IAOTE: an adaptive fault diagnosis method for rotors under hybrid imbalanced small samples
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摘要:
提出了改进性自适应过采样技术（improved adaptive oversampling technique，IAOTE）。该技术融合自适应噪声处理策略（noise-immunity，NI）与改进自适应半监督加权过采样机制（improving adaptive semi-unsupervised weighted oversampling，IA-SUWO），首先利用NI策略对糅杂不均衡数据进行去噪，随后采用K均值聚类算法处理去噪数据以识别聚类边界样本，并嵌入IA-SUWO机制合成新样本。进而，本文将IAOTE与最小二乘支持向量机（least squares support vector machines，LS-SVM）分类器集成，构建故障诊断框架，确保分类可解释性并集成参数优化机制。实验表明：在20个诊断实例中，IAOTE的敏感性（sensitivity）指标最高达到99.76%，几何平均（G-mean）指标最高达到99.25%，F值（F-measure）指标最高达到99.42%，受试者操作曲线下的面积（AUC）指标最高达到99.26%，且累积误差值最低，其更适用于糅杂不均衡小样本下转子早期故障诊断。
Abstract:Improved adaptive oversampling technique (IAOTE) was proposed to address the problems of imbalanced health state data and ineffective mainstream sampling algorithms in the early steam turbine rotor self-scaling fault diagnosis modeling. This technique integrated the adaptive noise-immunity (NI) processing strategy with the improving adaptive semi-unsupervised weighted oversampling (IA-SUWO). Firstly, the NI strategy was used to denoise the mixed imbalanced data, and then the K-means clustering algorithm was used to process the denoised data to recognize the imbalanced data. The NI strategy was used to denoise the blended imbalanced data, and then the K-means clustering algorithm was used to process the denoised data to identify the cluster boundary samples and embed the IA-SUWO mechanism to synthesize the new samples. Furthermore, IAOTE was integrated with least squares support vector machines (LS-SVM) classifiers to construct a fault diagnosis framework to ensure classification interpretability and integrate parameter optimization mechanisms. Experiments showed that among 20 diagnostic examples, IAOTE achieved the highest sensitivity index of 99.76%, the highest G-mean index of 99.25%, the highest F-measure index of 99.42%, the highest area under curve (AUC) index of 99.26%, and the lowest cumulative error, which made IAOTE more suitable for early rotor fault diagnosis in small samples under the mix of imbalance.
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图 4 所提故障监测方法的总体流程图
Figure 4. Overall flowchart of the proposed fault monitoring method
表 1 10种采样算法在汽轮机转子数据集上的实验结果比较
Table 1. Comparison of experimental results of ten sampling algorithms on turbine rotor dataset
% 数据 评价标准 ROS SMOTE BSMOTE IA-SUWO Safe-level-SMOTE Cluster-SMOTE A-SUWO MWMOTE NI-MWMOTE IAOTE 转子数据1 Sensitivity 46.16±4.78 49.19±4.07 44.53±6.53 86.63±5.96 50.70±4.56 60.70±7.47 83.26±8 80.93±3.69 67.56±5.18 96.86±3.68 G-mean 63.97±2.92 65.35±2.93 64.29±5.10 79.04±4.36 66.83±3.18 68.60±3.20 74.28±3.15 71.44±4.13 73.37±2.28 92.77±3.17 F-measure 58.61±3.84 60.59±3.65 58.69±6.47 81.21±2.55 62.40±3.89 66.43±3.20 77.14±2.25 74.43±2.61 71.98±2.72 94.24±2.55 AUC 67.56±2.07 68.08±2.55 68.90±4.040 79.73±3.68 69.53±2.92 69.59±2.76 75.22±2.64 72.15±3.44 73.78±2.27 92.92±3.09 转子数据2 Sensitivity 50.58±2.53 50.93±6.64 49.77±4.38 79.19±6.52 56.63±4.32 54.77±5.36 80.35±6.68 81.63±4.51 65.35±7.06 99.07±0.92 G-mean 66.05±2.11 67.64±3.93 65.06±3.63 79.42±3.74 68.74±4.58 67.30±3.41 76.25±5.11 66.35±2.85 70.36±3.38 97.20±1.38 F-measure 61.63±2.34 63.22±5.11 60.47±4.30 79.57±4.10 65.43±5.16 63.69±4.14 77.57±5.11 71.72±2.60 68.95±4.29 97.88±0.96 AUC 68.49±2.42 70.64±2.83 67.5±3.55 79.53±3.74 70.06±4.60 68.90±3.12 76.48±5.37 67.85±2.76 70.76±3.26 97.23±1.36 转子数据3 Sensitivity 56.63±4.93 57.91±5.97 50.70±3.69 74.65±4.99 57.44±3.43 54.65±4.28 71.28±3.99 84.19±3.73 56.74±5.39 98.02±2.05 G-mean 69.18±2.76 69.25±3.89 66.62±3.23 79.06±2.35 70.22±2.76 67.97±2.82 77.83±3.72 69.64±5.00 68.73±3.14 96.93±1.78 F-measure 65.82±3.51 66.17±4.67 62.18±3.88 78.28±2.83 66.97±3.22 64.30±3.35 76.63±3.90 74.41±3.52 65.39±4.07 97.57±1.36 AUC 70.70±2.42 70.52±3.69 69.19±3.11 79.27±2.25 71.69±2.69 69.71±2.80 78.17±3.74 70.99±4.44 70.12±2.60 96.96±1.74 转子数据4 Sensitivity 61.51±6.68 60.58±4.54 61.05±6.16 77.79±5.73 64.30±4.35 61.05±5.38 74.88±4.94 78.84±3.98 61.28±6.32 99.07±0.74 G-mean 73.04±4.59 71.11±1.89 71.78±4.11 80.85±3.96 73.48±3.26 69.51±3.66 78.48±2.88 68.17±2.81 68.91±4.03 98.72±0.85 F-measure 70.36±5.44 68.44±2.50 69.11±4.93 80.34±4.38 71.32±3.71 67.09±4.42 77.81±3.37 71.73±2.48 66.70±4.65 98.96±0.65 AUC 74.24±4.19 72.15±1.68 72.85±3.82 80.95±3.88 74.19±3.15 70.17±3.36 78.62±2.75 68.95±2.66 69.53±3.94 98.73±0.84 转子数据5 Sensitivity 64.42±5.18 62.79±6.60 60.58±5.71 78.26±4.62 65.12±4.65 58.37±6.15 78.37±4.91 83.72±4.1 74.88±4.11 95.81±2.64 G-mean 73.00±3.49 72.80±4.01 71.91±3.19 81.67±2.92 75.54±2.49 71.40±4.17 80.85±4.21 67.62±4.54 74.73±3.02 94.02±1.74 F-measure 70.92±3.98 70.43±4.75 69.11±4.04 80.67±3.17 73.37±3.04 68.21±5.09 80.52±4.23 73.24±2.56 74.84±2.83 95.09±1.35 AUC 73.66±3.36 73.78±3.74 73.08±2.69 81.19±2.91 76.45±2.16 72.97±3.62 80.95±4.16 69.36±3.63 74.83±3.03 94.08±1.69 转子数据6 Sensitivity 65.81±6.72 65.81±5.26 61.51±7.58 78.60±3.16 66.51±3.83 59.42±2.65 82.21±4.52 78.49±3.21 56.28±7.40 99.19±0.78 G-mean 74.07±3.71 74.60±3.27 71.31±5.03 81.01±2.24 74.55±2.22 69.74±1.78 82.56±1.93 67.38±2.65 67.81±4.47 98.62±1.01 F-measure 72.09±4.69 72.63±3.90 68.87±5.93 80.73±2.04 72.75±2.49 66.97±1.89 82.61±2.17 71.16±2.27 64.39±5.77 98.90±0.79 AUC 74.71±3.26 75.29±3.04 72.38±4.61 81.13±2.25 75.12±2.17 70.70±1.88 82.63±1.89 68.20±2.54 69.19±3.57 98.63±1.01 转子数据7 Sensitivity 58.37±5.42 57.79±6.80 55.23±7.34 76.51±4.45 58.84±3.96 52.91±3.56 80.81±2.81 83.26±3.48 60.35±4.47 98.26±2.53 G-mean 68.55±3.07 69.00±4.13 68.97±4.76 80.25±2.61 69.92±1.99 66.78±3.50 81.97±2.85 66.61±2.75 68.88±2.30 97.92±1.28 F-measure 65.66±3.81 65.90±5.11 65.26±6.01 80.17±2.82 66.97±2.56 62.81±3.85 81.87±2.80 72.42±2.23 66.44±2.82 98.19±1.25 AUC 69.59±2.86 70.29±3.74 70.87±3.93 81.02±2.57 71.05±1.75 68.66±3.57 82.00±2.85 68.31±2.55 69.59±2.28 97.93±1.26 转子数据8 Sensitivity 64.42±5.29 65±6.26 61.05±4.82 76.51±3.09 70.35±3.77 57.91±4.55 80.93±4.15 81.74±5.26 61.51±3.40 97.09±1.26 G-mean 74.8±2.64 74.01±3.64 71.92±2.63 79.89±2.15 78.87±2.86 69.09±3.99 82.54±2.74 68.93±2.63 70.82±1.98 94.97±1.48 F-measure 72.57±3.29 71.91±4.47 69.22±3.34 79.38±2.13 77.38±2.98 66.03±4.48 82.33±2.99 73.10±2.91 68.35±2.45 95.88±1.06 AUC 75.76±2.34 74.77±3.21 72.97±2.25 80.02±2.23 79.42±2.94 70.23±3.93 82.58±2.72 74.42±2.76 71.57±1.81 95.01±1.44 转子数据 9 Sensitivity 80.81±5.78 84.30±4.69 74.07±6.78 91.05±3.05 84.77±3.82 83.60±2.97 85.00±3.53 86.63±3.21 82.44±3.53 97.67±1.64 G-mean 87.14±3.73 88.30±2.85 82.34±4.00 91.37±1.85 88.38±3.01 84.95±1.70 88.98±1.79 84.90±2.50 85.44±1.96 97.58±1.07 F-measure 86.48±4.06 87.89±3.09 81.12±4.66 91.47±1.16 88.04±3.12 84.79±1.71 88.69±1.95 85.19±2.44 85.04±2.17 97.79±0.98 AUC 87.44±3.61 88.43±2.80 82.91±3.64 91.42±1.15 88.49±3.00 85.00±1.73 89.11±1.73 84.94±2.49 85.52±1.91 97.59±1.07 转子数据10 Sensitivity 60.12±5.64 56.28±4.29 56.05±6.29 78.02±5.68 57.91±5.37 61.74±4.67 73.37±4.19 75.12±5.70 58.84±6.74 95.81±3.43 G-mean 70.42±4.46 67.13±2.45 66.86±4.09 80.64±2.84 69.92±3.28 66.96±3.20 79.76±1.84 65.42±4.79 65.81±2.00 90.08±2.20 F-measure 67.76±5.03 63.87±3.14 63.53±5.15 80.31±3.01 66.74±4.14 65.31±3.63 78.68±2.25 68.88±4.51 63.69±3.32 92.57±1.91 AUC 71.45±4.40 68.26±2.16 68.02±3.59 80.84±2.75 71.28±2.82 67.27±3.11 80.10±1.68 66.10±4.76 66.54±1.81 90.29±2.17 转子数据11 Sensitivity 85.00±3.17 84.30±5.06 79.07±5.51 90.81±2.82 83.95±4.45 83.37±2.45 88.14±4.45 85.81±4.45 76.05±3.52 96.63±2.65 G-mean 86.41±1.64 86.81±3.29 85.01±2.93 91.38±1.80 87.01±2.64 85.43±1.19 90.63±2.00 83.55±2.53 80.79±2.81 97.89±1.33 F-measure 86.24±1.75 86.54±3.47 84.23±3.33 91.40±1.79 86.72±2.74 85.14±1.34 90.47±2.17 83.99±2.52 80.01±2.92 97.92±1.35 AUC 86.45±1.65 86.92±3.28 85.29±2.76 91.41±1.79 87.15±2.61 85.47±1.16 90.72±1.95 83.66±2.52 80.99±2.85 97.91±1.30 转子数据12 Sensitivity 67.56±5.6 65.23±5.97 63.02±4.31 80.23±5.34 69.53±3.75 68.02±5.29 75.23±4.87 78.6±4.69 69.77±6.46 97.56±1.39 G-mean 76.06±2.97 73.43±5.06 73.06±2.18 83.34±3.04 76.62±2.68 72.41±2.57 81.61±3.37 72.21±4.19 71.89±3.84 97.25±1.00 F-measure 74.29±3.57 71.47±5.61 70.71±2.68 82.92±3.39 75.16±2.96 71.27±3.09 80.62±3.79 74.07±3.99 71.35±4.25 97.56±0.85 AUC 76.74±2.67 74.01±4.96 73.95±2.03 83.47±2.94 77.03±2.72 72.67±2.5 81.91±3.24 72.5±4.17 72.09±3.84 97.26±1.00 转子数据13 Sensitivity 73.14±6.14 76.98±4.87 69.42±4.10 82.91±3.20 77.91±4.17 75.47±2.97 83.49±5.39 89.88±2.85 72.67±6.37 96.28±2.04 G-mean 80.80±3.02 82.84±2.29 79.97±2.81 86.61±1.69 84.16±2.06 83.39±1.58 88.22±2.86 83.63±1.92 78.78±3.60 98.55±1.14 F-measure 79.57±3.61 81.98±2.65 78.31±3.21 86.32±1.66 83.35±2.35 82.34±1.80 87.81±3.19 84.81±1.56 77.57±4.33 96.06±0.98 AUC 81.34±2.73 83.14±2.23 80.81±2.66 86.75±1.70 84.48±1.96 83.84±1.50 88.41±2.70 83.90±1.80 79.19±3.33 98.57±1.12 转子数据14 Sensitivity 62.44±2.95 62.33±7.46 60.81±3.92 77.44±5.38 63.60±5.83 61.63±8.06 79.07±4.10 74.53±6.21 63.49±5.54 97.21±2.58 G-mean 71.31±2.99 69.96±4.51 69.46±2.62 79.86±3.61 69.40±3.44 67.29±4.77 80.06±2.71 68.76±3.51 68.15±4.75 96.08±1.70 F-measure 69.04±3.09 67.76±5.55 67.01±3.11 79.47±4.01 67.69±4.19 65.46±5.63 79.98±2.76 70.60±3.94 66.78±4.92 96.81±1.49 AUC 71.98±3.05 70.58±4.13 70.12±2.47 79.96±3.55 69.77±3.28 67.73±4.65 80.12±2.69 69.07±3.65 68.43±4.83 96.10±1.69 转子数据 15 Sensitivity 67.33±3.78 68.26±4.65 62.56±3.28 82.09±2.96 64.77±4.21 63.02±2.67 80.23±4.25 63.27±6.78 69.30±6.78 98.95±1.16 G-mean 71.08±2.02 69.65±3.46 66.84±2.93 84.24±2.89 68.45±3.29 64.20±3.57 80.59±2.88 61.27±2.91 67.69±4.36 99.10±0.81 F-measure 70.07±2.15 69.23±3.72 65.49±2.94 84.00±2.86 67.33±3.54 63.89±2.93 80.64±2.96 62.17±2.91 68.21±4.84 99.18±0.74 AUC 71.28±2.05 69.71±3.45 67.03±3.00 84.28±2.89 68.60±3.27 64.30±3.64 80.65±2.87 61.45±3.06 67.85±4.25 99.19±0.81 转子数据16 Sensitivity 61.06±6.04 61.53±3.64 61.06±3.94 74.47±4.11 67.06±3.19 61.06±6.80 78.00±3.92 69.65±5.34 60.59±7.04 98.71±0.67 G-mean 69.56±3.74 69.81±2.86 67.71±2.48 78.95±2.80 73.48±1.80 67.69±3.38 81.22±1.95 64.41±3.34 64.67±3.67 96.00±1.26 F-measure 67.18±4.51 67.51±3.12 65.71±2.74 78.17±3.05 71.90±2.12 65.69±4.25 80.79±1.95 66.32±3.51 63.23±4.75 97.22±0.80 AUC 70.29±3.58 70.41±2.87 68.18±2.53 79.14±2.78 73.82±1.74 68.29±3.33 81.38±1.96 64.71±3.33 65.00±3.49 96.05±1.23 转子数据17 Sensitivity 64.00±3.85 61.88±3.89 60.59±6.93 77.29±5.46 68.71±4.41 60.12±6.38 79.29±4.05 76.59±6.87 63.76±4.36 99.76±0.50 G-mean 73.62±2.91 70.44±2.40 70.57±2.87 80.56±3.60 76.13±3.29 68.42±3.03 81.39±2.28 67.50±3.22 69.10±2.70 99.25±0.81 F-measure 71.43±3.31 68.15±2.77 67.95±3.91 80.11±3.93 74.56±3.60 65.97±3.98 81.25±2.31 70.54±3.74 67.62±3.20 99.42±0.61 AUC 74.41±2.92 71.12±2.41 71.65±2.40 80.70±3.53 76.59±3.24 69.18±2.76 81.51±2.28 68.18±3.33 69.38±2.59 99.26±0.81 转子数据18 Sensitivity 71.06±6.08 68.59±5.63 64.71±3.72 78.82±5.38 69.88±4.34 68.35±4.05 77.18±2.67 79.29±4.12 65.88±6.56 97.53±1.61 G-mean 78.92±3.99 74.47±3.62 73.80±3.05 83.13±2.91 77.95±2.90 75.46±2.54 81.68±2.67 72.27±2.28 73.69±4.32 97.68±1.06 F-measure 77.51±4.50 73.09±4.12 71.69±3.41 82.60±3.26 76.40±3.33 73.88±2.94 81.10±2.63 74.33±2.27 71.85±4.93 97.99±1.06 AUC 79.47±3.82 74.82±3.59 74.77±3.00 83.33±2.78 78.47±2.73 75.88±2.43 81.84±2.71 72.65±2.24 74.29±4.24 97.68±1.21 转子数据19 Sensitivity 60.71±5.72 58.35±4.55 59.41±7.17 76.94±2.30 64.12±5.93 58.59±6.65 78.82±3.46 67.18±5.61 64.82±5.33 95.41±2.32 G-mean 65.87±3.07 64.20±2.80 66.66±3.83 79.48±2.38 68.19±3.33 61.60±3.47 80.59±3.54 60.50±2.50 65.26±2.31 93.20±1.94 F-measure 64.17±3.82 62.18±3.33 64.32±4.97 79.19±2.16 66.89±4.13 60.45±4.40 80.51±3.17 63.27±2.13 65.08±3.23 94.42±1.51 AUC 66.24±2.99 64.59±2.71 67.29±3.45 79.55±2.40 68.41±3.21 61.88±3.39 80.68±3.49 61.12±2.16 65.35±2.29 93.25±1.91 转子数据20 Sensitivity 63.06±4.65 61.53±5.02 60.47±4.16 77.65±3.88 62.71±6.97 60.00±6.08 81.88±4.12 72.35±4.34 63.65±4.91 94.50±4.37 G-mean 71.28±3.34 67.25±4.08 67.04±1.93 80.45±3.09 69.30±4.31 65.58±4.23 82.83±3.13 63.94±3.24 67.12±2.95 94.64±1.51 F-measure 69.12±3.84 65.46±4.45 65.02±2.31 80.05±3.16 67.38±5.18 63.76±4.78 82.82±3.13 67.08±2.88 66.12±3.50 95.45±1.61 AUC 71.88±3.20 67.59±4.00 67.53±2.00 80.55±3.14 69.82±4.08 66.00±4.18 82.91±3.19 64.53±3.04 67.30±2.89 94.71±1.47 
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表 2 Holm测试的P值（控制算法：IAOTE）
Table 2. P-value of Holm’s test （control algorithm: IAOTE）
采样算法
序号采样算法
名称Sensitivity G-mean F-measure AUC α0.05 P值 α0.05 P值 α0.05 P值 α0.05 P值 1 ROS 0.0085124 1.9507×10−33 0.012741 1.7986×10−28 0.010206 3.4654×10−30 0.012741 1.5958×10−28 2 SMOTE 0.0073008 9.584×10−34 0.010206 6.2812×10−30 0.0085124 1.8177×10−31 0.010206 3.5736×10−30 3 BSMOTE 0.005683 5.5683×10−38 0.0073008 3.2104×10−32 0.005683 2.3445×10−34 0.0085124 6.2284×10−32 4 IA-SUWO 0.05 2.7823×10−13 0.05 4.9177×10−14 0.05 1.1742×10−13 0.05 9.2633×10−15 5 Safe-level-
SMOTE0.012741 1.0087×10−30 0.016952 1.3463×10−26 0.012741 6.0839×10−28 0.016952 5.9701×10−27 6 Cluster-
SMOTE0.0063912 9.8983×10−35 0.0063912 7.5071×10−33 0.0063912 6.3669×10−34 0.0063912 1.9993×10−33 7 A-SUWO 0.025321 1.6108×10−13 0.025321 1.0408×10−14 0.025321 4.0998×10−14 0.025321 2.0209×10−15 8 MWMOTE 0.016952 1.0403×10−14 0.005683 1.7275×10−34 0.016952 1.43952×10−27 0.005683 8.6959 ×10−359 NI-MWMOTE 0.010206 2.3003×10−31 0.0085124 3.7707×10−32 0.0073008 2.5064×10−32 0.0073008 3.5821×10−33
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