Model Fit Monitor — System Identification/Validation

Model Fit Monitor

System Identification / Validation

Reports how well a model's output tracks the signal it is meant to predict, as a running NRMSE fit updated every sample:

fit = 1 − √(S_e ÷ (S_y + ε)), where S_e is the exponentially weighted energy of the error y − ŷ and S_y the exponentially weighted variance of y about its own running mean.

• 1 – the model reproduces y exactly.
• 0 – the model is no better than predicting y's own mean.
• Negative – the model is worse than that. This is deliberately not clamped: it is the most useful thing the block can tell you, and a floor at zero would hide it.

Because the sums are exponentially weighted rather than taken over the whole run, the number follows the model live: a plant that drifts away from its identified model shows the fit falling on the canvas while the simulation is still running, which a fit computed at the end cannot do.

Ports

• y – the measured signal, a scalar. This is the reference: the denominator is its running variance, so it is not interchangeable with the other port.
• yhat (ŷ) – the model's output for the same instant, a scalar.
• fit – the running fit, a scalar, as a fraction (not the percentage MATLAB's compare prints – multiply by 100).

Parameters

• Forgetting Factor – λ in (0, 1]. The memory is roughly 1 ÷ (1 − λ) samples: 0.98 averages over about 50, 0.9 over about 10. Smaller reacts faster and is noisier; 1 makes it an ordinary cumulative fit over the whole run with no forgetting at all.
• Epsilon – a floor on the variance divisor, not a branch. A constant y has zero running variance, and without this the fit would divide by zero the moment a signal settles. Keep it small relative to the variance you expect; it biases the fit slightly upward.
• Initial Reference Mean – the seed for y's running mean. It decays with λ like any other sample, so it matters only for the first few multiples of the memory; set it to y's expected level to stop the fit reading low while the mean converges from zero.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. λ, ε and the seed are baked into the emitted arithmetic rather than exposed as tunable parameters: they define what the number means, so retuning one on the target would silently change the metric rather than the model.

The three HDL targets are simulation-only real arithmetic. A square root and a per-sample division do not belong in a Q16.16 datapath, and this block needs both.

Simulink bridge

None. Simulink has no block that reports a running fit – the NRMSE conventions this follows live in System Identification Toolbox functions (goodnessOfFit, compare), which run after a simulation over a whole logged signal rather than inside one, and which no ParamRule could carry across the bridge in any case. The block therefore has no parity testbench, which is the documented consequence of Support::None rather than a gap.

Notes

• Stateful, with three scalars: the running mean of y and the two weighted sums. It is a discrete-only block – a fit has no derivative to integrate.
• The mean is updated before it is used. S_y takes the deviation from the new mean, not the previous one. The two conventions differ by order (1 − λ) every sample.
• The output is the current sample's fit, not the previous one: the sums are advanced and then published, which is the opposite order to the filter blocks.
• The fit is a ratio of two weighted sums, so the weighting constants cancel and no normalisation by the sample count is needed – which is also why a warm-up period is visible in the number rather than hidden by one.