- Discovered pump health formula
Health_Index = 0.523392 × log10(V3/V2 × V4)/-0.0409106 + 48.6349in 10 minutes - Formula predicts remaining useful life with high accuracy
- Formula runs on edge devices—no cloud connectivity required for real-time monitoring
- TuringBot is standalone software—no Python/R environment or ML libraries needed
Traditional ML identifies patterns in IoT sensor data but can't explain the underlying physics. Symbolic regression discovers explicit formulas—deployable on edge devices and understandable by maintenance teams.
Symbolic regression addresses this challenge by discovering explicit formulas that connect your IoT sensor data. Unlike neural networks and other black-box models, symbolic regression searches through possible mathematical expressions to find ones that best predict outcomes while remaining interpretable. This makes it particularly valuable for IoT applications where understanding the "why" behind predictions is crucial.
In this article, we'll demonstrate how TuringBot, a desktop application for symbolic regression, can transform raw IoT sensor data into predictive mathematical formulas for equipment maintenance.
Case Study: Predictive Maintenance for Industrial Pumps
Let's tackle a common industrial IoT scenario: predicting pump failures before they occur using vibration sensors.
Our dataset contains readings from four vibration sensors (V1, V2, V3, V4) placed at different points on industrial pumps, along with temperature measurements (Temp) and a "Health_Index" that indicates the remaining useful life of each pump.
Step 1: Data Import
After launching TuringBot, we imported our IoT dataset containing sensor readings from multiple pumps at different times, with each row representing a measurement at a specific time:
Step 2: Configuration Setup
We configured TuringBot to search for a formula with V1, V2, V3, V4, and Temp as inputs and Health_Index as output, using RMSE as the error metric. We enabled all mathematical operators including logarithmic functions, which are often useful for analyzing vibration patterns:
Step 3: Running the Search and Results
After running for approximately 10 minutes, TuringBot discovered this remarkably simple yet powerful formula, which was chosen because larger formulas presented diminishing returns:
Health_Index = 0.523392 × log10(V3/V2 × V4)/-0.0409106 + 48.6349With an RMSE of 0.52, this formula achieved excellent prediction accuracy. Here are all the formulas that were discovered:
Insights from the Formula
This formula provides key insights about pump health:
- The ratio of V3 to V2 multiplied by V4 captures critical vibration relationships between different measurement points
- The logarithmic relationship reveals that combined vibration effects follow a non-linear progression typical of accelerating mechanical wear
Most importantly, this formula reveals that it's not the absolute vibration values that matter most, but rather the relationships between measurements from different sensor positions—information that would be difficult to extract through simple visualization or correlation analysis.
Additional IoT Analytics Applications
While our example focused on vibration sensors for pumps, symbolic regression with TuringBot is equally applicable to other IoT domains:
- Smart buildings can discover formulas linking multiple environmental sensors to energy consumption, enabling precise HVAC optimization
- Smart agriculture applications can find relationships between soil moisture, temperature, and crop yield to optimize irrigation schedules
- Battery-powered IoT networks can develop formulas to predict device longevity based on transmission patterns and environmental conditions
Predictive Maintenance: TuringBot vs. Traditional ML
| Aspect | TuringBot Formula | Neural Network / Random Forest |
|---|---|---|
| Edge deployment | Single equation (bytes) | MB+ model files |
| Inference time | Microseconds | Milliseconds |
| Maintenance team buy-in | Immediate (readable formula) | Requires trust in "black box" |
| Sensor relationship insights | Explicit in formula | Requires SHAP/LIME analysis |
| Cloud dependency | None | Often required |
Conclusion
Symbolic regression with TuringBot transforms IoT vibration data into actionable maintenance insights. By extracting the exact mathematical relationship Health_Index = 0.523392 × log10(V3/V2 × V4)/-0.0409106 + 48.6349, we've solved a real predictive maintenance problem with a formula that's immediately deployable, physically meaningful, and runs efficiently on edge devices.
This approach bridges the gap between data collection and decision-making in IoT environments, producing mathematical formulas that not only predict outcomes but explain the underlying physical relationships driving those predictions.