Making Unknown Systems Identifiable (with Real Measurements)

In this video, I show how to extract meaningful subsystem parameters from a system where individual components cannot be measured directly. Using an ultrasonic transmitter/receiver setup, I demonstrate how time and frequency-domain measurements can be used to separate transducer behavior from acoustic propagation effects. Then I identify which parameters belong to which transducer. Errata: In this video, I conflate observability and identifiability. That is my mistake, as u/Craizersnow82 pointed out in my reddit post. This video shows how changing the measurement structure turns a non-identifiable system into an identifiable one. In particular, due to an inherent scaling ambiguity, the internal subsystem gains are only identifiable up to a reference choice. While the fitted models are consistent with all measurements, the internal states cannot be uniquely reconstructed without additional assumptions. 0:00 - Intro 1:24 - Building the Test Fixture 3:07 - Time Domain Measurements 4:03 - Frequency Domain Measurements 5:59 - Modeling the Systems (Magnitude) 9:42 - Modeling the Systems (Group Delay) 12:20 - Making it Identifiable 15:57 - Thanks and Questions Shoutouts to the following makers on thingiverse: https://www.thingiverse.com/thing:4877332 (Extrusion cap) https://www.thingiverse.com/thing:5177513 (Extrusion Slot Cover) Further reading on transducer modeling: https://wiki.idiot.io/_media/piezoacoustic.pdf https://www.research.unipd.it/retrieve/2e9d5113-1801-47b4-ae38-05ea52edcb97/Evaluation_of_the_Electrical_Parameters_of_a_Piezoelectric_Transducer_Using_a_Low-Cost_Set-Up_and_FFT_Analysis.pdf Made with manim and love