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考虑泥沙颗粒影响的长距离供水工程单向塔水锤防护

汪怡然, 俞晓东, 韩笑笑, 张健

汪怡然, 俞晓东, 韩笑笑, 张健. 考虑泥沙颗粒影响的长距离供水工程单向塔水锤防护[J]. 农业工程学报, 2023, 39(4): 84-91. DOI: 10.11975/j.issn.1002-6819.202211238
引用本文: 汪怡然, 俞晓东, 韩笑笑, 张健. 考虑泥沙颗粒影响的长距离供水工程单向塔水锤防护[J]. 农业工程学报, 2023, 39(4): 84-91. DOI: 10.11975/j.issn.1002-6819.202211238
WANG Yiran, YU Xiaodong, HAN Xiaoxiao, ZHANG Jian. One-way surge tank protection of sediment-laden water hammer on long-distance water supply projects[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2023, 39(4): 84-91. DOI: 10.11975/j.issn.1002-6819.202211238
Citation: WANG Yiran, YU Xiaodong, HAN Xiaoxiao, ZHANG Jian. One-way surge tank protection of sediment-laden water hammer on long-distance water supply projects[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2023, 39(4): 84-91. DOI: 10.11975/j.issn.1002-6819.202211238

考虑泥沙颗粒影响的长距离供水工程单向塔水锤防护

基金项目: 国家自然科学基金资助项目(52179062;51879087)

One-way surge tank protection of sediment-laden water hammer on long-distance water supply projects

  • 摘要: 长距离供水工程的安全稳定运行离不开水锤防护,然而传统的水锤计算模型和分析方法忽略了泥沙颗粒影响。该研究基于浆体水锤波速公式和管路当量摩阻公式构建特征线方程进行数值计算,并通过水库-管道-阀门系统(RPV)关阀水锤试验的压力数据进行模型验证;结合单向塔边界数学模型,探究了泥沙颗粒参数对某工程输水管路单向塔水锤防护效果的影响。结果表明:无防护掉电时,含沙工况下泵后的降压波幅值更大,较清水多出1.22 m;含沙水管路沿线的最小内水压力均低于清水,插值最大为1.18 m。采用清水单向塔防护方案,除部分颗粒参数条件外(含沙量<10 kg/m3,颗粒直径=0.01 mm),含沙管路沿线均会出现负压;其内水压力最小值随着颗粒直径和含沙量的增大而减小,最低可达-2.41 m。在给定的颗粒参数范围内,提出满足工程防护需求的含沙水单向塔防护方案,其塔高较清水方案需要提高4 m。相关研究成果可为高含沙流域长距离供水工程的水锤防护设计提供一定的参考。
    Abstract: Abstract The safety and stability of long-distance water supply projects can be closely related to the reasonable protection of water hammers. However, the traditional transient flow in the method of characteristic cannot consider the influence of natural water sediment particles on the evaluation of water hammer protection. In this study, the pipeline head loss model was constructed, according to the sediment-laden water pipeline resistance model of Chen Guangwen and the single particle settlement formula of Zhang Ruijin. The method of characteristic was improved to simulate the sediment-laden water hammer pressure, according to the wave velocity formula of the water hammer on the slurry by Han Wenliang and the equivalent friction formula of sediment-laden water pipeline flow. The improved model was validated by the pressure data of reservoir-pipe-valve (RPV) water hammer closing valve test with water. The pressure of the sediment-laden water hammer with the low-concentration particle parameter was close to the experimental value of water. Combined with the boundary conditions of a one-way surge tank, one specific pipeline system of the water supply project was selected to determine the effect of sediment with different concentrations and particle diameters on water hammer protection under different initial pump heads. The results show that when the pump head of sediment-laden water was adjusted until the water level of downstream reservoir is consistent, the internal water pressure along the pipeline was higher, because of the higher initial pump head with sediment-laden water. After the power failure and pump stopped, the pressure dropping behind the pump of sediment-laden water was larger than that of water, and the minimum internal water pressure of sediment-laden water along the pipeline was lower than that of water. The lowest pressure at the node behind the pump was -15.76 m, whereas there was -37.82 m along the pipeline. The internal water pressure along the pipeline was greater than 0m under the original one-way surge tank protection. In the sediment-laden water, the minimum pressure decreased gradually with the increase of particle diameters and sediment concentrations, where the minimum reached -2.41 m. Except for some conditions with the low concentration particle parameter (S<10 kg/m3, d=0.01 mm), the negative pressure occurred along the pipeline of sediment-laden water, and the minimum pressure points were always located 19.7 km behind the pump. Therefore, there was different influence of sediment particles on the minimum internal water pressure at different positions of the pipeline. In order to increase the internal pressure along the pipeline, the water make-up capacity of the one-way surge tank should be increased. As such, the one-way surge tank protection scheme was obtained for the sediment-laden water. There was no negative pressure along the pipeline of sediment-laden water under the particle parameters conditions of S=100 kg/m3 and d=0.1 mm. The pressure deviation of the pipeline before 10.5 km was small, not more than 1 m, and then exceeded 2.5 m within the range of 11.3-21.8 km, compared with the minimum internal water pressure along the pipeline of the two protection schemes. The maximum pressure deviation reached 3.29 m at the point 21.8 km behind the pump. The method of characteristic was of great significance to improve the numerical simulation of multiphase transient flow. The finding can provide a strong reference for the sediment-laden water hammer protection and stable operation on long-distance water supply projects of high sediment concentration basins.
  • 随着农业装备不断向现代化、智能化和规模化发展[1],工业机器人的应用范围扩展至农业装备领域是必然趋势。旋转矢量(rotate vector,RV)减速器具有体积小、传动比范围大、质量轻、精度保持稳定、效率高等特点,农业机械经常需要大比例减速的情况,常选用RV减速器[2]。RV减速器作为农业机器人及农业机械的核心传动部件,其健康状况直接决定了传动精度、可靠性、生产效率和农机寿命。然而,由于RV减速器结构复杂,且在实际工作中工况多变,作业环境恶劣,随时发生故障[3]。RV减速器故障严重时会导致生产停滞,造成巨大的经济损失。因此,研究农业机器人RV减速器的故障诊断方法,及早发现并处理故障,缩短维护时间,对保障机器人安全运行、提高企业生产效率和经济效益具有重大意义。

    振动信号能够有效反映部件的健康状态,在故障诊断中得到广泛应用[4]。近年来,许多学者对此开展了研究,提出了神经网络[5]、深度学习[6]、时频分析[7]、盲反卷积[8]等方法。汪久根等[9]采用残差网络提高了RV减速器不同故障的分类准确率。YIN等[10]开发了一种基于知识和数据双驱动的传输网络用于RV减速器故障诊断。彭鹏等[11]提出了一种抗干扰的 RV 减速器故障识别卷积神经网络模型。韩特等[12]在深度特征嵌入空间下构建特征图,通过标签传播算法生成伪标签,利用信息熵评估健康状态概率的分布。上述关于RV减速器的故障诊断精度较高,主要采用神经网络、深度学习、机械学习等算法,但是此类算法的实现需要大量不同类型的数据支撑。而基于时域、频域或时频域的分析方法能够在少量数据的支撑下完成故障诊断。XIE等[13]提出了一种基于电流信号的瞬时频率趋势图与参数自适应变分模态分解算法相结合的RV减速器故障诊断方法,实现了RV减速器太阳轮故障特征提取。GUO等[14]将计算阶跟踪和同步平均相结合识别了RV减速器行星齿轮齿根裂纹故障。雷亚国等[15]利用脊线提取完成RV减速器振动信号的平稳数据截取,有效提取了RV减速器行星轮的故障信息。由于RV减速器因润滑、制造误差和不合理受力会引起各种机械故障,使得实际运行中裂纹、点蚀等故障往往同时或先后出现,传感器采集的信号往往是多个故障源相互耦合的结果,使故障诊断变得非常困难。文献[13-15]提出的故障诊断方法适于单一故障诊断,对RV减速器复合故障检测能力下降甚至失效。因此,如何在复合故障相互耦合以及往复运动、时变转速工况下,精确分离提取耦合故障特征是RV减速器故障诊断领域亟待攻克的难题。盲源分离(blind source separation,BSS)技术可以在传输通道未知的情况下,从混合信号中把多个信号源分离出来。独立成分分析(independent component analysis,ICA) [16]和稀疏分量分析(sparse component analysis,SCA) [17] 是常用的以信号处理技术求解BSS问题。ICA算法的前提是源信号是统计独立的,且每个独立分量必须符合非高斯分布。而现代机械设备难以满足统计独立性的假设,但SCA方法的稀疏性假设相对容易满足。

    SCA算法中,聚类方法是混合矩阵估计的首选。WANG等[18]提出了一种两阶段的聚类算法,从而提高了混合矩阵的估计精度。NORSALINA等[19]引入自适应时频阈值提高混合矩阵估计的精度。DING等[20]利用同步压缩S变换估计含谐波传输阻抗的混合矩阵。密度峰值聚类算法(density peak clustering,DPC)考虑局部密度和相对距离绘制决策图,快速识别簇中心并完成聚类。 DPC具有唯一输入参数,无需先验知识和迭代[21]。在解决振动源数目估计方面有一定的潜力。SCA算法还包括了源信号的恢复,主流方法有两类:一是通过优化逼近L0范数的函数恢复源信号。BU等[22]使用光滑的连续函数来近似L0范数。ZHANG等[23]用复三角函数逼近L0范数。但是上述方法具有源信号射入方向越近恢复精度越低。二是压缩感知(compressed sensing,CS)重构算法[24],该方法使用L1范数优化取代L0范数优化恢复源信号,避免了L0范数优化的NP-Hard问题。正交匹配追踪算法(orthogonal matching pursuit,OMP)克服匹配追踪算法的缺陷,在算法迭代过程中,残差能够与已经选择的原子正交,保证相同索引不会被重复选择,迭代过程在有限的次数内收敛[25],在重构信号算法的研究中发挥了重要作用。

    结合上述分析,本文提出一种基于时频图像脊线提取与改进稀疏分量分析相结合的RV减速器复合故障盲提取方法,旨在实现往复运动、时变转速、故障源数目未知工况下的RV减速器复合故障诊断。首先使用时频图像脊线提取(ridge extraction from time-frequency images,RETF)从时频图中提取脊线,完成对平稳信号的同步截取,然后利用sinC函数改进形态滤波(sinC-morphological filtering,SMF)、DPC和OPM相结合的盲源分离方法(SMF-DPC-OMP)实现平稳信号复合故障的分离提取,采用SMF对观测信号进行滤波降噪处理,在提高信噪比的同时突出信号的冲击分量,并对滤波后的信号进行密度峰值聚类处理,得到聚类中心,构建传感矩阵;接着将滤波后的信号转换到频域以满足SCA的稀疏性要求;最后利用OMP算法在频域重构源信号,在提高计算速度和适应性的同时,实现复合故障特征的提取。

    盲源分离是指在源信号和信号传输通道均未知的情况下,仅依赖传感器拾取的观测信号恢复和估计源信号的技术[26]。含噪声SCA的数学模型为

    {{\boldsymbol{X}}_{m \times t}} = {{\boldsymbol{A}}_{m \times n}}{{\boldsymbol{S}}_{n \times t}} + {{\boldsymbol{V}}_{m \times t}} (1)

    式中 {\boldsymbol{X}} 为观测矩阵,即采集到的振动信号; {\boldsymbol{A}} 为混合矩阵; {\boldsymbol{S}} 是具有稀疏性的未知源信号; {\boldsymbol{V}} 为噪声或其他随机干扰成分; m 为传感器数量; n 为源信号数量; t 为观测时间,s。

    短时傅里叶变换(short-time fourier transform,STFT)是有效捕获时变频率的方法之一,其定义为[27]

    Q\left( {t,f} \right) = \int\limits_R {x\left( \tau \right){h_\sigma }\left( {\tau - t} \right){{\text{e}}^{ - {j}_0 2{\text{π }}f\tau }}{\text{d}}\tau } (2)

    式中x\left( \tau \right) 为多分量信号;Q\left( {t,f} \right)是信号的时频表达(time frequency representation,TFR);{h_\sigma }\left( {\tau - t} \right)是长度为\tau 的高斯窗;R为实数集;t为时间;f为频率;j表示复数。

    从TFR中提取时频脊线估计瞬时频率(instantaneous frequency,IF)是完全非参数的,并且能适应不同的情况。有效的脊线提取方法是寻找TFR的最大位置[27],其定义如下:

    \overline {{D}} (t) = \mathop {\arg \max }\limits_{f \in J} \left| {Q(t,f)} \right|,{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} t = {t_0}, \ldots ,{t_{N - 1}} (3)

    式中 \overline {{D}} (t) 表示得到的脊线,是理论 {{D}}(t) 的估计, J 是频率的集合,N 为信号截止时间。RETF算法的具体实现步骤如下:

    1)初始化参数,并创建一个预存矩阵{{\boldsymbol{K}}_i}

    2)对时域信号x\left( t \right)进行STFT变换,得到其时频分布Q\left( {t,f} \right)

    3)寻找并标记最大能量点\left[ \begin{gathered} {t_0} \\ {f_0} \\ \end{gathered} \right],将该点存储为{\boldsymbol{K}}矩阵的第一列;

    4)使Q\left( {{t_0},f} \right)在最大值点{t_0}附近时刻归0,即Q\left( {{t_0},f} \right) = 0f \in \left[ {{f_0} - \Delta f,{f_0} + \Delta f} \right],其中\Delta f为滤波带宽惩罚参数,控制滤波带宽;

    5)在Q\left( {{t_0},f} \right)的邻域内寻找下一个最大能量点 \left[ \begin{gathered} t_{0}' \\ f_{0}' \\ \end{gathered} \right] = \ {\mathrm{\max}} _{\left( {{t_\alpha },{f_\alpha }} \right)}Q\left( {t,f} \right) {t_\alpha } \in \left[ {{t_0} - 1,{t_0} + 1} \right] {f_\alpha } \in \left[ {f_0} -F,{f_0} + F \right]H为选定的窗参数,控制迭代中 \overline {{D}} (t) 增量的平滑程度,H越小, \overline {{D}} (t) 增量越平滑;

    6)将 \left[ \begin{gathered} t_0' \\ f_0' \\ \end{gathered} \right] 存储为{\boldsymbol{K}}矩阵的下一列;

    7)使Q\left( {t_0',f} \right)在最大值点t_0'附近时刻归0,即Q\left( {t_0',f} \right) = 0f \in \left[ {{f_0} - \Delta f,{f_0} + \Delta f} \right]

    8)如果时间指标{t_\alpha }和频率指标{f_\alpha }未达到TFR矩阵的边界,返回步骤5);否则返回步骤1),并创建一个新的预存矩阵{{\boldsymbol{K}}_{i + 1}}

    9)当剩余TFR能量小于阈值\varepsilon 时停止算法(每一个预存矩阵,即是一条时频脊线)。

    \sin C函数又称辛格函数,定义如下:

    \sin C\left( x \right) = \frac{{\sin \left( {{\text{π}}x} \right)}}{{{\text{π}}x}} (4)

    本文选取 \sin C 函数作为结构元素时主要定义长度L和主瓣比p。长度是指整个图像的长度,主瓣比是指从中间截取整个图像的百分比。图1L = 20 p = 50\text{%} {\mathrm{sin}} C 结构元素。

    图  1  sinC函数参数图
    Figure  1.  Parameter diagram of sinC function

    形态滤波器的构建主要包括结构元素和形态算子。结构元素的选择包括结构元素的形状、长度、高度(振幅)等。在处理一维信号时 ,结构元素的形状一般有线形、三角形、半圆形、正弦等,本文选择 sin C函数作为结构元素 ,结合形态算子腐蚀Θ、膨胀\oplus 、形态开○和形态闭●,构建基于sinC函数的SMF平均组合滤波器。

    设原信号f\left( n \right)和结构元素g\left( m \right)为分别定义在F\left( {1,2, \ldots ,n - 1} \right)G = \left( {1,2, \ldots, m - 1} \right)上的离散函数, N \geqslant M。则f\left( n \right)关于g\left( m \right)的腐蚀运算、膨胀运算、开运算和闭运算[28]分别为

    (f\Theta g)(n) = \min[f(n + m) - g(m)] (5)
    (f \oplus g)(n) = \max [f(n - m) + g(m)] (6)
    (f \circ g){\kern 1pt} (n) = (f\Theta g \oplus g)(n) (7)
    (f \bullet g){\kern 1pt} (n) = (f \oplus g\Theta g)(n) (8)

    通常使用形态开和形态闭的级联形式去除信号中的正、负噪声。TANG[28]为了去除信号中的正、负噪声,定义了形态闭-开(closing-opening,CO)和开-闭(opening-closing,OC)滤波器:

    {\mathrm{CO}}{\kern 1pt} (f(n)) = (f \bullet g \circ g)(n) (9)
    {\mathrm{OC}}{\kern 1pt} (f(n)) = (f \circ g \bullet g)(n) (10)

    为了抑制统计偏倚,本文采用结合OC和CO的平均组合滤波器[28]:

    y(n) = [{\mathrm{OC}}(f(n) + {\mathrm{CO}}(f(n)]/2 (11)

    为了验证基于{\mathrm{sin}}\; C 函数的SMF滤波效果,生成模拟轴承外圈故障的仿真信号并添加信噪比(signal-to-noise ratio,SNR)为−3 dB的白噪声。图2为含噪声的仿真信号及滤波后的时域波形图,SMF降噪后的信噪比为0.7 dB,说明SMF较好的滤除干扰噪声,突显了信号的冲击特性。

    图  2  滤波前后信号波形对比
    Figure  2.  Comparison of signal waveforms before and after filtering

    将本文的SMF滤波器与文献[29]中的直线型滤波器(幅值为0,长度为10)进行对比,滤波器参数及滤波效果如图3所示。分析图3可知无论滤波器的参数如何选择,SMF的滤波后的信噪比总是要优于直线型滤波器。

    图  3  滤波参数及滤波效果对比
    Figure  3.  Comparison of filtering parameters and filtering effect

    DPC算法主要基于2个假设:1)聚类中心周围是低密度的点;2)聚类中心与密度较高的样本点之间的距离较大。设数据集U{{ = }}\left\{ {{u_1},{u_2}, \cdots, {u_R}} \right\} {u_i}{{ = }}{\left( {{u_{i1}},{u_{i2}}, \cdots, {u_{io}}} \right)^{\mathrm{T}}} ,其中i = 1,2, \cdots ,R{u_{ij}}表示数据点ij维属性,j = 1,2, \cdots ,OR为总体样本数。

    1)计算局部密度\rho

    对于每个数据点{u_i}i = 1,2, \cdots ,R,局部密度{\rho _i}可以被认为是距离点{u_i}较近的点的数量,{\rho _i}的定义如下[30]

    {\rho _i} = \sum\limits_{j,j \ne i} {\chi \left( {{d_{ij}} - {d_c}} \right)} (12)

    式中\chi \left( x \right)为分段函数,x < 0时,\chi \left( x \right){\text{ = }}1,否则\chi \left( x \right){\text{ = 0}}{d_{ij}}表示ij之间的距离(通常为欧氏距离),{d_c}表示截断距离。

    2)计算最近邻距离\delta

    每个点的最近邻距离{\delta _i}

    {\delta _i} = \left\{ \begin{gathered} \mathop {\min \left( {{d_{ij}}} \right)}\limits_{j:{\rho_j} > {\rho_i}} ,{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\rho _i} < \max \left( \rho \right) \\ \mathop {\max \left( {{d_{ij}}} \right)}\limits_j ,{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\rho _i} = \max \left( \rho \right) \\ \end{gathered} \right. (13)

    对于密度较低的样本点,计算该样本点与高于其密度的最近样本点之间的距离;而对于密度最高的样本点,则计算该点与最远样本点之间的距离。

    3)选取聚类中心 V

    聚类中心定义为同时具有高密度{\rho _i}和较大距离{\delta _i}的点{x_i},令{V_i} = {\rho _i}{\delta _i},取 V > \dfrac{2}{N}\displaystyle\sum\limits_{i = 1}^N {{V_i}} 为聚类中心。由于聚类对象为RV故障信号,{V_i}大多为0。为保证不遗漏正确的聚类中心,因此选取大于均值2倍的数据点为聚类中心。

    利用压缩感知重构算法中的OMP算法对源信号进行重构。将 m 个长度为 t 的观测信号表示为 {\boldsymbol{y}} = ({y_{11}}, {y_{12}}, \cdots {y_{1\;t}}, \cdots ,{y_{m1}},{y_{m2}}, \cdots {y_{mt}})^{\mathrm{T}}

    利用聚类中心 {\boldsymbol{V}}(m \times n) 构造传感矩阵 {\boldsymbol{W}} 。根据压缩感知模型,当混合信号长度为 mt \times 1 ,其传感矩阵 {\boldsymbol{W}} 的长度为 mt \times nt 。利用傅里叶变换正交矩阵 {{\boldsymbol{E}}_{t \times t}} 扩充矩阵 {\boldsymbol{V}} 的元素值,变换关系为 {{\boldsymbol{B}}_{ij}} = {{\boldsymbol{E}}_{t \times t}}{{\boldsymbol{V}}_{ij}} ,具体变换如式(14)所示。

    {\boldsymbol{y}} = \left[ \begin{gathered} {{\boldsymbol{{\boldsymbol{B}}}}_{11}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {{\boldsymbol{B}}_{12}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \cdots {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {{\boldsymbol{B}}_{1n}} \\ {{\boldsymbol{B}}_{21}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {{\boldsymbol{B}}_{21}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \cdots {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {{\boldsymbol{B}}_{2n}} \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \vdots {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \vdots {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \vdots {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \vdots \\ {{\boldsymbol{B}}_{m1}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {{\boldsymbol{B}}_{m2}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \cdots {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {{\boldsymbol{B}}_{mn}} \\ \end{gathered} \right]{\boldsymbol{x}} (14)

    {\boldsymbol{x}} = {({x_{11}},{x_{12}}, \cdots ,{x_{1\;t}}, \cdots ,{x_{n1}},{x_{n2}}, \cdots ,{x_{nt}})^{\mathrm{T}}} 的长度是 (nt \times 1) 。至此,盲源分离的重构模型构建完成。

    OMP是一种常用的压缩感知重构算法。首先在每次迭代过程中对所有选定的原子进行Schmidt正交化,以确保每次迭代的结果都是最优解。利用OMP算法进行重构的核心思想是构造频域感知矩阵。具体算法步骤如下:

    1)初始化残差 {r_0} ,迭代次数 \ell ,傅立叶正交变换矩阵 {{\boldsymbol{E}}_{t \times t}} ,并根据 {{\boldsymbol{B}}_{ij}} = {{\boldsymbol{E}}_{t \times t}}{{\boldsymbol{V}}_{ij}} 构造传感矩阵 {\boldsymbol{W}}{\kern 1pt} {\kern 1pt} {\text{ = }}{\kern 1pt} {\kern 1pt} {\kern 1pt} \left[ \begin{gathered} {{\boldsymbol{B}}_{11}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {{\boldsymbol{B}}_{12}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \cdots {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {{\boldsymbol{B}}_{1n}} \\ {{\boldsymbol{B}}_{21}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {{\boldsymbol{B}}_{21}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \cdots {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {{\boldsymbol{B}}_{2n}} \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \vdots {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \vdots {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \vdots {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \vdots \\ {{\boldsymbol{B}}_{m1}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {{\boldsymbol{B}}_{m2}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \cdots {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {{\boldsymbol{B}}_{mn}} \\ \end{gathered} \right]

    2)使用内积法计算传感矩阵 {\boldsymbol{W}} 的列向量与残差{r_i}的投影系数,并记录最大投影系数相对应的位置 {{\boldsymbol{\beta}} _i} ,随后将最大投影系数所对应的传感矩阵 {\boldsymbol{W}} 的列置0;

    3)使用最小二乘法计算本次迭代的重构信号的估计值 {x_i} = {({{\boldsymbol{\beta}} _i}^{\mathrm{T}} \cdot {{\boldsymbol{\beta}} _i})^{ - 1}} \cdot {{\boldsymbol{\beta}} _i}^{\mathrm{T}} \cdot {{\boldsymbol{r}}_i}

    4)更新残差 {r_{i + 1}} = {r_i} - {x_i} ,并重复步骤2),直到迭代结束;

    5)使用 {E_{t \times t}} 做逆傅立叶变换得到维数为 (kt \times 1) 的时域信号 x ,并根据聚类中心的维数k,将维数为 (kt \times 1) 的时域信号 x 分割为k个维数为\left( {t \times 1} \right)的时域信号,从而完成信号的盲源分离。

    1)平稳阶段截取:提取一组观测信号x\left( t \right)并进行STFT得到其时频表达Q\left( {t,f} \right)。随后提取时频脊线并截取恒速时段信号,获得平稳信号{x_1}\left( t \right)

    2)信号预处理:构造基于 \sin C 结构元素的平均组合滤波器,并对平稳信号{x_1}\left( t \right)进行滤波降噪,得到滤波信号{x_2}\left( t \right)

    3)估计混合矩阵:对滤波信号{x_2}\left( t \right)进行DPC得到聚类中心,即混合矩阵;

    4)源信号重构:利用步骤3)的混合矩阵构造传感矩阵,使用OMP算法在频域重构源信号;

    5)故障识别:对重构源信号进行快速傅里叶变换(fast Fourier transform,FFT)处理,根据分离信号频谱中的频率进行故障识别。

    本文算法的总体流程图如图4所示。

    图  4  RETF-SMF-DPC-OMP算法流程图
    Figure  4.  Flowchart of RETF-SMF-DPC-OMP algorithm

    试验信号来自于模拟农业机器人单关节臂往复运动的RV减速器试验台,如图5所示。将2个型号为333B30的PCB加速度传感器相互垂直安装于减速器保持架上拾取信号。水平方向为传感器1,垂直方向为传感器2。其中,试验台基座7上安装减速器保持架4,通过减速器保持架4装RV减速器5,型号为SV-X2MH100C-B2 LN的电机6输出轴通过RV减速器5连接关节臂1。图6为故障齿轮的实物图,图6a为太阳轮磨损图,图6b为行星轮磨损图。

    图  5  试验台及传感器位置示意图
    1. 关节臂 2. 加速度传感器1 3. 加速度传感器2 4. 减速器保持架 5. RV减速器 6. 电机 7. 基座
    Figure  5.  Diagram of position of test platform and sensor
    1. Articulated arm 2. Acceleration sensor 1 3. Acceleration sensor 2 4. Reducer cage 5. RV reducer 6. Motor 7. Test stand base
    图  6  故障齿轮
    Figure  6.  Faulty gear

    试验选用RV40E型减速器并以针轮固定的方式固定于试验台,减速比121、行星齿轮数目为2,太阳轮齿数{Z_1} = 12,行星轮齿数{Z_2} = 42,摆线轮齿数{Z_3} = 39,针轮齿数{Z_4} = 40。采集系统包括NI-USB9234采集卡与单向加速度传感器,采样频率为25.6 kHz。试验预设摆臂运动范围为0°~90°(单次抬升或下降90°),运行速度为100°/s。RV减速器的各个特征频率计算式见表1

    表  1  RV减速器各零件的工作频率
    Table  1.  Working frequency of each part of RV reducer
    名称Name 计算公式Calculation formula
    电机主轴转速
    Motor spindle speed {n_1}/(r·min−1)
    {n_1} = 60f/P
    太阳轮转频
    Sun gear rotation frequency {f_1}/Hz
    {f_1} = {n_1}/60
    行星轮转频
    Planetary gear rotation frequency {f_2}/Hz
    {f_2} = \dfrac{{{z_1}{z_4}}}{{({z_3} - {z_4})\left( {{z_1} + {z_2}{z_4}} \right)}}{f_1}
    一级啮合频率
    First stage engagement frequency {f_{1c}}/Hz
    {f_{1c}} = \dfrac{{{z_1}{z_2}{z_4}}}{{{z_1} + {z_2}{z_4}}}{f_1}
    注:P为伺服电机磁极对数,{{\textit{z}}_1}为太阳轮齿数,{{\textit{z}}_2}为行星轮齿数,{{\textit{z}}_3} 为摆线轮齿数,{{\textit{z}}_4} 为针轮齿数。
    Note: P is the number of magnetic poles of the servo moto, {{\textit{z}}_1} is the number of solar gear, {{\textit{z}}_2} is the number of planetary gear, {{\textit{z}}_3} is the number of cycloidal gear, and {{\textit{z}}_4} is the number of needle gear.
    下载: 导出CSV 
    | 显示表格

    行星轮故障频率{f_p}为行星轮相对于行星架的旋转频率,{f_p} = {f_2} - {f_3};太阳轮故障频率{f_s}为太阳轮相对于行星架的旋转频率,{f_s} = {f_1} + {f_3}。由于摆臂转速=100(°)/s =0.27 Hz,即支撑盘转频{f_3}=0.27 Hz。根据表1及太阳轮故障频率计算式计算可得太阳轮故障频率{f_s}为38.34 Hz,行星轮故障频率{f_p}为10.83 Hz。

    由传感器1和传感器2采集的2组信号都具有相同的运动状态,即同时加速或同时减速。因此本文在平稳阶段选取水平方向传感器1的振动信号用以分析机械臂的运动状态。图7为选取的振动信号进行STFT获得的时频图。可以看出,由于RV减速器的瞬时冲击过大,无法通过时频图区分出机械臂的3种运动状态,即启动加速阶段,恒速运动阶段以及减速停滞阶段。

    图  7  基于STFT的时频图
    Figure  7.  Time-frequency diagram based on STFT

    时频图中的脊线对应时频域中能量最大的路径,可以近似看作设备瞬时频率的时频轨迹。对时频图进行脊线提取,结果如图8所示。分析脊线走势能够较为清楚地区分机械臂的不同运行阶段,包括启动加速阶段,平稳运行阶段以及减速停滞阶段(后续分析均为此阶段)。图9a为水平方向传感器1采集信号的时域波形,图9b为垂直方向传感器2采集信号的时域波形。图9时域波形体现了机械臂启动、平稳到停止整个工作过程幅值的变化。依据图8中脊线的平稳阶段区间,在图9中标注同步截取相应时段的时域振动信号(后续分析皆是截取后的振动信号)。

    图  8  基于时频图像提取的时频脊线
    Figure  8.  Time-frequency ridges extracted from TFR

    图10a为截取平稳阶段传感器1的信号波形,图10b为截取平稳阶段传感器2信号波形。对图10振动信号进行SMF处理,对图10振动信号进行SMF处理,传感器2的滤波前后的信号波形对比如图11所示,从图11b中能够观测到故障所导致的冲击更加明显。

    图  9  基于时频脊线的传感器信号同步截取
    Figure  9.  Synchronous sensor signal interception based on time-frequency ridge
    图  10  恒速阶段的时域波形
    Figure  10.  Time domain waveform of constant velocity phase
    图  11  传感器2的滤波前后信号波形对比
    Figure  11.  Comparison of signal waveforms of sensor 2 before and after filtering

    对滤波后的信号进行包络谱分析,如图12所示,传感器1和传感器2滤波信号的频谱分别如图12a、12b所示。分析图12a、12b发现,太阳轮与行星轮的故障特征频率成分完全混合在一起,故障类型判断困难。

    图  12  恒速阶段的频域波形
    Figure  12.  Frequency domain waveform of constant velocity phase

    经SMF-DPC-OMP算法处理的频谱如图13所示,图13a的频率谱线集中在37.5 Hz及其倍频,与太阳轮理论计算故障频率38.34 Hz接近,故可推断图13a为太阳轮故障。图13b的频率谱线分布在10.94 Hz及其倍频,与行星轮理论计算故障频率10.83 Hz逼近,故识别其为行星轮故障。相比图12图13中的频率混合现象已经完全被消除,说明本文方法可实现复合故障的完全分离。采用文献[29]提出的结合形态滤波与稀疏分量分析(MF-SCA)的盲分离算法进行对比进一步验证本文方法的有效性,结果如图14所示,分析可见,图14a、14b均存在太阳轮和行星轮故障特征频率,说明MF-SCA方法无法有效实现RV减速器复合故障的分离。与MF-SCA方法相比,SMF-DPC-OMP算法能够节省约75%的时间运行成本。

    图  13  复合故障频谱SMF-DPC-OMP分离结果
    注:fs为太阳轮故障频率,fp为行星轮故障频率,Hz。
    Figure  13.  Separation composite faults spectrum by SMF-DPC-OMP
    Note: fs is the Sun gear fourlty frequency, fp is the planetary gear fourlty frequency, Hz.
    图  14  复合故障频谱MF- SCA分离结果
    Figure  14.  Separation composite faults spectrum by MF-SCA

    本文结合时频图像脊线提取、\sin C函数改进形态滤波和密度峰值聚类改进的稀疏分量分析各算法的优点,提出一种新的往复运动、变转速工况的RV减速器复合故障盲分离方法。通过RETE算法提取的脊线解决旋转机械变转速的问题,利用SMF-DPC-OMP实现了RV减速器复合故障的分离提取。试验台采集的RV减速器的太阳轮和行星轮磨损复合故障信号的分析结果显示,本文方法能够有效地完成复合故障的盲分离任务,主要结论如下:

    1)RETE算法能够在变转速工况导致时频图较为模糊的情况下,识别出RV减速器的运动状态;

    2)SMF-DPC-OMP算法能够在故障源数目未知的情况下,有效完成复合故障的盲分离任务;

    3)与MF-SCA方法比较,SMF-DPC-OMP算法能够节省约75%的时间运行成本,使得频谱更为简洁,抑制精细侧频和干扰分量。

    本文今后的工作将重点放在欠定条件下的故障提取上,或者进一步将该算法推广到旋转机械声信号的故障诊断中。

  • [1] 中国工程院"21世纪中国可持续发展水资源战略研究"项目组. 中国可持续发展水资源战略研究综合报告[J]. 中国工程科学,2000,2(8):1-17. Project Group of "Strategic Research on Sustainable Development of Water Resource in China in 21st Century". Strategic research on sustainable development of water resource in China[J]. Chinese Academy of Engineering, 2000, 2(8): 1-17. (in Chinese with English abstract)
    [2] 张春娟,郑新让,张迪. 冯家山水库引水工程爆管事故分析[J]. 中国农村水利水电,2005(5):81-82. ZHANG Chunjuan, ZHENG Xinrang, ZHANG Di. Analysis on pipe burst accident of Fengjiashan Reservoir Diversion Project[J]. China Rural Water and Hydropower, 2005(5): 81-82. (in Chinese with English abstract)
    [3] 王振华,马习贺,李文昊,等. 基于改进4-方程摩擦模型的输水管道水锤压力计算[J]. 农业工程学报,2018,34(7):114-120. WANG Zhenhua, MA Xihe, LI Wenhao, et al. Calculation of water hammer pressure of flow pipeline based on modified four-equation friction model[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2018, 34(7): 114-120. (in Chinese with English abstract)
    [4] 张巧玲,黄铋匀,杨振东,等. 基于特征线法的含气输水管道水锤特性分析[J]. 农业工程学报,2022,38(5):79-86. ZHANG Qiaolin, HUANG Biyun, YANG Zhendong, et al. Water hammer properties of gas-bearing water pipeline using characteristics method[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2022, 38(5): 79-86. (in Chinese with English abstract)
    [5] WANG H, ZHOU L, LIU D, et al. CFD approach for column separation in water pipelines[J]. Journal of Hydraulic Engineering, 2016, 142(10): 04016036.
    [6] 富友,蒋劲,李燕辉,等. 改进双流体模型计算有液柱分离的管路水锤压力[J]. 农业工程学报,2018,34(15):58-65. FU You, JIANG Jin, LI Yanhui, et al. Calculation of pipe water hammer pressure with liquid column separation by improved two-fluid model[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2018, 34(15): 58-65. (in Chinese with English abstract)
    [7] 韩凯,丁法龙,茅泽育. 半解析法求解水柱分离与断流弥合水锤问题及机理分析[J]. 农业工程学报, 2019, 35(15):33-39. HAN Kai, DING Falong, MAO Zeyu. Solving water column separation and cavity collapse for pipelines by semi-analytical method[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2019, 35(15): 33-39. (in Chinese with English abstract)
    [8] 高金良,郑成志,刁美玲,等. 高起伏长输管线水锤模拟及防护方案优选[J]. 哈尔滨工业大学学报, 2012, 44(8):24-26,38. GAO Jinliang, ZHENG Chengzhi, DIAO Meiling, et al. Study on optimal surge protection for high-undulate long-distance water transmission pipeline[J]. Journal of Harbin Institute of Technology, 2012, 44(8): 24-26, 38. (in Chinese with English abstract)
    [9] 齐敦哲,郝建志,吴福臣,等. 长管道工程中空气阀与单向调压塔水锤防护比较与优化[J]. 中国农村水利水电,2012(12):134-136. QI Dunzhe, HAO Jianzhi, WU Fuchen, et al. Comparison and optimization of water hammer protection between air valve and one-way surge tank in long pipeline engineering[J]. China Rural Water and Hydropower, 2012(12): 134-136. (in Chinese with English abstract)
    [10] 刘梅清,冯卫民. 单向调压塔防水锤特性的数值模拟与研究[J]. 水利学报,1995(10):23-28,34. LIU Meiqing, FENG Weiming. Numerical simulation and research on the characteristics of water hammer with one-way surge tank protection[J]. Journal of Hydraulic Engineering, 1995(10): 23-28, 34. (in Chinese with English abstract)
    [11] 徐进,张健. 长距离输水复杂管线下单向塔布置方案优化[J]. 水电能源科学,2009,27(5):139-141,135. XU Jin, ZHANG Jian. Study on optimal layout of one-way surge tank in complex long-distance water transfer project[J]. Water Resources and Power, 2009, 27(5): 139-141, 135. (in Chinese with English abstract)
    [12] 张健,索丽生,胡建永,等. 长距离供水工程单向塔设置分析[J]. 水力发电学报, 2011, 30(1):49-56. ZHANG Jian, SUO Lisheng, HU Jianyong, et al. Study on water hammer control by one-way surge tank in long-distance water-supply project[J]. Journal of Hydroelectric Engineering, 2011, 30(1): 49-56. (in Chinese with English abstract)
    [13] 胡建永,杨飞. 设置单向塔的输水工程爆管影响分析[J]. 中国农村水利水电,2013(12):122-124,129. HU Jianyong, YANG Fei. The influence of pipe burst on water supply projects with one-way surge tanks[J]. China Rural Water and Hydropower, 2013(12): 122-124, 129. (in Chinese with English abstract)
    [14] CHEN X, ZHANG J, YU X, et al. Study on impedance size optimization of a one-way surge tank in a long-distance water supply system[J]. Water Supply, 2021, 21(2): 868-877.
    [15] WYLIE E B, STREETER V L, SUO L S. Fluid Transients in Systems[M]. Englewood Cliffs, NJ: Prentice Hall, 1993.
    [16] 王新宏,龚立尧,吴巍,等. 高含沙河流供水水库运用方式研究:以王瑶水库为例[J]. 泥沙研究, 2018, 43(2):33-39. WANG Xinhong, GONG Liyao, WU Wei, et al. Reservoir operation patterns of water-supply reservoir in sediment-laden river: A case study on the Wangyao Reservior[J]. Journal of Sediment Research, 2018, 43(2): 33-39. (in Chinese with English abstract)
    [17] HAN W L, DONG Z N, CHAI H G. Water hammer in pipelines with hyperconcentrated slurry flows carrying solid particles[J]. Science in China (Series E: Technological Sciences), 1998(4): 337-347.
    [18] 韩文亮,王光谦,韩军. 两相流水击模型对输送防护措施效果的计算分析[J]. 水利学报,2000(3):39-43. HAN Wenliang, WANG Guangqian, HAN Jun. Computational analysis of water hammer prevention devices for solid-liquid two-phase flow pipelines[J]. Journal of Hydraulic Engineering, 2000(3): 39-43. (in Chinese with English abstract)
    [19] KODURA A, STEFANEK P, WEINEROWSKA-BORDS K. An experimental and numerical analysis of water hammer phenomenon in slurries[J]. Journal of Fluids Engineering, 2017, 139(12).
    [20] 汪怡然,俞晓东,石林,等. 输水管道含沙水锤模型及特性研究[J]. 水利学报,2022,53(8):984-990. WANG Yiran, YU Xiaodong, SHI Lin, et al. Models and characteristics of sand-contained water hammer in heterogeneous flow water transfer conduit[J]. Journal of Hydraulic Engineering, 2022, 53(8): 984-990. (in Chinese with English abstract)
    [21] 李珊珊,李国栋,张巧玲,等. 管道输沙阻力损失规律的多相流数值模拟研究[J]. 西安理工大学学报, 2017, 33(1):29-35. LI Shanshan, LI Guodong, ZHANG Qiaoling, et al. Numerical simulation of multiphase flow on the law of resistance loss of pipeline transportation[J]. Journal of Xi'an University of Technology, 2017, 33(1): 29-35. (in Chinese with English abstract)
    [22] 宗全利,汤骅,安杰. 低压灌溉管道输浑水阻力损失试验与建模[J]. 农业机械学报,2013,44(6):148-155. ZONG Quanli, TANG Hua, AN Jie, et al. Experiment and modelling on resistance loss of muddy water delivery for irrigation in low-pressure pipeline system[J]. Transactions of the Chinese Society for Agricultural Machinery, 2013, 44(6): 148-155. (in Chinese with English abstract)
    [23] 陈广文,古德生,高泉. 浆体水平管道输送阻力损失计算探讨[J]. 中南矿冶学院学报,1994(2):162-166. CHEN Guangwen, GU Desheng, GAO Quan. Exploration of drag losses calculation in slurry horizontal pipeline transportation[J]. Journal of Central-South Institute of Mining and Metallurgy, 1994(2): 162-166. (in Chinese with English abstract)
    [24] 赵立娟,倪福生,顾磊. 管道输沙Wasp阻力模型探讨[J]. 泥沙研究,2012(6):75-80. ZHAO Lijuan, NI Fusheng, GU Lei. Discussion on resistance calculation of sediment hydraulic transport in pipeline based on Wasp model[J]. Journal of Sediment Research, 2012(6): 75-80. (in Chinese with English abstract)
    [25] 邓祥吉,倪福生,罗荣民. 管道输沙阻力损失的2种计算模型[J]. 河海大学常州分校学报,2005,19(1):54-56,60. DENG Xiangji, NI Fusheng, LUO Rongmin. Two models for friction loss in slurry pipeline transport[J]. Journal of Hohai Universtiy Changzhou, 2005, 19(1): 54-56, 60. (in Chinese with English abstract)
    [26] 张瑞瑾. 河流动力学[M]. 北京:中国工业出版社,1961 .
    [27] YU C, YU X D, ZHANG L, et al. Approximate approach for improving pressure attenuation accuracy during hydraulic transients[J]. Water Supply, 2022, 22(3): 3387-3398.
    [28] 李岩,张金良,白玉川,等. 有压输沙管道脉动压强特性试验研究[J]. 水利学报,2020,51(8):967-978. LI Yan, ZHANG Jinliang, BAI Yuchuan, et al. Experimental study on characteristics of fluctuating pressure in sediment flow pipeline[J]. Journal of Hydraulic Engineering, 2020, 51(8): 967-978. (in Chinese with English abstract)
    [29] 李琳,付海林,谭义海,等. 新型异向流沉沙池泥沙沉降特性试验与机理分析[J]. 农业工程学报,2021,37(16):90-98. LI Lin, FU Hailin, TAN Yimei, et al. Hydraulic sediment characteristics test and mechanism analysis of a new type of anisotropic flow sedimentation basin[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2021, 37(16): 90-98. (in Chinese with English abstract)
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  • 收稿日期:  2022-11-28
  • 修回日期:  2023-02-11
  • 发布日期:  2023-02-27

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