1. Univ logo Piecewise Gaussian Process for System Identification Juan Yan Prof Kang Li and Prof Erwei Bai Queen’s University Belfast UKACC PhD Presentation Showcase

2. Univ logo Outline  Introduction  Gaussian Process(GP) Regression  Piecewise GP method  Results  Conclusion UKACC PhD Presentation Showcase Slide 2

3. Univ logo UKACC PhD Presentation Showcase Slide 3 Introduction  Gaussian Process is a global black-box non-parametric modelling method based on Bayesian inference. It uses the empirical data on the absence of the specific system model structure to estimate the most probable output and the chance of it.  Gaussian Process  Piecewise regression  When a system displays different characteristics in different intervals, it becomes necessary to model the system with varied parameters, structure, or even method. Splines are widely applied.

4. Univ logo Gaussian Process regression UKACC PhD Presentation Showcase Slide 4

5. Univ logo UKACC PhD Presentation Showcase Slide 5  GP regression results for different systems Gaussian Process regression

6. Univ logo Piecewise GP  In reality, it is not reasonable to expect a single Gaussian Process would cover a large interval, it makes sense to model an unknown f(x) by a number of Gaussian models. UKACC PhD Presentation Showcase Slide 6 Constraints:

7. Univ logo UKACC PhD Presentation Showcase Slide 7 Results: Piecewise GP compared with General GP noise ~ N (0, 0.2 ) The system is continuous on the whole interval and there are 20, 5, 10 data samples on the 3 segments respectively.

8. Univ logo UKACC PhD Presentation Showcase Slide 8 Results: Piecewise GP compared with Cubic splines noise ~ N (0,10) 48 data points in all

9. Univ logo UKACC PhD Presentation Showcase Slide 9 Conclusions  Piecewise GP shows better properties:  Compared with general GP, it suites better for large interval regression, and saves computational complexity;  Compared with Cubic splines, it fits better for high order system with noise.  Future work  Comparison needs to be implemented between GP and other piecewise methods (like piecewise polynomial);  Identification of multidimensional systems will be carried out with piecewise GP;  Adaptive methods will be studied for interval partition and non-uniform points sampling during the implementation of piecewise GP.

10. Univ logo Thank you for your attention UKACC PhD Presentation Showcase Slide 10