Curve fitting - Creep Coefficient

[MB_12486492]

I am trying to perform curve fitting using mathcad 13 to determine the best coefficients, "alpha" and "beta," that can approximate the equation of the three-parameter model (red line) to the creep equation according to Eurocode 2 (blue line).

I cannot change the expression of the parameters in the three-parameter model equation. At this point, I have already tried using functions like "genfit."

        

However, the parameters I am finding are less accurate than those obtained using the trial-and-error method.

I would greatly appreciate any help or suggestions you can provide.

[Werner_E · Accepted solution]

I am not sure but it may be hat you got confused about the time units?

Anyway, I just used your vectors X and Y and the function type you provided.
It looks to me that you had provided bad guess values.

But the function type seems not suit the data very well.

There may be other function types better suited. Some examples see below

[MB_12486492]

Thank you very much for your attention, Mr. Werner.

I have reviewed your solution; however, I am unable to open the file in my version of Mathcad (version 13.0).

  

Would it be possible to convert the file to a compatible format?

I appreciate your assistance.

[Werner_E]

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Would it be possible to convert the file to a compatible format?

Sure! Fortunately we are using real Mathcad here and not Prime. So its possible to save back in an older version format without problems.

Attached is the file in MC13 format but he pictures in my last post already showed it all, nothing hidden 😉

In future question please state which version of the software you are using.

[MB_12486492]

Mr. Werner_E,

Is it possible to use the function inside Genfit, alfa1(t, t0) = beta1(t, t0), without specifying specific points of the matrices X and Y?

[Werner_E]

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@MB_12486492 wrote:

Mr. Werner_E,

Is it possible to use the function inside Genfit, alfa1(t, t0) = beta1(t, t0), without specifying specific points of the matrices X and Y?

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I am not sure what you mean!?
The first two arguments of the "genfit" function must be vectors of scalars.
And "genfit" tries to find the best (scalar) parameters (alpha, beta in your case) for the function type (last "genfit" argument, based on the third function argument (guess values).

I am not sure what you have in mind when you write alfa1(t,t0), etc. alfa1 and beta1 are variables with scalar values returned by the "genfit" function and not functions in two variables ....?

I see that you have defined functions alpha_bct and beta_bct in two variables but I can't see how these functions should be used in fitting the X Y data.

EDIT: I am now stabbing in the blue (or in the dark), but maybe your goal is to approximate the function beta_bct by a function of the type you defined for f ???
Because genfit just works on vectors of values, its necessary to create the vectors of time and function values (T and Beta).

The guess values have to be provided in a vector and a vector in Mathcad is not allowed to hold quantities of different dimensions. Therefore we have to make T dimensionless so that beta and alpha both are unitless parameters.

Then we can use these vectors, your matrix F and appropriate guess values to find suitable parameters alpha and beta.

But then I am absolutely not sure if this really is what you are looking for ...

MC15 sheet attached

[MB_12486492]

The X and Y data were extracted from the function φ(t, t0), where X corresponds to specific points on the x-axis and Y to specific points on the y-axis.

Is there any possibility of using the function itself instead of specific points from the matrix?

For example, one idea would be something like this:

The other idea I mentioned above involves using alfa1(t, t0) and beta1(t, t0), where these coefficients would also vary over time to better fit the creep curve. I'm not sure if it would work this way, but I'm thinking and trying solutions for a better automatic adjustment.

[Werner_E]

genfit fits points to a specific function. So if you want to find a function f of a specific type which approximates another, different function Phi, you have to do as I just had shown - you must create data vectors.

Concerning function alpha(t) and beta(t): Guess this is possible, but probably not the way you have in mind.

Instead of

you would have to define the type of functions for alpha and beta, depending on some parameters and  use these functions in the definition of f

That means that you will have to know or suspect in which way alpha and beta are changing over time

Looks like my arbitrary choice of functions and/or my guess values are not much better than the original constants 😉

[MB_12486492]

Thank you for your time and attention, Mr. Werner.

The alternative equations you suggested would fit much better; however, I must work with the basic equation I initially shared, as it represents the solution to the differential equation I am focusing on.

I am attaching an article containing parts of my research, where the next step involves refining this curve as accurately as possible using a programming routine.

Any criticism, considerations, or suggestions are always welcome.

[LucMeekes]

Bom dia,

I fail to see the point of curve fitting. Following your sheet I find:

that define:

and:

that define:

to finally define:

So the function you are trying to approximate is actually

With the values:

this plots as:

So the shape of your function is determined with only four parameters.

Why settle for less accurate results in two or three parameters?

Success!
Luc

[MB_12486492]

Hi Mr. Luc Meeks,

I truly appreciate your attention to my question and your opinion.

Indeed, the creep coefficient depends on many factors, such as the age of the concrete at the time of load application, curing conditions, environmental factors like relative humidity, the level of applied stress, the duration and history of loading, the dimensions of the concrete elements, the material composition, and other factors.

I am attempting to simplify this by using an equation that depends on the modulus of elasticity and the viscosity modulus of the concrete.  While it may not achieve 100% precision, will provide a good level of accuracy.

I am attaching an article containing parts of my research, where the next step involves refining this curve as accurately as possible using a programming routine.

Any criticism, considerations, or suggestions are always welcome.