# Introduction to the Content

This page collects the abstracts and presentations that were part of the different editions of the Workshop on Nonlinear System Identification Benchmarks, the results of recent invited sessions based upon the benchmarks featured on this website, and benchmark results published in other journal or conference papers. You can find the different, keynotes, and regular talks of the past workshops, the list of invited sessions, and the papers published on the different benchmarks below.

Is your publication missing on this page? Would you want to feature additional material (slides, code, toolbox, ...)? Please contact us and we will include your research results on this webpage!

# Workshop Keynotes

## 2019

**Gianluigi Pillonetto**, University of Padova, Italy

Keynote:**Regularization networks for system identification**,**slides****Oliver Nelles**, University of Siegen, Germany

Keynote:**Challenges in nonlinear system identification**,**slides****Fredrik Lindsten**, Linkoping University, Sweden

Keynote:**Learning dynamical systems with particle stochastic approximation EM**,**slides****Elizabeth Cross**, The University of Sheffield, United Kingdom

Keynote:**Grey-Box models for structural dynamics**.

## 2018

**Eleni Chatzi**, ETH Zürich, Switzerland

Keynote:**Data-Driven Assessment of Engineered Systems: Beyond LTI**,**slides****Alfred Schouten**TU Delft, The Netherlands

Keynote:**Nonlinear cortical responses in EEG evoked by continuous wrist manipulations**,**slides****Johan Suykens**, KU Leuven, Belgium

Keynote:**Function estimation, model representations and nonlinear system identification**,**slides****Peter Young**, University of Lancaster, UK

Keynote:**State-Dependent Parameter (SDP) Nonlinear Models and a Hydrological Identification Benchmark**,

**slides**,**demo and background material****Jorge Goncalves**, University of Luxembourg, Luxembourg

Keynote:**Challenges in system identification of biochemical systems**,**slides**

## 2017

**David Barton**, University of Bristol

Keynote:**Control-based continuation - from models to experiments**,**slides****Lennart Ljung**, Linköping University

Keynote:**Non-linear system identification: A palette from off-white to pit-black**,**slides****Carl Edward Rasmussen**and**Johan Schoukens**, University of Cambridge and Vrije Universiteit Brussel

Keynote:**Bayesians methods in system identification: equivalences, differences, and misunderstanding**,

**updated slides**, slides 26/04/2017**Bart Peeters**, Siemens PLM Software

Keynote:**Structural non-linearities – an industrial view**,**slides**

## 2016

**Gaëtan Kerschen**, Université de Liège

Keynote:**Identification of Nonlinear Mechanical Systems: State of the Art and Recent Trends**,**slides**

**Carl Edward Rasmussen**, University of Cambridge

Keynote:**Variational Inference in Gaussian Processes for Non-Linear Time Series**,**slides**

**Thomas Schön**, Uppsala Universitet

Keynote:**Solving Nonlinear Inference Problems using Sequential Monte Carlo**,**slides**

**Johan Schoukens**, Vrije Universiteit Brussel

Keynote:**Data Driven Discrete Time Modeling of Continuous Time Nonlinear Systems: Problems, Challenges, Success Stories**,**slides**

**Keith Worden**, The University of Sheffield

Keynote:**Is System Identification Just Machine Learning?**,**slides**

# Workshop Regular Talks

## 2019

The complete **book of abstracts** of the 2019 Workshop on Nonlinear System Identification Benchmarks can be found __here__. Some of the presentations, sometimes completed by the code used to generate the presented results, can be found below.

- M. Schüssler, T.O. Heinz, and O. Nelles,
**Local Model State Space Networks for Hysteresis Identification**, Workshop on Nonlinear System Identification Benchmarks, 2019. - J. Decuyper, K. Tiels and J. Schoukens,
**Reducing nonlinear state-space models through polynomial Decoupling**, Workshop on Nonlinear System Identification Benchmarks, 2019.**slides** - K. Karami and D. Westwick,
**Polynomial Constrained Factoring in P-NARX Identification**, Workshop on Nonlinear System Identification Benchmarks, 2019.**slides** - A.C. Schouten, M.P. Vlaar, T. Solis-Escalante, Y. Yang and F.C.T. van der Helm,
**Cortical responses evoked by wrist joint manipulation**, Workshop on Nonlinear System Identification Benchmarks, 2019.**slides** - Z. Tuza and G.-B. Stan,
**Identifying Evoked Cortical Responses Using Block-Sparse Bayesian Learning**, Workshop on Nonlinear System Identification Benchmarks, 2019. - R.G. Junker and R. Relan,
**Continuous-time Stochastic Grey-box Model of the Nonlinear Feedback System based on Residual Analysis**, Workshop on Nonlinear System Identification Benchmarks, 2019.**slides** - T.J. Rogers and E.J. Cross,
**Particle MCMC Approaches to the Silverbox Benchmark**, Workshop on Nonlinear System Identification Benchmarks, 2019. - P. Gardner and R.J. Barthorpe,
**Estimation of Model Discrepancy using a Bayesian History Matching and Importance Sampling Approach**, Workshop on Nonlinear System Identification Benchmarks, 2019. - K. Tiels and J. Decuyper,
**PNLSS 1.0**, Workshop on Nonlinear System Identification Benchmarks, 2019.**slides**,**Matlab demo** - T. Krivec and L. Žnidarič,
**Sparse Gaussian Process Regression for System Identification**, Workshop on Nonlinear System Identification Benchmarks, 2019. - H. Zhou and W. Pan,
**Sparse Bayesian Deep Neural Networks for Nonlinear System Identification**, Workshop on Nonlinear System Identification Benchmarks, 2019. - A.H. Ribeiro, C. Andersson, K. Tiels, N. Wahlström and T.B. Schön,
**Deep Convolutional Networks are Useful in System Identification**, Workshop on Nonlinear System Identification Benchmarks, 2019.**slides** - B. Peeters, P.Z. Csurcsia,
**Structural nonlinearities – an industrial view**, Workshop on Nonlinear System Identification Benchmarks, 2019. - R. Fuentes, K. Worden and E.J. Cross,
**Equation Discovery using Sparse Bayesian Learning, applied to the Electro-Mechanical Positioning System**, Workshop on Nonlinear System Identification Benchmarks, 2019. - D. Khandelwal, M. Schoukens and R. Tóth,
**Automating System Identification Using Grammar and Genetic Programming**, Workshop on Nonlinear System Identification Benchmarks, 2019.**slides** - K. Tatsis, T. Simpson, E. Chatzi,
**Bayesian and Genetic Methods for Model Selection of Greybox Modelling on the Silverbox**, Workshop on Nonlinear System Identification Benchmarks, 2019. - T.O. Heinz and O. Nelles,
**LMN-Tool: Matlab-Toolbox for Local Model Networks**, Workshop on Nonlinear System Identification Benchmarks, 2019. - M. Schoukens and R. Tóth,
**Identification of Nonlinear LFR Systems starting from the Best Linear Approximation**, Workshop on Nonlinear System Identification Benchmarks, 2019.**slides** - K. Batselier,
**Lifting the curse of dimensionality in nonlinear system identification with tensor networks**, Workshop on Nonlinear System Identification Benchmarks, 2019.**slides**

## 2018

The complete **book of abstracts** of the 2018 Workshop on Nonlinear System Identification Benchmarks can be found __here__. Some of the presentations, sometimes completed by the code used to generate the presented results, can be found below.

- T.O. Heinz, T. Münker and O. Nelles,
**Identification of Systems with Hysteretic Behavior Using NOBF Local Model Networks**, Workshop on Nonlinear System Identification Benchmarks, 2018. - K. Karami, D. Westwick and J. Schoukens,
**Identification of Decoupled Polynomial NARX Models using Simulation Error Minimization**, Workshop on Nonlinear System Identification Benchmarks, 2018.**slides** - J. Decuyper, A. Fakhrizadeh Esfahani, K. Tiels and J. Schoukens,
**Retrieving highly structured models starting from a black box state-space model: a case study on the Bouc-Wen hysteresis model**, Workshop on Nonlinear System Identification Benchmarks, 2018.**slides** - B. Peeters, P.Z Csurcsia and J. Schoukens,
**The use of exotic multisines in MIMO structural dynamics and acoustic applications**, Workshop on Nonlinear System Identification Benchmarks, 2018.**slides** - M. Perne and M. Stepančič,
**Regressor selection using Lipschitz quotients on the F-16 aircraft benchmark**, Workshop on Nonlinear System Identification Benchmarks, 2018.**slides**,**Matlab code** - M. Mazzoleni, M. Scandella and F. Previdi,
**Kernel manifold regression for the coupled electric drives dataset**, Workshop on Nonlinear System Identification Benchmarks, 2018.**slides**,**Matlab code** - M.R.-H. Abdalmoaty and H. Hjalmarsson,
**Application of a Linear PEM estimator to a stochastic Wiener-Hammerstein Benchmark Problem**, Workshop on Nonlinear System Identification Benchmarks, 2018. - G. Birpoutsoukis and M. Schoukens,
**From the Volterra series to a Wiener-Hammerstein model**, Workshop on Nonlinear System Identification Benchmarks, 2018. - M. Stepančič, M. Perne and J. Kocijan,
**Regularised NFIR identification with Gaussian process model**, Workshop on Nonlinear System Identification Benchmarks, 2018. - D. Bouvier, T. Hélie and D. Roze,
**Phase-based homogeneous order separation for improving Volterra series identification**, Workshop on Nonlinear System Identification Benchmarks, 2018.**slides**,**Python Toolbox** - N. Simidjievski, L. Todorovski, S. Džeroski, and J. Kocijan,
**Nonlinear System Identification with Equation Discovery**, Workshop on Nonlinear System Identification Benchmarks, 2018. - P.Z. Csurcsia, J. Schoukens and B. Peeters,
**Nonparametric Approximation of the Nonlinear SilverBox Data: a Linear Time-varying Approach**, Workshop on Nonlinear System Identification Benchmarks, 2018. - J. Schoukens,
**Simulation and Prediction Errors in the Presence of Model Errors: a Case Study on the Silverbox**, Workshop on Nonlinear System Identification Benchmarks, 2018. - R. Hostettler, F. Tronarp and S. Särkkä,
**Nonparametric Drift Model for Stochastic Differential Equations**, Workshop on Nonlinear System Identification Benchmarks, 2018.**slides** - M. Schoukens and R. Tóth,
**From Nonlinear Identification to Linear Parameter Varying Models: Benchmark Examples**, Workshop on Nonlinear System Identification Benchmarks, 2018.**slides**,**Matlab code** - A. Montazeri, M.M. Arefi and M. Kazemi,
**An Investigation of the Wiener Approach for Nonlinear System Identification Benchmarks**, Workshop on Nonlinear System Identification Benchmarks, 2018.**slides**,**Matlab Toolbox**

## 2017

The complete **book of abstracts** of the 2017 Workshop on Nonlinear System Identification Benchmarks can be found __here__. Some of the presentations, sometimes completed by the code used to generate the presented results, can be found below.

- T. Dossogne, J.P. Noël and G. Kerschen,
**Nonlinear system identification of an F-16 aircraft using the acceleration surface method**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides**,**toolbox** - K. Tiels,
**Polynomial nonlinear state-space modeling of the F-16 aircraft benchmark**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides** - P. Dreesen, K. Tiels and M. Ishteva,
**Decoupling nonlinear models for the F-16 ground vibration test benchmark**, Workshop on Nonlinear System Identification Benchmarks, 2017. - G. Hollander, P. Dreesen, M. Ishteva and J. Schoukens,
**Nonlinear model decoupling using a tensor decomposition initialization**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides** - T. Münker, T.O. Heinz and O. Nelles,
**Regularized local FIR model networks for a Bouc-Wen and a Wiener-Hammerstein system**, Workshop on Nonlinear System Identification Benchmarks, 2017. - E. Zhang and M. Schoukens,
**Fast location of process noise for nonlinear system identification**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides**,**Matlab script**

*Readme in the Matlab script.* - B. Tang, M.J. Brennan and G. Gatti,
**On the interaction of an electro-dynamic shaker and a beam with stiffness nonlinearity**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides** - G. Giordano and J. Sjöberg,
**Maximum likelihood identification of Wiener-Hammerstein models in presence of process noise**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides** - R. Relan, D. Verbeke and K. Tiels,
**One step ahead prediction of the WH benchmark with process noise using kernel adaptive learning**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides** - M. Rébillat and M. Schoukens,
**A methodology to compare two estimation methods for parallel Hammerstein models**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides** - L. Ljung,
**Matlab System Identification Toolbox demonstration**, Workshop on Nonlinear System Identification Benchmarks, 2017.**toolbox**,**Matlab script**

*Note that the Matlab script requires Matlab2016b or higher to work, also the F-16 ground vibration test benchmark data should be downloaded.* - M. Schoukens,
**Interpolated linear modeling of the F16 benchmark**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides**,**Matlab script**

*Readme in the Matlab script.* - P.Z. Csurcsia, G. Birpoutsoukis and J. Schoukens,
**Transient elimination and memory saving possibilities for multidimensional nonparametric regularization illustrated on the cascaded water tanks benchmark problem**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides** - S.R. Hassan,
**System identification of dynamic force transducers**, Workshop on Nonlinear System Identification Benchmarks, 2017. - A.F. Esfahani, P. Dreesen, J.P. Noël, K. Tiels, J. Schoukens,
**Decoupled polynomial nonlinear state space models of a Bouc-Wen hysteretic system**, Workshop on Nonlinear System Identification Benchmarks, 2017. - D. Westwick, G. Hollander and J. Schoukens,
**The decoupled polynomial NARX model: parameter reduction and structural insights for the Bouc-Wen benchmark**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides**

## 2016

The complete **book of abstracts** of the 2016 Workshop on Nonlinear System Identification Benchmarks can be found __here__. Some of the presentations, sometimes completed by the code used to generate the presented results, will be posted below.

- K. Tiels,
**PNLSS 1.0 - A polynomial nonlinear state-space Matlab toolbox**, Workshop on Nonlinear System Identification Benchmarks, 2016.**slides** - A. Svensson, F. Lindsten, T.B. Schön,
**Particle methods for the Wiener-Hammerstein system**, Workshop on Nonlinear System Identification Benchmarks, 2016. - E. Zhang, M. Schoukens, J. Schoukens,
**Structural modeling of Wiener-Hammerstein system in the presence of the process noise**, Workshop on Nonlinear System Identification Benchmarks, 2016.**slides** - G. Holmes, T. Rogers, E.J. Cross, N. Dervilis, G. Manson, R.J. Barthorpe, K. Worden,
**Cascaded Tanks Benchmark: Parametric and Nonparametric Identification**, Workshop on Nonlinear System Identification Benchmarks, 2016. - G. Giordano, J. Sjöberg,
**Cascade Tanks Benchmark**, Workshop on Nonlinear System Identification Benchmarks, 2016. - J.P. Noël, A.F. Esfahani, G. Kerschen, J. Schoukens,
**A nonlinear state-space solution to a hysteretic benchmark in system identification**, Workshop on Nonlinear System Identification Benchmarks, 2016. - A.F. Esfahani, P. Dreesen, K. Tiels, J.P. Noël, J. Schoukens,
**Using a polynomial decoupling algorithm for state-space identification of a Bouc-Wen system**, Workshop on Nonlinear System Identification Benchmarks, 2016. - R. Gaasbeek, R. Mohan,
**Control-focused identification of hysteric systems: Selecting model structures? Think about the final use of the model!**, Workshop on Nonlinear System Identification Benchmarks, 2016. - A. Bajrić,
**System identification of a linearized hysteretic system using covariance driven stochastic subspace identification**, Workshop on Nonlinear System Identification Benchmarks, 2016. - R. Relan, K. Tiels, A. Marconato,
**Identifying an Unstructured Flexible Nonlinear Model for the Cascaded Water-tanks Benchmark: Capabilities and Short-comings**, Workshop on Nonlinear System Identification Benchmarks, 2016. - P. Mattson, D. Zachariah, P. Stoica,
**Identification of a PWARX model for the cascade water tanks**, Workshop on Nonlinear System Identification Benchmarks, 2016. - G. Birpoutsoukis, P.Z. Csurcsia,
**Nonparametric Volterra series estimate of the cascaded tank**, Workshop on Nonlinear System Identification Benchmarks, 2016. - M. Rébillat, K. Ege, N. Mechbal, J. Antoni,
**Repeated exponential sine sweeps for the autonomous estimation of nonlinearities and bootstrap assessment of uncertainties**, Workshop on Nonlinear System Identification Benchmarks, 2016. - M. Schoukens,
**Identification of Wiener-Hammerstein systems with process noise using an Errors-in-Variables framework**, Workshop on Nonlinear System Identification Benchmarks, 2016.**slides** - K. Worden, G. Manson, R.J. Barthorpe, E.J. Cross, N. Dervilis, G. Holmes, T. Rogers,
**Wiener-Hammerstein Benchmark with process noise: Parametric and Nonparametric Identification**, Workshop on Nonlinear System Identification Benchmarks, 2016. - G. Manson, R.J. Barthorpe, E.J. Cross, N. Dervilis, G. Holmes, T. Rogers, K. Worden,
**Bouc-Wen Benchmark: Parametric and Nonparametric Identification**, Workshop on Nonlinear System Identification Benchmarks, 2016. - E. Louarroudi, S. Vanlanduit, R. Pintelon,
**Identification of non-linear restoring forces through linear time-periodic approximations**, Workshop on Nonlinear System Identification Benchmarks, 2016. - M. Schoukens, F.G. Scheiwe,
**Modeling Nonlinear Systems Using a Volterra Feedback Model**, Workshop on Nonlinear System Identification Benchmarks, 2016.**slides** - A. Svensson, F. Lindsten, T.B. Schön,
**First principles and black box modeling of the cascaded water tanks**, Workshop on Nonlinear System Identification Benchmarks, 2016.

# Invited Sessions

## SYSID 2018

Two invited sessions were organized at the 18th IFAC Symposium on System Identification in Stockholm, Sweden. It featured the following talks:

- G. Giordano, J. Sjöberg,
**Maximum Likelihood Identification of Wiener-Hammerstein System with Process Noise**, 18th IFAC Symposium on System Identification (SYSID 2018), 2018, 401-406. - A. Svensson, D. Zachariah, T.B. Schön,
**How Consistent Is My Model with the Data? Information-Theoretic Model Check**, 18th IFAC Symposium on System Identification (SYSID 2018), 2018, 407-412. - J.G. Stoddard, J. Welsh,
**Regularized Basis Function Estimation of Volterra Kernels for the Cascaded Tanks Benchmark**, 18th IFAC Symposium on System Identification (SYSID 2018), 2018, 413-418. - M. Schoukens, R. Toth,
**From Nonlinear Identification to Linear Parameter Varying Models: Benchmark Examples**, 18th IFAC Symposium on System Identification (SYSID 2018), 2018, 419-424. - R. Hostettler, F. Tronarp, S. Särkä
**Modeling the Drift Function in Stochastic Differential Equations Using Reduced Rank Gaussian Processes**, 18th IFAC Symposium on System Identification (SYSID 2018), 2018, 778-783. - M.R.H Abdalmoaty, H. Hjalmarsson,
**Application of a Linear PEM Estimator to a Stochastic Wiener-Hammerstein Benchmark Problem**, 18th IFAC Symposium on System Identification (SYSID 2018), 2018, 784-789. - S. Pan, J. Welsh,
**An Application of Indirect Inference to the Cascaded Tanks Nonlinear Benchmark**, 18th IFAC Symposium on System Identification (SYSID 2018), 2018, 790-795. - D. Westwick, G. Hollander, K. Karami, J. Schoukens,
**Using Decoupling Methods to Reduce Polynomial NARX Models**, 18th IFAC Symposium on System Identification (SYSID 2018), 2018, 796-801.

## IFAC World Congress 2017

An open invited track was organized at the 2017 IFAC World Congres in Toulouse, France. It featured the following talks:

- M. Schoukens, J.P. Noël,
**Three Benchmarks Addressing Open Challenges in Nonlinear System Identification**, 20th World Congress The International Federation of Automatic Control, 2017, 448-453.**slides** - R. Relan, K. Tiels, A. Marconato, J. Schoukens,
**An Unstructured Flexible Nonlinear Model for the Cascaded Water-Tanks Benchmark**, 20th World Congress The International Federation of Automatic Control, 2017, 454-459. - A. Fakhrizadeh Esfahani, P. Dreesen, K. Tiels, J.P. Noël, J. Schoukens,
**Polynomial State-Space Model Decoupling for the Identification of Hysteretic Systems**, 20th World Congress The International Federation of Automatic Control, 2017, 460-465. - M. Brunot, A. Janot, F. Carrillo,
**Continuous-Time Nonlinear Systems Identification with Output Error Method Based on Derivative-Free Optimisation**, 20th World Congress The International Federation of Automatic Control, 2017, 466-471. - J. Belz, T. Münker, T.O. Heinz, G. Kampmann, O. Nelles,
**Automatic Modeling with Local Model Networks for Benchmark Processes**, 20th World Congress The International Federation of Automatic Control, 2017, 472-477. - G. Birpoutsoukis, P.Z. Csurcsia, J. Schoukens,
**Nonparametric Volterra Series Estimate of the Cascaded Water Tanks Using Multidimensional Regularization**, 20th World Congress The International Federation of Automatic Control, 2017, 478-483.

# Publications on the Featured Benchmarks

## Coupled Electric Drives (2017)

You can find a list of contributions working on the Coupled Electric Drives below. You could also check the citing papers of the Coupled Electric Drives dataset description through Google Scholar for a more up-to-date overview.

- T. Wigren and M. Schoukens,
**Coupled Electric Drives Data Set and Reference Models**, Technical Report, Department of Information Technology, Uppsala University, Department of Information Technology, Uppsala University, 2017.**pdf** - P. Wachel,
**Wiener system modelling by exponentially weighted aggregation**, International Journal of Control, 2017, 90, 2480-2489. - F. Sabahi and M. Reza Akbarzadeh-T,
**Extended Fuzzy Logic: Sets and Systems**, IEEE Transactions on Fuzzy Systems, 2016, 24, 530-543. - H. Nejib, O. Taouali and N. Bouguila,
**Identification of nonlinear systems with kernel methods**, IEEE International Conference on Systems, Man, and Cybernetics (SMC), 2016, 577-581. - D. Aleksovski, D. Dovžan, S. Džeroski and J. Kocijan,
**A comparison of fuzzy identification methods on benchmark datasets**, 4th IFAC Conference on Intelligent Control and Automation SciencesICONS, 2016, 31-36. - A. Carini and G.L. Sicuranza,
**A study about Chebyshev nonlinear filters**, Signal Processing, 2016, 122, 24-32. - M. Scarpiniti, D. Comminiello, R. Parisi and A. Uncini,
**Novel Cascade Spline Architectures for the Identification of Nonlinear Systems**, IEEE Transactions on Circuits and Systems—I, 2015, 62, 1825-1835. - H.V.H. Ayala, L.F. da Cruz, R.Z. Freire and L. dos Santos Coelho,
**Cascaded free search differential evolution applied to nonlinear system identification based on correlation functions and neural networks**, IEEE Symposium on Computational Intelligence in Control and Automation (CICA), 2014, 1-7.

## F-16 Ground Vibration Test (2017)

You can find a list of contributions working on the F-16 Ground Vibration Test below. You could also check the citing papers of the F-16 Ground Vibration Test dataset description through Google Scholar for a more up-to-date overview.

- T. Dossogne, J.P. Noël and G. Kerschen,
**Nonlinear system identification of an F-16 aircraft using the acceleration surface method**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides**,**toolbox** - K. Tiels,
**Polynomial nonlinear state-space modeling of the F-16 aircraft benchmark**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides** - P. Dreesen, K. Tiels and M. Ishteva,
**Decoupling nonlinear models for the F-16 ground vibration test benchmark**, Workshop on Nonlinear System Identification Benchmarks, 2017. - L. Ljung,
**Matlab System Identification Toolbox demonstration**, Workshop on Nonlinear System Identification Benchmarks, 2017.**toolbox**,**Matlab script**

*Note that the Matlab script requires Matlab2016b or higher to work, also the F-16 ground vibration test benchmark data should be downloaded.* - M. Schoukens,
**Interpolated linear modeling of the F16 benchmark**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides**,**Matlab script**

*Readme in the Matlab script.*

## Cascaded Tanks System (2016)

You can find a list of contributions working on the Cascaded Tanks System below. You could also check the citing papers of the Cascaded Tanks System dataset description through Google Scholar for a more up-to-date overview. It is also worthwhile checking the papers citing the 2017 IFAC WC contribution on the Cascaded Tanks System trhough Google Scholar.

- A. Svensson, T.B. Schön,
**A flexible state space model for learning nonlinear dynamical systems**, Automatica, 2017, 80, 189-199. - M. Schoukens, J.P. Noël,
**Three Benchmarks Addressing Open Challenges in Nonlinear System Identification**, 20th World Congress The International Federation of Automatic Control, 2017, 448-453.**slides** - R. Relan, K. Tiels, A. Marconato, J. Schoukens,
**An Unstructured Flexible Nonlinear Model for the Cascaded Water-Tanks Benchmark**, 20th World Congress The International Federation of Automatic Control, 2017, 454-459. - M. Brunot, A. Janot, F. Carrillo,
**Continuous-Time Nonlinear Systems Identification with Output Error Method Based on Derivative-Free Optimisation**, 20th World Congress The International Federation of Automatic Control, 2017, 466-471. - J. Belz, T. Münker, T.O. Heinz, G. Kampmann, O. Nelles,
**Automatic Modeling with Local Model Networks for Benchmark Processes**, 20th World Congress The International Federation of Automatic Control, 2017, 472-477. - G. Birpoutsoukis, P.Z. Csurcsia and J. Schoukens,
**Nonparametric Volterra Series Estimate of the Cascaded Water Tanks Using Multidimensional Regularization**, 20th World Congress The International Federation of Automatic Control, 2017, 478-483. - P.Z. Csurcsia, G. Birpoutsoukis and J. Schoukens,
**Transient elimination and memory saving possibilities for multidimensional nonparametric regularization illustrated on the cascaded water tanks benchmark problem**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides** - G. Holmes, T. Rogers, E.J. Cross, N. Dervilis, G. Manson, R.J. Barthorpe, K. Worden,
**Cascaded Tanks Benchmark: Parametric and Nonparametric Identification**, Workshop on Nonlinear System Identification Benchmarks, 2016. - G. Giordano, J. Sjöberg,
**Cascade Tanks Benchmark**, Workshop on Nonlinear System Identification Benchmarks, 2016. - R. Relan, K. Tiels, A. Marconato,
**Identifying an Unstructured Flexible Nonlinear Model for the Cascaded Water-tanks Benchmark: Capabilities and Short-comings**, Workshop on Nonlinear System Identification Benchmarks, 2016. - P. Mattson, D. Zachariah, P. Stoica,
**Identification of a PWARX model for the cascade water tanks**, Workshop on Nonlinear System Identification Benchmarks, 2016. - G. Birpoutsoukis, P.Z. Csurcsia,
**Nonparametric Volterra series estimate of the cascaded tank**, Workshop on Nonlinear System Identification Benchmarks, 2016. - M. Schoukens, F.G. Scheiwe,
**Modeling Nonlinear Systems Using a Volterra Feedback Model**, Workshop on Nonlinear System Identification Benchmarks, 2016.**slides** - A. Svensson, F. Lindsten, T.B. Schön,
**First principles and black box modeling of the cascaded water tanks**, Workshop on Nonlinear System Identification Benchmarks, 2016.

## Wiener-Hammerstein Process Noise System (2016)

You can find a list of contributions working on the Wiener-Hammerstein Process Noise System below. You could also check the citing papers of the Wiener-Hammerstein Process Noise System dataset description through Google Scholar for a more up-to-date overview. It is also worthwhile checking the papers citing the 2017 IFAC WC contribution on the Wiener-Hammerstein Process Noise System trhough Google Scholar.

- A. Svensson, T.B. Schön and F. Lindsten.
**Learning of state-space models with highly informative observations: a tempered Sequential Monte Carlo solution**, Mechanical Systems and Signal Processing, 2018, 104, 915-928. - M. Schoukens and J.P. Noël,
**Three Benchmarks Addressing Open Challenges in Nonlinear System Identification**, 20th World Congress The International Federation of Automatic Control, 2017, 448-453.**slides** - J. Belz, T. Münker, T.O. Heinz, G. Kampmann, O. Nelles,
**Automatic Modeling with Local Model Networks for Benchmark Processes**, 20th World Congress The International Federation of Automatic Control, 2017, 472-477. - T. Münker, T.O. Heinz and O. Nelles,
**Regularized local FIR model networks for a Bouc-Wen and a Wiener-Hammerstein system**, Workshop on Nonlinear System Identification Benchmarks, 2017. - E. Zhang and M. Schoukens,
**Fast location of process noise for nonlinear system identification**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides**,**Matlab script**

*Readme in the Matlab script.* - G. Giordano and J. Sjöberg,
**Maximum likelihood identification of Wiener-Hammerstein models in presence of process noise**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides** - R. Relan, D. Verbeke and K. Tiels,
**One step ahead prediction of the WH benchmark with process noise using kernel adaptive learning**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides** - K. Tiels,
**PNLSS 1.0 - A polynomial nonlinear state-space Matlab toolbox**, Workshop on Nonlinear System Identification Benchmarks, 2016.**slides** - E. Zhang, M. Schoukens, J. Schoukens,
**Structural modeling of Wiener-Hammerstein system in the presence of the process noise**, Workshop on Nonlinear System Identification Benchmarks, 2016.**slides** - M. Rébillat, K. Ege, N. Mechbal, J. Antoni,
**Repeated exponential sine sweeps for the autonomous estimation of nonlinearities and bootstrap assessment of uncertainties**, Workshop on Nonlinear System Identification Benchmarks, 2016. - M. Schoukens,
**Identification of Wiener-Hammerstein systems with process noise using an Errors-in-Variables framework**, Workshop on Nonlinear System Identification Benchmarks, 2016.**slides** - K. Worden, G. Manson, R.J. Barthorpe, E.J. Cross, N. Dervilis, G. Holmes, T. Rogers,
**Wiener-Hammerstein Benchmark with process noise: Parametric and Nonparametric Identification**, Workshop on Nonlinear System Identification Benchmarks, 2016.

## Bouc-Wen System (2016)

You can find a list of contributions working on the Bouc-Wen System below. You could also check the citing papers of the Bouc-Wen System dataset description through Google Scholar for a more up-to-date overview. It is also worthwhile checking the papers citing the 2017 IFAC WC contribution on the Bouc-Wen System trhough Google Scholar.

- M. Schoukens, J.P. Noël,
**Three Benchmarks Addressing Open Challenges in Nonlinear System Identification**, 20th World Congress The International Federation of Automatic Control, 2017, 448-453.**slides** - A. Fakhrizadeh Esfahani, P. Dreesen, K. Tiels, J.P. Noël, J. Schoukens,
**Polynomial State-Space Model Decoupling for the Identification of Hysteretic Systems**, 20th World Congress The International Federation of Automatic Control, 2017, 460-465. - M. Brunot, A. Janot, F. Carrillo,
**Continuous-Time Nonlinear Systems Identification with Output Error Method Based on Derivative-Free Optimisation**, 20th World Congress The International Federation of Automatic Control, 2017, 466-471. - J. Belz, T. Münker, T.O. Heinz, G. Kampmann, O. Nelles,
**Automatic Modeling with Local Model Networks for Benchmark Processes**, 20th World Congress The International Federation of Automatic Control, 2017, 472-477. - G. Hollander, P. Dreesen, M. Ishteva and J. Schoukens,
**Nonlinear model decoupling using a tensor decomposition initialization**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides** - T. Münker, T.O. Heinz and O. Nelles,
**Regularized local FIR model networks for a Bouc-Wen and a Wiener-Hammerstein system**, Workshop on Nonlinear System Identification Benchmarks, 2017. - M. Rébillat and M. Schoukens,
**A methodology to compare two estimation methods for parallel Hammerstein models**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides** - A.F. Esfahani, P. Dreesen, J.P. Noël, K. Tiels, J. Schoukens,
**Decoupled polynomial nonlinear state space models of a Bouc-Wen hysteretic system**, Workshop on Nonlinear System Identification Benchmarks, 2017. - D. Westwick, G. Hollander and J. Schoukens,
**The decoupled polynomial NARX model: parameter reduction and structural insights for the Bouc-Wen benchmark**, Workshop on Nonlinear System Identification Benchmarks, 2017.**slides** - J.P. Noël, A.F. Esfahani, G. Kerschen, J. Schoukens,
**A nonlinear state-space solution to a hysteretic benchmark in system identification**, Workshop on Nonlinear System Identification Benchmarks, 2016. - A.F. Esfahani, P. Dreesen, K. Tiels, J.P. Noël, J. Schoukens,
**Using a polynomial decoupling algorithm for state-space identification of a Bouc-Wen system**, Workshop on Nonlinear System Identification Benchmarks, 2016. - R. Gaasbeek, R. Mohan,
**Control-focused identification of hysteric systems: Selecting model structures? Think about the final use of the model!**, Workshop on Nonlinear System Identification Benchmarks, 2016. - A. Bajrić,
**System identification of a linearized hysteretic system using covariance driven stochastic subspace identification**, Workshop on Nonlinear System Identification Benchmarks, 2016. - M. Rébillat, K. Ege, N. Mechbal, J. Antoni,
**Repeated exponential sine sweeps for the autonomous estimation of nonlinearities and bootstrap assessment of uncertainties**, Workshop on Nonlinear System Identification Benchmarks, 2016. - G. Manson, R.J. Barthorpe, E.J. Cross, N. Dervilis, G. Holmes, T. Rogers, K. Worden,
**Bouc-Wen Benchmark: Parametric and Nonparametric Identification**, Workshop on Nonlinear System Identification Benchmarks, 2016. - E. Louarroudi, S. Vanlanduit, R. Pintelon,
**Identification of non-linear restoring forces through linear time-periodic approximations**, Workshop on Nonlinear System Identification Benchmarks, 2016. - M. Schoukens, F.G. Scheiwe,
**Modeling Nonlinear Systems Using a Volterra Feedback Model**, Workshop on Nonlinear System Identification Benchmarks, 2016.**slides**

## Parallel Wiener-Hammerstein System (2015)

You can find a list of contributions working on the Parallel Wiener-Hammerstein System below. You could also check the citing papers of the Parallel Wiener-Hammerstein System dataset description through Google Scholar for a more up-to-date overview.

- M. Schoukens, A. Marconato, R. Pintelon, G. Vandersteen, Y. Rolain,
**Parametric identification of parallel Wiener–Hammerstein systems**, Automatica, 2015, 51, 111-122. - M. Schoukens, K. Tiels, M. Ishteva, J. Schoukens,
**Identification of parallel Wiener-Hammerstein systems with a decoupled static nonlinearity**, 19th World Congress The International Federation of Automatic Control, 2014, 505-510.**slides** - P. Dreesen, M. Schoukens, K. Tiels, J. Schoukens,
**Decoupling static nonlinearities in a parallel Wiener-Hammerstein system: A first-order approach**, Instrumentation and Measurement Technology Conference (I2MTC), 2015, 987-992.

## Wiener-Hammerstein System (2009)

You can find a list of contributions working on the Wiener-Hammerstein System below. You could also check the citing papers of the Wiener-Hammerstein System dataset description through Google Scholar for a more up-to-date overview.

- F. Sabahi and M. Reza Akbarzadeh-T,
**Extended Fuzzy Logic: Sets and Systems**, IEEE Transactions on Fuzzy Systems, 2016, 24, 530-543. - A. Naitali, F. Giri,
**Wiener–Hammerstein system identification – an evolutionary approach**, International Journal of Systems Science, 2016, 47, 45-61. - A. Svensson, T.B. Schön, A. Solin, S. Särkkä,
**Nonlinear State Space Model Identification Using a Regularized Basis Function Expansion**, proceedings of the 6th IEEE international workshop on computational advances in multi-sensor adaptive processing (CAMSAP), Cancun, Mexico, December 2015, 213-221. - H. Ase, T. Katayama,
**A subspace-based identification of Wiener–Hammerstein benchmark model**, Control Engineering Practice, 2015, 44, 126-137. - E. de la Rosa, W. Yu, X. Li,
**Nonlinear system identification using deep learning and randomized algorithms**, IEEE International Conference on Information and Automation, 2015, 274-279. - M. Schoukens, R. Pintelon, Y. Rolain,
**Identification of Wiener–Hammerstein systems by a nonparametric separation of the best linear approximation**, Automatica, 2014, 50, 628-634. - L. Vanbeylen,
**A fractional approach to identify Wiener–Hammerstein systems**, Automatica, 2014, 50, 903-909. - A. Marconato, J. Sjöberg, J.A.K. Suykens, J. Schoukens,
**Improved Initialization for Nonlinear State-Space Modeling**, IEEE Transactions on Instrumentation and Measurement, 2014, 63, 972-980. - O. Taouali, I. Elaissi, H. Messaoud,
**Hybrid kernel identification method based on support vector regression and regularisation network algorithms**, IET Signal Processing, 2014, 8, 981-989. - A. Marconato, M. Schoukens, Y. Rolain, J. Schoukens,
**Study of the effective number of parameters in nonlinear identification benchmarks**, IEEE 52nd Annual Conference on Decision and Control (CDC), 2013, 4308-4313.**slides** - R. Frigola, C.E. Rasmussen,
**Integrated pre-processing for Bayesian nonlinear system identification with Gaussian processes**, IEEE 52nd Annual Conference on Decision and Control (CDC), 2013, 5371-5376. - H.M. Romero Ugalde, J.C. Carmona, V.M. Alvarado, J. Reyes-Reyes,
**Neural network design and model reduction approach for black box nonlinear system identification with reduced number of parameters**, Neurocomputing, 2013, 101, 170-180. - O. Taouali, I. Elaissi, H. Messaoud,
**Design and comparative study of online kernel methods identification of nonlinear system in RKHS space**, Artificial Intelligence Review, 2012, 37, 289-300. - O. Taouali, I. Elaissi, H. Messaoud,
**Online identification of nonlinear system using reduced kernel principal component analysis**, Neural Computing and Applications, 2012, 21, 161–169. - D.T. Westwick, J. Schoukens,
**Initial estimates of the linear subsystems of Wiener–Hammerstein models**, Automatica, 2012, 48, 2931-2936. - D.T. Westwick, J. Schoukens,
**Classification of the Poles and Zeros of the Best Linear Approximations of Wiener-Hammerstein Systems**, 16th IFAC Symposium on System Identification (SYSID), 2012, 470-475. - A. Wills, B. Ninness,
**Generalised Hammerstein–Wiener system estimation and a benchmark application**, Control Engineering Practice, 2012, 20, 1097-1108. - L. Piroddi, M. Farina, M. Lovera,
**Black box model identification of nonlinear input–output models: A Wiener–Hammerstein benchmark**, Control Engineering Practice, 2012, 20, 1109-1118. - J. Sjöberg, L. Lauwers, J. Schoukens,
**Identification of Wiener–Hammerstein models: Two algorithms based on the best split of a linear model applied to the SYSID'09 benchmark problem**, Control Engineering Practice, 2012, 20, 1119-1125. - A. Marconato, J. Sjöberg, J. Schoukens,
**Initialization of nonlinear state-space models applied to the Wiener–Hammerstein benchmark**, Control Engineering Practice, 2012, 20, 1126-1132. - J. Paduart, L. Lauwers, R. Pintelon, J. Schoukens,
**Identification of a Wiener–Hammerstein system using the polynomial nonlinear state space approach**, Control Engineering Practice, 2012, 20, 1133-1139. - A.H. Tan, H.K. Wong, K. Godfrey,
**Identification of a Wiener–Hammerstein system using an incremental nonlinear optimisation technique**, Control Engineering Practice, 2012, 20, 1140-1148. - Y. Han, R.A. de Callafon,
**Identification of Wiener–Hammerstein benchmark model via rank minimization**, Control Engineering Practice, 2012, 20, 1149-1155. - P.L. dos Santos, J.A. Ramos, J.M. de Carvalho,
**Identification of a Benchmark Wiener–Hammerstein: A bilinear and Hammerstein–Bilinear model approach**, Control Engineering Practice, 2012, 20, 1156-1164. - T. Falck, P. Dreesen, K. De Brabanter, K. Pelckmans, B. De Moor, J.A. Suykens,
**Least-Squares Support Vector Machines for the identification of Wiener–Hammerstein systems**, Control Engineering Practice, 2012, 20, 1165-1174. - F. Giri, E.W. Bai (Editors),
**Block-oriented Nonlinear System Identification**, Springer, 2010. - A. Marconato, J. Schoukens,
**Identification of Wiener-Hammerstein Benchmark Data by Means of Support Vector Machines**, 15th IFAC Symposium on System Identification (SYSID), 2009, 816-819. - T. Falck, K. Pelckmans, J.A. Suykens, B. De Moor,
**Identification of Wiener-Hammerstein Systems using LS-SVMs**, 15th IFAC Symposium on System Identification (SYSID), 2009, 820-825. - K. De Brabanter, P. Dreesen, P. Karsmakers, K. Pelckmans, J. De Brabanter, J. Suykens, Bart De Moor,
**Fixed-Size LS-SVM Applied to the Wiener-Hammerstein Benchmark**, 15th IFAC Symposium on System Identification (SYSID), 2009, 826-831. - P.L. dos Santos, J.A. Ramos, J.M. de Carvalho,
**Identification of a Benchmark Wiener-Hammerstein System by Bilinear and Hammerstein-Bilinear Models**, 15th IFAC Symposium on System Identification (SYSID), 2009, 832-837. - G. Pillonetto, A. Chiuso,
**Gaussian Processes for Wiener-Hammerstein system identification**, 15th IFAC Symposium on System Identification (SYSID), 2009, 838-843. - N.V. Truong, L. Wang,
**Benchmark Nonlinear System Identification using Wavelet based SDP Models**, 15th IFAC Symposium on System Identification (SYSID), 2009, 844-849. - L. Piroddi, M. Farina, M. Lovera,
**Polynomial NARX Model Identification: a Wiener–Hammerstein Benchmark**, 15th IFAC Symposium on System Identification (SYSID), 2009, 1074-1079. - J. Paduart, L. Lauwers, R. Pintelon, J. Schoukens,
**Identification of a Wiener-Hammerstein System Using the Polynomial Nonlinear State Space Approach**, 15th IFAC Symposium on System Identification (SYSID), 2009, 1080-1085. - A. van Mulders, J. Schoukens, M. Volckaert, M. Diehl,
**Two Nonlinear Optimization Methods for Black Box Identification Compared**, 15th IFAC Symposium on System Identification (SYSID), 2009, 1086-1091. - H. Ase, T. Katayama, H. Tanaka,
**A State-Space Approach to Identification of Wiener-Hammerstein Benchmark Model**, 15th IFAC Symposium on System Identification (SYSID), 2009, 1092-1097. - L. Lauwers, R. Pintelon, J. Schoukens,
**Modelling of Wiener-Hammerstein Systems via the Best Linear Approximation**, 15th IFAC Symposium on System Identification (SYSID), 2009, 1098-1103. - A. Wills, B. Ninness,
**Estimation of Generalised Hammerstein-Wiener Systems**, 15th IFAC Symposium on System Identification (SYSID), 2009, 1104-1109. - J. Schoukens, J. Suykens, L. Ljung,
**Wiener-Hammerstein Benchmark**, 15th IFAC Symposium on System Identification (SYSID), 2009.

## Silverbox (2004)

You can find a list of contributions working on the Silverbox System below. You could also check the citing papers of the Silverbox System dataset description through Google Scholar for a more up-to-date overview.

- C.L.C. Mattos, G.A. Barreto, G. Acuna,
**Randomized Neural Networks for Recursive System Identification in the Presence of Outliers: A Performance Comparison**, IWANN 2017: Advances in Computational Intelligence, 2017, 603-615. - F. Sabahi and M. Reza Akbarzadeh-T,
**Extended Fuzzy Logic: Sets and Systems**, IEEE Transactions on Fuzzy Systems, 2016, 24, 530-543. - A. Carini, G.L. Sicuranza,
**Recursive functional link polynomial filters: An introduction**, 24th European Signal Processing Conference (EUSIPCO), 2016, 2335-2339. - R. Castro, S. Mehrkanoon, A. Marconato, J. Schoukens, J.A.K. Suykens,
**SVD truncation schemes for fixed-size kernel models**, International Joint Conference on Neural Networks (IJCNN), 2014, 3922-3929. - A. Marconato, M. Schoukens, Y. Rolain, J. Schoukens,
**Study of the effective number of parameters in nonlinear identification benchmarks**, IEEE 52nd Annual Conference on Decision and Control (CDC), 2013, 4308-4313.**slides** - R. Frigola, C.E. Rasmussen,
**Integrated pre-processing for Bayesian nonlinear system identification with Gaussian processes**, IEEE 52nd Annual Conference on Decision and Control (CDC), 2013, 5371-5376. - A. Marconato, J. Sjöberg, J.A.K. Suykens, J. Schoukens,
**Identification of the Silverbox Benchmark Using Nonlinear State-Space Models**, 16th IFAC Symposium on System Identification (SYSID), 2012, 632-637. - E. Pepona, S. Paoletti, A. Garulli, P. Date,
**Identification of Piecewise Affine LFR Models of Interconnected Systems**, IEEE Transactions on Control Systems Technology, 2011, 19, 148-155. - M. Espinoza, J.A.K. Suykens, B. De Moor,
**Kernel based partially linear models and nonlinear identification**, IEEE Transactions on Automatic Control, 50, 2005, 1602-1606. - M. Espinoza, K. Pelckmans, L. Hoegaerts, J.A. Suykens, B. De Moor,
**A comparative study of ls-svm’s applied to the silver box identification problem**, 6th IFAC Symposium on Nonlinear Control Systems (NOLCOS), 2004, 369-374. - H. Hjalmarsson, J. Schoukens,
**On Direct Identification of Physical Parameters in Non-Linear Models**, 6th IFAC Symposium on Nonlinear Control Systems (NOLCOS), 2004, 375-380. - J. Paduart, G. Horvath, J. Schoukens,
**Fast identification of systems with nonlinear feedback**, 6th IFAC Symposium on Nonlinear Control Systems (NOLCOS), 2004, 381-385. - L. Sragner, J. Schoukens, G. Horváth,
**Modelling of a slightly nonlinear system: a neural network approach**, 6th IFAC Symposium on Nonlinear Control Systems (NOLCOS), 2004, 387-392. - Verdult, V.,
**Identification of Local Linear State-Space Models: The Silver-Box Case Study**, 6th IFAC Symposium on Nonlinear Control Systems (NOLCOS), 2004, 393-398. - L. Ljung, Q. Zhang, P. Lindskog, A. Juditski,
**Estimation of grey box and black box models for non-linear circuit data**, 6th IFAC Symposium on Nonlinear Control Systems (NOLCOS), 2004, 399-404.