An Industrial Signal Generation Method Based on Lightweight Conditional Diffusion Model
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摘要: 深度学习模型为缓解数据不均衡问题提供有效途径, 然而, 现有方法难以兼顾生成质量与计算效率, 例如生成对抗网络存在训练不稳定问题, 扩散模型的计算复杂度较高. 为提高工业信号可用性, 提出基于轻量化条件扩散模型的工业信号生成方法, 在保持扩散模型生成优势的同时显著提高训练效率, 并降低模型推理计算量. 该方法主要分为自编码器信号降维与扩散模型样本生成两阶段. 阶段一基于自编码器建立原始信号的隐变量分布结果, 构建轻量化的低维空间, 以提高整体模型的计算效率. 阶段二通过条件扩散模型的马尔可夫链噪声推理过程, 对阶段一的输出结果进行重建, 以获取高质量的工业信号. 针对轻量化空间取值有限导致的类别混叠问题, 以聚合同类并区分异类为目标, 设计对比学习损失提高空间中的类别区分度. 考虑到故障幅值分布特征表现为周期性衰减冲击, 提出分解损失函数挖掘信号隐藏特征并提升生成样本质量. 在两种数据集的实验结果表明, 该方法能够为工业系统提供可靠数据支持.Abstract: Deep learning models provide an effective approach to alleviating data imbalance. However, generation quality and computational efficiency are difficult to balance in existing methods. For example, generative adversarial networks suffer from unstable training, while diffusion models require high computational complexity. To improve the usability of industrial signals, an industrial signal generation method based on lightweight conditional diffusion model is proposed. The generation advantages of diffusion models are retained. Meanwhile, training efficiency is significantly improved, and the computational cost of model inference is reduced. The proposed method consists of two stages: Signal dimensionality reduction using an autoencoder and sample generation using a diffusion model. In the first stage, the latent variable distribution results of the original signal are learned by an autoencoder. A lightweight low-dimensional space is then constructed to improve the computational efficiency of the overall model. In the second stage, the output of the first stage is reconstructed through the Markov-chain-based denoising process of a conditional diffusion model. High-quality industrial signals are thereby generated. The limited range of values in the lightweight space may cause class confusion. To address this problem, a contrastive learning loss is designed to aggregate samples from the same class and separate samples from different classes. Consequently, class discriminability in the lightweight space is improved. Fault amplitude distributions are characterized by periodic decaying impulses. Therefore, a decomposition loss function is proposed to capture hidden signal characteristics and improve the quality of generated samples. Experimental results on two datasets demonstrate that the proposed method can provide reliable data support for industrial systems.
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Key words:
- generative model /
- neural network /
- diffusion model /
- autoencoder /
- contrastive learning
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图 2 基于自编码器的轻量化空间信号降维
Fig. 2 Autoencoder-based signal dimensionality reduction in the lightweight space
图 6 XJTU-SY数据集时频域波形
Fig. 6 Time- and frequency-domain waveforms of the XJTU-SY dataset
图 7 三轴轴承振动数据集实验平台
Fig. 7 Experimental platform for the triaxial bearing vibration dataset
图 8 三轴轴承振动数据集时频域波形
Fig. 8 Time- and frequency-domain waveforms of the triaxial bearing vibration dataset
图 9 XJTU-SY数据集生成信号的时频域分析
Fig. 9 Time- and frequency-domain analysis of signals generated on the XJTU-SY dataset
图 10 三轴轴承振动数据集生成信号的时频域分析
Fig. 10 Time- and frequency-domain analysis of signals generated on the triaxial bearing vibration dataset
图 11 XJTU-SY数据集上生成信号与真实样本之间的PSD重叠度
Fig. 11 PSD overlap between generated signals and real samples on the XJTU-SY dataset
图 12 XJTU-SY数据集外圈磨损的t-SNE降维可视化
Fig. 12 t-SNE dimensionality-reduction visualization of outer-race wear on the XJTU-SY dataset
图 13 三轴轴承振动数据集内圈磨损的PCA降维可视化(损伤直径为1.1 mm)
Fig. 13 PCA dimensionality-reduction visualization of inner-race wear on the triaxial bearing vibration dataset (damage diameter: 1.1 mm)
图 14 XJTU-SY数据集在1 : 2不均衡率下的混淆矩阵 (横轴: 预测类别, 纵轴: 真实类别)
Fig. 14 Confusion matrix for the XJTU-SY dataset at an imbalance ratio of 1 : 2 (horizontal axis: Predicted class, vertical axis: True class)
图 15 三轴轴承振动数据集在1 : 10不均衡率下的混淆矩阵 (横轴: 预测类别, 纵轴: 真实类别)
Fig. 15 Confusion matrix for the triaxial bearing vibration dataset at an imbalance ratio of 1 : 10 (horizontal axis: Predicted class, vertical axis: True class)
图 16 生成模型在不同分类器上的故障诊断结果
Fig. 16 Fault diagnosis results of generative models using different classifiers
图 17 不同类型工业信号生成样本的t-SNE可视化分析结果
Fig. 17 t-SNE visual analysis results of different types of industrial signal generated samples
表 1 实验设置和参数对比
Table 1 Comparison of experimental settings and parameters
模型 组成模块 训练批次 训练轮次
($ \times\,\; 10^{3} $)学习率
($ \times\,\; 10^{-4} $)优化器 CVAE – 128 50 5 Adam DDPM – 64 5 20 AdamW TTS-GAN – 128 10 50 AdamW DIFFUSION-TS – 32 20 2 Adam JiT – 64 1 1 AdamW TimeVQVAE A1 32 5 50 AdamW A2 32 5 50 AdamW LC-DiffAE B1 128 20 2 Adam B2 128 10 3 AdamW 注: A1表示VQ-VAE训练与码本生成, A2表示码本学习与数据生成. B1表示自编码器样本降维, B2表示扩散模型样本生成. 
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表 2 相似性、多样性指标的表达式及值域
Table 2 Expressions and value ranges of similarity and diversity metrics
指标 类型 定义 表达式 值域 JSD$ \downarrow $ 相似性指标 计算$P(x)$、$Q(x)$和$M(x)$的KL散度平均值, 以评估分布差异 $ \text{JSD}(P\|Q) = \dfrac{\mathrm{KL}(P\|M)+\mathrm{KL}(Q\|M)}{2} $ $ [0,\;1] $ WD$ \downarrow $ 相似性指标 衡量将概率分布$P(x)$转化为另一个分布$Q(x)$所需的最小传输代价 $ \text{WD}(P,\;Q) = \left( \inf\limits_{\gamma\in\Gamma(P,\;Q)} \int \|x-y\|^{p}\,\; \mathrm{d}\gamma(x,\;y) \right)^{1/p} $ $ [0,\;+\infty) $ MMD$ \downarrow $ 相似性指标 一种基于核的非参数度量, 用于估计分布在再生核希尔伯特空间中的均值嵌入差异 $ \begin{gathered} \text{MMD}^{2}(P,\;Q) = \mathrm{E}_{x,\;x'\sim P} \left[k(x,\;x')\right] +\\ \mathrm{E}_{y,\;y'\sim Q} \left[k(y,\;y')\right] - 2\mathrm{E}_{x\sim P,\;\,\;y\sim Q} \left[k(x,\;y)\right] \end{gathered} $ $ [0,\;+\infty) $ CS$ \downarrow $ 相似性指标 通过计算分布之间的交叉相关矩阵绝对误差, 衡量分布的一致性程度 $ \text{CS}(P,\;Q) = \dfrac{1}{D^{2}} \sum\limits_{i=1}^{D} \sum\limits_{j=1}^{D} \left| R_{P}(i,\;j)-R_{Q}(i,\;j) \right| $ $ [0,\;2] $ DS$ \downarrow $ 相似性指标 用于区分不同类型的数据分布, 以反映分布之间的相似性 $ \text{DS}(P,\;Q) = \left| \mathrm{accuracy}-0.5 \right| $ $ [0,\;0.5] $ ICD$ \uparrow $ 多样性指标 计算同一类别生成样本$x_i$与$x_j$之间的平均距离$d$ $ \text{ICD} = \dfrac{2}{N(N-1)} \sum\limits_{i<j} d(x_i,\;x_j) $ $ [0,\;1] $ BGS$ \uparrow $ 多样性指标 在距离上下界约束内, 通过贪心算法选择与已选样本集合$S$差异较大的样本 $ \text{BGS} = \dfrac{1}{|S|} \sum\limits_{x_i\in S} \left[ 1-d(x_i,\;x_j) \right] $ $ [0,\;1] $ MGS$ \uparrow $ 多样性指标 通过正交基向量$q_j$, 计算新样本相对于已有样本特征$z_i$的正交残差 $ \text{MGS} = \dfrac{1}{N} \sum\limits_{i=1}^{N} \left\| z_i- \sum\limits_{j=1}^{i-1} \left(q_j^{\mathrm{T}}z_i\right)q_j \right\|_{2} $ $ [0,\;1] $ 注: $ \downarrow $表示指标值越小, 分布间的相似程度越高; $ \uparrow $表示指标值越大, 生成样本的多样性越高.
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表 3 相似性指标度量结果
Table 3 Similarity metric evaluation results
数据集 指标 CVAE DDPM TTS-GAN DIFFUSION-TS JiT TimeVQVAE LC-DiffAE XJTU-SY JSD $ 0.145\pm0.021 $ $ 0.241\pm0.017 $ $ 0.162\pm0.013 $ $ 0.602\pm0.011 $ $ 0.156\pm0.008 $ $ 0.350\pm0.042 $ 0.123±0.013 WD $ 1.423\pm0.010 $ $ 5.600\pm0.108 $ $ 1.013\pm0.017 $ $ 2.784\pm0.044 $ $ 1.472\pm0.020 $ $ 2.355\pm0.032 $ 0.990±0.020 MMD $ 0.073\pm0.011 $ $ 0.075\pm0.007 $ $ 0.280\pm0.051 $ $ 0.161\pm0.012 $ $ 0.042\pm0.007 $ $ 0.126\pm0.012 $ 0.017±0.003 CS $ 0.011\pm0.003 $ $ 0.019\pm0.003 $ $ 0.039\pm0.011 $ $ 0.008\pm0.002 $ 0.004±0.002 $ 0.007\pm0.002 $ $ 0.009\pm0.002 $ DS $ 0.287\pm0.018 $ $ 0.270\pm0.019 $ $ 0.438\pm0.014 $ $ 0.431\pm0.022 $ 0.096±0.012 $ 0.450\pm0.026 $ $ 0.149\pm0.012 $ 三轴轴承振动 JSD $ 0.452\pm0.016 $ $ 0.420\pm0.013 $ $ 0.421\pm0.045 $ $ 0.620\pm0.019 $ $ 0.227\pm0.024 $ $ 0.491\pm0.043 $ 0.225±0.013 WD $ 3.715\pm0.096 $ $ 3.704\pm0.071 $ $ 3.670\pm0.067 $ $ 5.472\pm0.084 $ $ 2.971\pm0.089 $ $ 5.001\pm0.076 $ 1.423±0.025 MMD $ 0.147\pm0.005 $ $ 0.077\pm0.005 $ $ 0.244\pm0.005 $ $ 0.226\pm0.036 $ $ 0.073\pm0.014 $ $ 0.229\pm0.035 $ 0.015±0.003 CS $ 0.041\pm0.012 $ $ 0.026\pm0.002 $ $ 0.127\pm0.013 $ 0.009±0.002 $ 0.049\pm0.013 $ $ 0.036\pm0.004 $ $ 0.025\pm0.007 $ DS $ 0.478\pm0.012 $ 0.312±0.016 $ 0.470\pm0.011 $ $ 0.480\pm0.006 $ $ 0.469\pm0.013 $ $ 0.490\pm0.002 $ $ 0.476\pm0.005 $
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表 4 不同模型生成样本与真实样本之间的分布重叠度比较
Table 4 Comparison of distribution overlaps between generated and real samples from different models
模型 XJTU-SY 三轴轴承振动 PSD KDE PSD KDE CVAE 0.549 0.818 0.506 0.693 DDPM 0.391 0.618 0.430 0.580 TTS-GAN 0.311 0.823 0.333 0.508 DIFFUSION-TS 0.063 0.103 0.125 0.084 JiT 0.914 0.927 0.708 0.698 TimeVQVAE 0.184 0.282 0.025 0.272 LC-DiffAE 0.815 0.936 0.734 0.841
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表 5 多样性指标定量评估结果
Table 5 Quantitative evaluation results of diversity metrics
模型 XJTU-SY 三轴轴承振动 ICD BGS MGS ICD BGS MGS CVAE 0.803 0.739 0.749 0.646 0.457 0.499 DDPM 0.921 0.776 0.732 0.744 0.674 0.757 TTS-GAN 0.122 0.094 0.203 0.009 0.001 0.093 DIFFUSION-TS 0.015 0.040 0.109 0.084 0.056 0.211 JiT 0.974 0.777 0.763 0.834 0.371 0.542 TimeVQVAE 0.881 0.778 0.786 0.809 0.474 0.652 LC-DiffAE 0.969 0.882 0.887 0.899 0.701 0.723
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表 6 不同不均衡率下的分类结果
Table 6 Classification results under different imbalance ratios
不均
衡率数据集 指标 真实信号 CVAE DDPM TTS-GAN DIFFUSION-TS JiT TimeVQ VAE LC-DiffAE 1 : 2 准确率 $0.871 \pm 0.030$ $0.914 \pm 0.015$ $0.847 \pm 0.038$ $0.921 \pm 0.017$ $0.896 \pm 0.040$ $0.936 \pm 0.016$ $0.910 \pm 0.010$ 0.974±0.010 XJTU-
SY精确率 $0.873 \pm 0.021$ $0.922 \pm 0.018$ $0.850 \pm 0.043$ $0.928 \pm 0.013$ $0.920 \pm 0.017$ $0.944 \pm 0.014$ $0.917 \pm 0.011$ 0.974±0.009 召回率 $0.839 \pm 0.038$ $0.914 \pm 0.015$ $0.847 \pm 0.038$ $0.921 \pm 0.017$ $0.896 \pm 0.040$ $0.936 \pm 0.016$ $0.910 \pm 0.010$ 0.974±0.010 F1分数 $0.838 \pm 0.044$ $0.914 \pm 0.015$ $0.843 \pm 0.039$ $0.920 \pm 0.007$ $0.892 \pm 0.045$ $0.936 \pm 0.017$ $0.909 \pm 0.011$ 0.974±0.010 准确率 $0.977 \pm 0.014$ $0.931 \pm 0.019$ $0.952 \pm 0.015$ $0.963 \pm 0.016$ $0.929 \pm 0.020$ $0.977 \pm 0.026$ $0.971 \pm 0.008$ 0.987±0.012 三轴轴承
振动精确率 $0.974 \pm 0.016$ $0.951 \pm 0.007$ $0.963 \pm 0.011$ $0.967 \pm 0.012$ $0.932 \pm 0.018$ $0.978 \pm 0.016$ $0.974 \pm 0.005$ 0.987±0.009 召回率 $0.974 \pm 0.016$ $0.931 \pm 0.019$ $0.952 \pm 0.015$ $0.963 \pm 0.016$ $0.929 \pm 0.020$ $0.977 \pm 0.013$ $0.971 \pm 0.008$ 0.987±0.012 F1分数 $0.974 \pm 0.016$ $0.929 \pm 0.020$ $0.952 \pm 0.016$ $0.963 \pm 0.017$ $0.929 \pm 0.020$ $0.977 \pm 0.026$ $0.971 \pm 0.008$ 0.987±0.014 1 : 5 准确率 $0.932 \pm 0.005$ $0.908 \pm 0.056$ $0.843 \pm 0.032$ $0.921 \pm 0.013$ $0.853 \pm 0.074$ $0.943 \pm 0.017$ $0.902 \pm 0.010$ 0.961±0.010 XJTU-
SY精确率 $0.892 \pm 0.002$ $0.929 \pm 0.026$ $0.848 \pm 0.032$ $0.924 \pm 0.012$ $0.893 \pm 0.043$ $0.949 \pm 0.020$ $0.914 \pm 0.002$ 0.961±0.010 召回率 $0.864 \pm 0.010$ $0.908 \pm 0.056$ $0.843 \pm 0.032$ $0.921 \pm 0.013$ $0.853 \pm 0.074$ $0.943 \pm 0.017$ $0.902 \pm 0.010$ 0.961±0.010 F1分数 $0.867 \pm 0.015$ $0.902 \pm 0.064$ $0.841 \pm 0.032$ $0.920 \pm 0.012$ $0.833 \pm 0.091$ $0.943 \pm 0.009$ $0.900 \pm 0.011$ 0.960±0.010 准确率 $0.973 \pm 0.018$ $0.924 \pm 0.010$ $0.954 \pm 0.022$ $0.956 \pm 0.018$ $0.893 \pm 0.024$ $0.970 \pm 0.009$ $0.966 \pm 0.013$ 0.988±0.006 三轴轴承
振动精确率 $0.961 \pm 0.026$ $0.946 \pm 0.003$ $0.960 \pm 0.014$ $0.959 \pm 0.015$ $0.897 \pm 0.021$ $0.970 \pm 0.008$ $0.971 \pm 0.012$ 0.989±0.009 召回率 $0.958 \pm 0.028$ $0.924 \pm 0.010$ $0.954 \pm 0.022$ $0.956 \pm 0.018$ $0.893 \pm 0.024$ $0.970 \pm 0.009$ $0.966 \pm 0.013$ 0.988±0.006 F1分数 $0.958 \pm 0.029$ $0.918 \pm 0.013$ $0.953 \pm 0.012$ $0.955 \pm 0.020$ $0.893 \pm 0.023$ $0.970 \pm 0.009$ $0.965 \pm 0.021$ 0.988±0.012 1 : 10 准确率 $0.950 \pm 0.030$ $0.908 \pm 0.005$ $0.869 \pm 0.035$ $0.886 \pm 0.044$ $0.861 \pm 0.054$ 0.961±0.011 $0.916 \pm 0.008$ $0.952 \pm 0.015$ XJTU-
SY精确率 $0.871 \pm 0.053$ $0.919 \pm 0.011$ $0.871 \pm 0.035$ $0.896 \pm 0.040$ $0.893 \pm 0.032$ 0.966±0.008 $0.924 \pm 0.005$ $0.952 \pm 0.008$ 召回率 $0.836 \pm 0.096$ $0.908 \pm 0.005$ $0.869 \pm 0.035$ $0.886 \pm 0.044$ $0.861 \pm 0.054$ 0.961±0.011 $0.916 \pm 0.008$ $0.952 \pm 0.015$ F1分数 $0.818 \pm 0.126$ $0.907 \pm 0.005$ $0.867 \pm 0.037$ $0.884 \pm 0.043$ $0.845 \pm 0.068$ 0.960±0.012 $0.915 \pm 0.008$ $0.952 \pm 0.011$ 准确率 $0.980 \pm 0.006$ $0.882 \pm 0.018$ $0.940 \pm 0.014$ $0.975 \pm 0.012$ $0.830 \pm 0.049$ $0.958 \pm 0.024$ $0.960 \pm 0.016$ 0.986±0.006 三轴轴承
振动精确率 $0.961 \pm 0.010$ $0.917 \pm 0.012$ $0.949 \pm 0.010$ $0.978 \pm 0.009$ $0.835 \pm 0.051$ $0.962 \pm 0.017$ $0.966 \pm 0.014$ 0.987±0.008 召回率 $0.955 \pm 0.014$ $0.882 \pm 0.018$ $0.940 \pm 0.014$ $0.975 \pm 0.012$ $0.830 \pm 0.049$ $0.958 \pm 0.024$ $0.960 \pm 0.016$ 0.986±0.006 F1分数 $0.954 \pm 0.015$ $0.863 \pm 0.034$ $0.939 \pm 0.014$ $0.974 \pm 0.012$ $0.829 \pm 0.049$ $0.958 \pm 0.024$ $0.960 \pm 0.016$ 0.986±0.009
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表 7 各模型计算开销与生成性能对比
Table 7 Comparison of computational costs and generation performance among different models
模型 扩散模型 组成模块 训练时间 (s) (10轮) 采样时间 (s) 推理计算量 (GFLOPs) 参数量 (M) MMD PSD KDE 分类准确率1 : 5 CVAE 否 – 0.068 1.680 0.002 1.221 0.073 0.549 0.818 0.908 DDPM 是 – 35.170 546.282 0.053 1.985 0.075 0.391 0.618 0.843 TTS-GAN 否 – 9.018 2.441 0.008 13.008 0.280 0.311 0.823 0.921 DIFFUSION-TS 是 – 3.140 2001.260 2.282 3.488 0.161 0.063 0.103 0.853 JiT 是 – 91.140 3953.101 9.273 129.722 0.042 0.914 0.927 0.943 A1 59.956 1.980 0.015 0.353 TimeVQVAE 否 A2 30.016 3.134 0.026 1.803 0.126 0.184 0.282 0.902 完整模型 89.972 5.114 0.041 2.156 B1 0.682 1.958 0.003 1.333 LC-DiffAE 是 B2 7.411 142.132 0.004 1.984 0.017 0.816 0.936 0.961 完整模型 8.093 144.090 0.007 3.317
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表 8 消融实验结果
Table 8 Ablation study results
模型 JSD WD MMD PSD 分类准确率 1 : 2 1 : 5 1 : 10 A 0.123 0.990 0.017 0.816 0.974 0.961 0.952 B 0.554 2.956 0.238 0.035 0.923 0.919 0.925 $ \mathrm{B}^{\prime} $ 0.130 1.002 0.021 0.761 0.957 0.943 0.941 $ \mathrm{B}^{\prime\prime} $ 0.132 1.091 0.049 0.623 0.948 0.920 0.901 C 0.130 0.931 0.011 0.805 0.953 0.941 0.916 D 0.151 1.094 0.008 0.772 0.888 0.897 0.844 E 0.122 1.151 0.024 0.650 0.942 0.893 0.868 F 0.105 0.959 0.022 0.786 0.844 0.918 0.900
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表 9 $ c $、$ p $和$ \xi $指标的敏感度分析结果
Table 9 Sensitivity analysis results for $ c $, $ p $和$ \xi $
参数 指标 0.01 0.05 0.10 0.30 0.50 1.00 3.00 $ c $ JSD 0.083 0.082 0.082 0.082 0.082 0.082 0.083 WD 0.935 0.923 0.924 0.928 0.950 0.932 0.944 MMD 0.008 0.009 0.009 0.009 0.009 0.009 0.008 $ \xi $ JSD $ \times $ 0.082 0.082 0.083 0.081 0.082 0.082 WD $ \times $ 0.930 0.940 0.950 0.913 0.941 0.923 MMD $ \times $ 0.004 0.005 0.004 0.006 0.005 0.005 $ p $ JSD 0.084 0.083 0.082 0.083 0.085 - - WD 0.978 0.963 0.954 0.968 0.968 - - MMD 0.006 0.005 0.006 0.005 0.006 - - 注: $ \times $表示模型训练异常; -表示无对应结果.
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表 10 分解损失与对比损失权重参数的敏感度分析结果
Table 10 Sensitivity analysis results for the weight parameters of the decomposition and contrastive losses
参数 指标 0.01 0.10 0.20 0.50 1.00 $ \omega_1 $ JSD 0.084 0.084 0.083 0.082 0.081 WD 0.975 0.977 0.950 0.932 0.923 MMD 0.006 0.005 0.005 0.006 0.005 $ \omega_2 $ JSD 0.082 0.083 0.084 0.082 0.083 WD 0.925 0.950 0.969 0.939 0.945 MMD 0.004 0.005 0.005 0.005 0.007
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表 11 不同类型工业信号生成样本的质量评估结果
Table 11 Quality evaluation results for generated samples of different types of industrial signals
信号类型 JSD WD MMD PSD KDE ICD 振动 0.088 1.119 0.006 0.813 0.935 0.928 声音 0.095 1.754 0.014 0.849 0.985 0.956 温度 0.688 11.744 0.006 0.742 0.935 0.990 电流 0.070 0.495 0.009 0.978 0.980 0.979
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