Regression Modeling & Baseline Development

Abriliam Consulting — Industrial Energy Management

This notebook builds weather-normalized regression models to establish a performance baseline for the chiller plant. The baseline allows us to separate weather-driven variation from operational changes — answering the question: "Is the plant performing differently than expected for these conditions?"

We start with a simple single-variable regression (OAT vs chiller kW), then progress to a multivariable model incorporating load and occupancy, and finally apply CUSUM analysis to detect when operations changed.

Regression Statistics:
Slope: 31.95
Intercept: -56.84
R-squared: 0.8609
Mean Squared Error: 5054.89

Single-Variable Regression: OAT vs Chiller kW

The simple linear regression of chiller power against outdoor air temperature shows a positive relationship — as expected, warmer weather drives higher chiller loads. However, the R-squared is moderate, indicating that OAT alone explains only part of the variation. Load magnitude and occupancy are also significant drivers.

The scatter plot shows considerable spread around the regression line, particularly at higher temperatures. This spread represents the combined effects of varying occupancy patterns, time-of-day differences, and the operational changes we're investigating.

Multivariable Regression Statistics:
Intercept: 71.09
Coefficients: [ 8.90297424  2.26926092 -6.70189585]
R-squared: 0.9755
Mean Squared Error: 1098.75

Multivariable Regression: OAT + Tons + Occupancy

Adding cooling load (tons) and occupancy fraction dramatically improves the model. The residual analysis shows:

• Residual plot: Residuals are roughly centered around zero but show some heteroscedasticity (wider spread at higher predicted values). This is common in HVAC models — larger loads have more variability.
• Q-Q plot: The residuals approximate a normal distribution, validating the regression assumptions.
• Histogram: Roughly symmetric distribution of residuals, though with slightly heavier tails than a perfect normal.

This multivariable model forms the basis for our change detection — we can now ask whether residuals shift systematically at any point in time.

Hydraulic Trends

The three-panel spline plot reveals the key relationships:

• CHW flow and delta-T (top): Flow and temperature difference move inversely — when delta-T drops, flow must increase to maintain the same cooling output. This is the hydraulic signature of low-delta-T syndrome.
• CW flow and delta-T (middle): Condenser-side hydraulics are more stable, tracking load as expected.
• OAT and kW/ton (bottom): Outdoor temperature and efficiency are correlated, but the kW/ton trend shows drift beyond what weather alone explains.

OLS Regression Statistics (First 24 Hours):
Intercept: 47.49
Coefficients: [ 1.9129087   8.27215735 -1.22977881]
R-squared: 0.9447
Mean Squared Error: 301.46

CUSUM Change Detection

The CUSUM (Cumulative Sum) chart is a powerful tool for detecting when a process shifts. We trained a baseline model on the first 24 hours, then tracked cumulative residuals for the remaining data.

A flat CUSUM line means the process is behaving as the baseline predicts. A sustained upward slope means the plant is consistently consuming more energy than predicted — an operational change has occurred. The inflection point in the CUSUM identifies when the change happened, which can then be correlated with maintenance logs, control system changes, or equipment events.