Extended space method for parameter identifiability of DAE systems

Mathematical models of physical systems often have parameters that must be identified from physical data. This makes the analysis of the parameter identifiability of the given model system an essential prerequisite. Thus far, several methods have been proposed for analyzing the parameter identifiability of ordinary differential equation (ODE) systems. But, to the best of our knowledge, the parameter identifiability of differential algebraic equation (DAE) systems has scarcely been analyzed as a specific topic. Traditional differential algebraic (DA) methods developed for ODE systems are often applied directly on DAE systems. These methods, however, are not always applicable, e.g., when the prime ideal condition is not satisfied by a DAE system. In this paper, we propose a novel method to analyze the identifiability of DAE systems, based on the concept of space extension, through which the algebraic and differential variables can be decoupled. Furthermore, an inherent, low-dimensional, regular ODE system can be obtained, which is the external equivalent of the original DAE system. Subsequently, the differential algebraic (DA) method can then be used to analyze the identifiability of the low-dimension ODE system. Theoretical analysis is also presented for the proposed method. Two examples, including a simplified interaction model and an isothermal reactor system, are presented to illustrate the detailed steps and effectiveness of the proposed method.     

小型悬臂梁结构振动参数交互辨识方法

介绍了针对于小型悬臂梁结构振动参数辨识的交互方法,通过有限元计算结果和模态试验结果的相互修正,能减小传感器附加质量和有限元建模不准确对悬臂梁结构振动参数的辨识结果引入的误差,使得修正后的结果与结构实际振动参数更为接近.典型算例给出了方法的具体流程.     

DHEM: a deep heat energy method for steady-state heat conduction problems

Journal of Mechanical Science and Technology - Based on the deep energy method recently brought forward to handle linear-elastic or hyper-elastic finite deformation problems in solid mechanics, in...     

Estimation of heat fluxes during high-speed drilling

Heat fluxes on each cutting edge of a carbide double cutting drill are estimated during a high-speed machining process from temperature measurements in the drill tool and a direct model that has been established using the non integer system identification approach. A single experiment is required in order to characterize the transient thermal behavior of the tool. The non integer system identification method is based on the recursive linear least square algorithm. The inverse method is based on the constant function specification approach. Results obtained during machining lead to predict the tool wear and possible tool positioning defect.     

Kinematic modeling and parameter identification of a new circumferential drilling machine for aircraft assembly

Automated fastener hole drilling is a key technology for low-cost and high-quality assembly of aircrafts. In this paper, a new circumferential drilling machine for fuselage assembly of large aircrafts is introduced. In order to meet the required position accuracy of drilled holes, this paper focuses on the kinematic calibration of the machine in order to improve its positioning accuracy. A modeling strategy, which combines the Denavit-Hartenberg (D-H) method and a modified version of the Hayati-Mirmirani (H-M) method, is proposed to deal with the special kinematic structure of the arc-base drilling unit of the machine. Main issues in kinematic parameter identification such as definition of objective function, calibration data selection, acquisition of initial values, and setting of convergence criteria are also discussed. Experiments of repeatability testing and kinematic calibration have been performed, and the results show that the positioning accuracy of the arc-base drilling unit is comparable to its repeatability after calibration. This suggests that the proposed kinematic calibration method is effective. Actual drilling tests have been performed on a simulated aircraft fuselage after implementing the identified kinematic model in the machine’s control software. Position errors of drilled holes are within ±0.5 mm, which meets the requirement for fastener hole drilling in the fuselage assembly of large aircrafts.     

FEM-based prediction of workpiece transient temperature distribution and deformations during milling

In high-speed dry milling of thin-walled parts, the cutter-workpiece temperature rises asymptotically with cutting speed, causing excessive cutter tooth wear and workpiece thermal expansion, which in turn reduces the cutter life and produces dimensional and geometrical variabilities in the machined part. Therefore, a basic understanding of the thermal aspect of machining and the effecting parameters is essential for achieving better part quality with improved productivity. This paper presents a transient milling simulation model to assist manufacturing engineers in gaining in-depth understanding of the thermomechanical aspects of machining and their influence on resulted part quality. Based on the finite-element method approach, the model can predict transient temperature distributions and resulted elastic-plastic deformations induced during the milling of 2.5D prismatic parts comprising features like slots, steps, pockets, etc. The advantages of the proposed model over previous works are that it (1) performs feature-based machining simulation considering transient thermomechanical loading conditions; (2) allows modeling the effects of coolant on convective heat transfer rate; and (3) considers the nonlinear behavior of the workpiece due to its changing geometry, inelastic material properties, and flexible fixture–workpiece contacts. The prediction accuracy of the model was validated with experimental results obtained during the course of the research work. A good agreement between the numerical and experimental results was found for different test cases with varying part geometries and machining conditions.     

Nonlinear transient heat conduction analysis of hollow thick temperature-dependent 2D-FGM cylinders with finite length using numerical method

Nonlinear transient heat conduction analysis is developed for hollow thick temperature-dependent 2D-FGM cylinders subjected to transient non-uniform axisymmetric thermal loads. It is demonstrated here that the temperature-dependency in addition to the material properties variation in the 2D- FGM would lead to highly nonlinear governing equations. To do this, the graded finite element method is employed to model the structures and a quadratic Lagrange shape function has been used to improve the accuracy of the temperature distribution for the two-dimensional heat conduction analysis. Furthermore, time variation of the temperatures and the effects of material distribution variability in two radial and axial directions and the temperature-dependency of the material properties on the temperature are discussed in detail. It is assumed that the material, geometry and volume fraction distribution are axisymmetric but not uniform along the axial direction. According to the results, the variation of the material properties in two dimensions has significant effect on temperature distribution; therefore, it gives more designing flexibility benefits to the designers to implement this kind of material for the thermal barriers purposes.     

淬火过程换热系数反求法的有限元实现

在淬火过程的数值模拟中,换热系数的正确求解是工件温度场、应力/应变场模拟结果和实际相符的先决条件.分析换热系数反求法的数学模型,并采用有限元法实现该数学模型的求解.与有限差分求解法比较,用有限元方法求解的换热系数曲线连续、平滑,结果可靠,而且编程量小,用求得的换热系数计算试件中心的温度场变化曲线,计算结果和实测数据吻合.     

Parametric optimization for tumour identification: bioheat equation using ANOVA and the Taguchi method

Breast cancer is the number one killer disease among women. It is known that early detection of a tumour ensures better prognosis and higher survival rate. In this paper an intelligent, inexpensive and non-invasive diagnostic tool is developed for aiding breast cancer detection objectively. This tool is based on thermographic scanning of the breast surface in conjunction with numerical simulation of the breast using the bioheat equation. The medical applications of thermographic scanning make use of the skin temperature as an indication of an underlying pathological process. The thermal pattern over a breast tumour reflects the vascular reaction to the abnormality. Hence an abnormal temperature pattern may be an indicator of an underlying tumour. Seven important parameters are identified and analysis of variance (ANOVA) is performed using a 2n design (n = number of parameters, 7). The effect and importance of the various parameters are analysed. Based on the above 2(7) design, the Taguchi method is used to optimize the parameters in order to ensure the signal from the tumour maximized compared with the noise from the other factors. The model predicts that the ideal setting for capturing the signal from the tumour is when the patient is at basal metabolic activity with a correspondingly lower subcutaneous perfusion in a low temperature environment.     

Mechanism study of micro-electrical discharge drilling method during micro-dimpling

Journal of Mechanical Science and Technology - This paper reports the cutting mechanism in micro-electrical discharge drilling (uEDD) during a micro-dimpling process. A combination of fundamental...     

Adaptive finite element solution for the heat conduction with a moving heat source

We have demonstrated that some of the parabolic type problems encountered in such branches of engineering as heat conductions with a moving source can be analyzed successfully by means of the finite element method. Adapted mesh generation technique is implemented for solving heat transfer involving a moving heat source so that small elements can be used in areas of large time rates of change of temperature. It has been adjusted to steep gradients of the solution with respect to the relatively large time interval. A program has been developed for the case of two-dimensional triangular elements, and algorithm is possessed a number of usual advantages that made solutions very divergent. Numerical results have shown that the adaptive gridding scheme is effective in localizing oscillations due to the sharp gradients or discontinuities in the solution. Furthermore, the numerical results near the region of moving source from the present method are under and over estimated the solution of traditional finite element method by almost 3% respectively. The several examples are given to illustrate the validity and practicality of the method. The results of various sample solutions are evaluated and discussed.     

基于环境激励的结构模态参数识别方法

利用时域分析最小二乘复指数法(kast-Squares Complex Exponential,LSCE)推导出在脉冲响应下结构的模态参数,并利用ITD(Ibrahim Time Domain)法对随机振动响应的参数进行识别,为分析工作模态下结构的优化设计、损伤诊断和故障诊断打下基础.在充分研究了环境载荷对工程结构影响的基础上,重点分析了风载荷对大跨度工程结构的影响.利用有限元软件对空间桁架结构进行有限元工作模态分析,得出在环境载荷激励下的结构响应,进而利用参数识别方法得出模态参数,其结果与工程实际相符,证明了环境载荷处理的可行性和该理论体系的正确性.     

基于预测误差法的加速度传感器动态模型参数辨识

加速度传感器动态模型对研究与分析加速度传感器的动态特性与动态误差补偿具有重要作用。针对加速度传感器动态模型的参数辨识,提出了一种基于预测误差法的加速度传感器动态模型参数辨识方法,该方法将加速度传感器的状态空间模型转化为线性带外生输入的自回归滑动平均(ARMAX)模型,获得其最优一步预测输出的表达式,并通过求解加速度传感器最优一步预测输出极小化误差准则函数,实现加速度传感器动态模型参数的最优辨识。实验结果表明,该方法有效地实现了加速度传感器动态模型的参数辨识,所得加速度传感器动态模型具有较高的精度,能描述加速度传感器的动态特性。     

A bisection method for the milling of NURBS mapping projection curves by CNC machines

The concept of non-uniform rational B-spline (NURBS) mapping projection curves (NURBS-MPCs) is proposed in this work. A NURBS-MPC is a projection curve on a NURBS surface of a NURBS curve. The bisection method is used to interpolate NURBS-MPCs. Using an assigned chord, the interpolation of a NURBS-MPC can be obtained easily, and the milling precision of the NURBS-MPC can be controlled effectively. Based on the NURBS theory, the bisection method, and the parametric programming method, an online NURBS software package (NURBS-SP) for FANUC 0i-MB/MC/MD CNC system and an offline NURBS toolbox (NURBS-T) for Matlab have been developed. Using an example of a planar NURBS curve, a NURBS-MPC is created on a NURBS surface. The simulation and milling of the NURBS-MPC show that the bisection method is feasible and effective. The online NURBS-SP endows the NURBS interpolation function for those CNC systems only equipped with linear interpolation (G01) and circular interpolation (G02/G03) and extends the interpolation functions and machining capability of low-middle level three-axis milling machines. The interactive application of the NURBS-T and NURBS-SP can accomplish the design, simulation, and milling for NURBS-MPCs. This feature makes them to have broad application prospects in CNC machining industry.     

An emissivity-corrected method for the accurate radiometric measurement of transient surface temperatures during braking

The main difficulty encountered in brake disc infrared temperature measurements is the lack of knowledge of the disc surface emissivity, which is nonuniform and varies during braking. To provide information on the nonuniformity and variations of emissivity, brake disc surface temperatures were investigated by an original two-colour fibre optic pyrometer and an infrared camera. The first result is the measurements of the accurate surface temperature. Besides, it is shown that the local emissivity varies with friction due to modifications of surface properties. Thermal phenomena observed on the disc track are correlated with temporal changes of normal and tangential frictional forces.     

Voronoi based discrete least squares meshless method for heat conduction simulation in highly irregular geometries

A new technique is used in Discrete Least Square Meshfree(DLSM) method to remove the common existing deficiencies of meshfree methods in handling of the problems containing cracks or concave boundaries. An enhanced Discrete Least Squares Meshless method named as VDLSM(Voronoi based Discrete Least Squares Meshless) is developed in order to solve the steady-state heat conduction problem in irregular solid domains including concave boundaries or cracks. Existing meshless methods cannot estimate precisely the required unknowns in the vicinity of the above mentioned boundaries. Conducted researches are limited to domains with regular convex boundaries. To this end, the advantages of the Voronoi tessellation algorithm are implemented. The support domains of the sampling points are determined using a Voronoi tessellation algorithm. For the weight functions, a cubic spline polynomial is used based on a normalized distance variable which can provide a high degree of smoothness near those mentioned above discontinuities. Finally, Moving Least Squares(MLS) shape functions are constructed using a varitional method. This straight-forward scheme can properly estimate the unknowns(in this particular study, the temperatures at the nodal points) near and on the crack faces, crack tip or concave boundaries without need to extra backward corrective procedures, i.e. the iterative calculations for modifying the shape functions of the nodes located near or on these types of the complex boundaries. The accuracy and efficiency of the presented method are investigated by analyzing four particular examples. Obtained results from VDLSM are compared with the available analytical results or with the results of the well-known Finite Elements Method(FEM) when an analytical solution is not available. By comparisons, it is revealed that the proposed technique gives high accuracy for the solution of the steady-state heat conduction problems within cracked domains or domains with concave boundaries and at the same time possesses a high convergence rate which its accuracy is not sensitive to the arrangement of the nodal points. The novelty of this paper is the use of Voronoi concept in determining the weight functions used in the formulation of the MLS type shape functions.     

An innovational transfer alignment method based on parameter identification UKF for airborne distributed POS

Airborne distributed Position and Orientation System (POS) depends on transfer alignment to obtain high accuracy motion parameters of sub-systems by using accurate motion information of main system, including position, velocity and attitude. Complicated aircraft flexure will decrease the accuracy of transfer alignment. Usually, the flexure angle is idealized as Markov process with fixed parameters, while these parameters are unknown and time-varying in real application. Accordingly, the accuracy of state model and statistic characters of noise will be incorrect, which consequently increases the error of transfer alignment. To solve the mentioned problem, this paper proposes a parameter identification method and then combines it with UKF. As a result, transfer alignment based on parameter identification UKF (PIUKF) is designed, and verified by simulations and static experiment. The results show that transfer alignment method based on PIUKF improves the accuracy of sub-systems compared with those based on UKF and strong tracking UKF.     

Passive identification of heat equation coefficients with account for errors in estimating the state of the object and measuring system

This paper describes the problem of passive identification of heat equation coefficients with account for the noise of the behavior of the object dynamics model and for the noise of the measuring system model. The use of the finite difference method allowed for reducing the solution of partial differential equations to the solution of a system of linear finite-difference and algebraic equations described by models in the form of a state space. Presentation of the heat equation in form of such a model makes it possible to apply the Kalman filter algorithm for the reliable estimation of the behavior of the object under study.     

An approximate method for the study of large deformations of membranes

A method is described to give approximate solutions to problems concerned with the deformation of highly extensible, rubberlike membranes. This is based on a principle first described by Rayleigh, involving the minimization of the elastic strain energy of the membrane. The method, which enables rapid solution under a variety of boundary conditions, is applied to three typical problems with no known closed-form solutions, namely: the stretching of a clamped rubber sheet; the stretching of a rubber tube; and the axial movement of the inner ring of an annulus with respect to its outer periphery.     

An all-digital method for accurate measurements of mechanical deformations

In this paper, an experimental analysis method based on image treatment techniques for the quantitative evaluation of some polycrystal material deformations is presented. This method has been successfully developed for this purpose by adapting and developing algorithms suitable for the images under study. Details of the whole process as applied to a typical example are described and discussed.