Poisson theory and integration method for a dynamical system of relative motion

This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is established. The Jacobi last multiplier of the system is defined, and the relation between the Jacobi last multiplier and the first integrals of the system is studied. Our research shows that for a dynamical system of relative motion, whose configuration is determined by n generalized coordinates, the solution of the system can be found by using the Jacobi last multiplier if （2n-1） first integrals of the system are known. At the end of the paper, an example is given to illustrate the application of the results.

Dynamic Stiffness Deterioration of a Machining Center Based on Relative Excitation Method

The tool point frequency response function(FRF) is commonly obtained by impacting test or semi-analytical techniques.Regardless of the approach,it is assumed that the workpiece system is rigid.The assumption is valid in common machining,but it doesn’t work well in the cutting processes of thin-wall products.In order to solve the problem,a multi-degree-of-freedom dynamic model is employed to obtain the relative dynamic stiffness between the cutting tool and the workpiece system.The relative direct and cross FRFs between the cutting tool and workpiece system are achieved by relative excitation experiment,and compared with the tool point FRFs at x and y axial direction.The comparison results indicate that the relative excitation method could be used to obtain the relative dynamic compliance of machine-tool-workpiece system more actually and precisely.Based on the more precise relative FRFs,four evaluation criterions of dynamic stiffness are proposed,and the variation trend curves of these criterions during the last six months are achieved and analyzed.The analysis results show that the lowest natural frequency,the maximum and the average dynamic compliances at x axial direction deteriorate more quickly than that at y axial direction.Therefore,the main cutting direction and the large-size direction of workpieces should be arranged at y axial direction to slow down the deterioration of the dynamic stiffness of machining centers.The compliance of workpiece system is considered,which can help master the deterioration rules of the dynamic stiffness of machining centers,and enhance the reliability of machine centers and the consistency of machining processes.

Adjoint Method-Based Algorithm for Calculating the Relative Dispersion Ratio in a Hydrodynamic System

Relative dispersion ratio(RDR)can be used to quantify the deviation behavior of a water parcel’s trajectory caused by a disturbance in a hydrodynamic system.It can be calculated by using a standard method for determining relative dispersion(RD),which accounts for the growth of the deviation of a cluster of particles from a specific initial time.However,the standard method for computing RD is time consuming.It involves numerous computations on tracing many water parcels.In this study,a new method based on the adjoint method is proposed to acquire a series of RDR fields in one round of tracing.Through this method,the continuous variation in the RDR corresponding to a time series of the disturbance time t can be obtained.The consistency and efficiency of the new method are compared with those of the standard method by applying it to a double-gyre flow and an unsteady Arnold-Beltrami-Childress flow field.Results show that the two methods have good consistency in a finite time span.The new method has a notable speedup for evaluating the RDR at multiple t.

Inversion of focal mechanism and events identification using an improved relative amplitude method

The relative amplitude method （RAM） is more suitable for source inversion of low magnitude earthquakes because it avoids the modeling of short-period waveforms. We introduced an improved relative amplitude method （IRAM） which is more robust in practical cases. The IRAM uses a certain function to quantify the fitness between the observed and the predicted relative amplitudes among direct P wave, surface reflected pP and sP waves for a given focal mechanism. Using the IRAM, we got the fault-plane solutions of two earthquakes of mb4.9 and mb3.8, occurred in Issyk-Kul lake, Kyrgyzstan. For the larger event, its fault-plane solutions are consistent with the Harvard＇s CMT solutions. As to the smaller one, the strikes of the solution are consistent with those of the main faults near the epicenter. The synthetic long period waveforms and the predicted P wave first motions of the solutions are consistent with observations at some of regional stations. Finally, we demonstrated that fault-solutions cannot interpret the characteristics of teleseismic P waveforms of the underground nuclear explosion detonated in Democratic People＇s Republic of Korea （DPRK） on October 9, 2006.

Analysis and Application of the Synthetic Relative Measuring Method in On-Line Monitoring for Capacitive Equipment in Power Systems

On-line measurement for dielectric loss angle can effectively monitor the insulation condition of capacitive equipment in power systems. Synthetic relative measuring methods not only markedly overcome the shortcomings of traditional absolute measuring methods but also greatly improve the accuracy of dielectric loss angle measurement. However, synthetic relative measuring methods based on two or three pieces of capacitive equipment do not have the characteristic of generality. In this paper, a principle of synthetic relative measuring method is presented. The example of application for synthetic relative methods based on three and four pieces of capacitive equipment running in the same phase is taken to present the failure judgment matrices for N pieces of equipment. According to these matrices, the fault condition of N pieces of capacitive equipment can be watched, which is more general. Then some problems needing to be concerned along with two diagnostic methods used in diagnostic system are introduced. Finally, two programmable flow charts for the two methods are given and corresponding examples demonstrate their feasibility in practice.

Risk Assessment of Diary Cattle Brucellosis Based on Systematic Multilevel Grey Relation Entropy Method

[Objective] The study was to explore the major factors affecting diary cattle brucellosis risk assessment,as well as their strong-to-weak sequence,so as to provide theoretical basis for assessing diary cattle brucellosis risk level in different regions.[Method] From 4 dimensions of feeding and importing,breeding,housing and polyculture situation,an evaluation index system was set up,and diary cattle brucellosis risk survey was conducted in 3 typical regions.Finally,systematic multilevel grey relation entropy method was applied to perform data analysis.[Result] The strong-to-weak sequence of Level 1 impact factor of diary cattle brucellosis was as follows：feeding and importinghousingpolyculture situationbreeding;the sequence of Level 2 impact factor was U32〉U12〉U11〉U31〉U21〉U42〉U43〉U23〉U22〉U41;the risk level sequence of 3 typical regions was Province A（County A1,A2,A3）Province B（County B1,B2,B3）Province C（County C1,C2,C3）.[Conclusion] According to the weight of Level 1 index strata,administrative departments at all levels and dairy cattle farmers should lay emphasis on the aspects of feeding,importing and housing;viewed from the perspective of Level 2 index strata,dairy cattle farmers should value the siting of cattle field,the brucellosis surveillance before importing and milking modes most.According to the diary cattle brucellosis risk level of 3 typical regions,if administrative departments at all levels strengthen peoples＇ awareness of their personal health and increase investment in this area,with new healthy cultured atmosphere built,the risk level of diary cattle brucellosis will surly decline.

Response surface method using grey relational analysis for decision making in weapon system selection

A proper weapon system is very important for a na- tional defense system. Generally, it means selecting the optimal weapon system among many alternatives, which is a multiple- attribute decision making （MADM） problem. This paper proposes a new mathematical model based on the response surface method （RSM） and the grey relational analysis （GRA）. RSM is used to obtain the experimental points and analyze the factors that have a significant impact on the selection results. GRA is used to an- alyze the trend relationship between alternatives and reference series. And then an RSM model is obtained, which can be used to calculate all alternatives and obtain ranking results. A real world application is introduced to illustrate the utilization of the model for the weapon selection problem. The results show that this model can be used to help decision-makers to make a quick comparison of alternatives and select a proper weapon system from multiple alternatives, which is an effective and adaptable method for solving the weapon system selection problem.

Program evaluation and its application to equipment based on super-efficiency DEA and gray relation projection method

For the gray attributes of the equipment program and its difficulty to carry out the quantitative assessment of the equipment program information, the gray relation projection method is simply reviewed. Combining the super-data envelopment analysis（DEA） model and the gray system theory, a new super-DEA for measuring the weight is proposed, and a gray relation projection model is established to rank the equipment programs. Finally, this approach is used to evaluate the equipment program. The results are verified valid and can provide a new way for evaluating the equipment program.

Relative Chemical Shifts for Obtaining Accurate Chemical Shifts of Hydrogen Atoms in CH Groups

Accurate chemical shifts of hydrogen atoms in CH groups are difficult to obtain. To solve this problem, relative chemical shifts are introduced. Internal and external standard methods were used to measure the chemical shifts in a whole-concentration of N-methylacetamide- water system. Determination of the chemical shifts of hydrogen atoms, especially those of CH groups, according to the two methods yielded significant differences. Relative chemical shifts were proven to be independent of the reference and may be applied to other systems.

Optimization of cutting parameters with Taguchi and grey relational analysis methods in MQL-assisted face milling of AISI O2 steel

This study aims to examine the usability of environmentally harmless vegetable oil in the minimum quantity of lubrication(MQL)system in face milling of AISI O2 steel and to optimize the cutting parameters by different statistical methods.Vegetable oil was preferred as cutting fluid,and Taguchi method was used in the preparation of the test pattern.After testing with the prepared test pattern,cutting performance in all parameters has been improved according to dry conditions thanks to the MQL system.The highest tool life was obtained by using cutting parameters of 7.5 m cutting length,100 m/min cutting speed,100 mL/h MQL flow rate and 0.1 mm/tooth feed rate.Optimum cutting parameters were determined according to the Taguchi analysis,and the obtained parameters were confirmed with the verification tests.In addition,the optimum test parameter was determined by applying the gray relational analysis method.After using ANOVA analysis according to the measured surface roughness and cutting force values,the most effective cutting parameter was observed to be the feed rate.In addition,the models for surface roughness and cutting force values were obtained with precisions of 99.63%and 99.68%,respectively.Effective wear mechanisms were found to be abrasion and adhesion.

Convergence analysis for the Secant method based on new recurrence relations

A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided difference of order one of the nonlinear operator is Lipschitz continuous. The convergence conditions differ from some existing ones and are easily satisfied. The results of the paper are justified by numerical examples that cannot be handled by earlier works.

An ideal point method adopting grey relational entropy to estimate life cycle cost with effectiveness of torpedo

To making the decision of the developing blue prints,ideal point method was selected to estimate the life cycle cost with effectiveness of torpedo.At the same time,the concept of grey relational entropy of the grey system theory was adopted to compute the distance between each blue print and the ideal point(or negative ideal point).The blue print,nearest to the ideal point and farthest to the negative ideal point,is the best one.As an example,four blue prints of torpedo were estimated.The result indicates the practical value of this method.

Priority-sequence of mineral resources' development and utilization based on grey relational analysis method

Generally, the sequence decision of the development and utilization of Chinese mineral resources is based on national and provincial overall plan of the mineral resources. Such plan usually cannot reflect the relative size of the suitability of the development and utilization of mineral resources. To solve the problem, the paper has selected the gift condition, the market condition, the technological condition,socio-economic condition and environmental condition as the starting-points to analyze the influential factors of the priority-sequence of mineral resources' development and utilization. The above 5 conditions are further specified into 9 evaluative indicators to establish an evaluation indicator system. At last,we propose a decision model of the priority sequence based on grey relational analysis method, and figure out the observation objects by the suitability index of development. Finally, the mineral resources of a certain province in China were analyzed as an example. The calculation results indicate that silver(2.0057), coal(1.9955), zinc(1.9442), cement limestone(1.9077), solvent limestone(1.5624) and other minerals in the province are suitable for development and utilization.

Determining relative block structure rating for rock erodibility evaluation in the case of non-orthogonal joint sets

The most commonly used method for assessing the hydraulic erodibility of rock is Annandale's method.This method is based on a correlation between the erosive force of flowing water and the capacity of rock resistance. This capacity is evaluated using Kirsten's index, which was initially developed to evaluate the excavatability of earth materials. For rocky material, this index is determined according to certain geomechanical factors related to intact rock and rock mass, such as compressive strength of intact rock, rock block size, discontinuity shear strength and relative block structure. To quantify the relative block structure, Kirsten(1982) developed a mathematical expression that accounts for the shape and orientation of the blocks relative to the direction of flow. Kirsten's initial concept for assessing the relative block structure considers that the geological formation is mainly fractured by two joint sets forming an orthogonally fractured system. An adjusted concept is proposed to determine the relative block structure when the fractured system is non-orthogonal where the angle between the planes of the two joint sets is greater or less than 90°. An analysis of the proposed relative block structure rating shows that considering a non-orthogonally fractured system has a significant effect on Kirsten's index and, as a consequence, on the assessment of the hydraulic erodibility of rock.

New Refinement Relations of Z Specifications for Multiple Viewpoints Oriented Requirements Method

In this paper we develop several new refinement relations of Z for multiple viewpoints oriented requirements method (MVORM). The original motivation is that we found the standard Z refinement relation is not adequate or correct when considering specifications that have temporal relationships of operations. The concept of temporal state variables is introduced into Z. Then new implementation relations are defined and new refinement relations are deduced, mainly for temporal state variables to process temporal relationships of operations. We use state transition systems to abstract the temporal state transitions. A simple example is used to show the procedures of MVORM. Finally some directions of further work are forwarded.

Optimization of Tribological Performance of Al-6061T6-15% SiCp-15% Al₂O₃Hybrid Metal Matrix Composites Using Taguchi Method &Grey Relational Analysis

In this investigation, optimization of tribological performance parameters of Al-6061T6 alloy reinforced with SiC (15% by weight) and Al2O3 (15% by weight) particulates having particle size of 37 μm each has been presented. The wear and frictional properties of the hybrid metal matrix composites have been studied by performing dry sliding wear test using pin-on-disc wear tester. A L27 orthogonal array is selected for the analysis of the data. From the test results it is observed that sliding distance has the significant contribution in controlling the friction and wear behaviour of hybrid composites. A confirmation test is also carried out to verify the accuracy of the results obtained through the optimization. In addition an optical micrograph test is also performed on the wear tracks to study the wear mechanism.

Optimizing the Glass Fiber Cutting Process Using the Taguchi Methods and Grey Relational Analysis

This paper mainly describes a new approach to optimizing of the cutting glass fiber with multiple performance characteristics, based on reliability analysis, Taguchi and Grey methods. During the cutting process, the speed, the volume and the cutting load are optimized cutting parameters when the performance characteristics, which include Weibull modulus and blade wear, are taken into consideration. In this paper, optimization with multiple performance characteristics is found to be the highest cutting speed and the smallest cutting volume, and the medium cutting load. An analysis of the variance of the blade wear indicates that the cutting speed (47.21%), the cutting volume (14.62%) and the cutting load (12.20%) are the most significant parameters in the cutting process of glass fibers. In summary, the most optimal cutting parameter should be A3B1C2. The results of experiments have shown that the multiple performance characteristics of cutting glass fiber are improved effectively through this approach.

ON RELATIONS BETWEEN THE MODIFIED-ITERATIVE METHOD AND CHIEN’S PERTURBATION SOLUTION

In this paper, we gave analytical formulas of characteristic relation of circular plate in solving high-order solutions of modified-iterative method, which reduces the calculating quantities of the method. Having deduced the relations between the modified-iterative method and Chien's perturbation solution, we obtained the conclusion that the convergent regions of the two methods are the same.

Multi-Objective Optimization of Fused Deposition Modeling for Mechanical Properties of Biopolymer Parts Using the Grey-Taguchi Method

The urgent need to develop customized functional products only possible by 3D printing had realized when faced with the unavailability of medical devices like surgical instruments during the coronavirus-19 disease and the ondemand necessity to perform surgery during space missions.Biopolymers have recently been the most appropriate option for fabricating surgical instruments via 3D printing in terms of cheaper and faster processing.Among all 3D printing techniques,fused deposition modelling(FDM)is a low-cost and more rapid printing technique.This article proposes the fabrication of surgical instruments,namely,forceps and hemostat using the fused deposition modeling(FDM)process.Excellent mechanical properties are the only indicator to judge the quality of the functional parts.The mechanical properties of FDM-processed parts depend on various process parameters.These parameters are layer height,infill pattern,top/bottom pattern,number of top/bottom layers,infill density,flow,number of shells,printing temperature,build plate temperature,printing speed,and fan speed.Tensile strength and modulus of elasticity are chosen as evaluation indexes to ascertain the mechanical properties of polylactic acid(PLA)parts printed by FDM.The experiments have performed through Taguchi’s L27orthogonal array(OA).Variance analysis(ANOVA)ascertains the significance of the process parameters and their percent contributions to the evaluation indexes.Finally,as a multiobjective optimization technique,grey relational analysis(GRA)obtains an optimal set of FDM process parameters to fabricate the best parts with comprehensive mechanical properties.Scanning electron microscopy(SEM)examines the types of defects and strong bonding between rasters.The proposed research ensures the successful fabrication of functional surgical tools with substantial ultimate tensile strength(42.6 MPa)and modulus of elasticity(3274 MPa).

Multidimensional Relative Poverty of Farmers in Tibetan Areas - Based on a Data Analysis on Micro Surveys

In 2020,the issue of absolute poverty has been solved,and China is building a well-off society in an all-round way.The issue of relative poverty is an important content of poverty reduction.Based on a survey data from Danba County in October 2020,this paper uses the AF method to calculate the incidence of multidimensional poverty and the multidimensional poverty index.The results showed that 44.65%of the farmers have multidimensional deprivation of any three indicators of relative poverty,and 2.79%of the farmers have serious multidimensional deprivation;the incidence of one-dimensional poverty in terms of“educational level index of head of household,”“per capita non-transfer income of households in 2019,”and“per capita household income in 2019”is the highest;at the same time,the contribution rate of the three indicators to the multidimensional poverty index is also higher than other indicators.Therefore,several suggestions have been put forward to alleviate the multidimensional relative poverty in the region from the aspects of industry development and education.