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15 pages, 2705 KiB

Open AccessArticle

Countermeasures of Double Carbon Targets in Beijing–Tianjin–Hebei Region by Using Grey Model

by Zhenxiu Liu, Meng Wang and Lifeng Wu

Axioms 2022, 11(5), 215; https://doi.org/10.3390/axioms11050215 - 5 May 2022

Cited by 2 | Viewed by 2332

In this paper, by combining the development characteristics of the Beijing–Tianjin–Hebei region, the fractional accumulation GM (1,1) model was used to predict the peak time of the Beijing–Tianjin–Hebei region, and the carbon peak year was predicted to be 2044. Then, according to the [...] Read more.

In this paper, by combining the development characteristics of the Beijing–Tianjin–Hebei region, the fractional accumulation GM (1,1) model was used to predict the peak time of the Beijing–Tianjin–Hebei region, and the carbon peak year was predicted to be 2044. Then, according to the urbanization level and the proportion of the added value of the secondary industry in different regions in 2018, regions were divided into four categories: the first to reach the peak, the peak on schedule (easy), the peak on schedule (general), and the peak may be delayed. The Beijing–Tianjin–Hebei region plans to achieve a carbon peak by 2044 and proposes specific suggestions to achieve carbon neutrality by 2060 to achieve coordinated development of Beijing–Tianjin–Hebei and high-quality development. Full article

(This article belongs to the Special Issue Grey System Theory and Applications in Mathematics)

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11 pages, 821 KiB

Open AccessArticle

The Influence Factor Analysis of Symmetrical Half-Bridge Power Converter through Regression, Rough Set and GM(1,N) Model

by Shih-Kuen Changchien and Kun-Li Wen

Axioms 2022, 11(1), 18; https://doi.org/10.3390/axioms11010018 - 2 Jan 2022

Viewed by 1413

Abstract

Analysis of power converter performance has tended to be engineering-oriented, focusing mainly on voltage stability, output power and efficiency improvement. However, there has been little discussion about the weight relations between these factors. In view of the previous inadequacy, this study employs regression, [...] Read more.

Analysis of power converter performance has tended to be engineering-oriented, focusing mainly on voltage stability, output power and efficiency improvement. However, there has been little discussion about the weight relations between these factors. In view of the previous inadequacy, this study employs regression, rough set and GM(1,N) to analyze the relations among the factors that affect the converter, with a symmetrical half-bridge power converter serving as an example. The four related affecting factors, including the current conversion ratio, voltage conversion ratio, power conversion ratio and output efficiency, are firstly analyzed and calculated. The respective relative relations between output efficiency and the other three factors are obtained. This research can be referred to by engineers in their design of symmetrical half-bridge power converters. Full article

(This article belongs to the Special Issue Grey System Theory and Applications in Mathematics)

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15 pages, 1006 KiB

Open AccessArticle

Applying Grey Relational Analysis in the Evaluation of the Balance of Children with Intellectual Disability

by Chih-Sheng Chang

Axioms 2021, 10(4), 341; https://doi.org/10.3390/axioms10040341 - 11 Dec 2021

Viewed by 2280

Abstract

In addition to intellectual performance, children with intellectual disability also seem to have lower performance than children without intellectual disability in terms of balance. Therefore, they often experience walking instability or fall due to imbalance, causing injuries. With regard to balance training courses [...] Read more.

In addition to intellectual performance, children with intellectual disability also seem to have lower performance than children without intellectual disability in terms of balance. Therefore, they often experience walking instability or fall due to imbalance, causing injuries. With regard to balance training courses provided by medical or special education personnel for children with intellectual disability, although there are subjective observation scales that describe their balance in a qualitative way, there are still few direct measurement methods that can provide personnel with the ability to evaluate the training results of an intervention program. The purpose of this study was to provide a method for evaluating the balance of children with intellectual disability to facilitate a general inspection or evaluation of balance before and after the implementation of various intervention programs that help movement development. In recent years, the force platform system has been widely used in the research of the elderly balance, yet the research on balance assessment tools applied to children is rare. This study used the objective, fast, and accurate characteristics of the force platform system to analyze the key points of the sit-to-stand movement and the movement balance parameters of children with intellectual disability and children without intellectual disability. Using the grey relational analysis (GRA) method, the time factors and weight factors from the average performance of children without intellectual disabilities was used as the analysis data. After analyzing the relevance between each participant and the target, a norm for evaluating the balance of children with intellectual disability was established. Hence, this valuable result can provide researchers, special education teachers, and related professionals with an effective and time-saving evaluation of the balance of children with intellectual disability. Full article

(This article belongs to the Special Issue Grey System Theory and Applications in Mathematics)

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16 pages, 3840 KiB

Open AccessArticle

Advanced Proportional-Integral-Derivative Control Compensation Based on a Grey Estimated Model in Dynamic Balance of Single-Wheeled Robot

by Mao-Lin Chen, Chun-Yen Chen, Chien-Hung Wen, Pin-Hao Liao and Kai-Jung Chen

Axioms 2021, 10(4), 326; https://doi.org/10.3390/axioms10040326 - 30 Nov 2021

Viewed by 2374

Abstract

This paper aims to design a one-wheeled robot as regards its pitch freedom and balance control on the one hand and to assess the application feasibility of the GM (1,1) swing estimation controller on the other. System control focuses mainly on one-wheeled robot [...] Read more.

This paper aims to design a one-wheeled robot as regards its pitch freedom and balance control on the one hand and to assess the application feasibility of the GM (1,1) swing estimation controller on the other. System control focuses mainly on one-wheeled robot stability, body swings in position, and speed control. Mathematical modeling and GM (1,1) prediction control are under investigation. The mathematical modeling is firstly conducted through referencing to the Newtonian mechanics and the Lagrange equation, from which the robot transfer function and state-space differential equation are derived. Next, the linear quadratic regulator is applied as the control rule at the balance point. Applying GM (1,1) to assess the robot gyro signal at a dynamic state is a discussion. Next, model reference estimation control is processed, and a mathematical model of the balance control method is completed. Finally, a simulation is conducted to verify the feasibility of the GM (1,1) estimation reference model. The linear quadratic regulator, which is credited with tenacity, can provide pitch swing and balance control of the one-wheeled robot. Full article

(This article belongs to the Special Issue Grey System Theory and Applications in Mathematics)

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14 pages, 1035 KiB

Open AccessArticle

Establishing Effective Remedial Instruction Grouping Using the Rough Set Theory and Grey Structural Modeling

by Bor-Tyng Wang

Axioms 2021, 10(4), 299; https://doi.org/10.3390/axioms10040299 - 11 Nov 2021

Viewed by 1972

Abstract

In the field of education, the assessment of a student’s learning performance is based on his final course scores. Few people care about what is behind the numbers. Most of the time, the final scores represent the end of the course because students [...] Read more.

In the field of education, the assessment of a student’s learning performance is based on his final course scores. Few people care about what is behind the numbers. Most of the time, the final scores represent the end of the course because students have already passed the subject. Low-level students especially, still have a lot of misconceptions, but they do not know how to make up for their poor grasp of the subject in preparation for future study. Instead of just giving students their scores, teachers are encouraged to provide remedial instruction to students for their future learning. This study aims to establish an effective method using rough set theory and grey structural modeling to determine which attributes affect students’ final scores and to cluster students accordingly. A rough set algorithm generates a set of attributes for an assessment list. Grey structural modeling (GSM) is then used to cluster students who have the same weaknesses in English. GSM changes from one dimension to two dimensions, and calculates the relative distance, so that cluster analysis can be performed. Targeted remedial instruction can then be given to each similar ability student grouping. The results revealed that through integrating the two theories, teachers could more effectively sort students into groups. Students benefit by coming to understand their weaknesses in English instead of just receiving a single score at the end of the semester, and they can learn with their peers as well. Teachers can adjust their teaching strategies and syllabus design based on the analytical results to target the students’ needs. Full article

(This article belongs to the Special Issue Grey System Theory and Applications in Mathematics)

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14 pages, 2051 KiB

Open AccessArticle

Grey Estimator-Based Tracking Controller Applied to Swarm Robot Formation

by Yu-Ting Chen, Chian-Song Chiu and Ya-Ting Lee

Axioms 2021, 10(4), 298; https://doi.org/10.3390/axioms10040298 - 9 Nov 2021

Cited by 1 | Viewed by 1493

Abstract

Mobile robots are widely used in many applications, while various types of mobile robots and their control researches have been proposed in literature. Since swarm robots have higher flexibility and capacity for teamwork, this paper presents a grey estimator-based tracking controller for formation [...] Read more.

Mobile robots are widely used in many applications, while various types of mobile robots and their control researches have been proposed in literature. Since swarm robots have higher flexibility and capacity for teamwork, this paper presents a grey estimator-based tracking controller for formation trajectory tracking of swarm robots. First, wheel-type mobile robots are used and modeled for the controller design. Then, a grey dynamic estimator is developed to estimate the environmental disturbance and model uncertainty for linear feedback compensation. As a result, the asymptotic trajectory tracking is assured, so that the application on the swarm robot formation is achieved for a multi-agent system. The computational complexity is slightly reduced by the design. Finally, in order to verify the reliability of swarm robot formation, several types of formation are maintained by the grey estimator-based feedback linearization controller. Full article

(This article belongs to the Special Issue Grey System Theory and Applications in Mathematics)

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9 pages, 815 KiB

Open AccessArticle

GM(1,1;λ) with Constrained Linear Least Squares

by Ming-Feng Yeh and Ming-Hung Chang

Axioms 2021, 10(4), 278; https://doi.org/10.3390/axioms10040278 - 27 Oct 2021

Cited by 1 | Viewed by 1537

Abstract

The only parameters of the original GM(1,1) that are generally estimated by the ordinary least squares method are the development coefficient a and the grey input b. However, the weight of the background value, denoted as λ, cannot be obtained simultaneously [...] Read more.

The only parameters of the original GM(1,1) that are generally estimated by the ordinary least squares method are the development coefficient a and the grey input b. However, the weight of the background value, denoted as λ, cannot be obtained simultaneously by such a method. This study, therefore, proposes two simple transformation formulations such that the unknown parameters

a

,

b

and

λ

can be simultaneously estimated by the least squares method. Therefore, such a grey model is termed the GM(1,1;λ). On the other hand, because the permission zone of the development coefficient is bounded, the parameter estimation of the GM(1,1) could be regarded as a bound-constrained least squares problem. Since constrained linear least squares problems generally can be solved by an iterative approach, this study applies the Matlab function lsqlin to solve such constrained problems. Numerical results show that the proposed GM(1,1;λ) performs better than the GM(1,1) in terms of its model fitting accuracy and its forecasting precision. Full article

(This article belongs to the Special Issue Grey System Theory and Applications in Mathematics)

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12 pages, 8284 KiB

Open AccessArticle

A Novel Color Recognition Model for Improvement on Color Differences in Products via Grey Relational Grade

by Jeih-Jang Liou

Axioms 2021, 10(4), 266; https://doi.org/10.3390/axioms10040266 - 20 Oct 2021

Cited by 3 | Viewed by 1937

Abstract

ED light, a green energy-saving light source, can cause color cast. For this reason, LED light is seldom favored by designers. The purpose of the paper is to provide shoppers who are observing product colors in an LED-lighted setting with an innovative color [...] Read more.

ED light, a green energy-saving light source, can cause color cast. For this reason, LED light is seldom favored by designers. The purpose of the paper is to provide shoppers who are observing product colors in an LED-lighted setting with an innovative color identification model. Based on designers’ product color comparison, the paper employs high-reliability mechanic visual perception in combination with grey relational grade. Grey relational grade is applied to eliminate electrical fault pertaining to mechanic visual perception, whereby appropriate LED parameters and color cast inclination can be obtained. The paper first mimics retail store display windows. The color temperature and illuminance of LED light sources are adjustable. Two degrees of illuminance, including high illuminance (1500 lux) and low illuminance (500 lux), and two light source color temperatures, including yellow light (2700 K) and white light (4000 K), were assigned for study. Four colors, including red, yellow, blue and green of the natural color system, were selected as product colors. The mechanic visual perception sensor was used to identify the object (product) color, which is then converted into an RGB color model to serve as research data of color cast measurement, and the grey relational grade was applied to obtain the most appropriate LED light parameters and the color cast of the four colors. The data analysis reveals that green shows the least color cast when it is lighted by a yellow LED light source with low illuminance, yellow and blue have the least color cast when it is lighted by a white LED light source with high illuminance and red displays the least color cast when it is lighted by a white LED light source with low-illuminance. The analysis also indicates each color’s cast inclination in blackness, chromaticness and hue. As a result, LED light that is more acceptable to designers is suggested for display windows, thus reducing problems with product color cast. Full article

(This article belongs to the Special Issue Grey System Theory and Applications in Mathematics)

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