| T O P I C R E V I E W |
| computon |
Posted - 08/14/2009 : 04:15:56 AM
i think you don't understant my question.i used the pridiction band and confidence band in the nonlinear fitting process and gained the parameters' value and standard daviation,as you can see below.i want to know the uncertainty of the index temperature T41-J,σ(T41-J),it is can not be gained immediately after fitting and it must deduce.
i copy my question and revise the gibberish in my post ,as follows?
thank you for your patience and looking forward your detailed reply.
HI
i used boltzmann function to nonlinear fit the data of Charpy impact data(temparature ,Charpy Energy),as follows:
E=(A1-A2)/(1+exp(T-Tt)/θ1)
E-Charpy Energy;T-temperature; Tt-an index temperature at the mid-energy:0.5(A1+A2);θ1-parameter.
The experiment data is as follows:
T E
25 75
25 70
25 77.5
10 73
10 67
10 72
0 54.5
0 57
0 56.5
-10 57
-10 48
-10 54.5
-20 38.5
-20 40
-20 44
-30 36.5
-30 35.5
-30 36
-40 39
-40 33
-40 34
-50 30
-50 27
-50 27.5
-60 26
-60 33
-60 30
The fitting result is as follows:
Parameters A1 A2 Tt θ1
Unit. J J ℃
value 28.42±2.17 79.03±4.26 -6.72±2.90 13.65±2.85
Now i want to know the uncertainty of the energy?
can i use the equation to calculate the uncertainty of the energy?
σ(E)=(Σ((Ei-E(i-fit)^2)/(n-1))
Ei -the i-th charpy energy at the i-th temparature;
E(i-fit)-the calculating energy using the fitting function, Boltzmann function ,by inputing the i-th temperatue corresponding to the i-th charpy energy;
If i calculate an index temperature at the energy 41J,T-41J:
T-41J=θ1*ln((A2-A1)/(A2-41)-1)+Tt
how to calculate the uncertainty of the index tempaterature T-41J,θ(T-41J)?
can i use the equation as following:
σ(T-41J)=θ1*ln((A2-A1)/(A2-41)-1)-θ1*ln((A2-A1)/(A2-41+σ(E))-1)
what's the relationship between the parameter uncertainty in the fitting and the uncertainty of the curve /the index temprature T-4J?
thank you for you help and your reply?
|
|
|
