System modeling with Reservoir Computing
Francis Wyffels
[email protected] Benjamin Schrauwen
[email protected] Dirk Stroobandt
[email protected] Electronics and Information Systems Department, Ghent University, Sint-Pietersnieuwstraat 41, 9000 Gent, Belgium
Abstract Reservoir Computing is a novel technique which can be applied to a wide range of applications. In this work we demonstrate that Reservoir Computing can be used for black box nonlinear system modeling.We will use Reservoir Computing to model the output flow of a heating tank with variable deadtime.
K input nodes
Reservoir with N state nodes
L output nodes
- dotted lines: trained interconnections - solid lines: random but fixed interconnections
1. Introduction Many control engineering techniques, in particular Model Predictive Control strategies, are based on process models. These models are obtained from physical principles or data-driven models (Camacho et al., 2007). Most of the data-driven models are black box models based on Analog Neural Networks (Camacho et al., 2007) which cannot cope with problems that have a strong temporal aspect. Therefore some research has focused on the use of Recurrent Neural Networks which have memory due to the loops inside the network. But unfortunately Recurrent Neural Networks are hard to train. Reservoir Computing is a recently developed technique for very fast training of Recurrent Neural Networks which has been successfully used in many applications (Jaeger, 2001) such as speech recognition (Skowronski & Harris, 2007; Verstraeten et al., 2007), robot control (Antonelo et al., 2007) and time-series generation (Jaeger, 2001). To accomplish this, Reservoir Computing uses an untrained dynamic system (the reservoir), where the desired function is implemented by a linear, memory-less mapping from the full instantaneous state of the dynamical system to the desired output which can be trained by using linear regression techniques such as ridge regression (Wyffels et al., 2008a). A schematic overview is given in Figure 1. In this work we will use Reservoir Computing to model
Figure 1. Schematic overview of the Reservoir Computing technique.
the behavior of a nonlinear dynamical system with variable dead-time.
2. Experimental setup The task at hand is the modeling of a heating tank with a variable cold water inlet and a hot water outlet. The heating element of the tank has a constant power thus, the outlet temperature is controlled by varying the cold water flow. Because the temperature of the outlet flow is measured after flowing through a long small pipe, the system has a variable dead-time which adds an extra difficulty in predicting the model. A full description of the plant can be found in (Cristea et al., 2005). In contrast to most modeling techniques, we don’t make any assumptions about the plant neither we split up the plant in different parts. We model both, the tank and the outlet pipe, by using only one reservoir consisting of 400 randomly connected band-pass neurons (see (Wyffels et al., 2008b) for an introduction). The spectral radius was tuned to give the reservoir a near-stable behavior. In order to give the reservoir more nonlinear properties each neuron adds an auxil-
iary input with a constant bias. Because of the variable dead-time, we needed to increase the fading memory of the reservoir by adding feedback from the output to all the neurons. The readout function was trained using 10,000 samples of random input-output examples extracted by simulation. Next, the reservoir was left predicting 3,500 samples based on its input, 1,000 samples were discarded for warming up to eliminate transient effects.
This work was partially funded by FWO Flanders project G.0317.05 and the Photonics@be Interuniversity Attraction Poles program (IAP 6/10), initiated by the Belgian State, Prime Minister’s Services, Science Policy Office.
Antonelo, E. A., Schrauwen, B., & Campenhout, J. V. (2007). Generative modeling of autonomous robots and their environments using reservoir computing. Neural Processing Letters, 26, 233–249.
42 40 38 Outlet temperature (°C)
Acknowledgments
References
44
36
Camacho, E., Rubio, F., Berenguel, M., & Valenzuela, L. (2007). A survey on control schemes for distributed solar collector fields. part i: Modeling and basic control approaches. Solar Energy, 81, 1240– 1251.
34 32 30 28
Cristea, S., de Prada, C., & De Keyser, R. (2005). Predictive control of a process with variable dead-time. CD-Proceedings of the 16th IFAC World Congress.
26 24
in control engineering tasks.
200
400
600
800 1000 1200 Time (samples)
1400
1600
1800
2000
Figure 2. Validation of the model: real outlet temperature (gray solid line), predicted outlet temperature (dashed line).
3. Results In Figure 2, a comparison of the desired outlet temperature and the predicted outlet temperature is given. Using the previously described reservoir configuration, the outlet temperature was predicted in connection to a variable input flow which was not seen by the reservoir during training. One can see that the reservoir is able to give accurate predictions of the outlet temperature.
4. Conclusions In previous work, many techniques for system modeling are proposed. But most of them need a lot of experience in the application domain or are difficult to train. In this work we showed that by using Reservoir Computing one is able to model a nonlinear system with variable dead-time based on input-output recordings of the plant. No knowledge in the application domain was needed. For future work we wish to investigate the use of Reservoir Computing as a controller
Jaeger, H. (2001). The “echo state” approach to analysing and training recurrent neural networks (Technical Report GMD Report 148). German National Research Center for Information Technology. Skowronski, M. D., & Harris, J. G. (2007). 2007 Special Issue: Automatic speech recognition using a predictive echo state network classifier. Neural Networks, 20, 414–423. Verstraeten, D., Schrauwen, B., D’Haene, M., & Stroobandt, D. (2007). An experimental unification of reservoir computing methods. Neural Networks, 20, 391–403. Wyffels, F., Schrauwen, B., & Stroobandt, D. (2008a). Regularization methods for reservoir computing. Proceedings of the International Conference on Analog Neural Networks (ICANN). (submitted). Wyffels, F., Schrauwen, B., Verstraeten, D., & Stroobandt, D. (2008b). Band-pass reservoir computing. Proceedings of the International Joint Conference on Neural Networks.
