How can I fit 3-D scatter points with value?

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Zihao Huang 2020-8-7

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编辑： Abdolkarim Mohammadi 2020-8-8

Hi,

I have an output file from a fluent simulation. The output file contains the coordinates of each of the nodes and the pressure value of each node. In other words, each point has its coordinate (theta, r, z) and its pressure value p. Is there a way I could fit these scatter points and output an expression p(theta,r,z)?

Thank you,

Joseph

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Answer 1

Abdolkarim Mohammadi 2020-8-7

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编辑：Abdolkarim Mohammadi 2020-8-7

If your model for the relationship between (theta, r, z) triplets and the pressure is linear, use regress. Otherwise, use lsqcurvefit or nlinfit. You cannot use the curve fitting app (cftool) because it only supports up to two independent variables.

Regression page: mathworks.com/help/stats/regression-and-anova.html

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Abdolkarim Mohammadi 2020-8-7

编辑：Abdolkarim Mohammadi 2020-8-7

Statistical analyses are broadly classified into two categories:

(1) An exploratory analysis can find patterns and relationships within your dataset on its own. It only needs a dataset.

(2) A confirmatory analysis cannot find relationships within your dataset on their own. You need dataset and a parametric model, and the analysis tells you how good it could fit your model to your dataset.

For confirmatory analysis you have to provide a model in addition to the dataset. Curve fitting and regression are confirmatory analyses. You pass your dataset and a parametric model to them and they return you the coefficients for the model that minimize the error. You may have noticed in MATLAB's curve fitting app that you have to try different models (linear, power, polynomial, etc) to achieve a good fit. That's because curve fitting is a confirmatory analysis and cannot find model for the relationships between variables. Indeed finding a suitable model is not easy, especially for datasets with more than two independent variables. If you need a model in the form of

, you are seeking for a linear relationship. In the case of for example

, then you are looking for nonlinear curve fitting. In all cases, you have to first define a model and have MATLAB estimate

,

, and

.

It may also turn out that none of the above parametric models show good fit to your data. That's where you should use artificial neural networks or interpolation methods. None of these two analyses give you an explicit relationship (formula) but can be used to estimate the values in between your data points.

Zihao Huang 2020-8-7

Thank you for your clarification. In my dataset, I have only 3 sets of thetas, do you think I can maybe fit the surface (r,z,p) for a theta, and then move on to get all three equations, and find out the relationship between them? I tried cftool on (r,z,p) in theta 1, and it fits well using cubic interpolant method. However, I don't know how to export the function of that surface. Can you help me with this?

Abdolkarim Mohammadi 2020-8-7

编辑：Abdolkarim Mohammadi 2020-8-8

(1) When you split apart values of theta, you are treating it as a moderator variable. In other words, you are assuming that theta does not directly affect pressure; it is just affecting the model (r,z)=>p. This is in contrast with the assumption of the direct effect of theta in the model (r,p,theta)=>p.

(2) As I mentioned in my previous comment, interpolation does not produce equation. It just interpolates between your data points to fill the gaps between datapoints. For example, if you have only two data points of (x=0,y=0) and (x=1,y=2) then you create interpolation and evaluate the interpolation at x=0.5, then it returns y=1, which is the intermediate between your points.

(3) You should not judge the quality of interpolation models based on

. Any type of interpolation will always lead to

. It's because they do not produce error at datapoints.

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