Separation of Comprehensive Geometrical Errors of a 3-DOF Parallel Manipulator Based on Jacobian Matrix and Its Sensitivity Analysis with Monte-Carlo Method

Parallel kinematic machines （PKMs） have the advantages of a compact structure,high stiffness,a low moving inertia,and a high load/weight ratio.PKMs have been intensively studied since the 1980s,and are still attracting much attention.Compared with extensive researches focus on their type/dimensional synthesis,kinematic/dynamic analyses,the error modeling and separation issues in PKMs are not studied adequately,which is one of the most important obstacles in its commercial applications widely.Taking a 3-PRS parallel manipulator as an example,this paper presents a separation method of source errors for 3-DOF parallel manipulator into the compensable and non-compensable errors effectively.The kinematic analysis of 3-PRS parallel manipulator leads to its six-dimension Jacobian matrix,which can be mapped into the Jacobian matrix of actuations and constraints,and then the compensable and non-compensable errors can be separated accordingly.The compensable errors can be compensated by the kinematic calibration,while the non-compensable errors may be adjusted by the manufacturing and assembling process.Followed by the influence of the latter,i.e.,the non-compensable errors,on the pose error of the moving platform through the sensitivity analysis with the aid of the Monte-Carlo method,meanwhile,the configurations of the manipulator are sought as the pose errors of the moving platform approaching their maximum.The compensable and non-compensable errors in limited-DOF parallel manipulators can be separated effectively by means of the Jacobian matrix of actuations and constraints,providing designers with an informative guideline to taking proper measures for enhancing the pose accuracy via component tolerancing and/or kinematic calibration,which can lay the foundation for the error distinguishment and compensation.

Matrix description of differential relations of moment functions in structural reliability sensitivity analysis

In a structural system reliability analysis that lacks probabilistic information, calculating the numerical characteristics of the state functions, especially the first four moments of the state functions, is necessary. Based on that, the structural system reliability is analyzed with a fourth-order moment method. The reliability sensitivity is required to conduct the differential operation of the numerical characteristic functions. A reliability sensitivity analysis formula is then derived in combination with the relation of the differential operation. Based on the matrix theory and Kronecker algebra, this paper systematically derives a matrix expression of the first four moments of the state functions, and establishes the matrix relation between the first four moments of the state functions and those of the basic random variables. On this basis, a differential operation formula of the first four moments of the state functions is further derived against the first four moments of the basic random variables. The vector relation between the state functions and the multidimensional basic random variables is described by means of the matrix operation to extend the operation method. Finally, a concise and intuitive formula is obtained to explore the inherent essential relation between the numerical characteristics of the state functions and those of the basic random variables, leading to a universal equation for the two kinds of numerical characteristics.

Effect of stress sensitivity on displacement efficiency in CO_2 flooding for fractured low permeability reservoirs

Carbon dioxide flooding is an effective means of enhanced oil recovery for low permeability reservoirs. If fractures are present in the reservoir, CO2 may flow along the fractures, resulting in low gas displacement efficiency. Reservoir pore pressure will fluctuate to some extent during a CO2 flood, causing a change in effective confining pressure. The result is rock deformation and a reduction in permeability with the reduction in fracture permeability, causing increased flow resistance in the fracture space. Simultaneously, gas cross flowing along the fractures is partially restrained. In this work, the effect of stress changes on permeability was studied through a series of flow experiments. The change in the flowrate distribution in a matrix block and contained fracture with an increase in effective pressure were analyzed. The results lead to an implicit comparison which shows that permeability of fractured core decreases sharply with an increase in effective confining pressure. The fracture flowrate ratio declines and the matrix flowrate ratio increases. Fracture flow will partially divert to the matrix block with the increase in effective confining pressure, improving gas displacement efficiency.

Parameters Sensitivity Characteristics of Highly Integrated Valve-Controlled Cylinder Force Control System

Nowadays, a highly integrated valve?controlled cylinder(HIVC) is applied to drive the joints of legged robots. Although the adoption of HIVC has resulted in high?performance robot control, the hydraulic force system still has problems, such as strong nonlinearity, and time?varying parameters. This makes HIVC force control very diffcult and complex. How to improve the control performance of the HIVC force control system and find the influence rule of the system parameters on the control performance is very significant. Firstly, the mathematical model of HIVC force control system is established. Then the mathematical expression for parameter sensitivity matrix is obtained by applying matrix sensitivity analysis(PSM). Then, aimed at the sinusoidal response under(three factors and three levels) working conditions, the simulation and the experiment are conducted. While the error between the simulation and experiment can’t be avoided. Therefore, combined with the range analysis, the error in the two performance indexes of sinusoidal response under the whole working condition is analyzed. Besides, the sensitivity variation pattern for each system parameter under the whole working condition is figured out. Then the two sensitivity indexes for the three system parameters, which are supply pressure, proportional gain and initial displacement of piston, are proved experimentally. The proposed method significantly reveals the sensitivity characteristics of HIVC force control system, which can make the contribution to improve the control performance.

Acoustic design sensitivity analysis of structural sound radiation

This paper presents an acoustic design sensitivity(ADS)analysis on sound radiation of structures by using the boundary element method(BEM).We calculated the velocity distribution of the thin plate by analytical method and the surface sound pressure by Rayleigh integral,and expressed the sound radiation power of the structure in a positive definite quadratic form of the Hermitian with an impedance matrix.The ADS analysis of the plate was thus translated into the analysis of structure dynamic sensitivity and ...

Novel sensitivity analysis method and dynamics optimization for multiple launch rocket systems

This study establishes the launch dynamics method,sensitivity analysis method,and multiobjective dynamic optimization method for the dynamic simulation analysis of the multiple launch rocket system(MLRS)based on the Riccati transfer matrix method for multibody systems(RMSTMM),direct differentiation method(DDM),and genetic algorithm(GA),respectively.Results show that simulation results of the dynamic response agree well with test results.The sensitivity analysis method is highly programming,the matrix order is low,and the calculation time is much shorter than that of the Lagrange method.With the increase of system complexity,the advantage of a high computing speed becomes more evident.Structural parameters that have the greatest influence on the dynamic response include the connection stiffness between the pitching body and the rotating body,the connection stiffness between the rotating body and the vehicle body,and the connection stiffnesses among 14^(#),16^(#),and 17^(#)wheels and the ground,which are the optimization design variables.After optimization,angular velocity variances of the pitching body in the revolving and pitching directions are reduced by 97.84%and 95.22%,respectively.

Continuous Deformation Monitoring by Polymermatrix Carbon Fiber Sensitive Layer

Composite made of short-cut carbon fiber mat and vinyl ester resin was observed to be an effective sensor for tensile strain up to 6 000με. Based on its strain sensitivity, a skin-like sensitive layer which can continuously cover the structural surface to sense strain in large area was developed. The sensitive layer was applied to continuously monitor the deformation of a simply supported beam. The result indicates that the fractional change in electrical resistance of the sensitive layer reversibly reflects the beam deformation in each section and describes the distribution of the average strain of the beam. The effect of temperature change on the monitoring was studied by monitoring tests conducted at different temperatures ranging from 20 to 80 ℃, which reveals temperature sensitivity in the sensitive layer and the temperature dependence of the piezoresistive behavior when the temperature exceeds 50 ℃. By the application of differential conaection principle, a method for temperature compensation was established and the gauge factor for the monitoring was dramatically increased. This method was verified experimentally.

Dynamic Shafting Alignment Algorithms Considering Sensitivity Analysis and Its Application

A method for dynamic alignment calculation of a large turbogenerator shafting is proposed. The method can analyze bearing load and bearing load sensitivity. Shafting alignment is made up of two parts:static alignment and dynamic alignment. Static alignment forms the basis of dynamic alignment, its mathematical model is deduced by transfer matrix method, the shafting static characteristic parameters under specific alignment installation requirements were obtained afterwards. Based on superposition method, bearing sensitivity analysis is performed to find the impact of slight bearing elevation change of the static alignment result. Above static alignment, dynamic shafting alignment considers the internal geometry of bearing under rotating state, static Reynolds equation is solved by the finite difference method and the relative position relationship of the center of journal and bearing are obtained. For static characteristic parameters calculated by static alignment and bearing sensitivity analysis, the calculation accuracy is verified by finite element software. The alignment model and codes in this paper can be a tool for the installation and safety analysis of large-scale shafting with three-point or four-point supports.

DESIGN SENSITIVITY ANALYSIS OF ROTATING MACHINERY BY MODAL SYNTHESIS METHOD

A new method which is a combination of sensitivity analysis and modal synthesis technique was applied to the simple calculation of design sensitivities of the dynamic characteristics of substructurally combined rotating systems. In this paper the free interface mode method was introduced as a basic tool for the modal synthesis technique. As an example, the sensitivities of the critical speeds of a high-specd winding mechanism on textile machine with respect to design modifications were obtained by the new method introduced in this paper and compared with the values obtained by using another method.

A Reasonable Approach for the Development of Shale Gas Wells with Consideration of the Stress Sensitivity

High-pressure deep shale gas reservoirs are usually highly stress-sensitive.When the reasonable production mode of shale gas well is built,the impact of strong stress sensitivity should be fully considered.First,this study calculated the relationship between permeability and formation pressure under different elastic modulus based on the shale lithology of Long Ma Xi formation in Sichuan Basin by testing and analysing the mechanical parameters of the rock.According to numerical simulation result,when the elastic modulus exceeds 14.0 GPa,the stress sensitivity of the matrix will slight affect the cumulative gas production of shale gas.Second,the changing relation between fracture conductivity and permeability with fracture pressure and the time of pressure acts were experimentally studied.The numerical simulation result suggested that the 30-year cumulative gas production considering the stress sensitivity was reduced by 13.5%compared with the 30-year cumulative gas production without considering the stress sensitivity.Finally,the production of different production modes under different stress sensitive characteristics was predicted using numerical simulation method.When the matrix and fractures are fixed with a same stress-sensitive curve,the initial production allocation will not significantly impact the cumulative gas production.When the fractured fractures are subjected to a varying stress sensitive curve,the lower production allocation will result in higher post-production and cumulative gas production.

The Application of Sensitivity Analysis on Comprehensive Transportation Evaluation

Comprehensive transportation evaluation objects using multi-objective decision method is a process of choosing the best one from a few objects through calculating, analyzing, and comparing the index system. The result may be different because of the difference of the index weight and index value. Therefore, sensitivity analysis should be one of the necessary parts of the decision-making. It is desired to give the index with higher sensitivity and its varying scope to control the index strictly during the execution process. This paper derives transfer index weight, which changes the rank evaluation order of the projects. Meanwhile, a simple, effective and practical method based on sensitivity district and sensitivity matrix is proposed for the sensitivity analysis of decision-making. As an example, the index sensitivity in decision-making of some provinces comprehensive transportation objects, and their influence on the final decision are discussed.

Damage Identification under Incomplete Mode Shape Data Using Optimization Technique Based on Generalized Flexibility Matrix

A generalized flexibility–based objective function utilized for structure damage identification is constructed for solving the constrained nonlinear least squares optimized problem. To begin with, the generalized flexibility matrix (GFM) proposed to solve the damage identification problem is recalled and a modal expansion method is introduced. Next, the objective function for iterative optimization process based on the GFM is formulated, and the Trust-Region algorithm is utilized to obtain the solution of the optimization problem for multiple damage cases. And then for computing the objective function gradient, the sensitivity analysis regarding design variables is derived. In addition, due to the spatial incompleteness, the influence of stiffness reduction and incomplete modal measurement data is discussed by means of two numerical examples with several damage cases. Finally, based on the computational results, it is evident that the presented approach provides good validity and reliability for the large and complicated engineering structures.

高洁净度超光滑非球面的自动化干涉检测方法

为了实现应用于高能激光等领域对表面洁净度有着极高要求的超光滑非球面检测,排除检测人员带来的洁净度与空气扰动的影响,研究了高洁净度超光滑非球面的自动化干涉检测方法。通过建立补偿干涉法非球面失调量与波前像差之间的灵敏度矩阵,实现利用波前像差求解被测非球面失调量。以理想干涉系统的离焦、彗差与像散为优化目标,进行反馈控制,实现被测非球面的自动化调整,进而实现高洁净度超光滑非球面的自动化干涉检测。实验结果表明,在干涉图可测范围内,利用灵敏度矩阵通过几步迭代即可实现非球面失调量的收敛。结合Stewart六自由度调整台,分别实现2μm精度的平移误差调整、2"精度的光轴自动化对准,最终完成被测非球面的精密调整,实现高洁净度超光滑非球面的自动化干涉检测。采用灵敏度矩阵与六自由度调整的非球面自动化干涉检测方法可实现被测非球面失调量的快速求解与自动调整,降低人员和环境带来的扰动影响,提高了非球面的检测速度,并实现了高洁净度超光滑非球面的自动化干涉检测。

协方差驱动随机子空间辨识的参数敏感性分析

协方差驱动随机子空间辨识(Covariance-driven Stochastic Subspace Identification,SSI-cov)是近年来发展较为成熟的工作模态分析方法。针对其识别精度和效率对参数设置具有较高敏感性的问题,基于敏感性分析方法,利用奇异熵增量跳跃点明显程度、频率平均识别误差、阻尼比总变异系数、振型平均模态置信因子、运行时间5种评价指标以及稳定图,通过一经典五自由度层模型仿真算例,研究Toeplitz矩阵行块数、采样频率、数据长度对SSI-cov识别结果的影响规律。并给出既能满足精度要求又可控制程序运行时间的参数建议取值范围。最后,通过一缩尺三层框架模型在白噪声激励下实测数据对提出的根据SSI-cov改进参数设置进行验证,结果表明提出的各参数建议取值范围均较为合理。

基于L_(2)灵敏度最小化的数字滤波器状态空间实现稀疏化方法

为解决传统数字滤波器在有限精度实现时因有限字长(Finite Word Length,FWL)效应导致滤波器性能下降的问题,提出一种L_(2)灵敏度最小化的数字滤波器状态空间实现稀疏化方法.推导前向差分算子数字滤波器结构传输函数及其等效状态空间实现,根据可控及可观格莱姆矩阵得到基于相似变换矩阵的L_(2)灵敏度表达式,并进行稀疏化校准,将L_(2)灵敏度最小化问题转换为凸函数求最值问题,求导得到L_(2)灵敏度最小化表达式,代回即得前向差分算子数字滤波器的稀疏化状态空间实现.仿真结果表明,所提方法设计的数字滤波器具有更好的抗FWL效应.

直纹面面齿轮共轭小齿轮的滚齿加工研究

针对直纹面面齿轮与圆柱齿轮不满足共轭关系而限制其在小传动比应用场合的情况,提出与直纹面面齿轮共轭的小齿轮及其滚齿加工方法。首先建立了直纹面面齿轮及其共轭小齿轮的齿面方程,获得共轭小齿轮相比圆柱齿轮的齿面偏差形貌;随后推导了阿基米德齿轮滚刀的齿面方程,并根据滚齿加工运动坐标系和啮合原理建立了圆柱齿轮的数学模型;在滚齿加工圆柱齿轮的运动基础上,通过增加滚刀的径向移动和工件的附加转动使滚刀切削刃逼近共轭齿面,附加运动由泰勒多项式表示,通过建立敏感矩阵方程并采用奇异值分解法迭代求解方程获得附加数控运动多项式系数,最后获得数控加工齿面;为评价直纹面面齿轮副的传动性能,进行了齿面承载接触分析,并与传统面齿轮-圆柱齿轮副进行了对比。研究结果表明:相同参数下,直纹面面齿轮副与传统面齿轮副的承载性能基本相同,完全能够代替传统面齿轮副传动;数值算例和仿真加工对该方法的验证表明,其数值算例误差不超过1μm,仿真结果误差不超过6μm,证明了该方法的可行性和准确性。

基于有限元仿真的ECT感兴趣区域高分辨率图像重建

感兴趣区域的高分辨率图像重建是电容层析成像(electrical capacitance tomography,ECT)技术的研究热点之一。均匀电极分布的ECT模型仅在重建场域的边界位置具有较高的灵敏度系数,不适用于感兴趣区域成像。为改善感兴趣区域中的灵敏度分布,提高图像分辨率,提出了一种基于有限元仿真ECT感兴趣区域高分辨率图像重建方法,根据保角变换理论优化电极分布。进行了仿真实验,将均匀电极和优化电极分布的灵敏度矩阵代入Tikhonov算法、Landweber算法和ART算法,重建结果表明上述方法可有效提高感兴趣区域的图像重建精度。

基于宽频激励的平面电磁层析成像方法

为了实现对高低电导率材料的检测与成像,提出了一种基于宽频激励的平面电磁层析成像方法。根据线圈的电磁特性及实验测试结果,探讨了平面线圈阵列的优化方法。通过有限元仿真模型,采用场量提取法获取灵敏度矩阵,并针对灵敏度矩阵的均匀性问题提出了改进方法,提高了图像重建质量。通过仿真模型评估了不同电导率物体的图像重建质量,仿真结果证明了提出的平面电磁层析成像方法可以实现对高低电导率材料的成像。搭建了基于宽频激励的平面电磁层析成像实验系统,并对多种不同电导率物体进行了成像实验。实验结果表明,重建图像平均相关系数为0.77,平均定位误差为4.46 mm。

高分辨率磁共振参数联合血清MMP9、hs-CRP检测预测大脑中动脉粥样硬化性狭窄病人发生急性卒中的价值

目的:分析高分辨率磁共振(HRMRI)参数检测联合血清MMP9、hs-CRP指标对大脑中动脉粥样硬化性狭窄病人急性卒中发生的预测价值。方法:选取183例大脑中动脉粥样硬化性狭窄病人,根据住院期间是否发生急性卒中将其分为急性卒中组89例和无急性卒中组94例。分析狭窄程度及血清MMP9、hs-CRP水平预测大脑中动脉粥样硬化性狭窄病人急性卒中的价值。结果:急性卒中组易损斑块、狭窄程度、Essen卒中风险评分(ESRS)、血清MMP9、hs-CRP水平均高于无急性卒中组(P<0.05);狭窄程度及血清MMP9、hs-CRP水平预测大脑中动脉粥样硬化性狭窄病人发生急性卒中的AUC分别为0.886、0.857、0.634;三者联合预测的AUC为0.923。结论:血清MMP9、hs-CRP联合HRMRI参数检测可提高了评估急性卒中预测的准确性。

面向设备性能退化监测的分步参数估计策略

为通过预防性定期维护提升化工装置的精细化管理水平,探讨了关键设备的在线性能监测原理,针对设备性能参数可估计性差的问题,提出了一种基于机理模型分析设备性能退变的分步参数估计策略,根据灵敏度分析确定参数处理规则。首先以工业装置的严格机理模型为基础给出在线的粗粒度模型候选项,以历史数据拟合误差最小为目标完成初步参数估计,给出最优模型和各参数初值。然后基于灵敏度分析矩阵特征给模型参数排序,以表征性能退变的时变参数为界,前后不同顺位的定常参数采用不同策略依次处理。最后以滑动时间窗方式估计时变参数,实现设备性能监测。以反应釜夹套换热器的传热性能监测为例,按照分步策略获得设备性能参数的退变,剥离操作变量的影响,结果与工厂操作周期符合。表示该策略可以用于设备性能监测。