Data-driven prediction of dimensionless quantities for semi-infinite target penetration by integrating machine-learning and feature selection methods

This study employs a data-driven methodology that embeds the principle of dimensional invariance into an artificial neural network to automatically identify dominant dimensionless quantities in the penetration of rod projectiles into semi-infinite metal targets from experimental measurements.The derived mathematical expressions of dimensionless quantities are simplified by the examination of the exponent matrix and coupling relationships between feature variables.As a physics-based dimension reduction methodology,this way reduces high-dimensional parameter spaces to descriptions involving only a few physically interpretable dimensionless quantities in penetrating cases.Then the relative importance of various dimensionless feature variables on the penetration efficiencies for four impacting conditions is evaluated through feature selection engineering.The results indicate that the selected critical dimensionless feature variables by this synergistic method,without referring to the complex theoretical equations and aiding in the detailed knowledge of penetration mechanics,are in accordance with those reported in the reference.Lastly,the determined dimensionless quantities can be efficiently applied to conduct semi-empirical analysis for the specific penetrating case,and the reliability of regression functions is validated.

Effects of physical parameter range on dimensionless variable sensitivity in water flooding reservoirs

The similarity criterion for water flooding reservoir flows is concerned with in the present paper. When finding out all the dimensionless variables governing this kind of flow, their physical meanings are subsequently elucidated. Then, a numerical approach of sensitivity analysis is adopted to quantify their corresponding dominance degree among the similarity parameters. In this way, we may finally identify major scaling law in different parameter range and demonstrate the respective effects of viscosity, permeability and injection rate.

Novel Annulus-shaped Flexure Pivot in Rotation Application and Dimensionless Design

Large-deflection flexure pivot is widely used in high precision rotation application, but there are less flexure configurations and simple and convenient design methods, This paper presents a novel large-deflection curved-compliant annulus-shaped flexure pivot composed of six curved beam flexure elements. It can offer more than lO^angular stroke theoretically. Firstly, main-motion pseudo-rigid-body method is introduced to establish the flexure pivot model. Although pseudo-rigid-body method can be used to analyze the large-deformation flexure pivot performance, the method is definitely a laborious and difficult task for designing this novel flexure pivot. In order to simply the designing process, dimension-design graphs based on the parametric models and finite element analysis is presented. Using the dimension-design method as a tool, the designers can determine the optimal geometry rapidly, based on the stiffness and rotation demands of an annulus-shaped flexure pivot. Finally, dimension-design graph examples are given whose primary design aims to achieve a rotation stroke of annulus-shaped flexure pivot. The finite element analysis results show that the relative designing error between anticipative rotation stroke and graph design result is less than 4%. The dimensionless method used in designing annulus-shaped flexure pivot can reduce design process in both time and complexity. The novel annulus-shaped flexure pivot and dimension-design method are helpful supplement to configuration and design method of large-deflection flexure pivot.

Dimensionless Study on Secretion Clearance of a Pressure Controlled Mechanical Ventilation System with Double Lungs

A pressure controlled mechanical ventilator with an automatic secretion clearance function can improve secretion clearance safely and efficiently.Studies on secretion clearance by pressure controlled systems show that these are suited for clinical applications.However,these studies are based on a single lung electric model and neglect the coupling between the two lungs.The research methods applied are too complex for the analysis of a multi-parameter system.In order to understand the functioning of the human respiratory system,this paper develops a dimensionless mathematical model of doublelung mechanical ventilation system with a secretion clearance function.An experiment is designed to verify the mathematical model through comparison of dimensionless experimental data and dimensionless simulation data.Finally,the coupling between the two lungs is studied,and an orthogonal experiment designed to identify the impact of each parameter on the system.

Dimensionless Variation of Seepage in Porous Media with Cracks Stimulated by Low-Frequency Vibration

Pulse excitation or vibration stimulation was imposed on the low permeable formation with cracks to enhance the production or injection capacity.During that process,a coupling of wave-induced flow and initial flow in dual-porous media was involved.Researchers had done much work on the rule of wave propagation in fractured porous media,whereas attentions on the variation law of flow in developing low permeable formation with cracks under vibration stimulation were not paid.In this study,the effect of low-frequency vibration on the seepage in dual-porous media was examined for the application of wave stimulation technology in developing reservoirs with natural cracks.A model for seepage of single-phase liquid in porous media with cracks under low-frequency vibration excitation was built by combining wave propagating theory for porous media with cracks and dual-porous media seepage mechanics.A governing equation group for the model,which was expressed by dimensionless fluid and solid displacements,was derived and solved with a numerical method.Variable physical properties were simulated to check the applicability of external low-frequency vibration load on dual-porous media and a parametric study for various vibration parameters.Stimulation of low-frequency vibration affected flow velocities of crack and rock matrix fluids.Compared with that in single-porous media,the stimulation effect on the fluid inner matrix of dual-porous media was relatively weakened.Different optimal vibration parameters were needed to increase the channeling flow between the crack and rock matrix or to only promote the flow velocity in the rock matrix.The theoretical study examines wave-coupled seepage field in fractured porous media with results that are applicable for low-frequency stimulation technology.

Dimensionless model to determine spontaneous combustion danger zone in the longwall gob

According to spontaneous combustion propensity,the longwall gob is divided into three zones,including heat dissipation zone,self-heating zone and the choking zone.Only in the self-heating zone can temperature of coal rise due to oxidation.Studying the distribution of the "Three Zones" in gob is important for predicting and preventing spontaneous combustion in coalmine.In normal mining operations,temperature of coal is roughly constant.The process of mass transfer in the gob is considered to be steady.Based on mass conservation,gas species conservation,darcy's law,Ficks law of diffusion and coal oxidation 1-grade reaction rule,governing equation for air leakage intensity and species concentration are deduced.With critical value of coal spontaneous combustion and the size of longwall workface as basic dimension,a dimensionless steady coupled model of air flow diffusion and chemical reaction in loose coal of Fully Mechanized Top-Coal Caving Mining Workface(FMTCCMW) is setup.By solving the model numerically,regulation of three zones' distribution and spontaneous combustion in the gob can be obtained.The results can be easily popularized to prediction of spontaneous combustion in other coalmines' longwall gob.

A Unified Dimensionless Parameter for Finite Element Mesh for Beams Resting on Elastic Foundation

Discretising a structure into elements is a key step in finite element(FE)analysis.The discretised geometry used to formulate an FE model can greatly affect accuracy and validity.This paper presents a unified dimensionless parameter to generate a mesh of cubic FEs for the analysis of very long beams resting on an elastic foundation.A uniform beam resting on elastic foundation with various values of flexural stiffness and elastic supporting coefficients subject to static load and moving load is used to illustrate the application of the proposed parameter.The numerical results show that(a)Even if the values of the flexural stiffness of the beam and elastic supporting coefficient of the elastic foundation are different,the same proposed parameter“s”can ensure the same accuracy of the FE solution,but the accuracy may differ for use of the same element length;(b)The proposed dimensionless parameter“s”can indeed be used as a unified index to generate the mesh for a beam resting on elastic foundation,whereas the use of the same element length as a criterion may be misleading;(c)The errors between the FE and analytical solutions for the maximum vertical displacement,shear force and bending moment of the beam increase with the dimensionless parameter“s”;and(d)For the given allowable errors for the vertical displacement,shear force and bending moment of the beam under static load and moving load,the corresponding values of the proposed parameter are provided to guide the mesh generation.

The Analysis of Dimensionless Magnitudes in Economic Science

An economy consists of the economic system of a country or other unit of human society.It includes labor,capital,natural resources,production,trade,distribution and consumption of goods and services in the area where human society is active.These factors give context,content,and determine the conditions and parameters with which the economy operates.When searching with data mining techniques to identify or find out dimensionless groups(DGs)in technical literature,it is possible to meet errors/faults/omissions concerning both,the form and the content of such groups.In the present study,a methodological framework has been developed in terms of a logical flow chart,including 11 activity stages and seven decision nodes,to acquire/process/store/retrieve knowledge for reconstruction and identification of these groups.Case Based Reasoning(CBR),especially modified to meet the needs of this work,has been used for tracing causality paths by similarity and making correction suggestions.Two case examples are presented to prove the functionality of the proposed methodology.Non-dimensional groups are used in engineering but can also be used in economic science.Through this analysis,we can calculate the scale of industrial processes from laboratory to pilot and then factory scale.Still through the study of non-dimensional groups,it is easy to calculate economies of scale embedded in the production process.Synergy savings and target economies cause economies of scale in a production process and reduce the cost of production per unit of output when production is increased.Non-dimensional groups can be a quantitative and measurable indicator for calculating and predicting economies of scale in an industrial unit.The same can happen in an economic unit providing services,that is,intangible products.

Development of a dimensionless parameter for characterization of dielectric barrier discharge devices with respect to geometrical features

Non-thermal plasma（NTP） devices produce excited and radical species that have higher energy levels than their ground state and are utilized for various applications. There are various types of NTP devices, with dielectric barrier discharge（DBD） reactors being widely used. These DBD devices vary in geometrical configuration and operating parameters, making a comparison of their performance in terms of discharge power characteristics difficult. Therefore, this study proposes a dimensionless parameter that is related to the geometrical features, and is a function of the discharge power with respect to the frequency, voltage, and capacitance of a DBD. The dimensionless parameter, in the form of a ratio of the discharge energy per cycle to the gap capacitive energy, will be useful for engineers and designers to compare the energy characteristics of devices systematically, and could also be used for scaling up DBD devices.From the results in this experiment and from the literature, different DBD devices are categorized into three separate groups according to different levels of the energy ratio. The larger DBD devices have lower energy ratios due to their lower estimated surface discharge areas and capacitive reactance. Therefore, the devices can be categorized according to the energy ratio due to the effects of the geometrical features of the DBD devices, since it affects the surface discharge area and capacitance of the DBD. The DBD devices are also categorized into three separate groups using the Kriegseis factor, but the categorization is different from that of the energy ratio.

Unity Formulas for the Coupling Constants and the Dimensionless Physical Constants

In this paper in an elegant way will be presented the unity formulas for the coupling constants and the dimensionless physical constants. We reached the conclusion of the simple unification of the fundamental interactions. We will find the formulas for the Gravitational constant. It will be presented that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincare dodecahedral space. This article will be followed by the energy wave theory and the fractal space-time theory.

Mathematical modeling of electromagnetic dimensionless number for electromagnetic casting of metals and its application

In order to estimate the feasibility of electromagnetic casting (EMC) for different metals, a mathematical model named the electromagnetic dimensionless number (EMDN) was presented, and its validity was proved by the experiments of aluminum and Sn-3%Pb alloy. From the experiment and the analysis of EMDN it can be concluded that the EMC of steel can be attained only when the magnetic flux density is larger than 0.09T, while that required for aluminum is only 0.04T. The mathematical expression of the electromagnetic dimensionless number was given out.

Improved normalization method for ductile fracture toughness determination based on dimensionless load separation principle

This study successfully deals with the inhomogeneous dimension problem of load separation assumption, which is the theoretical basis of the normalization method. According to the dimensionless load separation principle, the normalization method has been improved by intro- ducing a forcible blunting correction. With the improved normalization method, the J-resistance curves of five different metallic materials of CT and SEB specimens are estimated. The forcible blunting correction of initial crack size plays an important role in the J-resistance curve estima- tion, which is closely related to the strain hardening level of material. The higher level of strain hardening leads to a greater difference in JQ determined by different slopes of the blunting line. If the blunting line coefficient recommended by ASTM E1820-11 is used in the improved nor- realization method, it will lead to greater fracture resistance than that processed by the blunting line coefficient recommended by ISO 12135-2002. Therefore, the influence of the blunting line on the determination of JQ must be taken into full account in the fracture toughness assessment of metallic materials.

Experimental Investigation of Dimensionless Velocity and Shearing Stress in Boundary Layer Flow on Continuous Moving Surface in Power Law Fluids

An analysis is carried out to study the steady flow characteristics from a continuous flat surface moving in a parallel free stream of non-Newtonian power law fluid. The constitutive equations of the fluid are transformed into dimensionless ones. The velocity field is measured by Particle Image Velocimetry. Experimental results are obtained for the distribution of velocity. The influence of wall velocity ratio parameter on boundary layer flow field is observed in the experiment. Dimensionless velocity distribution and shearing stress distribution are obtained by post-processing experimental results. The effects of various physical parameters like velocity ratio parameter and similarity variable on various momentum transfer characteristics are discussed in detail and shown graphically. It is indicated that dimensionless velocity increases with velocity ratio parameter and similarity variable, and that dimensionless shearing stress decreases with velocity ratio parameter and similarity variable.

Calibration of discrete element modeling: Scaling laws and dimensionless analysis

In this paper,dynamic similarity conditions are derived for discrete element simulations by non-dimensionalising the governing equations.These conditions must be satisfied so that the numerical model is a good representation of the physical phenomenon.For a pure mechanical system,if three independent ratios of the corresponding quantities between the two models are set,then the ratios of other quantities must be chosen according to the similarity principles.The scalability of linear and non-linear contact laws is also investigated.Numerical tests of 3D uni-axial compression are carried out to verify the theoretical results.Another example is presented to show how to calibrate the model according to laboratory data and similarity conditions.However,it is impossible to reduce computer time by scaling up or down certain parameters and continue to uphold the similarity conditions.The results in this paper provide guidelines to assist discrete element modelers in setting up the model parameters in a physically meaningful way.

Dimensionless variable groups for the free-fall grain dryer

Dimensionless variable groups(DGs)of free-fall grain dryer were developed by using the characteristic scaling method and engineering intuition.These DGs were intended for the analyses of drying characteristics and sizes of this dryer.Experiments of the free-fall rough rice dryer were carried out using different drying chambers(small and medium scales),drying air temperatures(100°C-150°C),and drying air speeds(1-3 m/s).Experimental data were used to study relationships and to validate similarities among these DGs.The results of the study showed the five appropriate dimensionless variables representing and describing the drying mechanism of the free-fall dryer.These DGs could be applied to design and analyze scaling up the dryer.In addition,the dimensionless correlation was established to predict the moisture contents of rough rice while being dried by the free-fall dryer.The predicted values from this correlation were in relatively good agreement with the experimental data under the proposed drying conditions(R2=0.989,MRD=1.82%and RMSE=0.0168).

Effect of dimensionless heat input during laser solid forming of high-strength steel

Laser solid forming(LSF)technology can be used to rapidly manufacture and repair high-strength steel parts with superior performance,but the value of the heat input during operation is difficult to quantify,which has a substantial impact on the microstructure and mechanical properties of the parts.A promising method to improve the forming efficiency and quality of LSFed parts is to accurately control the heat input and explore its relationship with the microstructure and mechanical properties.To remove the interference of other variables from the experiment,the dimensionless heat input Q;^(∗)was introduced.The Q^(∗)values were designed in advance to calculate the experimental parameters used to perform the LSF experiment.The microstructure was observed at different regions of the sample,and its mechanical properties were analyzed.From the results,the following conclusions were drawn.The Q;^(∗)value was directly related to the cooling rate and heat accumulation in the top structure,leading to the formation of different microstructures;it also modified the original structure at the bottom,affecting the subsequent thermal cycle and indirectly changing the tempered martensite morphology.The heat input also affected the mechanical properties of the sample.The hardness of the stable zone decreased with increasing Q;^(∗)value,and the lowest value was 190 HV.Similarly,the tensile strength and yield strength of the LSFed samples decreased considerably with increasing Q;^(∗)value,and the lowest values were 735 and 604 MPa,respectively.Only the elongation and reduction in the area increased after a slight decrease.The Q;^(∗)value had a significant effect on heat treatment.When Q;^(∗)=2.9,the increase in tensile strength and yield strength after heat treatment was the largest(29%and 44%,respectively).

综合评价方法中的最优无量纲化模型研究

针对综合评价过程中无量纲化方法选择盲目性较强的问题,文章首先引入综合评价结果优良性的度量指标,优化综合评价结果稳定性和区分度的度量函数,建立无量纲化有效性的统计检验方法;其次,以无量纲化有效为主要约束条件,分别以稳定性最高、区分度最高以及稳定性和区分度均最高为目标函数构建三类最优无量纲化模型,分析大平移尺度和小平移尺度约束条件对最优无量纲化模型的影响;最后,通过大量的数值模拟实验研究了6种常用综合评价方法中的最优无量纲化模型,并对结果进行深入分析。研究发现,大平移尺度约束下几种综合评价方法中的最优无量纲化结果均不同于现有无量纲化方法,小平移尺度约束下的最优无量纲化与均值化较为接近,但不完全相同;经过不断优化后的稳定性函数和区分度函数能更科学地度量综合评价结果的稳定性和区分度大小,无量纲化有效性的统计检验方法能准确判断指标间的量纲差异是否被有效消除;综合评价方法、目标函数和约束条件不同时所对应的最优无量纲化结果不同。

煤层透气性系数新的测试计算方法

煤层透气性系数是衡量煤层瓦斯流动难易程度的关键参数。现行的煤层透气性系数计算式中,将变压力非线性偏微分方程的系数假定为常数,理论推导结果存在较大缺陷,使得现场测定的透气性系数存在较大偏差。为解决煤层透气性系数测定失准的问题,推导了钻孔径向流量法测试煤层透气性系数的过程,并在推导过程中指出该方法存在的问题。以朗格缪尔式瓦斯含量和达西定律为基础,建立无量纲模型,将模型解算结果进行反演拟合,得到新的煤层透气性系数计算式,并通过现场实测钻孔数据进行验证,修正了现行的煤层透气性系数测试方法,提出准确可靠的计算煤层透气性系数的新方法。结果表明:用抛物线式表示煤层瓦斯含量并将变量煤层瓦斯压力p^(1.5)视为常量推导而来的煤层透气性系数计算式,相当于将瓦斯含量拟合成与压力平方成正比关系,理论与实际测算均存在较大误差。采用朗格缪尔式无量纲模型计算出的无因次瓦斯涌出速度Y’进行反演拟合,可解决现行计算方法的缺陷;当吸附常数b与原始瓦斯压力p_(0)的乘积(无因次原始瓦斯压力)不同时,Y’与无因次时间Fo’的函数曲线明显不同,由此得到了含有无因次原始瓦斯压力的透气性系数计算式;当煤层和钻孔条件一定时,由不同时间测试的瓦斯涌出量计算得到的煤层透气性系数λ值具有良好的再现性。新的煤层透气性系数现场测定方法与现行方法完全相同,不增加额外工作量,但新方法的计算更加精确可靠。

抑尘液滴对煤表面动态润湿特征模拟评估方法

在煤体表面喷洒抑尘液是涉煤工业企业常用抑尘手段,而抑尘液滴撞击煤表面的润湿过程对抑尘效果具有重要意义。为研究抑尘液滴在煤表面动态润湿过程以及进一步评估液滴润湿性能,提出了液滴撞击煤表面过程中动态润湿指标,基于CLSVOF数值模拟法研究了液滴在煤表面动态润湿过程;利用无量纲润湿长度和无量纲润湿面积评价该过程中体现的润湿性能,并得出最大无量纲润湿长度与最大无量纲润湿面积相关理论表达,同时与表面张力的润湿性评估能力进行了比较。结果表明:CLSVOF方法能够较好地模拟液滴在煤表面的撞击以及动态润湿过程,可用来评估液滴对煤的动态润湿能力。液滴滴落在煤表面上,首先展铺为圆盘状,达到最大展铺时,圆盘边缘与中心存在速度差。当速度差较小时,液滴回缩汇聚成为一个液滴;当速度差较大时,液滴出现断裂行为,形成许多微小液滴。液滴粒径越大,断裂行为越早出现、现象越明显。一旦液滴在煤表面发生破裂,无量纲润湿长度与无量纲润湿面积并不是保持着一致性变化趋势,无量纲润湿面积评估能力更佳。液滴粒径相同时,撞击煤表面的韦伯数越大,润湿能力越好;相同速度下增加粒径对液滴润湿能力影响较小。与表面张力相比,无量纲润湿长度和无量纲润湿面积具有更好的液滴润湿性评估能力,体现出在润湿剂评价、优选中的潜在应用价值。

微量水蒸气条件下低温表面结霜过程的实验研究

为研究微量水蒸气在低温表面上的结霜过程,搭建了低温表面微量水汽混合湿氮气的可视化结霜实验台。实验对比了常规湿度和微量水汽含量条件下,-180℃冷表面上常温氮气流中水蒸气结霜过程和形态,研究了不同微量水汽含量以及环境压力对低温结霜特性的影响。结果表明:相比于常规湿度条件下冷凝-冻结机制主导的结霜过程,微量水蒸气(体积分数71×10^(-6))在低温表面主要通过凝华机制生成微小冰晶沉积在冷表面,形成不均匀分布的无明显枝干的霜晶,随后形成平整疏松的霜层。凝华机制主导的霜层生长过程主要体现为霜层厚度的增大,而密度无明显增大。在微量水蒸气条件下,随着水汽含量由1.53×10^(-6)升高至500×10^(-6),霜层逐渐增厚并伴随着霜层形态由平坦均匀薄层向簇状霜团转变,增大的接触面积使霜层生长速率加快。环境压力由109 kPa升高至190 kPa时,增大的水蒸气分压本质上是由水蒸气绝对含量增加引起,霜层生长加快,表面的不平整程度会升高,霜晶形态更丰富。随时间推移,同一时刻不同环境压力下霜层厚度的差异逐渐增大。最后拟合了适用于低温表面上微量水蒸气条件下的无量纲霜层厚度关联式,整体误差在±20%以内。