1. EGR 301 Applications for ARIMA Simulations

7. Stabilizing the time series Simulating the time series

8. Purpose Parameterize the accelerogram. Relate parameters to source and site parameters. Simulate acceleration histories. Note Include cross-correlation for components and sites. Include parameter uncertainty to create CI envelopes. Used a frequency-constrained ARMA (2,2).

9. SCTI (recorded) Simulated (simulated)

10. Reliability-based Design of Wastewater Treatment Plants

11. Influent Effluent

12. 1. Simulate influent BOD mass loading Model (1-  B)(1-  B 7 )Z t = C + a t Application Reliability-based design

13. 2. Simulate upsets When BOD/(NH 3 +TON) > 10  upset BOD and NH 3 are positively correlated. Model (1-  B)(1-  B 7 )Z t = C + a t Diagonal, multivariate Application Reliability-based design Note: multi. ARMA predicts half of univ. upsets.

14. 3. Plant operation Permit: Weekly BOD effluent average < 20 mg/l 90% of time. Question: What should BOD effluent be? Model: (1-  B)ln(Z t ) = C + a t From simulations take weekly averages. (Present mean/present 99% reliability value) = (target mean/permit value) 3.14/5.9 = target mean/20  target mean = 10.6 mg/l Note: assume constant coefficient of variation (  )