A list of hosted nonlinear system datasets can be found below. Click on the link to jump to a more detailed description of the dataset you are interested in.

(7) F-16 Ground Vibration Test (2017)
(6) Cascaded Tanks System (2016)
(5) Wiener-Hammerstein Process Noise System (2016)
(4) Bouc-Wen System (2016)
(3) Parallel Wiener-Hammerstein System (2015)
(2) Wiener-Hammerstein System (2009)
(1) Silverbox (2004)

Do you have a great nonlinear system identification dataset ready to feature as a benchmark? Please contact us, maybe we can include it on this website!

F-16 Ground Vibration Test (2017)

The F-16 Ground Vibration Test benchmark features a high order system with clearance and friction nonlinearities at the mounting interface of the payloads.

The experimental data made available to the Workshop participants were acquired on a full-scale F-16 aircraft on the occasion of the Siemens LMS Ground Vibration Testing Master Class, held in September 2014 at the Saffraanberg military basis, Sint-Truiden, Belgium.

During the test campaign, two dummy payloads were mounted at the wing tips to simulate the mass and inertia properties of real devices typically equipping an F-16 in flight. The aircraft structure was instrumented with accelerometers. One shaker was attached underneath the right wing to apply input signals. The dominant source of nonlinearity in the structural dynamics was expected to originate from the mounting interfaces of the two payloads. These interfaces consist of T-shaped connecting elements on the payload side, slid through a rail attached to the wing side. A preliminary investigation showed that the back connection of the right-wing-to-payload interface was the predominant source of nonlinear distortions in the aircraft dynamics, and is therefore the focus of this benchmark study.

A detailed formulation of the identification problem can be found here. All the provided files and information on the F-16 aircraft benchmark system are available for download here. This zip-file contains a detailed system description, the estimation and test data sets, and some pictures of the setup. The data is available in the .csv and .mat file format.

Please refer to the F16 benchmark as:

J.P. Noël and M. Schoukens, F-16 aircraft benchmark based on ground vibration test data, 2017 Workshop on Nonlinear System Identification Benchmarks, pp. 19-23, Brussels, Belgium, April 24-26, 2017.

Previously published results on the F-16 Ground Vibration Test benchmark are listed in the history section of this webpage.

Special thanks to Bart Peeters (Siemens Industry Software) for his help in creating this benchmark.

The F-16 ground vibration test setup.

Cascaded Tanks System (2016)

The cascaded tanks setup.

The cascaded tanks system is a fluid level control system consisting of two tanks with free outlets fed by a pump. The input signal controls a water pump that delivers the water from a reservoir into the upper water tank. The water of the upper tank flows through a small opening into the lower tank, and finally through a small opening from the lower tank back into the reservoir. This benchmark combines soft and hard nonlinearities to be identified based on relatively short data records.

A detailed formulation of the identification problem can be found here. All the provided files and information on the cascaded tanks system are available for download here. This zip-file contains a detailed system description, the estimation and test data sets, and some pictures and a video of the setup. The data is available in the .csv and .mat file format.

Please refer to the Cascaded Tanks benchmark as:

M. Schoukens and J.P. Noël, Three Benchmarks Addressing Open Challenges in Nonlinear System Identification, 20th World Congress of the International Federation of Automatic Control, pp.448-453, Toulouse, France, July 9-14, 2017.

M. Schoukens, P. Mattsson, T. Wigren and J.P. Noël, Cascaded tanks benchmark combining soft and hard nonlinearities, Workshop on Nonlinear System Identification Benchmarks, pp.20-23, Brussels, Belgium, April 25-27, 2016.

Previously published results on the Cascated Tanks benchmark are listed in the history section of this webpage.

Special thanks to Torbjörn Wigren and Per Mattsson for their help in creating this benchmark.

Wiener-Hammerstein Process Noise System (2016)

The Wiener-Hammerstein system is a well-known block-oriented structure. It contains a static nonlinearity that is sandwiched in between two linear time-invariant (LTI) blocks. The presence of the two LTI blocks results in a problem that is harder to identify.

The Wiener-Hammerstein system proposed as a benchmark contains dominant process noise. The process noise enters the system before the static nonlinearity. Two much less significant noise sources are present in the measurement channels of the input and output.

A detailed formulation of the identification problem can be found here. All the provided files, data and information on the Wiener-Hammerstein system are available for download here. This zip-file contains a detailed system description with a signal generation guide, an example estimation data set, the test data sets, the datasets measured during the past measurement campaign(s), pictures of the measurement setup, and an indicative electrical circuit schematic of the system. It is possible that the actual implemented Wiener-Hammerstein system deviates at some points (resistor values, opamp type) from the electrical circuit provided here. The data is available in the .csv and .mat file format.

Please refer to the Wiener-Hammerstein benchmark as:

M. Schoukens and J.P. Noël, Three Benchmarks Addressing Open Challenges in Nonlinear System Identification, 20th World Congress of the International Federation of Automatic Control, pp.448-453, Toulouse, France, July 9-14, 2017.

M. Schoukens and J.P. Noël, Wiener-Hammerstein benchmark with process noise, Workshop on Nonlinear System Identification Benchmarks, pp.15-19, Brussels, Belgium, April 25-27, 2016.

Previously published results on the Wiener-Hammerstein process noise benchmark are listed in the history section of this webpage.


A Wiener-Hammerstein system with process noise: the red blocks represent linear time-invariant dynamics, while the blue block respresents a static nonlinearity.

Bouc-Wen System (2016)

Hysteresis is a dynamic nonlinearity commonly encountered in very diverse engineering and science disciplines, ranging from solid mechanics, electromagnetism and aerodynamics to biology, ecology and psychology. In particular, the Bouc-Wen model has been intensively exploited during the last decades to represent hysteretic effects in mechanical engineering, especially in the case of random vibrations.

It is proposed as a benchmark problem to identify a Bouc-Wen system based on synthetic input-output data. A detailed formulation of the identification problem can be found here. All the provided files and information on the Bouc-Wen system are available for download here. This zip-file contains a detailed system description with a signal generation guide and the test data sets. This benchmark requires MATLAB to run.

Please refer to the Bouc-Wen benchmark as:

M. Schoukens and J.P. Noël, Three Benchmarks Addressing Open Challenges in Nonlinear System Identification, 20th World Congress of the International Federation of Automatic Control, pp.448-453, Toulouse, France, July 9-14, 2017.

J.P. Noël and M. Schoukens, Hysteretic benchmark with a dynamic nonlinearity, Workshop on Nonlinear System Identification Benchmarks, pages. 7-14, Brussels, Belgium, April 25-27, 2016.

Previously published results on the Bouc-Wen benchmark are listed in the history section of this webpage.

Parallel Wiener-Hammerstein System (2015)

A Parallel Wiener-Hammerstein system is obtained by connecting multiple Wiener-Hammerstein systems in parallel. Each parallel branch contains a static nonlinearity that is sandwiched in between two linear time-invariant (LTI) blocks. The presence of the two LTI blocks, and the parallel branches results in a problem that is harder to identify.

The provided data was part of a previously published Automatica paper available online at Sciencedirect or as an ArXiv preprint. The Parallel Wiener-Hammerstein system, the measurement setup, and the input signals used are detailed in Section 10 of the aforementioned paper. The provided Parallel Wiener-Hammerstein datasets are available for download here. This zip-file contains the multisine estimation data set, the multisine and an increasing-amplitude test data set. The data is available in the .csv and .mat file format.

Please refer to the Parallel Wiener-Hammerstein benchmark as:

M. Schoukens, A. Marconato, R. Pintelon, G. Vandersteen and Y. Rolain, Parametric identification of parallel Wiener–Hammerstein systems, Automatica, vol. 51, pp.111-122, 2015.

Previously published results on the Parallel Wiener-Hammerstein benchmark are listed in the history section of this webpage.

Special thanks to Johan Pattyn for designing the parallel Wiener-Hammerstein system.

A two-branch Parallel Wiener-Hammerstein system: the red blocks represent linear time-invariant dynamics, while the blue blocks respresent a static nonlinearity.

Wiener-Hammerstein System (2009)

The Wiener-Hammerstein system is a well-known block-oriented structure. It contains a static nonlinearity that is sandwiched in between two linear time-invariant (LTI) blocks. The presence of the two LTI blocks results in a problem that is harder to identify. This benchmark can be considered to be the predecessor of the Parallel Wiener-Hammerstein and the Wiener-Hammerstein with Process Noise datasets (though the system parameters are different).

The provided data is part of a previously published benchmark available online at IFAC website. The benchmark description can be found here. All the provided files (.mat file format) and information on the Parallel Wiener-Hammerstein system are available for download here. This .mat file contains the estimation and test dataset as specified in the benchmark document. A .csv version of the benchmark dataset is available for download here.

Please refer to the Wiener-Hammerstein benchmark as:

J. Schoukens, J. Suykens, L. Ljung. Wiener-Hammerstein Benchmark. 15th IFAC Symposium on System Identification (SYSID 2009), July 6-8, 2009, St. Malo, France.

Previously published results on the Wiener-Hammerstein benchmark are listed in the history section of this webpage.

Special thanks to Johan Schoukens for creating this benchmark, to Gerd Vandersteen for designing the benchmark system and to the IFAC Technical Committee 1.1 on Modelling, Identification and Signal Processing for hosting this benchmark.

Silverbox (2004)

The Silverbox system can be seen as an electroninc implementation of the Duffing oscilator. It is build as a 2nd order linear time-invariant system with a 3rd degree polynomial static nonlinearity around it in feedback. This type of dynamics are, for instance, often encountered in mechanical systems.

The provided data is part of a previously published ECC paper available online. A technical note describing the silverbox benchmark can be found here. All the provided files (.mat file format) and information on the Parallel Wiener-Hammerstein system are available for download here. This .zip file contains the silverbox dataset as specified in the benchmark document (V1 is the input record, while V2 is the measured output). A .csv version of the benchmark dataset is available for download here.

Please refer to the Silverbox benchmark as:

T. Wigren and J. Schoukens. Three free data sets for development and benchmarking in nonlinear system identification. 2013 European Control Conference (ECC), pp.2933-2938 July 17-19, 2013, Zurich, Switzerland.

Previously published results on the Silverbox benchmark are listed in the history section of this webpage.

Special thanks to Johan Schoukens for creating this benchmark, and to Torbjörn Wigren for hosting this benchmark.

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