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Automatic calibration of hysteretic models through multiple responses
- 1. Corrado Chisari Gianvittorio Rizzano Massimo Latour Claudio Amadio
- 2. Phenomenological models Phenomenological models simulate the observed behaviour without caring of the underlying physics. They can represent relationships as stress-strain of fibres, force-displacement of rods, moment-rotation of beam-to-column joints, base shear-top displacement of buildings, etc. without conceptual differences. 2AUTOMATIC CALIBRATION OF HYSTERETIC MODELS THROUGH MULTIPLE RESPONSES Some parameters may not have clear physical meaning Model calibration
- 3. Model calibration Model calibration means finding the model parameters which, inserted in the numerical model of the a given test, provide the optimal fitting of the experimental response. 3 S1 S2 S3 S4 Experimental evidence Real test Numerical modelling Model calibration AUTOMATIC CALIBRATION OF HYSTERETIC MODELS THROUGH MULTIPLE RESPONSES
- 4. Multiple responses 4AUTOMATIC CALIBRATION OF HYSTERETIC MODELS THROUGH MULTIPLE RESPONSES We can define a discrepancy function, measuring the inconsistency between experimental data and computed response: 𝜔𝜔 𝒑𝒑 = 𝒚𝒚𝒆𝒆𝒆𝒆𝒆𝒆 − 𝒚𝒚𝒄𝒄 𝒑𝒑 𝒚𝒚𝒆𝒆𝒆𝒆𝒆𝒆 Model calibration is thus solved as an optimisation problem �𝒑𝒑 = arg min 𝒑𝒑∈𝑷𝑷 𝜔𝜔 𝒑𝒑 or, if NT responses are available, �𝒑𝒑 = arg min 𝒑𝒑∈𝑷𝑷 𝜔𝜔1 𝒑𝒑 , … , 𝜔𝜔𝑁𝑁𝑇𝑇 𝒑𝒑 MULTI-OBJECTIVE OPTIMISATION PROBLEM The general solution is the Pareto Front, the set of non-dominated solutions Genetic Algorithms
- 5. MultiCal software - input MultiCal Experimental tests • Responses to fit Hysteretic model • Parameters to calibrate Optimisation settings • Genetic Algorithms parameters 5AUTOMATIC CALIBRATION OF HYSTERETIC MODELS THROUGH MULTIPLE RESPONSES MultiCal (www.multical.unisa.it) addresses the need of a unique tool for calibrating hysteretic models onto multiple experimental tests.
- 6. MultiCal software - input MultiCal Experimental tests • Responses to fit Hysteretic model • Parameters to calibrate Optimisation settings • Genetic Algorithms parameters 6AUTOMATIC CALIBRATION OF HYSTERETIC MODELS THROUGH MULTIPLE RESPONSES MultiCal (www.multical.unisa.it) addresses the need of a unique tool for calibrating hysteretic models onto multiple experimental tests.
- 7. MultiCal software - input MultiCal Experimental tests • Responses to fit Hysteretic model • Parameters to calibrate Optimisation settings • Genetic Algorithms parameters 7AUTOMATIC CALIBRATION OF HYSTERETIC MODELS THROUGH MULTIPLE RESPONSES MultiCal (www.multical.unisa.it) addresses the need of a unique tool for calibrating hysteretic models onto multiple experimental tests.
- 8. MultiCal software - output MultiCal Pareto Front analysis Compromise solution Curves 8AUTOMATIC CALIBRATION OF HYSTERETIC MODELS THROUGH MULTIPLE RESPONSES
- 9. MultiCal software - output MultiCal Pareto Front analysis Compromise solution Curves 9AUTOMATIC CALIBRATION OF HYSTERETIC MODELS THROUGH MULTIPLE RESPONSES
- 10. MultiCal software - output MultiCal Pareto Front analysis Compromise solution Curves 10AUTOMATIC CALIBRATION OF HYSTERETIC MODELS THROUGH MULTIPLE RESPONSES Moment-rotation Envelope Energy
- 11. Examples 11AUTOMATIC CALIBRATION OF HYSTERETIC MODELS THROUGH MULTIPLE RESPONSES Repeated runs of the optimisation analysis may increase the confidence in the results and help assess uncertainty in the calibration
- 12. Examples 12AUTOMATIC CALIBRATION OF HYSTERETIC MODELS THROUGH MULTIPLE RESPONSES Innovative self-centering dissipative connection: phenomenological modelling Non-degrading flag- shape Degrading flag-shape
- 13. Examples 13AUTOMATIC CALIBRATION OF HYSTERETIC MODELS THROUGH MULTIPLE RESPONSES Dissipative L-stub: phenomenological modelling
- 14. Conclusions • MultiCal is a tool aimed at calibrating hysteretic models based on multiple tests, in the framework of multi-objective optimisation • It can dealt with up to 6 tests, and different response quantities (generalised force, envelope curve and energy) • The optimisation is governed by Genetic Algorithms (NSGA-II) • Several Opensees uniaxialMaterial models can be calibrated: more are planned to be implemented • Default parameters and template builder assist the user in the creation of input files • A graphical interface is under construction 14AUTOMATIC CALIBRATION OF HYSTERETIC MODELS THROUGH MULTIPLE RESPONSES