1. 5/24/2001 1 Modeling & Diagnostics of A Furnace System This work develops an efficient diagnostic methodology for a multi-zone batch furnace system using techniques based on multivariate statistics and sensor fusion strategies. SFR Workshop May 24, 2001 Jiangxin Wang, Costas Spanos Berkeley, CA

2. 5/24/2001 2 Furnace Model InsulatorHeater ThermocoupleWafer Boat Door T3T3 P5P5 C5C5 R5R5 R 34 P4P4 C4C4 R4R4 P1P1 C1C1 R1R1 P2P2 C2C2 R2R2 P3P3 C3C3 R3R3 R 45 R 23 R 12 T2T2 T1T1 T5T5 T4T4 A five-zone batch furnace system: Electrical Analogy:

3. 5/24/2001 3 T(k+1) = AT(k)+BP(k) Controller + Noise Diagnose Temperature Setting Temp Measurement Power Plant Comparison of Actual and Simulated system model

4. 5/24/2001 4 Diagnostic Goals Diagnostics Temperature Settings Temperature Sensor Readings Power Delivery Accurate System Model Is there any fault? What type of fault? Which sensor/which zone? How serious it is? (parameterization) Final Goal: Different combinations of faults can be distinguished and the corresponding fault parameters can be estimated with high accuracy.

5. 5/24/2001 5 Model Classification N E1 E2 E.g.: Selection Criterion Temperature Setting Normal Model Actual System Error Model 1 Error Model N Selection Criterion Temperature & Power readings Simulation

6. 5/24/2001 6 Least Squares Method for Drift Detection Error Whitening & Least Square Solution: 1. 2. 3. 4. Linear approximation Normal System (no faults): General System (all faults are considered):

7. 5/24/2001 7 Diagnostic Results by Least Square Approach * All results are based on experimental data collected on furnace tylan17 in Berkeley MicroLab

8. 5/24/2001 8 Sensor Fusion Experiment #1 Experiment #2 Experiment #K Diagnostic Algorithm Sensor Fusion I II K Fault Parameter Estimates Data Sets Fused Fault Parameter Estimates   Fusion:whereand

9. 5/24/2001 9 Discussion and Summary Under the assumption that the normal system is accurate, any fault combinations can be diagnosed almost perfectly (by simulation). In reality, inaccuracy in system modeling and limited experimental data types are the major causes for bad diagnostic performance. Single failure can be evaluated if the fault type is known, the accuracy depends on the accuracy of the system parameter estimates. Some important failure combinations can be effectively diagnosed by our approach using steady state data and/or cooling down data sets. Sensor fusion can be used to enhance diagnostic reliability.