基于小波有限元和遗传优化算法的转轴裂纹诊断

构造Rayleigh-Euler和Rayleigh-Timoshenko区间B样条小波梁单元,分别离散柔性转轴和刚性转盘,建立转子系统有限元模型.求解裂纹转子前三阶固有频率,并将其拟合成裂纹相对位置和相对深度的函数.将裂纹识别中的匹配追踪问题转化为多维优化问题,以实测固有频率作为输入,利用遗传算法寻优求解出与输入值相差最小的样本点,进而测出裂纹的相对位置和深度.试验研究表明,所提出的裂纹诊断方法具有较好的精度和鲁俸性,且易于在工程实践中进行裂纹转子定量诊断.     

基于区间B样条小波有限元的裂纹故障定量诊断

研究基于模型的结构裂纹故障诊断中的正反问题,即求解含裂纹参数结构的固有频率以及利用实测固有频率,定量识别裂纹参数。构造用于求解正问题的一维区间B样条小波裂纹单元,通过求解裂纹结构有限元模型,绘制以裂纹等效刚度与裂纹位置为变量的三阶频响函数解曲线,将实际测出的系统前三阶固有频率作为输入,根据曲线的交点定量预示出裂纹的位置和深度。实验研究表明,文中构造的区间B样条小波裂纹单元有效克服了传统有限元分析在求解裂纹奇异性问题时存在的效率低、精度差甚至难以收敛到正确解的缺陷,同时具有足够的辨识精度,为早期裂纹故障定量诊断提供新方法。     

梁类结构多裂纹微弱损伤的小波有限元定量检测方法

提出了一种定量检测梁类结构多裂纹参数的方法。利用适宜求解奇异性问题的小波有限元法,从动力学正问题入手,对裂纹梁进行有限元建模,获得裂纹故障在结构固有频率上反映的本质征兆,并利用曲面拟合技术绘制出以裂纹位置和深度作为变量的固有频率变化率曲面,然后对整个裂纹梁进行剖分,迭代求解出每个剖分单元上的结构损伤系数。损伤系数为正的单元诊断为裂纹单元,在每个裂纹单元上求出裂纹对应的前三阶固有频率变化率,并分别将其作为输入参数代入固有频率变化率曲面,做出前三阶模态的频率变化率等高线,最后通过三条等高线的交点预测出裂纹存在的位置和深度,算例分析验证了该算法的有效性。     

基于小波有限元法的悬臂梁裂纹识别的试验研究

利用小波有限元法求解了裂纹悬臂梁的前三阶固有频率,并将其拟合成以裂纹位置和深度作为变量的固有频率解曲面;将实测的裂纹梁前三阶固有频率作为裂纹识别反问题的输入,绘制出各阶固有频率等高线,三条等高线的交点预测出裂纹存在的位置和深度。试验结果验证了算法的有效性,这为其实际应用提供了有力的试验依据。     

工字截面梁轨结构裂纹损伤的小波有限元定量诊断

研究工字截面梁轨结构裂纹定量识别中的正反问题,即通过裂纹位置和深度求解结构的固有频率以及利用结构的固有频率,识别裂纹位置和深度.裂纹被看作为一扭转线弹簧,利用工字梁裂纹应力强度因子推导出线弹簧刚度,构造出结构的小波有限元刚度矩阵和质量矩阵,从而获得裂纹结构的前3阶固有频率.通过行列式变换,将反问题求解简化为只含线弹簧刚度一个未知数的一元二次方程求根问题,分别做出以不同固有频率作为输入值时裂纹位置与裂纹深度之间的解曲线,曲线交点预测出裂纹的位置与深度,试验结果验证算法的有效性.     

基于固有频率的悬臂梁裂缝识别

结构中裂缝的存在使其模态参数发生改变 ,如局部刚度减小、阻尼增大、固有频率降低。把裂缝梁模拟成由扭曲弹簧连接 ,并对其前三阶固有频率的变化与裂缝位置和深度之间的关系进行计算和分析 ;利用特征方程以及前三阶固有频率 ,通过作图法对裂缝参数进行识别。识别结果证明 ,这种方法精度较高、简单可行 ,可用于机械工程实时监测。     

基于高阶谱分析的转子裂纹的诊断

研究了基于高阶谱特性的转子裂纹的诊断 ,分析和实验表明无裂纹轴和有裂纹轴的高阶谱具有显著的差别 ,不同的裂纹深度、位置的转子裂纹的高阶谱 (主要是三阶谱 )也有较大的差别 ,利用高阶谱对转子裂纹的诊断具有良好的应用前景     

含横向裂纹管道固有频率的变化规律研究

基于应变能释放原理和线性断裂力学原理,推导了裂纹尖端方向与管道轴线方向成任意角度的横向裂纹的等效刚度的计算方程,得到了裂纹与管道固有频率的定量关系。进而研究了不同裂纹位置、深度和角度工况下结构的前3阶固有频率变化规律;通过对含裂纹管道进行实验,验证了含横向裂纹管道固有频率计算方法的有效性。     

基于遗传算法的平板裂纹识别

裂纹的识别是故障诊断领域研究的一个热点问题.基于构件的固有频率变化,从反问题的角度出发,把裂纹的识别问题转化为一个优化问题,将裂纹的相对位置及深度参数转化为二进制编码,提出基于遗传算法的平板构件裂纹的识别方法.为了减少遗传算法的计算量,对遗传算法作了一定的改进.计算结果表明算法计算精度高,计算量小,可广泛的应用于拉深件裂纹识别及结构损伤检测等场合.     

基于风力机叶片固有频率的裂纹定位方法

针对风力机叶片裂纹定位问题,基于裂纹叶片固有频率差值比参数只与损伤位置相关的关系,提出了固有频率差值比的裂纹位置参数,通过数值仿真计算,建立裂纹位置参数数据库,提出裂纹定位参数及裂纹定位准则,实现了叶片裂纹所属区间定位;同时,研究叶片裂纹定位参数在裂纹区间内的变化规律,建立了裂纹定位参数与区间相对位置间的映射关系,实现了叶片裂纹区间内的精确定位。通过数值仿真分析验证了该方法的有效性,且定位精度较高,为实际的应用提供有力的依据。     

Crack fault quantitative diagnosis based on finite element of B-spline wavelet on the interval

The model-based forward and inverse problems in the diagnosis of structural crack faults were studied. The forward problem is to solve the natural frequencies through a cracked structural model and the inverse problem is to quantitatively determine the crack parameters using the experimental testing frequencies. Then, the one-dimensional crack element of B-spline wavelet on the interval (BSWI) was built to solve the forward problem. Contour plots of normalized crack location versus normalized crack size were plotted by using the first three natural frequencies as the inputs. The intersection of the three curves predicted the normalized crack location and size. The experimental study verified the validity of the wavelet-based crack element in solving crack singular problems to overcome the disadvantages of the traditional finite element method (FEM), such as low efficiency, insufficient accuracy, slow convergence to correct solutions, etc. At the same time, it had adequate identification precision. The new method can be applied to prognosis and quantitative diagnosis of incipient crack. __________ Translated from Journal of Mechanical Strength, 2005, 27 (2) (in Chinese)     

Second Generation Wavelet Finite Element and Rotor Cracks Quantitative Identification Method

The presence of cracks in the rotor is one of the most dangerous and critical defects for rotating machinery. Defect of fatigue cracks may lead to long out-of-service periods, heavy damages of machines and severe economic consequences. With the method of finite element, vibration behavior of cracked rotors and crack detection was received considerable attention in the academic and engineering field. Various researchers studied the response of a cracked rotor and most of them are focused on the crack detection based on vibration behavior of cracked rotors. But it is often difficult to identify the crack parameters quantitatively. Second generation wavelets (SGW) finite element has good ability in modal analysis for singularity problems like a cracked rotor. Based on the fact that the feature of SGW could be designed depending on applications, a multiresolution finite element method is presented. The new model of SGW beam element is constructed. The first three natural frequencies of the rotor with different crack location and size were solved with SGW beam elements, and the database for crack diagnosis is obtained. The first three metrical natural frequencies are employed as inputs of the database and the intersection of the three frequencies contour lines predicted the normalized crack location and size. With the Bently RK4 rotor test rig, rotors with different crack location and size are tested and diagnosed. The experimental results denote the cracks quantitative identification method has higher identification precision. With SGW finite element method, a novel method is presented that has higher precision and faster computing speed to identify the crack location and size.     

Rotor crack detection based on high-precision modal parameter identification method and wavelet finite element model

In this paper, a new method based on high-precision modal parameter identification method and wavelet finite element (WFE) model is presented to determine the depth and location of a transverse surface crack in a rotor system. The rotor system is modeled using finite element method of B-spline wavelet on the interval (FEM BSWI), while the crack is equivalent as a weightless rotational spring. Additionally, a novel method based on empirical mode decomposition (EMD) and Laplace wavelet is proposed to acquire modal parameters with high precision, which is implemented to improve the precision of crack identification. By providing the first three natural frequencies, contours for the specified natural frequency are plotted in the same coordinate, and the intersection of the three curves predicts the crack location and size. The experimental results indicate that the proposed method can accurately identify the position and depth of different cracks. The effectiveness and reliability of the proposed method is verified.     

利用传递矩阵法对阶梯悬臂梁的裂纹参数识别

基于Bernoulli-Euler梁振动理论,以等效弹簧模拟裂纹引起的局部软化效应,利用传递矩阵法推导阶梯悬臂梁振动频率的特征方程,对于含多个裂纹以及复杂边界条件的阶梯梁,仅需求解4×4的行列式即可获得相应的频率特征方程。直接利用该特征方程,提出两种有效估计裂纹参数的方法———等值线法和目标函数最小化法,并应用两段阶梯悬臂梁的数值算例说明方法的有效性。算例结果表明,只需结构前三阶频率即可识别裂纹位置和深度。应用“零设置”可减小计算频率与理论频率不相等对识别结果的影响。等值线法可以直观给出裂纹位置和裂纹深度参数,目标函数最小化法可给出最优的裂纹参数结果,并且该方法可推广应用到含多个裂纹复杂梁(如非完全固支、弹性支撑等)结构的裂纹参数识别中。     

基于压电增益特性进行梁中缺陷的识别

驱动元件PZT片和传感元件PVDF膜粘贴于自由梁表面,通过测试压电增益,试验获取梁中不同缺陷尺寸下的固有频率,根据固有频率的变化,实现缺陷的识别,梁中的缺陷采用等效线性弹簧模拟,描绘出不同模态下刚度与缺陷可能位置曲线,根据曲线的交点,得出缺陷位置与尺寸,相比于实际的缺陷位置与尺寸,自由梁弯曲激振下识别的结果满足一定的精度。     

局部柔度变化在管道裂纹定量识别中的应用

局部柔度可描述结构上出现的裂纹,结构的模态参数将随着裂纹的扩展而改变,利用这一变化可辨识出裂纹发生的位置和深度。由此,建立了一种基于局部柔度变化的管道裂纹定量识别方法。该方法通过将管道结构沿径向离散为一系列依次嵌套的薄壁环,从而求得裂纹引起的局部柔度的变化规律,进而获得局部柔度与管道固有频率的特征关系,绘制裂纹管道的各阶固有频率曲面。采用实测前3阶固有频率去截取相应的固有频率曲面,获得各阶频率等高线,利用其交点定量诊断裂纹的位置与深度。实验结果验证了该方法的有效性。     

Four-beam model for vibration analysis of a cantilever beam with an embedded horizontal crack

As one of the main failure modes, embedded cracks occur in beam structures due to periodic loads. Hence it is useful to investigate the dynamic characteristics of a beam structure with an embedded crack for early crack detection and diagnosis. A new four-beam model with local flexibilities at crack tips is developed to investigate the transverse vibration of a cantilever beam with an embedded horizontal crack; two separate beam segments are used to model the crack region to allow opening of crack surfaces. Each beam segment is considered as an Euler-Bernoulli beam. The governing equations and the matching and boundary conditions of the four-beam model are derived using Hamilton's principle. The natural frequencies and mode shapes of the four-beam model are calculated using the transfer matrix method. The effects of the crack length, depth, and location on the first three natural frequencies and mode shapes of the cracked cantilever beam are investigated. A continuous wavelet transform method is used to analyze the mode shapes of the cracked cantilever beam. It is shown that sudden changes in spatial variations of the wavelet coefficients of the mode shapes can be used to identify the length and location of an embedded horizontal crack. The first three natural frequencies and mode shapes of a cantilever beam with an embedded crack from the finite element method and an experimental investigation are used to validate the proposed model. Local deformations in the vicinity of the crack tips can be described by the proposed four-beam model, which cannot be captured by previous methods.     

Identification of a crack in a beam by the boundary element method

A method to detect a crack in a beam is presented. The crack is not modeled as a massless rotational spring, and the forward problem is solved for the natural frequencies using the boundary element method. The inverse problem is solved iteratively for the crack location and the crack size by the Newton-Raphson method. The present crack identification procedure is applied to the simulation cases which use the experimentally measured natural frequencies as inputs, and the detected crack parameters are in good agreements with the actual ones. The present method enables one to detect a crack in a beam without the help of the massless rotational spring model.