Modeling Multiple Components Mechanical Signals by Means of Virtual Sample Generation Technique
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摘要: 采用具有多组分、非平稳、非线性等特性的机械振动/振声信号构建数据驱动软测量模型，是目前工业界测量高能耗旋转机械设备内部难以检测过程参数的常用手段.针对机械信号产生机理的复杂性导致模型解释性弱，以及工业过程连续不间断运行和机械设备旋转封闭的特殊性导致获取完备训练样本的经济性差和周期性长等问题，本文提出一种基于虚拟样本生成（Virtual sample generation，VSG）技术的多组分机械信号建模方法.首先，将机械信号自适应分解为具有不同时间尺度的平稳子信号并变换为多尺度谱数据；接着，采用适合于小样本高维数据建模的改进选择性集成核偏最小二乘（Selective ensemble kernel partial least squares，SENKPLS）算法构建面向真实训练样本的基于可行性的规划（Feasibility-based programming，FBP）模型，提出一种综合先验知识和FBP模型等手段面向高维谱数据的VSG技术，用以弥补真实训练样本的短缺问题；然后，基于互信息（Mutual information，MI）对由真实和虚拟训练样本组成的混合建模数据进行自适应特征选择；最后，基于约简的混合训练样本采用SENKPLS构建软测量模型.以近红外谱数据和磨矿过程实验球磨机的筒体振动/振声信号验证所提VSG技术和面向多组分机械信号建模方法的合理性和有效性.Abstract: Mechanical vibration & acoustic signals with characteristics of multiple components, nonstationarity and nonlinearity are always used to construct the data-driven soft sensor model of industrial processes. It is one of the main approaches to measure the difficulty-to-measure process parameters inside those high energy consumption mechanical devices. Duo to the complexity of the production mechanism of these mechanical signals, most of these soft sensor models are difficult to be explained. Moreover, the characteristics of the industrial process' continuous running and the mechanical equipment' operation modes lead to the difficulty of high economic cost and long period waiting to obtain sufficient training samples. To solve these problems, a new multi-component mechanical signal modeling method based on virtual sample generation (VSG) technology is proposed. Firstly, the mechanical signals are processed into a set of sub-signals with different time scales by using adaptive multi-component signal decomposition technique; then these sub-signals are transferred to high dimensional multi-scale spectral data. Secondly, an improved selective ensemble kernel partial least squares (SENKPLS) algorithm that suits to model small sample high dimensional data is used to construct a feasibility-based programming (FBP) model with the true training samples; then prior knowledge, FBP models and information entropy are integrated to produce virtual training samples. Thirdly, mutual information (MI) method is used to select the spectral features of the new mixing training samples based on the true and virtual ones. Finally, a soft sensor model is built by using these reduced mixing spectral data. Near-infra spectra data and mechanical vibration and acoustic singals of a laboratory-scale ball mill in grinding process validate the reasonability and effectiveness of the proposed VSG techniques and multi-component mechanical signals-based modeling approach.1) 本文责任编委 侯忠生
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图 1 基于VSG的多组分机械信号建模策略
Fig. 1 Multi-component mechanical signal modeling strategy based on VSG
图 7 基于不同数量的虚拟样本构建模型的训练误差
Fig. 7 Training errors of the constructed model based on virtual samples with different numbers
图 8 某选矿厂一段磨矿回路(GC Ⅰ)工艺流程
Fig. 8 Flow chart of the grinding circuit Ⅰ (GC Ⅰ) of some mineral grinding process
图 9 磨机筒体振动的VIMF1~10子信号的真实谱数据
Fig. 9 True spectra data of VIMF1~10 sub-signals from mill shell vibration signal
图 10 磨机振声AIMF1~10子信号的真实谱数据
Fig. 10 True spectra data of VIMF1~10 sub-signals from mill acoustic signal
图 11 磨机筒体振动VIMF1~10的虚拟谱数据
Fig. 11 Virtual spectra data of VIMF1~10 sub-signals from mill shell vibration signal
图 12 磨机振声AIMF1~10的虚拟谱数据
Fig. 12 Virtual spectra data of AIMF1~10 sub-signals from mill acoustic signal
图 13 基于不同${N_{{\rm{VSG}}}}$值构建的软测量模型测试误差的方差
Fig. 13 Variance of the testing errors based on soft sensor models using different ${N_{{\rm{VSG}}}}$ values
图 14 基于不同${N_{{\rm{VSG}}}}$值构建的软测量模型的测试误差
Fig. 14 Testing errors based on soft sensor models using different ${N_{{\rm{VSG}}}}$ values
表 1 基于PLS提取的潜在特征的贡献率
Table 1 Contribution of the latent features extracted based on PLS
LV# 输入单LV 输入累计 输出单LV 输出累计 1 88.85 88.85 23.78 23.78 2 10.96 99.8 19 42.78 3 0.17 99.97 20.8 63.57 4 0.01 99.98 21.77 85.35 5 0.01 99.99 8.63 93.98 
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表 2 基于混合样本建立的NIR模型统计结果
Table 2 Statistical results of NIR model based on mixed samples
真实样本数量 虚拟样本数量 核半径值 KLV数量 均值(Mean) 最大值(Max) 最小值(Min) 方差(Var) 15 0 600 10 7.188 9.0742 5.6867 0.9779 15 14 65 12 6.9473 9.3558 5.9747 0.8814 15 28 50 15 7.7808 11.2846 6.2231 1.2904 15 42 0.8 13 8.9316 10.3599 7.7212 0.7781 15 56 10 14 7.7027 12.2875 6.0686 1.6912 15 70 60 13 8.3782 11.6499 7.2438 1.0895 15 84 60 10 7.0026 7.6549 6.5843 0.3273 15 98 65 12 7.3832 8.4788 6.8142 0.4051 15 112 75 9 6.0723 6.8627 5.8029 0.2375 15 126 19 12 8.1114 10.0179 6.5984 0.8225
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表 3 用于产生虚拟样本的真实训练样本分布
Table 3 Distribution of the true training samples for generating virtual samples
样本序号 1 2 3 4 5 6 7 8 9 10 11 12 13 固定负荷(kg) 料10 料10 料10 水2 水2 水2 料20 料20 料20 水10 水10 水10 水10 变化负荷(kg) 水5 水15 水20 料10 料1 6 料20 水7.5 水12.5 水20 料24 料28 料35 料45
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表 4 面向CVR的谱特征选择的统计结果
Table 4 Statistical results of spectra feature selection for CVR
真实样本数量 虚拟样本数量 振动特征数量 振声特征数量 特征数量总和 MI阈值 13 9 1 344 190 1 534 0.8 13 18 473 71 514 0.9 13 27 3 388 1 878 5 266 0.2 13 36 895 175 1 070 0.8 13 45 3 396 1 870 5 266 0.2 13 54 3 387 1 869 5 256 0.2 13 63 3 403 1 880 5 283 0.1 13 72 3 384 1 865 5 249 0.2 13 81 3 403 1 879 5 282 0.1
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表 5 基于不同数量混合样本构建的软测量模型的统计结果
Table 5 Statistical results of soft sensor models based on mix samples with different number
真实样本数量 虚拟样本数量 RMSREP均值
(Mean)RMSREP最小值
(Min)RMSREP最大值
(Max)RMSREP方差
(Var)PLS 26 0 0.3445 0.1492 0.5803 0.0977 KPLS 26 0 0.1839 0.0704 0.4598 0.0947 文献[24] 26 0 0.1265 0.0381 0.4263 0.0677 文献[20] 26 0 0.3424 0.1967 0.4773 0.0778 文献[21] 26 0 0.2184 0.0968 0.4418 0.0858 本文 26 0 0.1708 0.0771 0.2829 0.0694 方法 26 9 0.1651 0.118 0.2591 0.0382 26 18 0.149 0.0966 0.2135 0.0288 26 27 0.1449 0.0916 0.2159 0.0337 26 36 0.1345 0.0994 0.1775 0.0172 26 45 0.1397 0.0909 0.2011 0.0286 26 54 0.1439 0.0981 0.1914 0.0266 26 63 0.1321 0.0987 0.1849 0.0208 26 72 0.1366 0.1069 0.1828 0.0203 26 81 0.129 0.0988 0.1749 0.0199 注: 表 5中的26个真实样本中, 仅是表 3中所示的13个用于产生虚拟样本.
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