Operationel Range

While working at Maersk there was a power-to-speed model used for planning, basically a polynomial inferred from a regression, taking in some extra inputs besides power and outputting speed. For this model there was defined valid input power levels. In this post I will talk about my thoughts on why it seems useful to define the operational range AND data type of an inferred function in an operational setting.

Basic Implementation

A very basic implementation of the operational range would be. If implementered in Python then I would also use dicts to specify the datatypes.

# dtype.py

# The range of variables in X.
X_RANGE = {'power': [0, 80000]}

# The range of variables in y.
Y_RANGE = {'speed': [0, 30]}

# The datatype of the inputs.
X_DTYPE = {'power': 'float64'}

# The datatype of the output.
Y_DTYPE = {'power': 'float64'}

Useful things you can do when you define the operational range:

• Test that predictions are within the operational range for input values in the operational range.
• Create standard reports to investigate yourself or ideally subject matter experts.
• Approximate the partial relationships between two variables by partial dependence plots (or a rough approximation to it).
• If the datatypes are specified then this it is easy to specify the spec of an API to users.
• If the datatypes is specified then parsing mistakes can be avoided by creating functions to load the data.

Related Thought: Basic Functional Relationships

To be even more specific one could specify a range on valid speed levels \([s_{min}(p), s_{max}(p)]\) for each power level \(p\). This would naturally lead to a lower bound on how bad the model is:

\[ \lvert \text{prediction}(p) - \text{actual}(p) \rvert \leq s_{max}(p) - s_{min}(p) \]

Related Thought: Sample of the data

With a sample of the data one can do similar thing but above could be faster to compute and easier to standardize.

A sample of the data with 1000 rows are however easy to keep as a pytest fixture so I would probably do this anyway.

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