Parameters estimation of Hammerstein–Wiener time-delay nonlinear model
Abstract
This paper discusses nonlinear system identification issue for a Hammerstein–Wiener time-delay model. The presented Hammerstein–Wiener model consists of two static nonlinear blocks sandwiching a dynamic linear block, and the nonlinear blocks are established using neuro-fuzzy networks, the dynamic linear block is constructed by a time-delay transfer function. To estimate the unknown parameters of the Hammerstein–Wiener time-delay model, we introduce the theory of separable signals. Initially, the output nonlinear block parameters are estimated through correlation analysis and cluster techniques based on available input-output of separable signals. Then, estimation of time-delay transfer function is facilitated by iteration method, so that time-delay parameter and transfer function parameters are alternately estimated. Finally, the input nonlinear block estimation is facilitated by integrating improved particle swarm optimization with cuckoo search techniques, which resulted in an improvement in the global search ability and convergence speed of neuro-fuzzy network. The simulation comparison results are finally verified via numerical case and state of charge estimation of lithium battery in terms of the feasibility and advantage of the developed Hammerstein–Wiener time-delay model identification.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Cites
Lui, C. F., Liu, Y., & Xie, M. (2022) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2022.3152856 · Cited by 188 · see citing works
Wang, D., Yang, Y. J., & Gu, T. (2023) · Journal of Energy Storage · doi:10.1016/j.est.2023.106831 · Cited by 138 · see citing works
Yang, R., Liu, Y., Yu, Y., et al. (2021) · Energy Reports · doi:10.1016/j.egyr.2021.08.120 · Cited by 67 · see citing works
Real-Time Reachable Set Control for Neutral Singular Markov Jump Systems With Mixed Delays
Zhang, L., Zhao, X., & Zhao, N. (2021) · IEEE Transactions on Circuits & Systems II Express Briefs · doi:10.1109/tcsii.2021.3118075 · Cited by 65 · see citing works
Short-Term Traffic Flow Forecasting Using Ensemble Approach Based on Deep Belief Networks
Jin, L., Wu, N., Qiao, Y., et al. (2020) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2020.3011700 · Cited by 61 · see citing works
Gaya, M. S., Yusuf, L. A., Mustapha, M., et al. (2017) · Indonesian Journal of Electrical Engineering and Computer Science · doi:10.11591/ijeecs.v5.i3.pp666-672 · Cited by 60 · see citing works
State of charge and state of health diagnosis of batteries with voltage-controlled models
Braun, J. A., Behmann, R., Schmider, D., & Bessler, W. G. (2022) · Journal of Power Sources · doi:10.1016/j.jpowsour.2022.231828 · Cited by 55 · see citing works
Vörös, J. (2014) · Nonlinear Dynamics · doi:10.1007/s11071-014-1804-4 · Cited by 54 · see citing works
Xu, K., Yang, H., & Zhu, C. (2019) · Neurocomputing · doi:10.1016/j.neucom.2019.05.049 · Cited by 54 · see citing works
Dong, X.-J., Shen, J.-N., He, G., et al. (2021) · Energy · doi:10.1016/j.energy.2021.121212 · Cited by 54 · see citing works
Nonlinear system modeling using self-organizing fuzzy neural networks for industrial applications
Zhou, H., Zhao, H., & Zhang, Y. (2020) · Applied Intelligence · doi:10.1007/s10489-020-01645-z · Cited by 53 · see citing works
Zeng, L., Ling, L., Zhang, D., & Jiang, W. (2022) · Applied Soft Computing · doi:10.1016/j.asoc.2022.109833 · Cited by 52 · see citing works
Hou, J., Wang, H., Su, H., et al. (2024) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2024.111329 · Cited by 52 · see citing works
Li, M., Chen, H., Shi, X. L., et al. (2019) · Applied Soft Computing · doi:10.1016/j.asoc.2019.105677 · Cited by 50 · see citing works
Data-driven predictive control of Hammerstein–Wiener systems based on subspace identification
Luo, X., & Song, Y. (2017) · Information Sciences · doi:10.1016/j.ins.2017.09.004 · Cited by 48 · see citing works
Li, J., Zong, T., Gu, J., et al. (2020) · Circuits Systems and Signal Processing · doi:10.1007/s00034-019-01329-1 · Cited by 47 · see citing works
Gu, Y., Zhu, Q., & Nouri, H. (2020) · IET Control Theory and Applications · doi:10.1049/iet-cta.2020.0104 · Cited by 45 · see citing works
Identification method of neuro‐fuzzy‐based Hammerstein model with coloured noise
Li, F., Jia, L., & Peng, D. (2017) · IET Control Theory and Applications · doi:10.1049/iet-cta.2017.0306 · Cited by 42 · see citing works
Self-citationHuang, S., Lin, N., Wang, Z., Zhang, Z., Wen, S., Zhao, Y., & Li, Q. (2024) · Journal of Power Sources · doi:10.1016/j.jpowsour.2024.234261 · Cited by 42 · see citing works
Identification scheme for fractional Hammerstein models with the delayed Haar wavelet
Kothari, K., Mehta, U., Prasad, V., et al. (2020) · IEEE/CAA Journal of Automatica Sinica · doi:10.1109/jas.2020.1003093 · Cited by 40 · see citing works
Li, F., Yang, Y., & Xia, Y. (2024) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2024.111631 · Cited by 40 · see citing works
Self-citationPrasad, V., & Mehta, U. (2021) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2021.108568 · Cited by 39 · see citing works
Li, F., Zheng, T., He, N., et al. (2022) · IEEE/CAA Journal of Automatica Sinica · doi:10.1109/jas.2022.105821 · Cited by 39 · see citing works
Self-citationFREQUENCY IDENTIFICATION OF HAMMERSTEIN-WIENER SYSTEMS WITH PIECEWISE AFFINE INPUT NONLINEARITY
Giri, F., Brouri, A., Amdouri, O., et al. (2014) · IFAC Proceedings Volumes · doi:10.3182/20140824-6-za-1003.00303 · Cited by 34 · see citing works
Liu, Q., Xiao, Y., Ding, F., et al. (2021) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.5576 · Cited by 32 · see citing works
Dong, J. (2021) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2021.3105745 · Cited by 30 · see citing works
Parameter Learning for the Nonlinear System Described by a Class of Hammerstein Models
Li, F., Zhu, X., & Cao, Q. (2022) · Circuits Systems and Signal Processing · doi:10.1007/s00034-022-02240-y · Cited by 30 · see citing works
Self-citationIdentification of Wiener model using step signals and particle swarm optimization
Tang, Y., Qiao, L., & Guan, X. (2009) · Expert Systems with Applications · doi:10.1016/j.eswa.2009.10.008 · Cited by 26 · see citing works
Xie, Y., Wang, J., Xie, S., & Chen, X. (2023) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2023.3322195 · Cited by 26 · see citing works
A hypervolume-based cuckoo search algorithm with enhanced diversity and adaptive scaling factor
Liang, M., Wang, L., Wang, L., et al. (2023) · Applied Soft Computing · doi:10.1016/j.asoc.2023.111073 · Cited by 21 · see citing works
Napole, C., Barambones, Ó., Calvo, I., et al. (2020) · Mathematics · doi:10.3390/math8112071 · Cited by 19 · see citing works
Identification of Wiener Time Delay Systems Based on Hierarchical Gradient Approach
Atitallah, A., Bedoui, S., & Abderrahim, K. (2015) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2015.05.040 · Cited by 18 · see citing works
Phase-based order separation for Volterra series identification
Bouvier, D., Hélie, T., & Roze, D. (2019) · International Journal of Control · doi:10.1080/00207179.2019.1694175 · Cited by 16 · see citing works
Adaptive TS fuzzy MPC based on Particle Swarm Optimization-Cuckoo Search algorithm
Taieb, A., Salhi, H., & Châari, A. (2022) · ISA Transactions · doi:10.1016/j.isatra.2022.05.018 · Cited by 16 · see citing works
Li, F., Zhou, S., & Liu, R. (2024) · Journal of Energy Storage · doi:10.1016/j.est.2024.114265 · Cited by 15 · see citing works
Self-citationAbouda, S. E., Abid, D. B. H., Elloumi, M., et al. (2020) · International Journal of Computer Applications in Technology · doi:10.1504/ijcat.2020.109340 · Cited by 11 · see citing works
An RNN-Based Adaptive Hybrid Time Series Forecasting Model for Driving Data Prediction
Seo, J. H., & Kim, K.-D. (2025) · IEEE Access · doi:10.1109/access.2025.3554803 · Cited by 10 · see citing works
Identification of Nonlinear Dynamic Systems Using Fuzzy Hammerstein-Wiener Systems
Abouda, S. E., Abid, D. B. H., Elloumi, M., et al. (2019) · International Conference on Sciences and Techniques of Automatic Control and Computer Engineering · doi:10.1109/sta.2019.8717218 · Cited by 9 · see citing works
Lu, K., & Wang, H. (2023) · IET Control Theory and Applications · doi:10.1049/cth2.12566 · Cited by 9 · see citing works
Identification of a precision motion stage based on the Hammerstein-Wiener model
Zhang, Z., Zhang, D., Zheng, H., et al. (2019) · Chinese Control Conference (CCC) · doi:10.23919/chicc.2019.8865318 · Cited by 6 · see citing works
Identification of Hammerstein-Wiener model with discontinuous input nonlinearity
Brouri, A., Mansouri, F. E. E., Chaoui, F. Z., et al. (2023) · Science China Information Sciences · doi:10.1007/s11432-022-3767-2 · Cited by 6 · see citing works
Parameter Identification for the Hammerstein-Wiener Nonlinear Time Delay Systems with Process Noises
Li, F., Han, J., He, N., et al. (2024) · Circuits Systems and Signal Processing · doi:10.1007/s00034-024-02900-1 · Cited by 6 · see citing works
Self-citationLiu, C., Wang, H., & Zhang, Q. (2024) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2024.107444 · Cited by 4 · see citing works
Parameters estimation for the Hammerstein‐Wiener models with colored noise based on hybrid signals
Li, F., & Han, J. (2023) · International Journal of Adaptive Control and Signal Processing · doi:10.1002/acs.3735 · Cited by 3 · see citing works
Self-citationBearing Dynamics Modeling Based on the Virtual State-Space and Hammerstein–Wiener Model
Jiang, G., Zhou, K., Li, Z., et al. (2024) · Sensors · doi:10.3390/s24165410 · Cited by 3 · see citing works
Pan, T., Liu, L., & Li, M. (2024) · IEEE Transactions on Semiconductor Manufacturing · doi:10.1109/tsm.2024.3392898 · Cited by 2 · see citing works
Balakrishnan, M., Rajendran, V., Prajwal Shettigar, J., et al. (2024) · Journal of Physics Conference Series · doi:10.1088/1742-6596/2818/1/012027 · Cited by 1 · see citing works
Flagged first, then by citations
Cited by
Still being checked.
- Authors
- Li, F., Zhu, Y., Zhou, S., & Cao, Q.
- Affiliations
- Jiangsu University of Technology (CN)
- Yangzhou University (CN)
- Corresponding author
- Li, Feng
- ORCID
- Venue
- Transactions of the Institute of Measurement and Control
- Publisher
- SAGE Publications
- Published
- 2025-09-23
- Volume
- 48
- Issue
- 12
- Pages
- 2990-3000
- ISSN
- 0142-3312 (ISSN-L)
- 1477-0369
- OpenAlex
- W4414483319
- Cited by
- 3
- References
- 47
- Citations by year
- 2026: 3
- FWCI
- 1.17
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Transactions of the Institute of Measurement and Control (publishedVersion)
- Funders
- National Natural Science Foundation of China (62003151)
- Postgraduate Research and Practice Innovation Program of Jiangsu University of Technology (XSJCX24_06)
- Qinglan Project of Jiangsu Province of China (2025[4])
- Zhongwu Youth Innovative Talents Support Program of Jiangsu University of Technology (202102003)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
- Physical Sciences › Engineering › Computational Mechanics › Advanced Adaptive Filtering Techniques
- Physical Sciences › Computer Science › Artificial Intelligence › Fuzzy Logic and Control Systems
- Keywords
- Hammerstein-Wiener model, time-delay systems, nonlinear system identification, parameter estimation, correlation analysis, clustering, fuzzy neural network, particle swarm optimization, cuckoo search algorithm
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review