Hi,
I would like to calculate the probability of failure using the convolution therom as described in this paper https://www.researchgate.net/publication/314278481_Reliability_Index_for_Non-normal_Distribution_of_Limit_State_Functions
First I wanted to write the code using examples of this paper (Please look at the attached screenshots). Unfortunately, I didn’t get the same results. I found a probabilty of failure Pf=3.82 10^-08 instead of 5.55 10^-02.
In addition, I am struggling to write the inverse function to derive the reliabilty index. I always leads to errors?
Can anyone explain the mistake?
Sigma= 1;
Mu=5;
PDF_Norm=@(x) exp(-0.5.*((x-Mu)/Sigma).^2)/(Sigma*sqrt(2*pi));
a=2;
b=1;
Gamma=@(x) x.^(a-1).*exp(-x/b)/((b^a).*gamma(a));
FUN=@(x) PDF_Norm(x).*Gamma(-x);
Pf=integral(@(x) FUN(x),-Inf,0);
sym x
Beta=finverse(F,x);Hi,
I would like to calculate the probability of failure using the convolution therom as described in this paper https://www.researchgate.net/publication/314278481_Reliability_Index_for_Non-normal_Distribution_of_Limit_State_Functions
First I wanted to write the code using examples of this paper (Please look at the attached screenshots). Unfortunately, I didn’t get the same results. I found a probabilty of failure Pf=3.82 10^-08 instead of 5.55 10^-02.
In addition, I am struggling to write the inverse function to derive the reliabilty index. I always leads to errors?
Can anyone explain the mistake?
Sigma= 1;
Mu=5;
PDF_Norm=@(x) exp(-0.5.*((x-Mu)/Sigma).^2)/(Sigma*sqrt(2*pi));
a=2;
b=1;
Gamma=@(x) x.^(a-1).*exp(-x/b)/((b^a).*gamma(a));
FUN=@(x) PDF_Norm(x).*Gamma(-x);
Pf=integral(@(x) FUN(x),-Inf,0);
sym x
Beta=finverse(F,x); Hi,
I would like to calculate the probability of failure using the convolution therom as described in this paper https://www.researchgate.net/publication/314278481_Reliability_Index_for_Non-normal_Distribution_of_Limit_State_Functions
First I wanted to write the code using examples of this paper (Please look at the attached screenshots). Unfortunately, I didn’t get the same results. I found a probabilty of failure Pf=3.82 10^-08 instead of 5.55 10^-02.
In addition, I am struggling to write the inverse function to derive the reliabilty index. I always leads to errors?
Can anyone explain the mistake?
Sigma= 1;
Mu=5;
PDF_Norm=@(x) exp(-0.5.*((x-Mu)/Sigma).^2)/(Sigma*sqrt(2*pi));
a=2;
b=1;
Gamma=@(x) x.^(a-1).*exp(-x/b)/((b^a).*gamma(a));
FUN=@(x) PDF_Norm(x).*Gamma(-x);
Pf=integral(@(x) FUN(x),-Inf,0);
sym x
Beta=finverse(F,x); integral, convolution MATLAB Answers — New Questions

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