梁结构裂纹参数的识别方法

以Bernoulli-Euler梁振动理论为基础,引入断裂力学中能量释放率的概念,得到承弯梁出现横向裂纹时其固有频率的变化与裂纹参数的简化表达式,讨论梁裂纹参数、几何参数对固有频率的影响。利用这一表达式,提出一种识别裂纹位置和深度的数值方法,最后,用含裂纹等截面悬臂梁的实验验证所提方法。结果表明,在固有频率误差较小的情况下,文中方法可给出梁结构中裂纹位置和深度,可为更精确的局部探伤指出探测范围。     

Model-free adaptive fractional order control of stable linear time-varying systems

This paper presents a new model-free adaptive fractional order control approach for linear time-varying systems. An online algorithm is proposed to determine some frequency characteristics using a selective filtering and to design a fractional PID controller based on the numerical optimization of the frequency-domain criterion. When the system parameters are time-varying, the controller is updated to keep the same desired performances. The main advantage of the proposed approach is that the controller design depends only on the measured input and output signals of the process. The effectiveness of the proposed method is assessed through a numerical example.     

层合薄膜电容式微加工超声换能器(CMUTs)谐振频率分析

电容式微加工超声换能器（Capacitive micromachined ultrasonic transducers,CMUTs）在3D超声成像、水下超声等领域具有重要应用价值。谐振频率决定着超声成像的分辨率,是CMUTs结构设计的重要参数之一。针对具有多层圆形薄膜的CMUTs结构,提出其薄膜结构和材料参数以及有效电极距离的等效方法,建立在直流偏置电压和交流电压共同作用下多层圆形薄膜的振动方程,并分别采用伽辽金法和能量等效法进行求解,获得多层薄膜CMUTs在偏置电压作用下的两类谐振频率解析式。基于有限元模型,利用数值解来验证谐振频率解析式的正确性,并开展参数化研究。结果显示,基于能量等效法的谐振频率解析式比基于伽辽金法的谐振频率解析式具有更高分析精度,适用于薄膜直径/厚度比在20~100范围内、空腔高度/薄膜厚度比不大于1的多层薄膜CMUTs的谐振频率分析;在从0 V到接近于塌陷电压的几乎整个偏置电压变化内,解析解与有限元仿真结果的相对误差小于5%。此外,利用所加工的具有三层薄膜的CMUTs芯片对谐振频率解析式进行试验验证,结果显示在不同偏置电压下谐振频率的试验测试值与理论分析值基本一致。因此,所提谐振频率的理论分析方法可广泛应用于多层薄膜CMUTs结构的设计与优化。     

An identification method for joint structural parameters using an FRF-based substructuring method and an optimization technique

A new method is proposed to identify the joint structural parameters of complex systems using a frequency response function (FRF)-based substructuring method and an optimization technique. The FRF method is used to estimate the joint parameters indirectly by minimizing the difference between the reference and calculated responses using a gradient-based optimization technique with analytical gradient information. To assess the robustness of the identification method with respect to noisy input data, FRFs contaminated by uniformly distributed random noise were tested in a numerical example. The effects of the random noise and the magnitude of the connection stiffness values on the accuracy of the method were investigated while identifying the joint parameters. When the FRFs were contaminated with random noise, the proposed procedure performed well when used to identify the stiffness values, but the accuracy of identification is deteriorative when used to identify the damping coefficients. The joint parameters of a real bolted structure were also identified by the proposed method. The results show that it can be applied successfully to real structures, and that a hybrid approach using both calculated and measured FRFs in the substructure model can enhance the quality of the identification results.     

Response sensitivity analysis of the dynamic milling process based on the numerical integration method

As one of the bases of gradient-based optimization algorithms, sensitivity analysis is usually required to calculate the derivatives of the system response with respect to the machining parameters. The most widely used approaches for sensitivity analysis are based on time-consuming numerical methods, such as finite difference methods. This paper presents a semi-analytical method for calculation of the sensitivity of the stability boundary in milling. After transforming the delay-differential equation with time-periodic coefficients governing the dynamic milling process into the integral form, the Floquet transition matrix is constructed by using the numerical integration method. Then, the analytical expressions of derivatives of the Floquet transition matrix with respect to the machining parameters are obtained. Thereafter, the classical analytical expression of the sensitivity of matrix eigenvalues is employed to calculate the sensitivity of the stability lobe diagram. The two-degree-of-freedom milling example illustrates the accuracy and efficiency of the proposed method. Compared with the existing methods, the unique merit of the proposed method is that it can be used for analytically computing the sensitivity of the stability boundary in milling, without employing any finite difference methods. Therefore, the high accuracy and high efficiency are both achieved. The proposed method can serve as an effective tool for machining parameter optimization and uncertainty analysis in high-speed milling.     

Analytical fractional PID controller design based on Bode’s ideal transfer function plus time delay

In this paper, a fractional order PID controller cascaded with a fractional filter is proposed for higher order processes. In this analytical design methodology, one or two reduced fractional orders plus time delay models are used to represent higher order system transfer functions. The controller parameters are determined so as to meet certain frequency domain specifications. A unity feedback reference model is employed where Bode’s ideal loop transfer function plus time delay of the fractional order model is placed in the forward path. The addition of this time delay provides the exact determination of frequency domain specifications if the system either intrinsically owns a time delay or a time delay is injected by its reduced order model. The proposed methodology is compared with two other related methodologies and it has been observed that the proposed controller performs much better than the others. Moreover, some empirical formulas for time domain characteristics of the reference model are numerically derived in terms of certain frequency domain specifications and time delay of the fractional reduced order model. The accuracy of these formulas is tested by simulations. The iso-damping, noise attenuation and load disturbance suppression performances of the proposed controller are also considered and compared with those of other related controllers.     

基于自运动控制的冗余度机器人运动学优化

基于自运动变量与雅可比矩阵零空间矢量的关系,提出了冗余度机器人自运动变量选取的新方法。基于线性化思想,建立了冗余度机器人运动学性能指标统一的表达式,并推导了性能指标的自运动变量解析式。利用非线性反馈,建立了基于自运动变量的优化控制系统,从而提出了冗余度机器人优化控制的新算法。该算法减少了系统的状态变量,从而简化了优化控制系统,比起以往的优化算法,如梯度投影法等,具有运算量小、优化能力强等优点,特别是在多冗余度机器人控制系统中具有很高的应用价值。利用计算机仿真证实了所提优化方法的可行性。     

Hybrid FE/ANN and LPR approach for the inverse identification of material parameters from cutting tests

Accuracy of numerical models based in finite elements (FE), extensively used for simulation of cutting processes, depends strongly on the identification of proper material parameters. Experimental identification of the constitutive law parameters for simulation of cutting processes involves unsolved problems such as the complex testing techniques or the difficulty to reproduce the stress triaxiality state during cutting. This work proposes a methodology for the inverse identification of the material parameters from cutting test. Two hybrid approaches are compared. One of them based on FE and artificial neural networks (ANN). The other one based on FE and local polynomial regression (LPR). Firstly, a FE model is validated with experimental data. Then, ANN and LPR are trained with FE simulations. Finally, the estimated ANN and LPR models are used for the inverse identification of material parameters. This identification is solved as an optimization problem. The FE/LPR approach shows good performance, outperforming the FE/ANN approach.     

On the prediction of side-wall wrinkling in sheet metal forming processes

Prediction and prevention of side-wall wrinkling are extremely important in the design of tooling and process parameters in sheet metal forming processes. The prediction methods can be broadly divided into two categories: an analytical approach and a numerical simulation using finite element method (FEM). In this paper, a modified energy approach utilizing energy equality and the effective dimensions of the region undergoing circumferential compression is proposed based on simplified flat or curved sheet models with approximate boundary conditions. The analytical model calculates the critical buckling stress as a function of material properties, geometry parameters and current in-plane stress ratio. Meanwhile, the sensitivities of various input parameters and integration methods of FEM models on the prediction of wrinkling phenomena are investigated. To validate our proposed method and to illustrate the sensitivity issue in the FEM simulation, comparisons with experimental results of the Yoshida buckling test, aluminum square cup forming and aluminum conical cup forming are presented. The results demonstrate excellent agreements between the proposed method and experiments. Our model provides a reliable and effective predictor for the onset of side-wall wrinkling in sheet metal forming processes.     

变频游梁式抽油系统运行参数的优化设计与性能仿真*

综合考虑电动机端电压频率的实时变化以及电动机负载扭矩波动对电动机瞬时转速的影响,建立了变频控制游梁式抽油系统曲柄运动规律、抽油杆柱纵向振动规律与系统动态参数的仿真模型。将抽汲参数、平衡装置参数、频率函数、电动机输出轴皮带轮转动惯量等系统运行参数作为优化设计变量,在保证油井产量不变、抽油机承载能力、抽油杆柱强度、平衡度和上下冲程时间分配等约束条件的基础上,以系统输入功率最低作为优化设计的目标函数,建立了变频游梁式抽油系统运行参数优化设计的数学模型。仿真与优化结果表明：① 在抽汲参数一定的条件下,优化实时频率可以显著改善游梁式抽油系统的动力性,具有明显的节电效果;② 优化电动机输出轴皮带轮转动惯量可以降低电动机输出功率的幅值与波动程度,进一步提高变频控制游梁式抽油系统的节电效果;③ 综合优化抽汲参数、平衡装置参数、频率函数与电动机输出轴皮带轮转动惯量可以显著改善系统的动力性能,降低系统能耗。     

Tracking control of nonlinear lumped mechanical continuous-time systems: A model-based iterative learning approach

This paper presents a nonlinear model-based iterative learning control procedure to achieve accurate tracking control for nonlinear lumped mechanical continuous-time systems. The model structure used in this iterative learning control procedure is new and combines a linear state space model and a nonlinear feature space transformation. An intuitive two-step iterative algorithm to identify the model parameters is presented. It alternates between the estimation of the linear and the nonlinear model part. It is assumed that besides the input and output signals also the full state vector of the system is available for identification. A measurement and signal processing procedure to estimate these signals for lumped mechanical systems is presented. The iterative learning control procedure relies on the calculation of the input that generates a given model output, so-called offline model inversion. A new offline nonlinear model inversion method for continuous-time, nonlinear time-invariant, state space models based on Newton's method is presented and applied to the new model structure. This model inversion method is not restricted to minimum phase models. It requires only calculation of the first order derivatives of the state space model and is applicable to multivariable models. For periodic reference signals the method yields a compact implementation in the frequency domain. Moreover it is shown that a bandwidth can be specified up to which learning is allowed when using this inversion method in the iterative learning control procedure. Experimental results for a nonlinear single-input-single-output system corresponding to a quarter car on a hydraulic test rig are presented. It is shown that the new nonlinear approach outperforms the linear iterative learning control approach which is currently used in the automotive industry on durability test rigs.     

Robust input design for nonlinear dynamic modeling of AUV

Input design has a dominant role in developing the dynamic model of autonomous underwater vehicles (AUVs) through system identification. Optimal input design is the process of generating informative inputs that can be used to generate the good quality dynamic model of AUVs. In a problem with optimal input design, the desired input signal depends on the unknown system which is intended to be identified. In this paper, the input design approach which is robust to uncertainties in model parameters is used. The Bayesian robust design strategy is applied to design input signals for dynamic modeling of AUVs. The employed approach can design multiple inputs and apply constraints on an AUV system’s inputs and outputs. Particle swarm optimization (PSO) is employed to solve the constraint robust optimization problem. The presented algorithm is used for designing the input signals for an AUV, and the estimate obtained by robust input design is compared with that of the optimal input design. According to the results, proposed input design can satisfy both robustness of constraints and optimality.     

基于递归理论的泵站压力管道运行状态监测

为了准确地识别建筑结构的模态参数,提出了一种基于多重信号分类算法（multiple signal classification,简称MUSIC）、经验小波变换（empirical wavelet transform,简称EWT）和同步提取小波变换（synchroextracting transform ,简称SET）的结构模态参数识别方法。首先,通过MUSIC-EWT对实测振动信号进行分解;其次,使用SET对单模态信号进行去噪处理;然后,采用自然环境激励技术（natural excitation technique,简称NExT）得到单模态信号的自由衰减响应;最后,利用Hilbert变换（hilbert transform,简称HT）和曲线拟合获得结构的自振频率和阻尼比。通过三层框架结构的数值模拟验证了该方法的准确性和鲁棒性。利用该方法对台风“达维”作用下广州中信广场的实测加速度数据进行分析,并将估计的结构模态参数和其他识别方法的分析结果进行对比,进一步证明了该方法的准确性和鲁棒性。     

基于递归理论的泵站压力管道运行状态监测

针对不利因素导致的管道运行异常问题,提出一种基于递归理论的泵站管道运行状态监测方法。首先,通过振动传感器提取压力管道关键部位的实测信息,并将同一位置不同方向的数据信息进行融合,得到一组反映结构整体动力特性的综合数据;其次,利用伪近临法与互信息法分别选取相空间重构参数m和τ;最后,绘制并计算代表管道动力特性的递归图及递归量化指标。将该方法应用于景泰川工程二期七泵站管道运行监测,通过设置不同的运行工况进行验证,结果表明：机组开关瞬间与稳定运行工况下,管道结构振动信号的递归图呈现不同模式,递归量化指标-确定性、对角线平均长度L、递归率及递归熵也呈现明显差异,能有效区分管道振动状态。该方法为压力管道的无损动态监测提供了新思路。     

子结构界面连接参数识别的波传播法

提出一种基于波传播法识别子结构连接界面刚度和阻尼的新方法。以子结构在平面内的弯曲振动为例,将单元的状态变量与波模式联系起来。通过单元波幅系数的识别,得到连接界面的位移和力向量,再由结点上位移连续及力平衡条件,求得连接界面各个自由度上的动刚度。在识别过程中,将动刚度分离为实部和虚部,以便于连接刚度和阻尼的独立识别。为了提高识别精度,选择一定的频率范围,在每一频率下求得连接界面的刚度和阻尼,最后求出统计平均值作为界面的连接参数。数值仿真算例表明本方法具有良好的识别精度和数值稳定性,是一种极有潜力的参数辨识方法。     

Second-order spectra for quadratic nonlinear systems by Volterra functional series: Analytical description and numerical simulation

Higher-order spectral analysis techniques are often used to identify nonlinearities in complex dynamical systems. More specifically, the auto- and cross-bispectrum have proven to be useful tools in testing for the presence of quadratic nonlinearities based on knowledge of a system's input and output. In this paper, analytical expressions for the auto- and cross-bispectrum are developed using a Volterra functional approach under the assumption of a zero-mean, stationary Gaussian input; proper simplifications are presented when the whiteness of the input signal is also imposed. These formulae show the contributions of the bispectrum in terms of the system frequency response function and elementary physical properties of the system. Simulations based on a stochastic numerical integration technique accompany the analytical solutions for a mechanical mass–spring–damper system possessing quadratic damping and stiffness coefficients and subjected to Gaussian white noise excitation. Subsequent estimates of the bispectrum based on the simulated signals show excellent agreement with theory. These results show how modes may interact nonlinearly producing intermodulation components at the sum and/or difference frequency of the fundamental modes of oscillation. The presence and extent of nonlinear interactions between frequency components are identified. Advantages of using higher-order spectra techniques will be revealed and pertinent conclusions will be outlined.     

基于并行计算的平面可调七杆机构动力学解析模型研究

基于运动学分析、凯恩动力学方程及数字-符号法,提出采用并行计算建立平面可调七杆机构动力学解析模型的方法,并研究了构件杆长及惯性参数变化对驱动力/力矩的影响.利用封闭矢量法对平面可调七杆机构进行运动学分析,得到各构件的速度和加速度表达式;将独立广义坐标、杆长及惯性参数作为符号量,其余参数处理为数值量,导出动力学解析模型的数字-符号表达式,并构造了解析模型的并行算法.由于动力学模型及实时代码优化是离线建立的,并且采用并行计算结构,减少了在线计算时间,从而为实时控制打下了基础.给出的仿真实例证明了此方法的有效性.     

A novel auto-tuning method for fractional order PI/PD controllers

Fractional order PID controllers benefit from an increasing amount of interest from the research community due to their proven advantages. The classical tuning approach for these controllers is based on specifying a certain gain crossover frequency, a phase margin and a robustness to gain variations. To tune the fractional order controllers, the modulus, phase and phase slope of the process at the imposed gain crossover frequency are required. Usually these values are obtained from a mathematical model of the process, e.g. a transfer function. In the absence of such model, an auto-tuning method that is able to estimate these values is a valuable alternative. Auto-tuning methods are among the least discussed design methods for fractional order PID controllers. This paper proposes a novel approach for the auto-tuning of fractional order controllers. The method is based on a simple experiment that is able to determine the modulus, phase and phase slope of the process required in the computation of the controller parameters. The proposed design technique is simple and efficient in ensuring the robustness of the closed loop system. Several simulation examples are presented, including the control of processes exhibiting integer and fractional order dynamics.     

Analytical modeling, optimization and testing of a compound bridge-type compliant displacement amplifier

This paper investigates a flexure-based compound bridge-type (CBT) displacement amplifier for piezoelectric drives. In addition to the advantages of large amplification ratio and compact size, the CBT amplifier has a larger lateral stiffness and is more suitable for actuator isolation and protection than the ordinary bridge-type amplifier. An analytical model for amplification ratio calculation is established based on the Euler-Bernoulli beam theory because other simple theoretical approaches cannot predict the ratio properly. The reason why those approaches fail is discovered by resorting to the elastic model. The input stiffness and resonance frequency of the amplifier are also analytically modeled and verified by finite-element analysis (FEA). The derived models are utilized to optimize the amplifier structure through particle swarm optimization (PSO) to obtain a large resonance frequency subject to other performance constraints. The performances of the fabricated amplifier with optimized parameters are confirmed by both FEA simulation and experimental studies. Because an output displacement over 1 mm is achieved by the designed amplifier, it is employable to develop micro/nanopositioning stages with a cubic millimeter sized workspace.     

Fast prediction of chatter stability lobe diagram for milling process using frequency response function or modal parameters

Prediction of chatter stability is important for planning and optimization of machining process in order to improve machining efficiency and reduce machining damage. Based on the classical analytical solution of chatter stability for milling process and in-depth analysis of the impact of modal parameters on the stability lobe diagram, a straight forward procedure for fast predicting stability lobe diagram directly using modal parameters of machining system was put forward. In consideration of the fact that the modal parameters of milling system can be estimated directly from the frequency response function using single DOF modal parameter estimation method, stability lobe diagram can be plotted directly using the tool tip’s frequency response function. The machining performances of a machining center with three different cutting tools were evaluated and the corresponding optimized cutting conditions were determined. The correctness of the proposed method was validated by good agreement of the predicted stability lobe diagram with that using the classical analytical method, and simulation results show that its calculation speed had been improved by 2–3 orders of magnitude. As a result, the proposed method of plotting stability lobe diagram using frequency response function can be utilized as an effective tool to select chatter-free cutting conditions in shop floor applications.