Inverse problems in measurement

The aim of a measurement procedure is to determine an input value from an output value and information about the measuring instrument. These are known in mathematical terms as inverse problems and this paper surveys the main methods of solving them. Practical examples, are given to show that the different methods are effective.     

基于MATLAB统计分析加工误差的零件质量控制

机械产品加工的工艺过程是一个复杂的系统工程,工件的加工误差是许多随机因素共同作用的结果.应用数理统计方法对加工过程中工件的尺寸误差进行了诊断分析,确定了一批工件加工误差的总体规律,找出了在工艺上控制误差的措施和解决问题的途径.可利用MATLAB软件在数学计算中的优势,结合机械加工中测量的数据,对数据进行高效和可靠的处理,绘制出直方图等可视化的图表,帮助工艺人员对误差产生的原因进行便捷和高效的分析,并运用适当的方法减少误差,提高加工精度.     

具有区间参数的不确定结构静力区间分析的一种算法

将结构系统中的不确定性参数用区间数来表示,用有限元法建立静力区间线性方程组。对该方程组的求解提出了一种区间逐步离散的方法。此方法通过令独立的不确定性参数取区间内的离散值,将区间线性方程组的求解转化为相应的确定性问题,再搜索各方程解中的最大最小值得到每个区间分量的边界。先用数学算例对该算法的正确性和有效性进行了验证,然后应用于静力区间分析的工程算例,并与其它算法进行了比较。计算结果表明该算法的计算效率和准确性较高。     

计算运动学中的数学方法

This paper summarizes several important mathematical methodologies appeared in modern computational kinematics. The developing history of these mathematical methods is depicted in classification threads together with time threads. Some trends of these mathematical methods applied in computational kinematics are pointed out. The paper can serve as a basic reference on choosing mathematical methods for solving complex kinematics problems.     

Excel在光学实验数据处理中的应用

回归分析是一类数学模型,其研究对象是一个随机变量同一个或多个非随机变量的关系问题,在提出一元和多元线性回归的基础上,通过比较最小二乘法解法和Excel函数解法,指出Excel函数解法可以简化复杂的数学运算,并配以图表,给求解过程带来方便.     

Feature-Enhancing Inverse Methods for Limited-View Tomographic Imaging Problems

In this paper we overview current efforts in the development of inverse methods which directly extract target-relevant features from a limited data set. Such tomographic imaging problems arise in a wide range of fields making use of a number of different sensing modalities. Drawing these problem areas together is the similarity in the underlying physics governing the relationship between that which is sought and the data collected by the sensors. After presenting this physical model, we explore its use in two classes of feature-based inverse methods. Microlocal techniques are shown to provide a natural mathematical framework for processing synthetic aperture radar data in a manner that recovers the edges in the resulting image. For problems of diffusive imaging, we describe our recent efforts in parametric, shape-based techniques for directly estimating the geometric structure of an anomalous region located against a perhaps partially-known background.     

Identifying and quantifying structural nonlinearities in engineering applications from measured frequency response functions

Engineering structures seldom behave linearly and, as a result, linearity checks are common practice in the testing of critical structures exposed to dynamic loading to define the boundary of validity of the linear regime. However, in large scale industrial applications, there is no general methodology for dynamicists to extract nonlinear parameters from measured vibration data so that these can be then included in the associated numerical models. In this paper, a simple method based on the information contained in the frequency response function (FRF) properties of a structure is studied. This technique falls within the category of single-degree-of-freedom (SDOF) modal analysis methods. The principle upon which it is based is effectively a linearisation whereby it is assumed that at given amplitude of displacement response the system responds at the same frequency as the excitation and that stiffness and damping are constants. In so doing, by extracting this information at different amplitudes of vibration response, it is possible to estimate the amplitude-dependent ‘natural’ frequency and modal loss factor. Because of its mathematical simplicity and practical implementation during standard vibration testing, this method is particularly suitable for practical applications. In this paper, the method is illustrated and new analyses are carried out to validate its performance on numerical simulations before applying it to data measured on a complex aerospace test structure as well as a full-scale helicopter.     

The application of the automatic search for visually similar geological layers in a borehole in introscopic camera recordings

The paper discusses the opportunities for obtaining valuable knowledge on the basis of video recordings from introscopic cameras, used to investigate mining boreholes. It also presents an original approach to the task of building a system, which would facilitate the process of searching for visually similar geological structures, and which would constitute an alternative to time-consuming manual profiling. The analysis of measurements performed with an introscopic camera is based on a feature space defined by the Authors, and uses the methods of mathematical morphology for processing video sequences, as well as data analysis for the decision-making process. As a result of the research, it was established that the methods of image processing and data analysis are an effective tool when it comes to automate the decision-making process with regards to the determination of the visual similarity of geological layers which make up a given, investigated area of a borehole. The methods in question yield a high percentage of correct decisions.     

函数展开法及高分子材料胶层的应力分析

以函数展开法并运用虚余功原理完成数学模型的建立过程,然后通过计算机运算指出高分子胶粘剂的一些重要使用性质－其在使用中所具有的力学性能,如应力、强度等。文中给出了计算实例,并得到了更合理的结果。     

Phenomenological and algorithmic methods for the solution of inverse problems of electromagnetic testing

Modern methods for the solution of inverse problems of nondestructive testing are described. The discussion is mainly focused on the methods based on a mathematical model of the respective physical phenomenon (so-called phenomenological methods) and the methods based on the algorithms for the analysis of digital signals (so-called algorithmic methods). The phenomenological methods involving a mathematical model assume that the configuration of the flaws in a tested specimen is varied until the norm of the mismatch between the model solution and the experimentally obtained signal is minimized. A good result is only guaranteed if the physics of the phenomenon in the model is close to reality. In algorithmic methods, the inversion procedure applied to experimental data is considered as an image-recognition problem. In this case, the signal is identified as a representative of the classes associated with known types of flaws. The classification algorithms, which are most frequently used for electromagnetic testing, are developed through identification of diagnostic signatures. This approach assumes the use of an artificial neural network trained with the signals from a predefined database that corresponds to a broad variety of flaws.     

多元统计分析在产品设计要素分析中的应用

研究多元统计分析的理论,利用感性工学的方法,建立适用于大多数产品的数学模型,为产品设计要素分析提供依据.使用系统聚类分析法对相近感性意象的产品图片进行筛选,选出具有典型感性意象的图片;利用主成份分析法和聚类法将描述产品图片的感性语义进行分类、合并,获得正式调研的产品语义.以实例分析,证实是一种比较适用可行的方法.     

Universal mechanism modeling method in virtual assembly environment

Motion simulation and performance analysis of mechanism are important methods for analyzing assembly quality after finishing assembly simulation in virtual assembly environment. However, most simulation systems have no function of mechanism motion simulation due to the randomicity of mechanism and lack of universal mechanism modeling method. In order to realize the simulation of any mechanism after finishing assembly simulation in a virtual environment, a new universal mechanism modeling method is presented. Two main models are contained in the mechanism model: information model and mathematical model. Firstly, the information model of mechanism is proposed to describe the data structure of mechanism which contains bottom geometry data, information of constraint, link, kinematic pair and physical data. Because the object of mechanism simulation is the assembly, which is assembled during the process of assembly simulation, the information of mechanism can be obtained automatically through mechanism automatic search method. Secondly, mathematical model of mechanism is presented. The mathematical model uses mathematical method to express the mechanism. In order to realize the automatic expression of any random mechanism, basic constraint library is presented, consequently random mechanism can be described based on the basic constraint library. Finally, two examples are introduced to validate the method in the prototype system named VAPP(Virtual Assembly Process Planning). The validation result shows that the mechanism modeling provides a universal modeling method for mechanism motion simulation in virtual assembly environment. This research has important effect on the development both of mechanism motion simulation and virtual assembly.     

BASIC THEORY AND METHOD OF WELDING ARC SPECTRAL INFORMATION

Arc spectral information is a rising information source which can solve many problems thatcan not be done with arc electric information and other arc information. It is of important signficanceto develop automatic control technique of welding process. The basic theory and methods on it play animportant role in expounding and applying arc spectral information. Using concemed equation inplasma physics and spectrum theory a system of equations including 12 equations which serve as basictheory of arc spectral information is set up. Through analyzing of the 12 equations, a basic view thatarc spectral information is the reflection of arc state and state variation, and is the most abundant in-formation resource reflecting welding arc process is drawn. Furthermore, based on the basic theory thebasic methods of test and control of arc spectral information and points out some applications of it arediscussesed.     

分布式机械CAD系统中确定性信息处理方法

为解决基于网络的机械CAD系统中输入输出数据、表格、图形与图像、公式、线图等确定性信息的处理问题,通过数据分析,应用了网络数据库存储管理计算数据、数表、图形和图像信息;应用了正则表达式方法编制网络工程计算器;此外,应用了插值、多项式拟合、数学形态学和人工神经网络等方法对设计线图进行优化处理,以提高CAD系统取值的精确性。     

A comparison of some methods for measuring the size distribution of two-dimensionally clustered latex particles in TEM images using mathematical morphology

The particle size distribution of polymer latexes of, for example, polybutadiene can be measured on transmission electron micrographs using image analysis methods. By taking suitable measures in preparing the sample it can be ensured that the image only consists of projections of two-dimensional clusters of adhering latex spheres. For the deagglomeration of these clusters a number of methods based on mathematical morphology are discussed. Speed and accuracy of the methods were tested on a personal-computer-based image analysis system and compared to manual measurements. Repeated openings or erosions applied to a binary image are relatively fast global methods with a low accuracy due to the fact that particle diameters are measured in whole numbers of pixels; only the horizontal diameters of rectangular pixels are measured. With an iterative method the individual components of the clusters are found by repeated conditional thickening of the erosion kernels. The method is accurate but very slow due to the large number of processing steps. The watershed method as applied to the original grey-scale transmission electron micrograph makes use of the sharp local maxima which arise at the interface of the projection of two adhering particles. This method is as accurate as the iterative method, but about eight times as fast.     

Scale-invariant analysis of wear particle morphology—a preliminary study

The importance of wear particle characterization is continuously growing, as the need for prediction and monitoring of wear increases. Accurate analysis of wear particles can, however, be limited by problems associated with particle characterization, especially of the wear particles' surface morphology. Since the shape and surface topography of wear particles often exhibit a fractal nature, fractal (scale-invariant) methods are, therefore, used in their characterization. However, the methods used to date ignore the fact that all fractal objects can be described by a small set of mathematical rules; although finding those rules which describe a particular fractal image is a difficult problem. No general solution exists to date and this paper attempts to redress this problem. A new analysis method, ‘scale-invariant analysis’, which is based on a partitioned iterated function system (PIFS), is proposed for the characterization of wear particle morphology. PIFS is a collection of contractive affine transformations. Each affine transformation transforms one part of a wear particle image onto another part of the same image. PIFSs were constructed for both computer generated and SEM images of wear particles. Results obtained in this study clearly demonstrate that the morphology of wear particles can effectively be characterized using the PIFS method.     

Decomposition method of complex optimization model based on global sensitivity analysis

The current research of the decomposition methods of complex optimization model is mostly based on the principle of disciplines, problems or components. However, numerous coupling variables will appear among the sub-models decomposed, thereby make the efficiency of decomposed optimization low and the effect poor. Though some collaborative optimization methods are proposed to process the coupling variables, there lacks the original strategy planning to reduce the coupling degree among the decomposed sub-models when we start decomposing a complex optimization model. Therefore, this paper proposes a decomposition method based on the global sensitivity information. In this method, the complex optimization model is decomposed based on the principle of minimizing the sensitivity sum between the design functions and design variables among different sub-models. The design functions and design variables, which are sensitive to each other, will be assigned to the same sub-models as much as possible to reduce the impacts to other sub-models caused by the changing of coupling variables in one sub-model. Two different collaborative optimization models of a gear reducer are built up separately in the multidisciplinary design optimization software iSIGHT, the optimized results turned out that the decomposition method proposed in this paper has less analysis times and increases the computational efficiency by 29.6%. This new decomposition method is also successfully applied in the complex optimization problem of hydraulic excavator working devices, which shows the proposed research can reduce the mutual coupling degree between sub-models. This research proposes a decomposition method based on the global sensitivity information, which makes the linkages least among sub-models after decomposition, and provides reference for decomposing complex optimization models and has practical engineering significance.     

A system for experimental studies of the dynamics of the process of cutting metal

An information system is described that enables one to solve applied problems of the physical and mathematical simulation of the dynamic processes that occur during vibration cutting of metals. The development and transformation of two types of mathematical models that describe vibration cutting and clipping of the trail left and adequately reproduce the actually observed cutting process are presented. Experimental data on the dynamics of the cutting process may be used for identifying parameters of different mathematical models that describe the process of constrained oblique cutting and for calculating the stability and free vibrations of metal cutting machines for different production parameters.     

权重信息不完全的产品绿色度综合评价方法

针对现有的产品绿色度评价方法不能处理不完全权重信息的不足，提出基于数据包络分析理论的绿色度评价方法。该方法首先对评价指标进行规范化处理，使规范化后的数据越大越好；其次建立只有输出指标且含有偏好信息的DEA模型，最后，利用交叉效率，建立交叉效率矩阵，并以平均交叉效率作为产品绿色度的量化指标。实验结果表明，该方法不仅能够处理区间数、序关系等形式的不完全权重信息，也能够处理完全确定及完全不确定权重信息的绿色度评价问题，且具有较好的鲁棒性、可操作性。