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Summary:
 Problem with choosing choosing an optimal curve based on integral, length and curvature, when it's created from descrete data points and not a analytical function
Main Question or Discussion Point
Hello,
I'm currently working on an assignment which requires me to choose an optimal curve of power generation based on data points generated by a script I wrote (attached for reference, TideHeight1s is the source data for the script, the txt file contains the code for the .m script).
The purpose is to present the potential for power generation from a tidal lagoon.
The power is therefore derived from the water discharge, which I calculate by iterating over a number of values for turbine shafts and height differences between lagoon water level and sea level, given in the form of discrete data points per 1 second interval.
The problem I have is that this generates several thousand possible power generation curves .
What I'm trying to do is choose one that is a balance between maximum total energy (area under the graph) delivered for the longest possible time most consistently (graph with the lowest curvature).
I have made attempts at that, as shown in the script itself, by playing around with taking a sum of all point and multiplying it by the time they're nonzero, taking the mode and multiplying that by the time and trying to include deviation from average for a flatter graph (that doesn't really work, because it preferres smallest graphs).
So basically, I don't know how to optimise for curvature based on discrete data.
I'm currently working on an assignment which requires me to choose an optimal curve of power generation based on data points generated by a script I wrote (attached for reference, TideHeight1s is the source data for the script, the txt file contains the code for the .m script).
The purpose is to present the potential for power generation from a tidal lagoon.
The power is therefore derived from the water discharge, which I calculate by iterating over a number of values for turbine shafts and height differences between lagoon water level and sea level, given in the form of discrete data points per 1 second interval.
The problem I have is that this generates several thousand possible power generation curves .
What I'm trying to do is choose one that is a balance between maximum total energy (area under the graph) delivered for the longest possible time most consistently (graph with the lowest curvature).
I have made attempts at that, as shown in the script itself, by playing around with taking a sum of all point and multiplying it by the time they're nonzero, taking the mode and multiplying that by the time and trying to include deviation from average for a flatter graph (that doesn't really work, because it preferres smallest graphs).
So basically, I don't know how to optimise for curvature based on discrete data.
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