Anomaly Detection on Irregular Signals in Adaptive Decay Reservoir Network Model Space

CHEN Ao; LI Wenpeng; XIE Xiaoyan; CHEN Pengpeng

doi:10.11999/JEIT260423

Article Contents

Article Navigation > Journal of Electronics & Information Technology > 2026 >

CHEN Ao, LI Wenpeng, XIE Xiaoyan, CHEN Pengpeng. Anomaly Detection on Irregular Signals in Adaptive Decay Reservoir Network Model Space[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260423

Citation:

CHEN Ao, LI Wenpeng, XIE Xiaoyan, CHEN Pengpeng. Anomaly Detection on Irregular Signals in Adaptive Decay Reservoir Network Model Space[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260423

Citation:

PDF( 2156 KB)

Anomaly Detection on Irregular Signals in Adaptive Decay Reservoir Network Model Space

doi: 10.11999/JEIT260423 cstr: 32379.14.JEIT260423

1.
School of Computer Science and Technology/School of Artificial Intelligence, China University of Mining and Technology, Xuzhou 221116, China
2.
Mine Digitization Engineering Research Center of the Ministry of Education, Xuzhou 221116, China
3.
Jiangsu Provincial Industrial Technology Engineering Center for Intelligent Sensing and Emergency IoT in Underground Space, Xuzhou 221116, China

Funds: the National Natural Science Foundation of China (62272462), the Natural Science Foundation of Jiangsu Province of China for Distinguished Young Scholars (BK20230045), Shenzhen Science and Technology Program (JCYJ20230807154300002)

Received Date: 2026-04-10
Accepted Date: 2026-08-13
Rev Recd Date: 2026-08-13

Available Online: 2026-08-25

Abstract

Abstract

Objective Signals acquired from industrial systems often exhibit irregular sampling due to sensor instability, intermittent operation, communication dropout, and multi-source asynchronous acquisition. This irregularity violates the uniform sampling assumption of most signal analysis methods and challenges anomaly detection. Interpolation and resampling may distort the underlying temporal dynamics, while continuous-time models based on neural ordinary differential equations as well as time-aware Transformers suffer from high training costs and strong dependence on large training sets, making them impractical under limited training resources. Model space learning offers an alternative by fitting each signal with a dynamic model and analyzing the fitted models instead of the raw signals. However, existing model space methods for irregular sampling rely on fixed reservoir configurations and lack adaptive optimization of the model space. This paper aims to develop an anomaly detection framework for irregularly sampled signals that is simultaneously robust to non-uniform intervals and efficient to train. Methods An adaptive model space learning framework based on the Adaptive Decay Reservoir Network (ADRN) is proposed (Fig. 1). ADRN extends the echo state network by introducing an exponential decay mechanism derived from a linear ordinary differential equation (Fig. 2). Between consecutive observations, the hidden state decays according to a learnable decay rate over the actual elapsed time, so that the state update naturally adapts to non-uniform sampling intervals without numerical ordinary differential equation solvers. Each new observation then updates the decayed state through a nonlinear activation. Ridge regression with a closed-form solution then fits a readout model mapping hidden states to the original signal, and the fitted readout weights serve as a compact fixed-dimensional representation regardless of signal length. The model space is further optimized by two complementary losses. A time-interval-weighted reconstruction loss assigns higher weights to larger intervals, preventing densely sampled segments from dominating the optimization and improving fitting quality under non-uniform sampling. A separability loss inspired by Fisher discriminant analysis acts through a learnable projection matrix to minimize intra-class scatter and maximize inter-class separation in the projected model space. The two losses are combined into a joint objective that simultaneously updates the reservoir parameters, the decay rate, and the projection matrix, and gradients propagate through the differentiable closed-form ridge regression to enable end-to-end optimization. A downstream classifier, namely a support vector machine on CWRU and SU and a random forest on the higher-dimensional TEP model space, performs the final detection. The echo state property of ADRN is formally established, and the resulting spectral-norm condition is more relaxed than the classical one, allowing richer reservoir dynamics. Results and Discussions Experiments cover the CWRU bearing dataset (five subsets, 50% missing rate), the SU gearbox dataset (30%, 50%, and 70% missing rates), and the Tennessee Eastman Process (TEP) chemical dataset (19 classes, three missing rates), with only 200 labeled signals per subset for training on CWRU and SU. The proposed method achieves the highest accuracy in 7 of the 8 CWRU and SU settings (Table 1), with accuracies ranging from 87.3% to 93.8% on CWRU. On SU, it maintains 94.4% accuracy even at a 70% missing rate, and the fluctuation across missing rates is only 2.8%, in contrast to 18.7% for ODE-RNN, while Neural CDE drops from 86.8% to 62.6%. Ablation studies confirm the contribution of each component (Table 1, Table 2). Removing the exponential decay reduces accuracy by up to 28.4 percentage points, and the interval weighting and the separability loss contribute complementary gains of 2.0 and 3.1 percentage points on SU at the 70% missing rate. t-SNE visualization shows that the optimized model space exhibits compact and clearly separated classes (Fig. 3). Training on a CWRU dataset completes in about 50 seconds, over two orders of magnitude faster than neural ordinary differential equation methods, which require 3000 to 7000 seconds (Table 3). Hyperparameter analysis indicates that a loss balance coefficient between 0.1 and 0.3 performs well and that a small reservoir suffices (Table 4). On TEP, a non-rotating-machinery industrial object whose faults manifest as changes in process dynamics, the proposed method attains the highest accuracy among all compared methods at every missing rate, with the largest margin of 7.0 percentage points at the highest missing rate (Table 5). Conclusions The ADRN based model space learning framework provides an effective solution for anomaly detection on irregularly sampled signals. The exponential decay mechanism enables interval-aware state updates without numerical ordinary differential equation solvers, ridge regression yields efficient closed-form readout fitting, and the joint optimization of the reconstruction and separability losses produces a model space with both high fitting quality and strong discriminative structure. The framework requires only a small reservoir of 10 to 50 dimensions and completes training within one minute, making it well suited to scenarios with limited training resources and irregular sampling. Future work includes adaptive reservoir sizing, extension to multivariate joint modeling, and validation in further domains such as structural health monitoring and biomedical or meteorological time series.
- Irregular signals,
- Anomaly detection,
- Adaptive decay reservoir network,
- Model space learning,
- Reservoir computing

FullText(HTML)

References(35)

References

[1]	ZAMANZADEH DARBAN Z, WEBB G I, PAN Shirui, et al. Deep learning for time series anomaly detection: A survey[J]. ACM Computing Surveys, 2025, 57(1): 15. doi: 10.1145/3691338.
[2]	王敏, 冯智彬, 吴德浩, 等. 非平稳过程异常监测方法: 综述与展望[J]. 中国科学: 信息科学, 2024, 54(8): 1807–1826. doi: 10.1360/SSI-2023-0377. WANG Min, FENG Zhibin, WU Dehao, et al. Overview and prospect of abnormal monitoring methods for non-stationary processes[J]. Scientia Sinica Informationis, 2024, 54(8): 1807–1826. doi: 10.1360/SSI-2023-0377.
[3]	孙晨峰, 吕卫民, 戴洪德, 等. 一种基于TimeGAN和OCSVM的多元退化设备小子样数据增广方法[J]. 电子学报, 2022, 50(11): 2678–2687. doi: 10.12263/DZXB.20220079. SUN Chenfeng, LÜ Weimin, DAI Hongde, et al. A small sample data augmentation method for multivariate degradation equipment based on TimeGAN and OCSVM[J]. Acta Electronica Sinica, 2022, 50(11): 2678–2687. doi: 10.12263/DZXB.20220079.
[4]	伍章俊, 许仁礼, 方刚, 等. 一种面向旋转机械多传感器故障诊断的模态融合深度聚类方法[J]. 电子与信息学报, 2025, 47(1): 244–259. doi: 10.11999/JEIT240648. WU Zhangjun, XU Renli, FANG Gang, et al. A modal fusion deep clustering method for multi-sensor fault diagnosis of rotating machinery[J]. Journal of Electronics & Information Technology, 2025, 47(1): 244–259. doi: 10.11999/JEIT240648.
[5]	JIA Xudong, PENG Wei, SHEN Chiran, et al. Spatio-temporal mixed graph neural controlled differential equations with adaptive connection sampling for irregular multivariate time series anomaly detection[C]. ICASSP 2025 - 2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Hyderabad, India, 2025: 1–5. doi: 10.1109/ICASSP49660.2025.10888536.
[6]	WANG Jun, DU Wenjie, YANG Yiyuan, et al. Deep learning for multivariate time series imputation: A survey[C]. Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence, Montreal, Canada, 2025: 10696–10704. doi: 10.24963/ijcai.2025/1187.
[7]	刘辉, 冯浩然, 马佳妮, 等. 融合空间自注意力感知的严重缺失多元时间序列插补算法[J]. 电子与信息学报, 2025, 47(10): 3917–3928. doi: 10.11999/JEIT250220. LIU Hui, FENG Haoran, MA Jiani, et al. Spatial self-attention incorporated imputation algorithm for severely missing multivariate time series[J]. Journal of Electronics & Information Technology, 2025, 47(10): 3917–3928. doi: 10.11999/JEIT250220.
[8]	CHE Zhengping, PURUSHOTHAM S, CHO K, et al. Recurrent neural networks for multivariate time series with missing values[J]. Scientific Reports, 2018, 8(1): 6085. doi: 10.1038/s41598-018-24271-9.
[9]	CHEN R T Q, RUBANOVA Y, BETTENCOURT J, et al. Neural ordinary differential equations[C]. Proceedings of the 32nd International Conference on Neural Information Processing Systems, Montréal, Canada, 2018: 6572–6583. doi: 10.5555/3327757.3327764.
[10]	KIDGER P, MORRILL J, FOSTER J, et al. Neural controlled differential equations for irregular time series[C]. Proceedings of the 34th Conference on Neural Information Processing Systems, 2020, 33: 6696–6707. (查阅网上资料, 本条文献会议地是线上, 请确认).
[11]	ZHANG Jiawen, ZHENG Shun, CAO Wei, et al. Warpformer: A multi-scale modeling approach for irregular clinical time series[C]. Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, Long Beach, USA, 2023: 3273–3285. doi: 10.1145/3580305.3599543.
[12]	CHEN Huanhuan, TIŇO P, RODAN A, et al. Learning in the model space for cognitive fault diagnosis[J]. IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(1): 124–136. doi: 10.1109/TNNLS.2013.2256797.
[13]	CHEN Huanhuan, TANG Fengzhen, TINO P, et al. Model metric co-learning for time series classification[C]. Proceedings of the 24th International Conference on Artificial Intelligence, Buenos Aires, Argentina, 2015: 3387–3394. doi: 10.5555/2832581.2832721.
[14]	CHEN Ao, ZHOU Xiren, FAN Yizhan, et al. Underground diagnosis based on GPR and learning in the model space[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024, 46(5): 3832–3844. doi: 10.1109/TPAMI.2023.3347739.
[15]	ZHOU Xiren, LIU Shikang, YAN Xinyu, et al. Reservoir-enhanced segment anything model for subsurface diagnosis[J]. Nature Communications, 2025, 16(1): 11080. doi: 10.1038/s41467-025-67382-4.
[16]	TANG Ziyu, ZHOU Xiren, CHEN Ao, et al. Inside and inside: Efficient anomaly detection by fully capturing the detailed dynamics[C]. ICASSP 2025 - 2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Hyderabad, India, 2025: 1–5. doi: 10.1109/ICASSP49660.2025.10888333.
[17]	CHEN Ao, ZHOU Xiren, and CHEN Huanhuan. Efficient anomaly detection of irregular sequences in Ct-Echo model space[C]. Proceedings of the 39th Annual AAAI Conference on Artificial Intelligence, Philadelphia, USA, 2025: 15731–15739. doi: 10.1609/aaai.v39i15.33727.
[18]	JAEGER H. The "Echo State" approach to analysing and training recurrent neural networks[R]. GMD Report 148, 2001.
[19]	任利强, 贾舒宜, 王海鹏, 等. 基于深度学习的时间序列分类研究综述[J]. 电子与信息学报, 2024, 46(8): 3094–3116. doi: 10.11999/JEIT231222. REN Liqiang, JIA Shuyi, WANG Haipeng, et al. A review of research on time series classification based on deep learning[J]. Journal of Electronics & Information Technology, 2024, 46(8): 3094–3116. doi: 10.11999/JEIT231222.
[20]	周平, 曾扬洋, 张宇, 等. 基于跨时空注意力机制的多变量时间序列异常检测[J]. 中国科学: 信息科学, 2025, 55(5): 1157–1176. doi: 10.1360/SSI-2024-0274. ZHOU Ping, ZENG Yangyang, ZHANG Yu, et al. Multivariable time series anomaly detection based on cross spatial-temporal attention mechanism[J]. Scientia Sinica Informationis, 2025, 55(5): 1157–1176. doi: 10.1360/SSI-2024-0274.
[21]	唐伦, 赵禹辰, 薛呈呈, 等. 一种基于时间序列分解和时空信息提取的云服务器异常检测模型[J]. 电子与信息学报, 2024, 46(6): 2638–2646. doi: 10.11999/JEIT230679. TANG Lun, ZHAO Yuchen, XUE Chengcheng, et al. A cloud server anomaly detection model based on time series decomposition and spatiotemporal information extraction[J]. Journal of Electronics & Information Technology, 2024, 46(6): 2638–2646. doi: 10.11999/JEIT230679.
[22]	黄昱哲, 管永原, 魏松杰. 面向时序异常检测的可变视距多向扫描方法[J]. 电子学报, 2025, 53(9): 3410–3424. doi: 10.12263/DZXB.20250385. HUANG Yuzhe, GUAN Yongyuan, and WEI Songjie. Variable horizon multi-directional scanning method for time series anomaly detection[J]. Acta Electronica Sinica, 2025, 53(9): 3410–3424. doi: 10.12263/DZXB.20250385.
[23]	郭铁峰, 贺建军, 申帅, 等. 基于动态规整与改进变分自编码器的异常电池在线检测方法[J]. 电子与信息学报, 2024, 46(2): 738–747. doi: 10.11999/JEIT230084. GUO Tiefeng, HE Jianjun, SHEN Shuai, et al. Abnormal battery on-line detection method based on dynamic time warping and improved variational auto-encoder[J]. Journal of Electronics & Information Technology, 2024, 46(2): 738–747. doi: 10.11999/JEIT230084.
[24]	RUBANOVA Y, CHEN R T Q, and DUVENAUD D K. Latent ordinary differential equations for irregularly-sampled time series[C]. Proceedings of the 33rd Conference on Neural Information Processing Systems, Vancouver, Canada, 2019: 5297–5307.
[25]	SHUKLA S N and MARLIN B. Multi-time attention networks for irregularly sampled time series[C]. International Conference on Learning Representations, Vienna, Austria, 2021.
[26]	CORTES C and VAPNIK V. Support-vector networks[J]. Machine Learning, 1995, 20(3): 273–297. doi: 10.1007/BF00994018.
[27]	JAEGER H, LUKOŠEVIČIUS M, POPOVICI D, et al. Optimization and applications of echo state networks with leaky- integrator neurons[J]. Neural Networks, 2007, 20(3): 335–352. doi: 10.1016/j.neunet.2007.04.016.
[28]	FISHER R A. The use of multiple measurements in taxonomic problems[J]. Annals of Eugenics, 1936, 7(2): 179–188. doi: 10.1111/j.1469-1809.1936.tb02137.x.
[29]	Case Western Reserve University. Bearing Data Center[EB/OL]. https://engineering.case.edu/bearingdatacenter/welcome, 2024.
[30]	SHAO Siyu, MCALEER S, YAN Ruqiang, et al. Highly accurate machine fault diagnosis using deep transfer learning[J]. IEEE Transactions on Industrial Informatics, 2019, 15(4): 2446–2455. doi: 10.1109/TII.2018.2864759.
[31]	DOWNS J J and VOGEL E F. A plant-wide industrial process control problem[J]. Computers & Chemical Engineering, 1993, 17(3): 245–255. doi: 10.1016/0098-1354(93)80018-I.
[32]	CHIANG L H, RUSSELL E L, and BRAATZ R D. Fault Detection and Diagnosis in Industrial Systems[M]. London, UK: Springer, 2001: 103–112. doi: 10.1007/978-1-4471-0347-9.
[33]	KEINER J, KUNIS S, and POTTS D. Using NFFT 3---A software library for various nonequispaced fast Fourier transforms[J]. ACM Transactions on Mathematical Software, 2009, 36(4): 19. doi: 10.1145/1555386.1555388.
[34]	HORN M, MOOR M, BOCK C, et al. Set functions for time series[C]. International Conference on Learning Representations, Addis Ababa, Ethiopia, 2020: 4353–4363.
[35]	ZHANG Xiang, ZEMAN M, TSILIGKARIDIS T, et al. Graph-guided network for irregularly sampled multivariate time series[C]. Proceedings of the Tenth International Conference on Learning Representations, 2022. (查阅网上资料, 本条文献会议地是线上, 请确认).