Risk assessment model of tunnel water inrush based on improved attribute mathematical theory

Tunnel water inrush is one of the common geological disasters in the underground engineering construction.In order to effectively evaluate and control the occurrence of water inrush,the risk assessment model of tunnel water inrush was proposed based on improved attribute mathematical theory.The trigonometric functions were adopted to optimize the attribute mathematical theory,avoiding the influence of mutation points and linear variation zones in traditional linear measurement functions on the accuracy of the model.Based on comprehensive analysis of various factors,five parameters were selected as the evaluation indicators for the model,including tunnel head pressure,permeability coefficient of surrounding rock,crushing degree of surrounding rock,relative angle of joint plane and tunnel section size,under the principle of dimension rationality,independence,directness and quantification.The indicator classifications were determined.The links among measured data were analyzed in detail,and the objective weight of each indicator was determined by using similar weight method.Thereby the tunnel water inrush risk assessment model is established and applied in four target segments of two different tunnels in engineering.The evaluation results and the actual excavation data agree well,which indicates that the model is of high credibility and feasibility.

Mathematical Model, Optimal Control and Transmission Dynamics of Avian Spirochaetosis

Avian Spirochaetosis is an acute endemic tick-borne disease of birds, caused by Borrelia anserins, a species of Borrelia bacteria. In this paper, we present a compartmental mathematical model of the disease for the bird population and Tick population. The disease steady-state and the conditions for reaching a stable disease-free steady state are determined. The analysis by Lyapunov method shows both local and global stability. Further investigation involves the introduction of controls to the model;the existence and uniqueness of optimal control are established. Finally, the effect of the controls is investigated using numerical solutions.

Semantic model and optimization of creative processes at mathematical knowledge formation

The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the formation of deductive theory is represented as the development of a certain informational space, the elements of which are structured in the form of the orientated semantic net. This net is properly metrized and characterized by a certain system of coverings. It allows injecting net optimization parameters, regulating qualitative aspects of knowledge system under consideration. To regulate the creative processes of the formation and realization of mathematical know- edge, stochastic model of formation deductive theory is suggested here in the form of branching Markovian process, which is realized in the corresponding informational space as a semantic net. According to this stochastic model we can get correct foundation of criterion of optimization creative processes that leads to “great main points” strategy (GMP-strategy) in the process of realization of the effective control in the research work in the sphere of mathematics and its applications.

A methodology for laser tool setters calibration and its precise mathematical model

On-machine tool setting is a pivotal approach in achieving intelligent manufacturing,and laser tool setters have become a crucial component of smart machine tools.Laser tool setters play a crucial role in precisely measuring the dimensions of cutting tools during the part machining process,focusing on tool length and diameter.As a measuring instrument,the positions of the laser axis of the laser tool setter need to be accurately calibrated before use.However,in actual calibration scenarios,traditional calibration methods face challenges due to installation errors in the tool setter and geometric errors in the measuring rod.To address this issue,this study proposes a novel calibration method.Initially,the calibration mechanism of the laser beam axis is established.Based on the accurate mathematical model of the laser beam and the measuring rod,and using the polygon clipping algorithm,the mathematical mechanism of the laser tool setter’s work is established.Then,a novel method is introduced to calculate the compensation distance between the laser beam reference point and the rod bottom center point at each moment during calibration.Furthermore,by utilizing the kinematic chain of the tool setter calibration system,a new calibration method is developed to accurately calibrate the position of the laser beam axis in the machine tool coordinate system.Finally,the accuracy of the calibration method is verified through simulation experiments and calibration tests.This method improves the calibration accuracy of the tool setter,and the mathematical model of the laser tool setter can be extended to the measurement of tools,thereby improving the precision of tool measurements.This research significantly improves the efficient production performance of smart machine tools.

基于孔压变化的瓦斯压力预判

为了缩短煤层瓦斯压力测压周期,提高瓦斯压力测量的精确度,对前人的主动式压力测定研究进行了总结和分析,提出了存在瓦斯压力预判研究不足的问题。针对该问题进行了瓦斯压力测定的模拟实验研究,研究发现压力测定过程分为孔压急速上升期、缓慢上升期、趋于稳定期与达到稳定期4个阶段,急速上升期孔压变化率远大于其他3个阶段。并构建了基于煤层瓦斯压力、模拟煤层孔隙大小、模拟钻孔内压力变化率3参数的瓦斯压力预判数学模型,使用该模型对煤层瓦斯压力进行了合理区间的验证,结果表明,与真实瓦斯压力相比存在较小误差,为主动式煤层瓦斯压力测定中补偿气体最佳注气压力的确定提供了理论依据。

面向任务的CMM圆度测量不确定度建模与优化

精密仪器正趋向于智能化以及功能多样化发展,评估精密仪器的测量不确定度因此也变得更加复杂。以CMM中的圆度测量为例,以面向任务的不确定度评定方法,实现快速、可靠地评估出CMM测量任务的不确定度。根据误差传播的实际情况,结合计算机模拟的蒙特卡洛方法,提出了一种误差分布多状态下的不确定度代数和合成方法。针对测量不确定度初次评定存在过量估计的问题,提出了优化评估方案。给出圆度测量任务的不确定度评定与优化实例,验证评定模型和优化方法的可行性与有效性。系统性解决CMM面向任务的不确定度评定难题,对于解决其他高精度仪器测量结果的不确定度评估、提高仪器的实际使用价值,均具有重要参考意义。

氢化物发生-原子荧光光谱法测定煤中砷含量测量不确定度分析与评定

使用氢化物发生-原子荧光光谱法检测煤中砷含量的不确定度,进一步探讨不确定度的根本原因,最终结果的精准度受到样品处理、检测试剂、检测环境等诸多因素的影响。创新设计一个数学模型,从测量重复性、试剂溶液浓度、煤样处理等多个角度入手,对不确定度的根本因素展开研究探讨,核算出煤中砷的合成标准不确定度是0.133 ug/g,样品砷含量检测数据是(1.75±0.27)μg/g,包含因子k=2。各测量不确定度的核心影响因素有三个:其一是标准工作曲线拟合,其二是测量重复性,其三是煤样处理,因此在测定时应加强样品处理、试剂溶液、测定条件等影响因素的控制。

复杂环境下飞机零部件孔参数测量算法研究

现有孔参数测量方法,难以适用于复杂环境条件测量需要,急需设计新的满足工程实际应用的方法。基于此,设计了识别测量算法,包含了同数控加工机床主轴配置的孔图像获取装置,构建了基于残差卷积网络用于提取孔特征的数学模型,用于精细识别孔径回归数学模型与孔位度量数学模型。采集加工现场零部件孔表面状态图像进行分析,提出方法较主流CH、RH、SH、Hh方法,20组测试样本半径偏差累积分别降低为原来的5/16、1/3、5/16、1/4,累积孔位偏差分别降低为原来的5/39、5/32、5/29、10/83,孔口缺陷平均F1-score值为0.94达到了工业应用0.9的标准。基于实验结果,说明了说提出算法更优的半径拟合与孔位测量能力,满足实际识别检测需要的同时可有效助力航空装置智能化转型升级。

基于数学物理模拟和高温测速的拉速对吹氩结晶器流场行为的影响

通过结晶器的流场优化可以降低连铸坯的炼钢缺陷,从而提高汽车外板的表面质量。结合数值模拟、水模拟和高温定量测速3种手段研究了拉速对结晶器流场的影响。研究结果表明,随着拉速提高,结晶器1/4宽度附近的表面流速增大,数值模拟、水模拟和高温定量测速的结果吻合良好。在结晶器断面尺寸为1190 mm×230 mm,氩气流量为8 L/min,水口浸入深度为170 mm时,随着拉速从1.2 m/min增加至1.3、1.4、1.5、1.6 m/min,结晶器流场的流动形态均为双循环流,结晶器窄面附近和1/4宽度附近的钢液从窄面向水口方向流动,水口附近的钢液从水口向外流动。随着拉速增大,窄面附近和1/4宽度附近的表面流速逐渐增大,水口附近的表面流速逐渐减小。此外,窄面附近和1/4宽度附近的液面波动都逐渐增大,容易形成气泡卷渣。因此应根据连铸生产中汽车外板的质量要求,将拉速控制在一个合理的范围内。

热轧厚规格带钢卷取温度控制优化及应用

热轧厚规格带钢卷取温度受钢种变换、带钢表面发生沸腾换热产生汽雾造成温度实测值受到严重干扰、设备跟踪精度等因素的影响,CTC数学模型的预报精度较薄规格产品普遍偏低,换规格轧制时卷取温度偏离目标值较多,同时厚规格带钢干头长度控制偏长,严重影响了厚规格产品的成材率。基于此,结合实际生产中出现的问题,对模型穿带速度、加速度等参数进行回归分析及优化;对C3模型服务器进行升级,并调整现场仪表响应时间,将厚规格带钢干头长度由4 m以上降到1.8 m左右,提高了厚规格产品成材率;同时对检测仪表位置进行优化调整,提高了厚规格带钢卷取温度命中率。优化实施后,厚规格带钢卷取温度命中率由85.26%提高到92.13%,成材率提高1.26%。

永磁同步电机转子位置信息控制技术分析

永磁同步电机因结构紧凑、运行稳定等特点,在工业、汽车、电力领域广泛应用,随着技术不同进步,在船舶、航天系统应用程度越来越高,在恶劣条件下,永磁同步电机的调速系统受到干扰,无法正常测量位置和转速等信息,这已成为永磁同步电机进一步应用的瓶颈,因此,加强永磁同步电机控制技术的研究迫切需要,首先分析国内外研究现状,然后建立数学模型,通过不同控制策略下仿真比较,最终得出改进后评估结果。

Numerical modeling of DPSK pressure signals and their transmission characteristics in mud channels

A numerical model and transmission characteristic analysis of DPSK （differential phase shift keying） pressure signals in mud channels is introduced. With the control logic analysis of the rotary valve mud telemetry, a logical control signal is built from a Gate function sequence according to the binary symbols of transmitted data and a phase-shift function is obtained by integrating the logical control signal. A mathematical model of the DPSK pressure signal is built based on principles of communications by modulating carrier phase with the phase-shift function and a numerical simulation of the pressure wave is implemented with the mathematical model by MATLAB programming. Considering drillpipe pressure and drilling fluid temperature profile along drillpipes, the drillpipe of a vertical well is divided into a number of sections. With water-based drilling fluids, the impacts of travel distance, carrier frequency, drillpipe size, and drilling fluids on the signal transmission were studied by signal transmission characteristic analysis for all the sections. Numerical calculation results indicate that the influences of the viscosity of drilling fluids and volume fraction of gas in drilling fluids on the DPSK signal transmission are more notable than the others and the signal will distort in waveform with differential attenuations of the signal frequent component.

Kinetic Models for Drying Techniques—Food Materials

Drying operations can help in reducing the moisture content of food materials for avoidance of microbial growth and deterioration, for shelf life elongation, to minimize packaging and improving storage for easy transportation. Thin-layer drying of materials is necessary to understand the fundamental transport mechanism and a prerequisite to successfully simulate or scale up the whole process for optimization or control of the operating conditions. Researchers have shown that to rely solely on experimental drying practices without mathematical considerations for the drying kinetics, can significantly affect the efficiency of dryers, increase the cost of production, and reduce the quality of the dried product. An effective model is necessary for the process design, optimization, energy integration and control;hence, the use of mathematical models in finding the drying kinetics of agricultural products is very important. The statistical criteria in use for the evaluation of the best model(s) has it that coefficient of determination (R2) has to be close to unity while the rest statistical measures will have values tending to zero. In this work, the essence of drying using thin-layer, general approaches to modeling for food drying mechanisms thin layer drying models and optimization of the drying processes have been discussed.

High Accuracy When Measuring Physical Constants: From the Perspective of the Information-Theoretic Approach

The practical value of high-precision models of the studied physical phenomena and technological processes is a decisive factor in science and technology. Currently, numerous methods and criteria for optimizing models have been proposed. However, the classification of measurement uncertainties due to the number of variables taken into account and their qualitative choice is still not given sufficient attention. The goal is to develop a new criterion suitable for any groups of experimental data obtained as a result of applying various measurement methods. Using the “information-theoretic method”, we propose two procedures for analyzing experimental results using a quantitative indicator to calculate the relative uncertainty of the measurement model, which, in turn, determines the legitimacy of the declared value of a physical constant. The presented procedure is used to analyze the results of measurements of the Boltzmann constant, Planck constant, Hubble constant and gravitational constant.

Statistical Data Analyses on Aircraft Accidents in Japan: Occurrences, Causes and Countermeasures

We investigate the major characteristics of the occurrences, causes of and counter measures for aircraft accidents in Japan. We apply statistical data analysis and mathematical modeling techniques to determine the relations among economic growth, aviation demand, the frequency of aircraft/helicopter accidents, the major characteristics of the occurrence intervals of accidents, and the number of fatalities due to accidents. The statistical model analysis suggests that the occurrence intervals of accidents and the number of fatalities can be explained by probability distributions such as the exponential distribution and the negative binomial distribution, respectively. We show that countermeasures for preventing accidents have been developed in every aircraft model, and thus they have contributed to a significant decrease in the number of accidents in the last three decades. We find that the major cause of accidents involving large airplanes has been weather, while accidents involving small airplanes and helicopters are mainly due to the pilot error. We also discover that, with respect to accidents mainly due to pilot error, there is a significant decrease in the number of accidents due to the aging of airplanes, whereas the number of accidents due to weather has barely declined. We further determine that accidents involving small and large airplanes mostly occur during takeoff and landing, whereas those involving helicopters are most likely to happen during flight. In order to decrease the number of accidents, i) enhancing safety and security by further developing technologies for aircraft, airports and air control radars, ii) establishing and improving training methods for crew including pilots, mechanics and traffic controllers, iii) tightening public rules, and iv) strengthening efforts made by individual aviation-related companies are absolutely necessary.

高炉炼铁大数据技术的发展现状与思考

因缺少废钢资源,我国钢铁生产将长期采用高炉-转炉长流程工艺,高炉操作至今仍主要依赖于人类专家的经验。从高炉数学模型、炼铁知识获取与应用、过程数据的获取等方面阐述了高炉炼铁大数据技术的发展现状,并提出了推进高炉炼铁大数据技术的思考。认为各种类型的数学模型是工业软件,在炼铁大数据技术中处于核心地位,但需要针对不同高炉的具体条件研究开发;对高炉内衬工作状态、炉缸内渣铁蓄积量、风口回旋区煤气焦炭,以及滴落带渣铁行为等的在线监测需要先进的检测技术;加强高炉下部焦炭降级行为的研究是高炉炼铁大数据技术发展的迫切需要。

高淀粉甘薯品种龙薯24号的肥料施加与栽培密度优化配置

为实现良种良法配套,筛选出高淀粉甘薯品种龙薯24号最佳栽培密度与肥料施加的优化配置组合,利用栽培密度、氮、磷、钾4因素5水平二次通用旋转组合设计,研究4个因素对龙薯24号产量的影响.结果表明,获得产量>2850 kg/667 m^(2)的农艺措施优化配置组合方案为栽培密度3913.5~4100.0株/667 m^(2),尿素施用量16.77~18.70 kg/667 m^(2),钙镁磷肥施用量34.22~38.32 kg/667 m^(2),硫酸钾施用量36.04~39.29 kg/667 m^(2).4个因素对产量的影响大小:施钾量>施氮量>栽培密度>施磷量.增施钾肥、适量施加氮肥、合理密植、控制磷肥用量对提高龙薯24号甘薯产量是有益的.

机器视觉技术在轨道交通中弯道测距的应用研究

实时检测列车之间的距离是保障轨道交通安全并提高列车运能的重要途径。位于弯轨上列车之间的距离测量是测距的难点。为了推算和优化列车在弯道处的实时测距计算式,文中提出了一种基于机器视觉在轨运行列车的弯道测距方法。该方法通过单目摄像机对轨道进行图像采集,利用OpenCV算法对采集到的图片进行处理和分析,采用神经网络方法拟合弯轨轨道线,实现动态提取所需要的轨道特征点。通过搭建数学模型可以推算和优化列车之间的测距计算式。实验结果表明,在时间间距为40~50 ms时,测距系统的整体误差率小于9.11%,测距与图像中获得到的其他信息可进行有效融合与集成,且能作为提高列车安全性能的重要判据之一。

原子荧光光谱法测定煤中砷的不确定度评定

煤中砷含量测量结果的准确性对控制煤炭质量、推进煤炭高效清洁利用及环保政策实施具有重要意义。使用原子荧光光谱法测定煤中砷含量,其测定结果的准确性受到样品处理、试剂溶液、测定条件等因素的影响。通过建立数学模型,从测量重复性、煤样称量、标准工作溶液浓度、标准曲线拟合、样品稀释过程及煤样处理等不确定度来源进行分析,计算原子荧光光谱法测定煤中砷的合成标准不确定度为0.050μg/g,样品砷含量测定结果为(17.8±1.0)μg/g,包含因子k=2。标准工作曲线拟合、测量重复性及煤样前处理引入的不确定度为各测量不确定度来源的最主要来源,在测定时应加强样品处理、试剂溶液、测定条件等影响因素的控制。

A MATHEMATICAL MODEL OF MIGRATION AND EXPANSION OF MEANDER LOOPS

This article presents a mathematical model of the plane evolution of alluvial meandering streams,through downstream migration and lateral expansion of meander loops.Under the conditions prevailing in natural streams,the channel centerlines follow sine-generated curves,with an assumed steady-state turbulent and subcritical flow,of large width-to-depth ratio（≥ 15,for example） and small Froude number（Fr ）.The plane deformation of the channel is caused by the action on the banks of the convective vertically-averaged meandering flow.The growth（migration and expansion） of meander loops is attributed to the regime-trend.The computational results of the model show that the obtained migration and expansion patterns of the meander loops are in good agreement with those of observations and measurements in similar meandering streams.