Superimpose DELs weighted on different lifetime

Wind & Water Structural Analysis
1

Hi everybody,

I have got a likely pretty straightforward question.

Let assume that I have a DEL value weighted over 20 years and a second value weighted over 0.25 years: is it possible to get a overall DEL weighted over a 20.25 years lifetime, starting from the two above? Nref = 1E+08 cycles and Woehler slope m=4.

I would expect the solving formula to look like:

DEL(20.25) = (((DEL(20)^m20 + DEL(0.25)^m0.25)*Nref/(20.25))^(1/m))/Nref

Am I on the right track or not? Please shed a light.

I thank you all in advance.

2

Dear Francesco,

The damage-equivalent load (DEL) is defined as follows:

DEL = ( SUM( n_k*L_k^m, k = 1, 2, …, N )/n_eq )^(1/m)

where,
k = load-range bin counter
N = number of load-range bins
n_k = number of cycle counts in the k’th load-range bin
L_k = k’th load range
n_eq = number of equivalent cycle counts
m = Whoeler material exponent

I’m not exactly sure how you are defining Nref. I’m assuming you mean that Nref is the number of equivalent cycle counts per year, such that 20*Nref is the number of equivalent cycle counts in 20 years.

I’m also not clear on how you are defining DEL(20) and DEL(0.25). If you mean that DEL(20) is a DEL based on Nref that acts for 20 years out of a 20.25-year period and DEL(0.25) is a DEL based on Nref that acts for 0.25 years out of a 20.25-year period, and my assumption about Nref is correct, than DEL(20.25) is:

DEL(20.25) = ( ( 20NrefDEL(20)^m + 0.25NrefDEL(0.25)^m )/( 20.25*Nref ) )^(1/m)

Notice that Nref cancels out, leaving:

DEL(20.25) = ( ( 20DEL(20)^m + 0.25DEL(0.25)^m )/( 20.25 ) )^(1/m)

However, there could be other interprations of Nref, DEL(20), and DEL(0.25). If my interprations are not correct, please clarify.

Best regards,

3

Dear Jason,

your thoughts about Nref, DEL(20) and DEL(20.25) are absolutely right. Indeed, I myself came up with the same formula you wrote down 10’ after posting my question.

I just wanted to have my idea supported by somebody who has a more consistent knowledge than me.

I really thank you in advance.

Kindest regards from Germany.

4

Dear Jason,

Can I estimate the Lifetime DEL based on Short-term DEL using the following method?

Annualized DEL = Sum(DEL(i) * f(i)) for i = 1, …, n,
where DEL(i) is the ith Short-term DEL, and f(i) is its corresponding frequency.
Lifetime DEL = Annualized DEL * Tlife
where Tlife is the design life of the equipment.
@Jason.Jonkman

5

Dear @Yuan.Hu,

I’m not following your approach.

The method MLife uses to compute the lifetime DEL is documented in the MLife Theory Manual: https://www.nrel.gov/wind/nwtc/assets/pdfs/mlife-theory.pdf.

Best regards,

7

Dear @Yuan.Hu,

MLife can use the Weibull wind distribution; it can also use a user-specified distribution, including multiple dimensions. See the documentation User_Probability_Distributions.pdf in the MLife archive for more information.

I’m still not sure I understand your equation for lifetime DEL in your step 3, which seems to differ from what MLife uses, but I agree with steps 1 and 2 in your method. Also, 20 seeds in step 1 may be more than you need (the IEC design standards only require 6 seeds, although it is questionable whether 6 is enough to ensure statistical convergence; 10 seeds may be more reasonable).

Best regards,

8

Dear Jason,
I have read the User_Probability_Distributions.pdf file and know the file format of distribution table, but how should I go about generating the binary file of distribution table?

9

Dear @Yuan.Hu,

In the MLife archive, there is a MATLAB function write_joint_pdfm.m that can be used to write the user-specified distribution to a binary file used via DistribName in MLife.

Best regards,