Clarification of Hass integral (Riemann sum) sensors

I need help understanding things better, so I had aomg conversation with chat gpt. It changed its recommendation after ingesting some Hass docs.

Here is a snippet that helps describe why you should use X method. This is in relation to a power (watts) sensor for my dryer. Other sensor data may need a different method.

You’re right to ask for clarification! Let’s break this down:

My Initial Explanation (Trapezoidal):

I initially recommended the trapezoidal method because it works well for fluctuating data, averaging the values at the start and end of each interval. This is generally a good fit for scenarios where the data fluctuates between values, especially with smooth transitions.

Home Assistant Documentation (Left Method):

The Home Assistant documentation introduces a new context, specifically designed for rectangular or square wave-like data, like your dryer power sensor. It states that the left method is actually better for situations where the sensor remains at a stable value for long periods and changes rapidly, which seems to fit your dryer’s behavior.

Why the Documentation is Important:

The Home Assistant docs are tailored to the Riemann Sum approximation within the specific context of how Home Assistant’s sensors work. If your dryer’s power consumption behaves like a square wave (long periods of steady power with sudden changes), the left method is optimized for this because:

It assumes stability between transitions and accurately captures rectangular functions like a power spike from an appliance.

The trapezoidal rule assumes a more gradual change between data points, which isn’t as accurate when you have sudden jumps.

So, Which is Correct?

For general mathematical integration over fluctuating data, trapezoidal might seem better. However, in your specific case (square wave power consumption from the dryer), the left method is actually better suited, according to Home Assistant’s documentation, because it accurately models sudden shifts with long stable periods.

Conclusion:

For your dryer, use the left method because it best captures the characteristics of your sensor data (sudden changes between high and low power). The trapezoidal method would be better for smoothly fluctuating data, which isn’t the case here.

Can anyone else offer some insight (or correlate chat gpt) into this so I can understand things better? From the Hass docs, my interpretation was that trapezoid method would be best because the source sensor fluctuates.