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Sports intensity and energy consumption based on fractional linear regression equation

APPLIED MATHEMATICS AND NONlinear SCIENCES 2022年第2期7卷 115-126页

作者： Hao, Haitao Albarakati, Abdullah China Jiliang Univ Hangzhou 310018 Peoples R China King Abdulaziz Univ Fac Comp & Informat Technol Dept Informat Syst Jeddah Saudi Arabia

Objective The objective is to analyse and explore the characteristics of physical exercise intensity, energy expenditure and substrate metabolism using Baduanjin and the ninth broadcast gymnastics as examples. Methods The indirect calorimetry of German CORTEX Metamax 3B portable gas met bolometer was used to determine the resting energy consumption of different age and sex of healthy people and related indexes such as the energy consumption and fat metabolism ratio in the ninth set of radio gymnastic exercises. Results The metabolic equivalents of Baduanjin and radio gymnastics were 2.68 and 5.07, and the average heart rate was 76.14 l/min and 97.3 l/min, which were higher than those at rest (P < 0.01). In radio gymnastics, the energy consumption level of men is higher than that of women (P < 0.05), but the proportion of fat metabolism of women is higher than that of men (P < 0.05). For 20-39 years old, when they are quiet, do Baduanjinhe and do radio gymnastics, the energy consumption of the subjects was 1828.7 kcal/d, 4008.8 kcal/d and 6355.6 kcal/d, respectively and for the ages of 40-59, they were 1822.6 kcal/d, 4047.4 kcal/d, and 8204.13 kcal/d, respectively. The ratios are significantly different;the energy consumption and fat energy supply ratio of the exercise group in the radio gymnastics group are significantly higher than those in the Baduanjin group, and the exercise group is significantly higher than that in the quiet group (P < 0.05);The heart rate and weight were calculated and the energy consumption equations of Ba Duan Jin and radio gymnastics were established. The equations have statistical significance. Conclusion Ba Duan Jin is a low-intensity exercise while radio gymnastics is a medium-intensity exercise;Comparing energy consumption and fat of Ba Duan Jin and the ninth set of radio gymnastics, the energy ratio of the energy consumption of the ninth set of broadcast gymnastics body was significantly higher than Baduanjin movement;linear regressio

关键词： physical exercise intensity energy expenditure linear regression equation

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Optimal control of unknown nonlinear systems via online parameter estimation with interval excitation

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NONlinear DYNAMICS 2025年第10期113卷 11779-11792页

作者： Luo, Rui Liu, Qiaoling Peng, Zhinan Shi, Kaibo Ghosh, Bijoy Kumar Chengdu Univ Sch Elect Informat & Elect Engn Chengdu 610106 Peoples R China Univ Elect Sci & Technol China Sch Automat Engn Chengdu 611731 Peoples R China Texas Tech Univ Dept Math & Stat Lubbock TX 79409 USA

This paper proposes an identifier-critic (IC) framework for optimal control of nonlinear systems with completely unknown dynamics. Unlike existing indirect adaptive/approximate dynamic programming algorithms, the developed IC framework consists of two adaptive neural networks (NNs): identifier and critic networks. The identifier networks are established to estimate the unknown dynamics, while the critic networks are applied to formulate the optimal control for an affine nonlinear system. To facilitate easy implementation and online computation, a linear regression method is introduced to establish the parameter estimation problem for the unknown weights in the NNs. Moreover, an interval excitation assumption, which is weaker than the persistence of excitation condition, is developed to ensure the convergence of the unknown weights in the IC framework within a finite time. The convergence of the weight estimation and the stability of the closed-loop system are theoretically demonstrated via Lyapunov theory. Finally, numerical simulation results are presented to demonstrate the effectiveness of the proposed control method.

关键词： Identifier-critic neural network linear regression equation Unknown nonlinear systems Optimal control Relaxed persistence of excitation condition

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Continuous-time model identification of fractional-order models with time delays

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IET CONTROL THEORY AND APPLICATIONS 2011年第7期5卷 900-912页

作者： Narang, A. Shah, S. L. Chen, T. Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 2V4 Canada Univ Alberta Dept Elect & Comp Engn Edmonton AB T6G 2V4 Canada

Modelling of real physical systems having long memory transients and infinite dimensional structures using fractional-order dynamic models has significantly attracted interest over the last few years. For this reason, many identification techniques both in the frequency domain and time domain have been developed to model these fractional-order systems. However, in many processes time delays are also present and estimation of time delays along with continuous-time fractional-order model parameters have not been addressed anywhere. This study deals with the continuous-time model identification of fractional-order system models with time delays. In this study, a new linear filter is introduced for simultaneous estimation of all model parameters for commensurate fractional-order system models with time delays. The proposed method simultaneously estimates time delays along with other model parameters in an iterative manner by solving simple linear regression equations. For the case when the fractional order is unknown, we also propose a nested loop optimisation method where the time delay along with other model parameters are estimated iteratively in the inner loop and the fractional order is estimated in the non-linear outer loop. The applicability of the developed procedure is demonstrated by simulations on a fractional-order system model by doing Monte Carlo simulation analysis in the presence of white noise. The proposed algorithm has also been applied to identify a process of thermal diffusion in a wall in simulation, which are characterised by fractional-order behaviour.

关键词： fractional order system model Optimisation techniques Monte Carlo simulation analysis fractional order behaviour non-linear outer loop fractional order dynamic model nested loop optimisation method continuous time model identification time domain infinite dimensional structure modelling thermal diffusion frequency domain linear regression equation delays identification continuous time systems linear filter Monte Carlo methods continuous time fractional order model parameter time delays optimisation Simulation, modelling and identification Distributed parameter control systems

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Effect of Measurement Accuracy and Range of Variation of a Physical Quantity on the Correlation Coefficient

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MEASUREMENT TECHNIQUES 2015年第10期57卷 1113-1120页

作者： Sandomirski, S. G. Natl Acad Sci Belarus Joint Inst Mech Engn Minsk BELARUS

We establish bounds on the maximal achievable value of the correlation coefficient between the measurements and the true values of a physical quantity, determined by the relative measurement error and its range of variation. A formula is developed for estimating the maximal correlation coefficient as a function of the relative error and its range of variation. A critical analysis is given of the possible reasons for getting abnormally high correlation coefficients in some indirect magnetic measurements.

关键词： physical measurements the range of variation of a physical quantity relative error linear regression equation correlation coefficient

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Parametric Reshaping of Portrait Images for Weight-change

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IEEE COMPUTER GRAPHICS AND APPLICATIONS 2018年第1期38卷 77-90页

作者： Zhao, Haiming Jin, Xiaogang Huang, Xiaojian Chai, Menglei Zhou, Kun Zhejiang Univ State Key Lab CAD & CG Hangzhou Zhejiang Peoples R China Zhejiang Univ Hangzhou Zhejiang Peoples R China Zhejiang Univ Comp Sci Dept Hangzhou Zhejiang Peoples R China

We present an easy-to-use parametric image retouching method for thinning or fattening a face in a single portrait image while maintaining a close similarity to the source image. First, our method reconstructs a 3D face from the input face image using a morphable model. Second, according to the linear regression equation derived from the depth statistics of the soft tissue in the face and the user-set parameters of weight-change degree, we calculate the new positions of the feature points. The Laplacian deformation method is then used for non-feature points in the 3D face model. Our model-based reshaping process can achieve globally consistent editing effects without noticeable artifacts. We seamlessly blend the reshaped face region with the background using image retargeting method based on mesh parametrization. The effectiveness of our algorithm is demonstrated by experiments and user study.

关键词： Computer Graphics Face Recognition Image Reconstruction Mesh Generation regression Analysis Solid Modelling Parametric Reshaping Portrait Images Easy To Use Parametric Image Retouching Method Source Image Input Face Image Morphable Model linear regression equation Depth Statistics Soft Tissue Weight Change Degree Feature Points Laplacian Deformation Method Nonfeature Points Reshaping Process Globally Consistent Editing Effects Reshaped Face Region Image Retargeting Method Mesh Parametrization 3 D Face Model Rendering Computer Graphics Three Dimensional Displays Solid Modeling Mathematical Model Two Dimensional Displays Computational Modeling linear regression Applications Facial Reshaping Portrait Retouching Image Retargeting Computer Graphics Picture Image Generation

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Effect of zinc concentration and experimental parameters on high stress abrasive wear behaviour of Al-Zn alloys: A factorial design approach

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MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING 2005年第1-2期406卷 24-33页

作者： Mondal, DP Das, S Rajput, V CSIR Reg Res Lab Bhopal 462026 Madhya Pradesh India

High stress abrasive wear behaviour of Al-Zn alloys containing high zinc concentration at varying applied load and abrasive size has been studied through two-level full factorial design approach. The upper level of zinc concentration, applied load and abrasive size is selected as 70 wt%, 7 N and 180 mu m, respectively. The lower level of zinc concentration, applied load and abrasive size is taken as 30 wt%, I N and 60 mu m, respectively. The linear regression equation, for the wear rate (W-r) as a function of these parameters (applied load, abrasive size and Zn-concentration) and their interaction, has been developed as: W-r = 17.34 + 1.81C + 12.23L + 3.27A + 1.27CL + 3.36LA + 1.68CA + 1.14CLA where C, L and A are coded values of Zn-concentration, applied load and abrasive size, respectively, and the multiplication factor for the wear rate and the coefficients is 10(-11) m(3)/m. The positive value of the coefficients associated with coded values of various parameters and their interactions in the above equation suggests that abrasive wear rate increases with zinc concentration, abrasive size and applied load. The validity of the developed equation has been checked with experimental values at randomly selected experimental parameters within the selected experimental domain. The results have been explained with selected worn surfaces and debris analysis. (c) 2005 Elsevier B.V. All rights reserved.

关键词： abrasive wear aluminium zinc alloys linear regression equation factorial design approach interaction effects

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Determination of Pb²⁺ ions by square-wave anodic stripping voltammetry using silver nanoparticles grown on indium tin oxide substrate

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MICRO & NANO LETTERS 2014年第11期9卷 766-769页

作者： Bin Huang, Rong Zheng, Yi Fan Zhejiang Univ Technol Coll Chem Engn Hangzhou 310032 Zhejiang Peoples R China Zhejiang Univ Technol Res Ctr Anal & Measurement Hangzhou 310014 Zhejiang Peoples R China

Silver (Ag) nanoparticles with a pure face-centred cubic phase were grown on indium tin oxide (ITO) substrate via the electrodeposition method. The products were characterised by scanning electron microscopy, energy-dispersive X-ray analysis and X-ray diffraction. Ag nanoparticles deposited on the ITO substrate were first used as an electrode for the electrochemical analysis of lead ions. A linear response was observed for Pb2+ in the range of 0.1-8 mu M. The linear regression equation was I = 0.129 + 0.368C (unit of C is M) and the correlation coefficient was 0.9993. The detection limit was 70 nM Pb2+ (S/N = 3). The results open new possibilities for the fabrication of novel electrodes for the construction of simple, low-cost and reliable electrochemical sensors for the quantification of trace levels of Pb2+.

关键词： voltammetry (chemical analysis) scanning electron microscopy X-ray chemical analysis correlation methods indium compounds regression analysis electrodeposition X-ray diffraction nanoparticles silver lead lead ion determination square wave anodic stripping voltammetry silver nanoparticles indium tin oxide substrate face centred cubic phase electrodeposition scanning electron microscopy energy dispersive X-ray analysis X-ray diffraction linear regression equation correlation coefficient electrochemical sensors Ag ITO Pb2+

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Applying quantitative spatial phenotypes analysis to the investigation of peltate glandular trichomes development pattern in Perilla frutescens

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PLANT METHODS 2023年第1期19卷 1-17页

作者： Jiang, Zheng Zhou, Peina Shao, Yongfang Zhang, Qianqian Yue, Wei Qu, Cheng Wu, Qinan Nanjing Univ Chinese Med Coll Pharm Nanjing 210023 Peoples R China Collaborat Innovat Ctr Chinese Med Resources Indus Nanjing 210023 Peoples R China Natl & Local Collaborat Engn Ctr Chinese Med Resou Nanjing 210023 Peoples R China

Background Glandular trichomes, often referred to as "phytochemical factories", plays a crucial role in plant growth and metabolism. As the site for secretion and storage, the development of glandular trichomes is related to the dynamic biosynthesis of specialised metabolites. The study aims to explore the relationship between spatial phenotype and dynamic metabolism of glandular trichomes, and establish a novel approach for the exploration and study of the regulatory mechanism governing the development of glandular *** In this study, we proposed a technical route based on the relative deviation value to distinguish the peltate glandular trichomes (PGTs) from the background tissues and extract their spatial phenotype. By defining glandular trichome developmental stages based on the leaf vein growth axis, we found that young PGTs were densely distributed near the proximal end of growth axis of the leaf veins, where perillaketone, a primary metabolite of PGTs, is predominantly accumulated. Conversely, mature PGTs are typically found near the distal end of the mid-vein growth axis and the lateral end of the secondary vein growth axis, where the accumulation rate of isoegomaketone and egomaketone exceeds that of perillaketone in PGTs. We further identified spatial phenotypic parameters, L-sum and d, as independent variables to construct a linear regression model that illustrates the relationship between the spatial phenotypes and metabolite content of PGTs, including perillaketone (R-2 = 0.698), egomaketone (R-2 = 0.593), isoegomaketone (R-2 = 0.662) and the sum of the amount (R-2 = 0.773).Conclusions This model proved that the development of PGTs was correlated with the growth of the entire leaf, and the development stage of PGTs can be identifined by spatial phenotypes based on the leaf veins. In conclusion, the findings of this study enhance our understanding of correlation between spatial phenotype and development of glandular trichomes and offer a new

关键词： Growth axis linear regression equation Leaf veins Peltate glandular trichomes Perilla frutescens Spatial phenotype

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Application of 3D reconstruction through CT to measure the abdominal cavity volume in the treatment of external abdominal hernia

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HERNIA 2021年第4期25卷 971-976页

作者： Gong, X. Pan, Z. -Y. Chen, J. Yang, S. Jiang, T. Shen, Y. -M. Beijing Chao Yang Hosp Dept Radiol 5 JingYuan Rd Beijing 100043 Peoples R China Beijing Chao Yang Hosp Dept Hernia & Abdominal Wall Surg 5 JingYuan Rd Beijing 100043 Peoples R China

Objective To evaluate 3D reconstruction through CT in the measurement of abdominal cavity volume. Methods From January 1, 2019 to December 31, 2019, 61 patients diagnosed as external abdominal hernia were included in this prospective study. Multislice computed tomography (MSCT) was applied to patients scanning, and the images were transferred to post-processing workstation for further analysis. We measured the abdominal cavity volumes using volume rendering (VR) method and diameter rendering (DR) method, and the results were used to test whether there is a correlation between them. In addition, the time required for the measurement was recorded and analyzed. Results In this study, we found that there was no significant difference in the abdominal cavity volumes between these two groups (VR vs. DR = 7857.316 +/- 2035.786 cm(3) vs. 7967.268 +/- 2925.792 cm(3), P > 0.05). Besides, the correlation analysis between the measured values of VR method and DR method showed there was a significant positive correlation (r = 0.922, P < 0.01). The linear regression equation based on the scatter plot was established as follows: y = 0.6417x + 2745, R-2 = 0.8504. Furthermore, this regression equation was simplified as follows: y = 0.64x + 2800, R-2 = 0.8499. Meanwhile, the time required for measurement of VR was significantly longer than that of DR (VR vs. DR = 64.3 +/- 7.1 min vs. 2.6 +/- 0.6 min, P < 0.01). Conclusion In conclusion, the DR method can quickly measure and calculate the abdominal cavity volume, and its accuracy can more suitable for clinical requirement.

关键词： Abdominal cavity volume Volume rendering Diameter rendering Accuracy linear regression equation

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Rapid detection of nandrolone residues in chicken by surface-enhanced Raman spectroscopy

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IFAC-PapersOnLine 2018年第17期51卷 666-672页

作者： Xu, Ning Liu, Muhua Yuan, Haichao Zhao, Jinhui Tao, Jinjiang Guo, Hongqing Chen, Jian Optics-Electrics Application of Biomaterials Lab College of Engineering Jiangxi Agricultural University Nanchang330045 China

Using colloidal gold particles as active substrate and magnesium sulfate solution as active agent, surface-enhanced Raman spectroscopy (SERS) was applied to rapidly detect nandrolone residues in chicken. Firstly, the Raman characteristic peaks of nandrolone solution and nandrolone in chicken extract were analyzed. Secondly, the single factor analysis method was used to optimize the experiment conditions. When the concentration of nandrolone in chicken extract was 0.5~10mg/L, the quantitative analysis was conducted. There was a good linear relationship between the concentrations of nandrolone in chicken extract and the SERS intensities at 1079cm-1. The linear regression equation was y=323.8x+734.93, and the determination coefficient (R2) was 0.9241. And the minimum detection limit was 0.5mg/L. The experimental result showed that this method could detect nandrolone residues in chicken rapidly. © 2018

关键词： Raman spectroscopy Animals Gold metallography Gold nanoparticles Light transmission Magnesium compounds Magnesium metallography Sols Spectrum analysis Substrates Sulfur compounds Au nanoparticle chicken Colloidal gold particles Determination coefficients linear regression equation Magnesium sulfate solution Nandrolone Surface enhanced Raman spectroscopy

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