The following are some recommended conceptual self-assessment questions for the lesson called The general and special forms of a functional model. They’re intended for you to work through to test your own understanding of the key concepts we covered there.
There are three forms of functional model: combined, parametric, and condition.
a) If I ask you to parametrize a situation, which form am I after?
b) If I ask you to develop the observation equations for a situation, which form will you develop?
c) If you develop a functional model and find you have terms in which you can’t separate the measurements from the parameters, what form of model is it?
In Example 6 we saw how to build a condition model for the internal angles of a triangle. Do the same thing for the internal angles of any quadrilateral (any shape with four straight sides).
a) Provide an example from the lessons above where the number of equations in your vector function F isn’t the same as the number of measurements.
b) For which of the three types of functional models, i.e. combined, parametric, condition, does this happen? (You know enough to answer this already, but you might also want to revisit your answer after the next lesson in which we summarize the different kinds of models.)
In Example 5, we saw how to develop the functional model for ‘best fitting’ a line to some data. It was based on the simple equation N – mE – b = 0.
I used b and m to relate it to the familiar equation for a line, y = mx + b. But instead of b for the y-intercept and m for slope, we could have used the variables x0 and x1 , giving us the following which frames the functional modeling task as setting things up to fit a first order polynomial to the data:
N = x1E + x0
a) Extend the work we did in that example by developing the functional model that would be needed to fit a second order polynomial to the data, i.e. where:
N = x2E2 + x1E + x0 = 0
You don’t need to fit a polynomial to any data here. Just write out the parameter vector, the measurement vector, and the functional model that would be used to do so.
b) Which of the three forms of functional model did you end with here, i.e. combined, parametric, or condition?
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