogen, alkaline hydrolysable nitrogen, and available potassium, as well as the pH of the soil in the dolomite shrubland, were higher than those in the limestone shrubland. The total potassium, total phosphorus, and available phosphorus contents of soil in the limestone shrubland were higher than those in the dolomite shrubland. Among the four types of land-use most strongly affected by human activities (paddy field, dryland, flue-cured tobacco field, and pear orchard), the nutrient contents (except potassium in the upper soil layer) were higher than those in the lower layer. The differences in nutrient contents between upper and lower layers were relatively small in the dryland and the pear orchard, whereas they were large for the paddy field and flue-cured tobacco field. The gray relational degree of various land-use types decreased in the following order: dolomite shrubland > forest > grass slope > pear orchard > limestone shrubland > paddy field > dryland > flue-cured tobacco field. The dolomite shrubland had the best soil quality, while the flue-cured tobacco field had the worst. Of the four types of land use most strongly affected by human activities, pear orchard had the best soil quality. This study can provide reference for soil nutrient management and sustainable management in karst areas.

Grey Correlation Analysis of Economic Growth and Cultural Industry Competitiveness

The influence of cultural industry competitiveness on economic growth is analyzed by using grey relational degree method. Then, the influence of cultural industry on the three industries is analyzed and compared in the same way. On this basis, further from the cultural industry, the impacts of core layer, outer layer, and related layer on economic growth were compared and analyzed. Finally, the economic growth model is used to measure the impact of investment, labor, and innovation in cultural industry on economic growth. The results show that cultural industry has a great influence on economic growth. The cultural industry has an obvious driving effect on the tertiary industry. The correlative layer of cultural industry has the greatest influence on economic growth. Cultural industry innovation has a huge pulling effect on economic growth. The SPSS software was used to process the data, and the data indicators were screened. Finally, the grey relational degree model was constructed. Then, the improved diamond model was used to select the influential factors of the development of cultural industry, and the main influencing factors were found out through the grey relational degree analysis. This paper analyzes the factors affecting economic benefits and puts forward countermeasures. The results show that it is of great significance to pay attention to the development of cultural manufacturing industry in cultural industry and promote cultural innovation to promote economic growth.

Bond Behavior of Steel-Recycled Aggregate Concrete Interface After High Temperatures and Spraying Water Cooling

Using recycled aggregate concrete (RAC) in steel-reinforced concrete structure is an effective way to eliminate the adverse effects of recycled aggregate, which has an excellent application prospect. Fire has a great destructiveness to steel-reinforced recycled aggregate concrete (SRRAC) structure; hence, the bond performance of SRRAC after high temperature, as the prerequisite for the composite between steel and RAC, is the key problem for structural safety and the corresponding safety assessment after fire. In this article, the residual bond behaviors of steel-recycled aggregate concrete interface after different high temperatures and spraying water cooling were studied through the push-out test. The failure modes and load–slip curves were examined. The ultimate bond strength, residual bond strength, and elastic bond shear stiffness of specimens after high temperature and cooling for the regime of spraying water were evaluated and compared to that of natural air. A parametric analysis of temperature, replacement percentage, and studs was conducted. A calculation approach for the ultimate bond strength and residual bond strength of SRRAC after high temperature was developed based on the sensitive analysis of gray system theory and regression analysis. Results showed that the bond properties of SRRAC specimens after high temperature were decreased as exposure temperature increased. The cooling regime of spraying water has a more significant influence on the ultimate strength and residual strength than that of natural air. The specimens with studs on both flange and web have the highest bond properties after high temperature. In all the factors, the number of studs showed the largest gray relational degree to the bond strength of SRRAC. The developed approach provided a reliable prediction of bond strength for SRRAC after high temperature.

Load Forecasting Based on Weighted Grey Relational Degree and Improved ABC-SVM

The present study proposes a short-term load forecasting method based on weighted grey relational degree and improved support vector machines with the artificial bee colony algorithm (ABC-SVM). The entropy weight method was employed to obtain the weight of load-related physical information, and the historical and forecast load data selected based on the weighted grey relational degree were input into the support vector machine (SVM) to build a forecasting model. Meanwhile, the SVM parameters were optimized by the improved artificial bee colony algorithm before the model was used to perform load forecasting. The experimental results show that the proposed method could effectively improve the accuracy of the forecasting model and simplify the calculation, thus having research and practical value.

Comprehensive evaluation of 47 tea [Camellia sinensis (L.) O. Kuntze] germplasm based on entropy weight method and grey relational degree

China has the most abundant tea resources in the world. In oder to scrutinize superior accessions suitable for popularization and planting, the quality characteristics of distinctive tea resources were analyzed by examining their key evaluation indexes and comprehensive evaluation methods. In this study, 29 indexes of 47 tea germplasms were detected, including agronomic characters, chemical compositions, quality of green tea and stress resistance. The key evaluation indexes were selected by factor analysis and cluster analysis, whereas the weight value of the indexes was determined by analytic hierarchy process (AHP) and entropy weight method. Furthermore, the comprehensive evaluation of tea varieties was carried out by grey correlation degree and entropy weight method. Our results showed that drastic differences of character indexes existed among tea varieties, and the 29 character indexes demonstrated complex information overlapping with each other. After simplification, 12 key evaluation indexes, namely score of green tea quality, total free amino acids, growth potential, water extract, yield, epigallocatechin gallate (EGCG), epigallocatechin (EGC), one bud one leaf stage, insect resistance, germination density, bud leaf color, and gallic acid (GA) were chosen. The weight value of each index was also determined. Since the rank of some varieties in these two evaluation methods was different, based on the comprehensive evaluation results of grey correlation degree method and entropy weight method, it was more rational to combine these two evaluation methods in selecting superior varieties. Consequently, nine excellent tea varieties were selected. This study not only provides an innovative method for comprehensive evaluation of tea resources, but also an approach to promote genetic improvement of the selected excellent tea varieties.

A Hybrid Neural Network Model for Marine Dissolved Oxygen Concentrations Time-Series Forecasting Based on Multi-Factor Analysis and a Multi-Model Ensemble

Dissolved oxygen (DO) is an important indicator of aquaculture, and its accurate forecasting can effectively improve the quality of aquatic products. In this paper, a new DO hybrid forecasting model is proposed that includes three stages: multi-factor analysis, adaptive decomposition, and an optimization-based ensemble. First, considering the complex factors affecting DO, the grey relational (GR) degree method is used to screen out the environmental factors most closely related to DO. The consideration of multiple factors makes model fusion more effective. Second, the series of DO, water temperature, salinity, and oxygen saturation are decomposed adaptively into sub-series by means of the empirical wavelet transform (EWT) method. Then, five benchmark models are utilized to forecast the sub-series of EWT decomposition. The ensemble weights of these five sub-forecasting models are calculated by particle swarm optimization and gravitational search algorithm (PSOGSA). Finally, a multi-factor ensemble model for DO is obtained by weighted allocation. The performance of the proposed model is verified by time-series data collected by the pacific islands ocean observing system (PacIOOS) from the WQB04 station at Hilo. The evaluation indicators involved in the experiment include the Nash–Sutcliffe efficiency (NSE), Kling–Gupta efficiency (KGE), mean absolute percent error (MAPE), standard deviation of error (SDE), and coefficient of determination (R2). Example analysis demonstrates that: ① The proposed model can obtain excellent DO forecasting results; ② the proposed model is superior to other comparison models; and ③ the forecasting model can be used to analyze the trend of DO and enable managers to make better management decisions.

Fuzzy Clustering Method Based on Improved Weighted Distance

As an essential data processing technology, cluster analysis has been widely used in various fields. In clustering, it is necessary to select appropriate measures to evaluate the similarity in the data. In this paper, firstly, a cluster center selection method based on the grey relational degree is proposed to solve the problem of sensitivity in initial cluster center selection. Secondly, combining the advantages of Euclidean distance, DTW distance, and SPDTW distance, a weighted distance measurement based on three kinds of reach is proposed. Then, it is applied to Fuzzy C-MeDOIDS and Fuzzy C-means hybrid clustering technology. Numerical experiments are carried out with the UCI datasets. The experimental results show that the accuracy of the clustering results is significantly improved by using the clustering method proposed in this paper. Besides, the method proposed in this paper is applied to the MUSIC INTO EMOTIONS and YEAST datasets. The clustering results show that the algorithm proposed in this paper can also achieve a better clustering effect when dealing with practical problems.