《计算机应用》唯一官方网站 ›› 2026, Vol. 46 ›› Issue (10): 3206-3214.DOI: 10.11772/j.issn.1001-9081.2025080971
• 数据科学与技术 • 上一篇
收稿日期:2025-08-25
修回日期:2025-09-11
接受日期:2025-09-29
发布日期:2025-11-07
出版日期:2026-10-10
通讯作者:
童英华
作者简介:刘晟(1998—),男,江西吉安人,硕士研究生,CCF会员,主要研究方向:物联网系统的可靠性、深度学习
基金资助:
Sheng LIU1, Yinghua TONG1,2(
)
Received:2025-08-25
Revised:2025-09-11
Accepted:2025-09-29
Online:2025-11-07
Published:2026-10-10
Contact:
Yinghua TONG
About author:LIU Sheng, born in 1998, M. S. candidate. His research interests include IoT system reliability, deep learning.
Supported by:摘要:
针对现有Transformer类模型在趋势性信息提取方面存在的不足,以及传感器异构性导致的变量相关性建模失真等问题,提出一种基于转置自注意力机制(TSA)与卷积自编码器(CAE)的多元时序数据分析方法。该方法通过构建转置一维CAE结构,从时间维度实现时序数据的特征重建,有效捕获多元时序数据中的长期趋势信息;同时,将TSA机制引入多变量相关性分析过程,显著提升变量间关联关系的建模精度。与近年主流方法的预测性能对比实验结果表明,所提方法的平均均方误差(MSE)为0.545,相较于iTransformer和DLinear分别降低了11.4%和7.4%。此外,在5个公共数据集上的异常检测实验结果表明,该方法的平均F1分数为84.92%,优于所有基线方法。在真实水质监测数据集上的预测实验结果表明,所提方法的平均绝对误差(MAE)和MSE相较于Autoformer分别降低了46.2%和42.9%,验证了该方法在实际应用场景中的有效性。
中图分类号:
刘晟, 童英华. 基于转置自注意力机制与卷积自编码器的多元时序数据分析方法[J]. 计算机应用, 2026, 46(10): 3206-3214.
Sheng LIU, Yinghua TONG. Multivariate time series data analysis method based on transposed self-attention mechanism and convolutional autoencoder[J]. Journal of Computer Applications, 2026, 46(10): 3206-3214.
| 方法 | Illness 36-36 | Illness 36-60 | ECL 96-96 | ECL 96-192 | ETTh1 96-96 | ETTh1 96-336 | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | |
| iTransformer | 2.268 | 0.972 | 2.274 | 0.979 | 0.148 | 0.260 | 0.178 | 0.269 | 0.392 | 0.410 | 0.490 | 0.462 |
| TimeMixer | 2.057 | 0.929 | 2.296 | 1.094 | 0.153 | 0.246 | 0.165 | 0.256 | 0.375 | 0.400 | 0.484 | 0.459 |
| TimesNet | 1.972 | 0.920 | 2.027 | 0.928 | 0.168 | 0.272 | 0.184 | 0.289 | 0.384 | 0.402 | 0.491 | 0.469 |
| DLinear | 1.963 | 0.963 | 2.368 | 1.096 | 0.140 | 0.237 | 0.169 | 0.267 | 0.375 | 0.399 | 0.489 | 0.457 |
| Autoformer | 3.103 | 1.287 | 2.700 | 1.125 | 0.201 | 0.317 | 0.222 | 0.334 | 0.477 | 0.478 | 0.566 | 0.525 |
| 本文方法 | 1.847 | 0.865 | 1.959 | 0.906 | 0.138 | 0.235 | 0.165 | 0.261 | 0.409 | 0.418 | 0.482 | 0.457 |
| 方法 | ETTm1 96-96 | ETTm1 96-336 | Exchange 96-96 | Exchange 96-336 | Weather 96-96 | Weather 96-336 | ||||||
| MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | |
| iTransformer | 0.338 | 0.373 | 0.426 | 0.422 | 0.091 | 0.216 | 0.331 | 0.417 | 0.174 | 0.214 | 0.278 | 0.297 |
| TimeMixer | 0.320 | 0.356 | 0.390 | 0.405 | 0.089 | 0.211 | 0.339 | 0.420 | 0.163 | 0.210 | 0.251 | 0.289 |
| TimesNet | 0.338 | 0.375 | 0.410 | 0.411 | 0.107 | 0.234 | 0.367 | 0.448 | 0.172 | 0.220 | 0.280 | 0.306 |
| DLinear | 0.328 | 0.362 | 0.400 | 0.406 | 0.092 | 0.213 | 0.305 | 0.414 | 0.176 | 0.237 | 0.259 | 0.322 |
| Autoformer | 0.526 | 0.488 | 0.593 | 0.521 | 0.197 | 0.323 | 0.509 | 0.524 | 0.266 | 0.336 | 0.359 | 0.395 |
| 本文方法 | 0.327 | 0.363 | 0.418 | 0.422 | 0.088 | 0.208 | 0.277 | 0.303 | 0.161 | 0.208 | 0.272 | 0.297 |
表1 预测实验结果对比
Tab. 1 Forecasting experimental results
| 方法 | Illness 36-36 | Illness 36-60 | ECL 96-96 | ECL 96-192 | ETTh1 96-96 | ETTh1 96-336 | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | |
| iTransformer | 2.268 | 0.972 | 2.274 | 0.979 | 0.148 | 0.260 | 0.178 | 0.269 | 0.392 | 0.410 | 0.490 | 0.462 |
| TimeMixer | 2.057 | 0.929 | 2.296 | 1.094 | 0.153 | 0.246 | 0.165 | 0.256 | 0.375 | 0.400 | 0.484 | 0.459 |
| TimesNet | 1.972 | 0.920 | 2.027 | 0.928 | 0.168 | 0.272 | 0.184 | 0.289 | 0.384 | 0.402 | 0.491 | 0.469 |
| DLinear | 1.963 | 0.963 | 2.368 | 1.096 | 0.140 | 0.237 | 0.169 | 0.267 | 0.375 | 0.399 | 0.489 | 0.457 |
| Autoformer | 3.103 | 1.287 | 2.700 | 1.125 | 0.201 | 0.317 | 0.222 | 0.334 | 0.477 | 0.478 | 0.566 | 0.525 |
| 本文方法 | 1.847 | 0.865 | 1.959 | 0.906 | 0.138 | 0.235 | 0.165 | 0.261 | 0.409 | 0.418 | 0.482 | 0.457 |
| 方法 | ETTm1 96-96 | ETTm1 96-336 | Exchange 96-96 | Exchange 96-336 | Weather 96-96 | Weather 96-336 | ||||||
| MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | |
| iTransformer | 0.338 | 0.373 | 0.426 | 0.422 | 0.091 | 0.216 | 0.331 | 0.417 | 0.174 | 0.214 | 0.278 | 0.297 |
| TimeMixer | 0.320 | 0.356 | 0.390 | 0.405 | 0.089 | 0.211 | 0.339 | 0.420 | 0.163 | 0.210 | 0.251 | 0.289 |
| TimesNet | 0.338 | 0.375 | 0.410 | 0.411 | 0.107 | 0.234 | 0.367 | 0.448 | 0.172 | 0.220 | 0.280 | 0.306 |
| DLinear | 0.328 | 0.362 | 0.400 | 0.406 | 0.092 | 0.213 | 0.305 | 0.414 | 0.176 | 0.237 | 0.259 | 0.322 |
| Autoformer | 0.526 | 0.488 | 0.593 | 0.521 | 0.197 | 0.323 | 0.509 | 0.524 | 0.266 | 0.336 | 0.359 | 0.395 |
| 本文方法 | 0.327 | 0.363 | 0.418 | 0.422 | 0.088 | 0.208 | 0.277 | 0.303 | 0.161 | 0.208 | 0.272 | 0.297 |
| 模型 | 参数量/106 | 计算量/GMAC |
|---|---|---|
| iTransformer | 3.256 | 1.250 |
| TimeMixer | 1.128 | 57.980 |
| TimesNet | 36.744 | 676.854 |
| DLinear | 0.018 | 0.005 |
| Autoformer | 5.822 | 21.153 |
| 本文方法 | 1.431 | 0.011 |
表2 模型复杂度
Tab. 2 Method complexity
| 模型 | 参数量/106 | 计算量/GMAC |
|---|---|---|
| iTransformer | 3.256 | 1.250 |
| TimeMixer | 1.128 | 57.980 |
| TimesNet | 36.744 | 676.854 |
| DLinear | 0.018 | 0.005 |
| Autoformer | 5.822 | 21.153 |
| 本文方法 | 1.431 | 0.011 |
| 方法 | ECL 96-96 | ECL 96-192 | ETTm1 96-96 | ETTm1 96-336 | Exchange 96-96 | Exchange 96-336 | Weather 96-96 | Weather 96-336 |
|---|---|---|---|---|---|---|---|---|
| iTransformer | 0.045 | 0.065 | 0.056 | 0.081 | 0.016 | 0.003 | 0.003 | 0.027 |
| TimeMixer | 0.022 | 0.574 | 0.124 | 0.036 | 0.621 | 0.004 | 0.434 | 0.021 |
| TimesNet | 0.171 | 0.005 | 0.024 | 0.060 | 0.007 | 0.002 | 0.001 | 0.025 |
| DLinear | 0.361 | 0.026 | 0.108 | 0.339 | 0.017 | 0.046 | 0.010 | 0.080 |
| Autoformer | 0.001 | 0.012 | 0.001 | 0.003 | 0.000 | 0.001 | 0.001 | 0.003 |
表3 本文方法与基线方法的t检验结果
Tab. 3 t-test results of proposed method and baseline methods
| 方法 | ECL 96-96 | ECL 96-192 | ETTm1 96-96 | ETTm1 96-336 | Exchange 96-96 | Exchange 96-336 | Weather 96-96 | Weather 96-336 |
|---|---|---|---|---|---|---|---|---|
| iTransformer | 0.045 | 0.065 | 0.056 | 0.081 | 0.016 | 0.003 | 0.003 | 0.027 |
| TimeMixer | 0.022 | 0.574 | 0.124 | 0.036 | 0.621 | 0.004 | 0.434 | 0.021 |
| TimesNet | 0.171 | 0.005 | 0.024 | 0.060 | 0.007 | 0.002 | 0.001 | 0.025 |
| DLinear | 0.361 | 0.026 | 0.108 | 0.339 | 0.017 | 0.046 | 0.010 | 0.080 |
| Autoformer | 0.001 | 0.012 | 0.001 | 0.003 | 0.000 | 0.001 | 0.001 | 0.003 |
| 方法 | MSL | PSM | SMAP | ||||||
|---|---|---|---|---|---|---|---|---|---|
| 精确率 | 召回率 | F1分数 | 精确率 | 召回率 | F1分数 | 精确率 | 召回率 | F1分数 | |
| OmniAnomaly | 89.02 | 86.37 | 87.67 | 88.39 | 74.46 | 80.83 | 92.49 | 61.99 | 74.21 |
| iTransformer | 87.65 | 70.37 | 78.07 | 98.10 | 93.09 | 95.53 | 90.69 | 53.36 | 67.19 |
| TimesNet | 89.54 | 75.36 | 81.84 | 98.51 | 96.31 | 97.40 | 90.01 | 55.06 | 68.33 |
| DLinear | 89.86 | 75.12 | 81.83 | 98.28 | 89.26 | 93.55 | 89.90 | 54.04 | 67.50 |
| Autoformer | 77.27 | 80.92 | 79.05 | 99.08 | 88.15 | 93.29 | 90.40 | 58.62 | 71.12 |
| 本文方法 | 83.86 | 81.35 | 82.58 | 96.43 | 96.81 | 96.62 | 87.40 | 56.10 | 68.33 |
| 方法 | SMD | SWAT | 平均F1分数 | ||||||
| 精确率 | 召回率 | F1分数 | 精确率 | 召回率 | F1分数 | ||||
| OmniAnomaly | 83.68 | 86.82 | 85.22 | 81.42 | 84.30 | 82.83 | 82.16 | ||
| iTransformer | 87.58 | 78.77 | 82.94 | 92.18 | 93.08 | 92.63 | 83.27 | ||
| TimesNet | 87.62 | 79.98 | 83.63 | 88.31 | 96.24 | 92.10 | 84.66 | ||
| DLinear | 83.62 | 71.52 | 77.10 | 80.91 | 95.30 | 87.52 | 81.50 | ||
| Autoformer | 78.44 | 65.10 | 71.15 | 89.85 | 95.81 | 92.74 | 81.47 | ||
| 本文方法 | 86.25 | 81.10 | 83.59 | 93.76 | 93.26 | 93.51 | 84.92 | ||
表4 不同模型在不同数据集上的异常检测结果 (%)
Tab. 4 Anomaly detection results of different models on different datasets
| 方法 | MSL | PSM | SMAP | ||||||
|---|---|---|---|---|---|---|---|---|---|
| 精确率 | 召回率 | F1分数 | 精确率 | 召回率 | F1分数 | 精确率 | 召回率 | F1分数 | |
| OmniAnomaly | 89.02 | 86.37 | 87.67 | 88.39 | 74.46 | 80.83 | 92.49 | 61.99 | 74.21 |
| iTransformer | 87.65 | 70.37 | 78.07 | 98.10 | 93.09 | 95.53 | 90.69 | 53.36 | 67.19 |
| TimesNet | 89.54 | 75.36 | 81.84 | 98.51 | 96.31 | 97.40 | 90.01 | 55.06 | 68.33 |
| DLinear | 89.86 | 75.12 | 81.83 | 98.28 | 89.26 | 93.55 | 89.90 | 54.04 | 67.50 |
| Autoformer | 77.27 | 80.92 | 79.05 | 99.08 | 88.15 | 93.29 | 90.40 | 58.62 | 71.12 |
| 本文方法 | 83.86 | 81.35 | 82.58 | 96.43 | 96.81 | 96.62 | 87.40 | 56.10 | 68.33 |
| 方法 | SMD | SWAT | 平均F1分数 | ||||||
| 精确率 | 召回率 | F1分数 | 精确率 | 召回率 | F1分数 | ||||
| OmniAnomaly | 83.68 | 86.82 | 85.22 | 81.42 | 84.30 | 82.83 | 82.16 | ||
| iTransformer | 87.58 | 78.77 | 82.94 | 92.18 | 93.08 | 92.63 | 83.27 | ||
| TimesNet | 87.62 | 79.98 | 83.63 | 88.31 | 96.24 | 92.10 | 84.66 | ||
| DLinear | 83.62 | 71.52 | 77.10 | 80.91 | 95.30 | 87.52 | 81.50 | ||
| Autoformer | 78.44 | 65.10 | 71.15 | 89.85 | 95.81 | 92.74 | 81.47 | ||
| 本文方法 | 86.25 | 81.10 | 83.59 | 93.76 | 93.26 | 93.51 | 84.92 | ||
| 方法 | ill_national 36-36 | ill_national 36-60 | ECL 96-96 | ECL 96-192 | ETTh1 96-96 | ETTh1 96-336 | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | |
| 去除自注意力机制 | 2.403 | 1.001 | 2.176 | 0.935 | 0.147 | 0.244 | 0.173 | 0.264 | 0.520 | 0.484 | 0.522 | 0.477 |
| 去除归一化 | 2.200 | 0.965 | 2.170 | 0.942 | 0.156 | 0.255 | 0.163 | 0.258 | 0.471 | 0.459 | 0.503 | 0.472 |
| 去除卷积自编码器 | 2.428 | 0.983 | 2.633 | 1.045 | 0.156 | 0.260 | 0.158 | 0.253 | 0.395 | 0.409 | 0.488 | 0.461 |
| 替换自编码器 | 2.203 | 0.919 | 2.165 | 0.957 | 0.140 | 0.237 | 0.178 | 0.283 | 0.424 | 0.439 | 0.483 | 0.458 |
| 去除动态权重 | 2.549 | 1.016 | 2.492 | 1.047 | 0.180 | 0.289 | 0.170 | 0.264 | 0.395 | 0.410 | 0.504 | 0.473 |
| 本文方法 | 1.847 | 0.865 | 1.959 | 0.906 | 0.138 | 0.235 | 0.155 | 0.251 | 0.409 | 0.418 | 0.486 | 0.460 |
| 方法 | ETTm1 96-96 | ETTm1 96-336 | Exchange 96-96 | Exchange 96-336 | Weather 96-96 | Weather 96-336 | ||||||
| MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | |
| 去除自注意力机制 | 0.332 | 0.363 | 0.447 | 0.426 | 0.095 | 0.219 | 0.336 | 0.420 | 0.170 | 0.216 | 0.275 | 0.300 |
| 去除归一化 | 0.337 | 0.371 | 0.443 | 0.433 | 0.095 | 0.216 | 0.327 | 0.414 | 0.166 | 0.213 | 0.281 | 0.304 |
| 去除卷积自编码器 | 0.333 | 0.368 | 0.446 | 0.432 | 0.096 | 0.217 | 0.326 | 0.414 | 0.162 | 0.208 | 0.265 | 0.292 |
| 替换自编码器 | 0.336 | 0.369 | 0.427 | 0.422 | 0.087 | 0.208 | 0.332 | 0.417 | 0.164 | 0.215 | 0.269 | 0.293 |
| 去除动态权重 | 0.367 | 0.391 | 0.419 | 0.416 | 0.088 | 0.211 | 0.343 | 0.425 | 0.166 | 0.215 | 0.283 | 0.307 |
| 本文方法 | 0.327 | 0.364 | 0.418 | 0.422 | 0.088 | 0.209 | 0.277 | 0.303 | 0.161 | 0.208 | 0.272 | 0.297 |
表5 消融实验结果
Tab. 5 Results of ablation experiments
| 方法 | ill_national 36-36 | ill_national 36-60 | ECL 96-96 | ECL 96-192 | ETTh1 96-96 | ETTh1 96-336 | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | |
| 去除自注意力机制 | 2.403 | 1.001 | 2.176 | 0.935 | 0.147 | 0.244 | 0.173 | 0.264 | 0.520 | 0.484 | 0.522 | 0.477 |
| 去除归一化 | 2.200 | 0.965 | 2.170 | 0.942 | 0.156 | 0.255 | 0.163 | 0.258 | 0.471 | 0.459 | 0.503 | 0.472 |
| 去除卷积自编码器 | 2.428 | 0.983 | 2.633 | 1.045 | 0.156 | 0.260 | 0.158 | 0.253 | 0.395 | 0.409 | 0.488 | 0.461 |
| 替换自编码器 | 2.203 | 0.919 | 2.165 | 0.957 | 0.140 | 0.237 | 0.178 | 0.283 | 0.424 | 0.439 | 0.483 | 0.458 |
| 去除动态权重 | 2.549 | 1.016 | 2.492 | 1.047 | 0.180 | 0.289 | 0.170 | 0.264 | 0.395 | 0.410 | 0.504 | 0.473 |
| 本文方法 | 1.847 | 0.865 | 1.959 | 0.906 | 0.138 | 0.235 | 0.155 | 0.251 | 0.409 | 0.418 | 0.486 | 0.460 |
| 方法 | ETTm1 96-96 | ETTm1 96-336 | Exchange 96-96 | Exchange 96-336 | Weather 96-96 | Weather 96-336 | ||||||
| MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | |
| 去除自注意力机制 | 0.332 | 0.363 | 0.447 | 0.426 | 0.095 | 0.219 | 0.336 | 0.420 | 0.170 | 0.216 | 0.275 | 0.300 |
| 去除归一化 | 0.337 | 0.371 | 0.443 | 0.433 | 0.095 | 0.216 | 0.327 | 0.414 | 0.166 | 0.213 | 0.281 | 0.304 |
| 去除卷积自编码器 | 0.333 | 0.368 | 0.446 | 0.432 | 0.096 | 0.217 | 0.326 | 0.414 | 0.162 | 0.208 | 0.265 | 0.292 |
| 替换自编码器 | 0.336 | 0.369 | 0.427 | 0.422 | 0.087 | 0.208 | 0.332 | 0.417 | 0.164 | 0.215 | 0.269 | 0.293 |
| 去除动态权重 | 0.367 | 0.391 | 0.419 | 0.416 | 0.088 | 0.211 | 0.343 | 0.425 | 0.166 | 0.215 | 0.283 | 0.307 |
| 本文方法 | 0.327 | 0.364 | 0.418 | 0.422 | 0.088 | 0.209 | 0.277 | 0.303 | 0.161 | 0.208 | 0.272 | 0.297 |
| 方法 | 96-96 | 96-192 | ||
|---|---|---|---|---|
| MSE | MAE | MSE | MAE | |
| iTransformer | 0.276 | 0.666 | 0.336 | 1.143 |
| TimeMixer | 0.283 | 0.671 | 0.342 | 0.659 |
| DLinear | 0.375 | 0.650 | 0.362 | 0.594 |
| Autoformer | 0.445 | 1.103 | 0.532 | 1.311 |
| 本文方法 | 0.250 | 0.612 | 0.308 | 0.688 |
表6 白洋淀水质环境监测数据预测的实验结果对比
Tab. 6 Comparison of experimental results of water quality monitoring data forecasting in Baiyangdian Lake
| 方法 | 96-96 | 96-192 | ||
|---|---|---|---|---|
| MSE | MAE | MSE | MAE | |
| iTransformer | 0.276 | 0.666 | 0.336 | 1.143 |
| TimeMixer | 0.283 | 0.671 | 0.342 | 0.659 |
| DLinear | 0.375 | 0.650 | 0.362 | 0.594 |
| Autoformer | 0.445 | 1.103 | 0.532 | 1.311 |
| 本文方法 | 0.250 | 0.612 | 0.308 | 0.688 |
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