Multi-Model Identification of HVAC System
Abstract
:1. Introduction
2. The Proposed Simultaneous Clustering and Regression Method
Algorithm 1 |
Step 1—Select proper values for m, h and construct regressor and observation vector . Step 2—Initialize the probability vector for each cluster i by a random number generator. Step 3—Iterate the algorithm until converges or termination criterion is satisfied. Step 4—Update residual values for each cluster i. Step 5—Update parameters , and . Step 6—Update as Step 7—Go to step 3, and repeat until convergence. |
3. Gap Metric
- (1)
- .
- (2)
- The gap metric is an extension of common distance measures between two linear systems such as the infinity norm. For instance, the distances between two systems and in the sense of infinity norm and gap metric are infinity and 0.1, respectively.
- (3)
- One pro of the gap metric is that it measures the ‘distance’ in the closed-loop sense instead of the open-loop sense. In other words, a small distance between two systems in the gap metric sense means that there exists at least one feedback controller that stabilizes both systems and the distance between the closed loops is small in the infinity norm sense. For instance, for the distance between two systems and the gap metric is about 0.2 [13].
3.1. Proper Number of Mode Selection
- (1)
- Initialize the operation regions and calculate the nonlinear measure index for each operating region. Select enough operation points in each operating region.
- (2)
- Collect enough data from the system around the operating point OPi, use the proposed Algorithm 1 and get the linear models Pi.
- (3)
- Compute the gap metric between all pairs of linear models Pi and Pj (i.e., ).
- (4)
- Prescribe a threshold level τ. Cluster the local models that satisfy δj ≤ τ.
3.2. Local Model Weights
4. Simulation and Validation
4.1. Simulation Results
4.2. Test on Real-World Data
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Model Parameters | ||||||
---|---|---|---|---|---|---|
Cluster | ||||||
i = 1 | 2.967 | −2.935 | 0.9676 | 0.0274 | −0.05466 | 0.02726 |
i = 2 | 1.744 | −0.7323 | −0.0119 | −0.08569 | 0.2612 | −0.1751 |
i = 3 | 2.304 | −1.624 | 0.3201 | 0.07934 | −0.147 | 0.06769 |
i = 4 | 1.077 | 0.8135 | 0.89 | −0.0528 | 0.126 | −0.073 |
i = 5 | 2.927 | −2.855 | 0.9282 | 0.0168 | −0.0325 | 0.0157 |
Model Parameters | ||||||
---|---|---|---|---|---|---|
Cluster | ||||||
i = 1 | 2.967 | −2.935 | 0.9676 | 0.0274 | −0.05466 | 0.02726 |
i = 2 | 1.744 | −0.7323 | −0.0119 | −0.08569 | 0.2612 | −0.1751 |
i = 3 | 2.304 | −1.624 | 0.3201 | 0.07934 | −0.147 | 0.06769 |
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Alipouri, Y.; Zhong, L. Multi-Model Identification of HVAC System. Appl. Sci. 2021, 11, 668. https://doi.org/10.3390/app11020668
Alipouri Y, Zhong L. Multi-Model Identification of HVAC System. Applied Sciences. 2021; 11(2):668. https://doi.org/10.3390/app11020668
Chicago/Turabian StyleAlipouri, Yousef, and Lexuan Zhong. 2021. "Multi-Model Identification of HVAC System" Applied Sciences 11, no. 2: 668. https://doi.org/10.3390/app11020668