Estimating gas-turbine NOx from operating measurements
An emissions estimator can support analysis of turbine operating conditions alongside physical measurements. This example predicts NOx from environmental and process variables and tests a selected neural network on held-out records.
1. Industrial challenge
Gas-turbine operating data can support an emissions estimator when direct measurements and operating context remain available. The example examines NOx error and a local response to turbine after temperature.
Operating conditions
Use ten inputs from the prepared turbine records.
Emission estimate
Assess NOx predictions and errors in the dataset units.
Local response
Inspect the directional curve at its fixed reference operating point.
2. Data set
The prepared dataset contains 36,733 records from the UCI Gas Turbine CO and NOx Emission dataset. The supplied final model retains ten inputs and selects ten hidden neurons. It was trained with the Quasi-Newton method recorded in the new report.
The downloadable project, saved report and supplied source CSV define the exact version used here. Repository: original dataset/source record.
| Subset | Records |
|---|---|
| Training | 22041 |
| Validation / selection | 7346 |
| Testing | 7346 |
| Unused | 0 |
| Variable | Role | Type | Encoding | Unit |
|---|---|---|---|---|
| ambient_temperature | Input | Numeric | As supplied | |
| ambient_pressure | Input | Numeric | As supplied | |
| ambient_humidity | Input | Numeric | As supplied | |
| air_filter_difference_pressure | Input | Numeric | As supplied | |
| gas_turbine_exhaust_pressure | Input | Numeric | As supplied | |
| turbine_inlet_temperature | Input | Numeric | As supplied | |
| turbine_after_temperature | Input | Numeric | As supplied | |
| turbine_energy_yield | Input | Numeric | As supplied | |
| compressor_discharge_pressure | Input | Numeric | As supplied | |
| CO | Input | Numeric | As supplied | |
| NOx | Target | Numeric | mg/m³ |
Interactive chart: NOx distribution. Enable JavaScript to explore it.
Interactive chart: NOx Pearson correlations chart. Enable JavaScript to explore it.
Interactive chart: NOx vs. ambient_temperature scatter chart. Enable JavaScript to explore it.
3. Model
The final model has 10 encoded input features and 1 outputs. The following dimensions describe the final saved network.
| Layer | Input shape | Output shape | Activation |
|---|---|---|---|
| Scaling | 10 | 10 | — |
| Dense | 10 | 10 | Tanh |
| Dense | 10 | 1 | Identity |
| Unscaling | 1 | 1 | — |
| Clamping | 1 | 1 | — |
The final output is a continuous estimate. Scaling, unscaling and any bounds follow the saved implementation; the calculator does not silently impose physical constraints.
4. Training strategy
The saved training configuration uses NormalizedSquaredError with QuasiNewton. Training minimizes the recorded objective; the validation subset monitors generalization during fitting. The testing subset is used for the evaluation below.
Interactive chart: Quasi-Newton method error history. Enable JavaScript to explore it.
Quasi-Newton method results
| Measure | Value |
|---|---|
| Epochs number | 146 |
| Elapsed time | 00:00:01 |
| Stopping criterion | Minimum loss decrease |
| Training error | 0.229 |
| Validation error | 0.229 |
5. Model selection
The following search results are recorded in the saved report. Selection used the validation subset. These are the selected settings within the tested search; they do not establish a globally optimal model.
Interactive chart: Growing neurons training/selection errors plot. Enable JavaScript to explore it.
Growing neurons results
| Measure | Value |
|---|---|
| Optimal neurons number | 10 |
| Optimum training error | 0.1428 |
| Optimum selection error | 0.146 |
| Epochs number | 10 |
| Stopping criterion | Maximum neurons reached |
| Elapsed time | 00:01:05 |
6. Testing analysis
The final model is evaluated on 7,346 testing observations. MAE, RMSE and prediction R² below are computed from the exact testing pairs stored by Neural Designer. Errors retain each target’s original units.
| Target | Unit | MAE | RMSE | Prediction R² | Pearson r² |
|---|---|---|---|---|---|
| NOx | mg/m³ | 3.073 | 4.562 | 0.842 | 0.842 |
The native goodness-of-fit task reports squared Pearson correlation (r²). Prediction R² here is 1 − squared prediction error / squared deviation from the test mean. They measure different properties: a strongly correlated prediction can still have a bias or an incorrect scale.
Interactive chart: NOx goodness-of-fit chart. Enable JavaScript to explore it.
7. Model deployment
Validated inputs → saved preprocessing → neural network → score or estimate → domain review. The ZIP contains the original project, source CSV, schema, test metrics and standalone interactive chart exports. The project hash in the schema identifies this exact version.
Directional response at a fixed reference point
Inspect the saved reference point
| Measure | Variable | Value |
|---|---|---|
| 1 | ambient_temperature | 26.837 |
| 2 | ambient_pressure | 1011.5 |
| 3 | ambient_humidity | 58.73 |
| 4 | air_filter_difference_pressure | 4.0851 |
| 5 | gas_turbine_exhaust_pressure | 25.805 |
| 6 | turbine_inlet_temperature | 1092.7 |
| 7 | turbine_after_temperature | 549.67 |
| 8 | turbine_energy_yield | 133.78 |
| 9 | compressor_discharge_pressure | 12.217 |
| 10 | CO | 2.6523 |
Interactive chart: NOx – turbine_after_temperature directional output. Enable JavaScript to explore it.
Explore the exported model
This research demonstration runs locally in your browser. Values outside the training range are outside the validated domain and are rejected. A valid input range does not guarantee that a combination is physically or operationally plausible.
This is not a certified control or protection system.
8. Scope and limitations
The saved split does not establish transfer to future years or another turbine. Use time-blocked or equipment-level validation, review sensor quality and evaluate extreme regimes. A directional response holds other variables fixed and is not a physically validated operating intervention or a compliance instrument.
No external validation or independent calibration study is included. Preprocessing statistics and model choices should be refitted within a prospective or grouped validation design. Correlations and directional responses describe associations, not causes. Human review is required before an operational decision.
