Signal Pairing
The indicators use two different references. Tracking indicators compare measured displacement to the numerical sub control point. Reference indicators compare numerical sub floors or measured displacement to the full FEM reference.
Notation
| Symbol | Meaning |
|---|---|
dm |
Measured actuator displacement response from the experiment at the interface/control point, approximately the zero-moment point around mid-column. |
dc |
Controller command displacement saved from logsout. |
dd |
Logged actuator command channel. It is retained in saved results but is not used for RTHS error evaluation or comparison plotting. |
fm |
Measured force. |
| numerical sub | Numerical sub FEM without the experimental column; measured feedback force fm is used to step this model forward. |
| full FEM | Complete FEM model driven by the same ground excitation a_g. This is also called the reference FEM. |
x1_r |
Full/reference FEM floor 1 response. |
x1_n |
Numerical sub FEM floor 1 response. |
x2_r |
Full/reference FEM floor 2 response. |
x2_n |
Numerical sub FEM floor 2 response. |
x3_r |
Full/reference FEM floor 3 response. |
x3_n |
Numerical sub FEM floor 3 response. |
d_r |
Full/reference FEM response at the interface/control point. |
d_n |
Numerical sub interface/control-point displacement command, recomputed by stepping the numerical sub with logged fm. |
Error Indicators
| Indicator | Code definition | Unit |
|---|---|---|
| J1 | Delay between measured dm and the numerical sub control point from finddelay(d_n, dm). |
ms |
| J2 | Normalized standard-deviation error between measured dm and the numerical sub control point.100 * std(dm - d_n) / std(d_n) |
% |
| J3 | Peak absolute error between measured dm and the numerical sub control point.100 * max(abs(dm - d_n)) / max(abs(d_n)) |
% |
| J4 | First-floor numerical sub response versus the first-floor full FEM reference. 100 * std(x1_n - x1_r) / std(x1_r) |
% |
| J5 | Second-floor numerical sub response versus the second-floor full FEM reference. 100 * std(x2_n - x2_r) / std(x2_r) |
% |
| J6 | Third-floor numerical sub response versus the third-floor full FEM reference. 100 * std(x3_n - x3_r) / std(x3_r) |
% |
| J7 | Normalized mean square error of measured dm against the full FEM control-point reference.100 * mean((dm - u_control_ref)^2) / mean(u_control_ref^2) |
% |
Code Sources
compare_hs_response_to_reference.m
Shared HS utility for saved RTHS and vHS comparisons. It uses numerical sub displacement d_n for J1-J3 and for comparison plotting.