PROPAG: Function for conducting joint propagation of uncertainty
In HYRISK: Hybrid Methods for Addressing Uncertainty in RISK Assessments
Description
Usage
Arguments
Details
Value
References
See Also
Examples
Description
Function for conducting joint propagation of probability, imprecise probability and possibilisty distributions (or intervals) using IRS (Baudrit et al., 2006) or hybrid method (Guyonnet et al., 2003).
Usage
1
2
Arguments
N
Integer corresponding to the number of random samples.
input
List of inputs as provided by the function CREATE_INPUT().
FUN
Model assessment function.
choice_opt
Option for the constrainted optimization algorithm:
"L-BFGS-B": Limited-memory BFGS based on optimr package.
"L-BFGS-B_MULTI": Limited-memory BFGS with multiple starts.
"GENOUD": genetic algorithm plus derivative optimizer based on rgenoud package, see Mebane & Sekhon (2011).
param_opt
Parameters needed by the optimization algorithm:
If "L-BFGS-B": param_opt=NULL.
If "L-BFGS-B_MULTI": param_opt specifies the number of multi starts (e.g. 10).
If "GENOUD": param_opt specifies vector of paramters (population size, maxixmum of generations, solution tolerance), see Mebane & Sekhon (2011).
mode
Type of hybrid uncertainty propagation:
"IRS" Independent Random Sampling of Baudrit et al. (2007).
"HYBRID" Hybrid propagation described by Baudrit et al. (2006).
corr
Tolerance to avoid empty alpha-cuts. By default, corr=0.01.
NL
Integer to specify the number of alpha-cuts needed for hybrid propagation described by Baudrit et al. (2006). By default, NL=10.
Details
Details of the theory and example 1 in Dubois & Guyonnet (2011), available at:
https://hal-brgm.archives-ouvertes.fr/file/index/docid/578821/filename/Uncertainties_RA_09_l_dg.pdf
Details on the representation via imprecise probability distributions in Pedroni et al. (2013).
Details on example 2 in Sch\"obi & Sudret (2016), available at:
https://arxiv.org/pdf/1608.05565.pdf
Value
Matrix Z0 of 2 rows and N columns (for IRS mode) or NxNL (for HYBRID mode).
This corresponds to the set of random intervals (row Number 1: lower bound; row Number 2: upper bound), which can be summarized in different forms, see Baudrit et al. (2006).
References
Baudrit, C., Dubois, D., & Guyonnet, D. 2006. Joint propagation and exploitation of probabilistic and possibilistic information in risk assessment. IEEE transactions on fuzzy systems, 14(5), 593-608.
Baudrit, C., Guyonnet, D., Dubois, D. 2007. Joint propagation of variability and partial ignorance in a groundwater risk assessment. Journal of Contaminant Hydrology, 93: 72-84.
Mebane, W., Jr. and Sekhon, J. S. 2011. Genetic Optimization Using Derivatives: The rgenoud package for R. Journal of Statistical Software, 42(11): 1-26.
Pedroni, N., Zio, E., Ferrario, E., Pasanisi, A., & Couplet, M. 2013. Hierarchical propagation of probabilistic and non-probabilistic uncertainty in the parameters of a risk model. Computers & Structures, 126, 199-213.
Sch\"obi, R., Sudret, B. 2016. Uncertainty propagation of p-boxes using sparse polynomial chaos expansions, https://arxiv.org/pdf/1608.05565.pdf
See Also
CREATE_INPUT
CREATE_DISTR
PLOT_CDF
Examples
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## Not run:
#################################################
#### EXAMPLE 1 of Dubois & Guyonnet (2011)
#### Probability and Possibility distributions
#################################################
#### Model function
FUN<-function(X){
UER=X[1]
EF=X[2]
I=X[3]
C=X[4]
ED=X[5]
return(UER*I*C*EF*ED/(70*70*365))
}
ninput<-5 #Number of input parameters
input<-vector(mode="list", length=ninput) # Initialisation
input[[1]]=CREATE_INPUT(
name="UER",
type="possi",
distr="triangle",
param=c(2.e-2, 5.7e-2, 1.e-1),
monoton="incr"
)
input[[2]]=CREATE_INPUT(
name="EF",
type="possi",
distr="triangle",
param=c(200,250,350),
monoton="incr"
)
input[[3]]=CREATE_INPUT(
name="I",
type="possi",
distr="triangle",
param=c(1,1.5,2.5),
monoton="incr"
)
input[[4]]=CREATE_INPUT(
name="C",
type="proba",
distr="triangle",
param=c(5e-3,20e-3,10e-3)
)
input[[5]]=CREATE_INPUT(
name="ED",
type="proba",
distr="triangle",
param=c(10,50,30)
)
####CREATION OF THE DISTRIBUTIONS ASSOCIATED TO THE PARAMETERS
input=CREATE_DISTR(input)
####VISU INPUT
PLOT_INPUT(input)
#################################################
#### PROPAGATION
#OPTIMZATION CHOICES
choice_opt=NULL #no optimization needed
param_opt=NULL
#PROPAGATION RUN
Z0_IRS<-PROPAG(N=1000,input,FUN,choice_opt,param_opt,mode="IRS")
Z0_HYBRID<-PROPAG(N=250,input,FUN,choice_opt,param_opt,mode="HYBRID")
#################################################
#### POST-PROCESSING
# VISU - PROPAGATION
PLOT_CDF(Z0_IRS,xlab="Z",ylab="CDF",main="EX 1",lwd=1.5)
PLOT_CDF(Z0_HYBRID,new=FALSE,color1=3,color2=4,lwd=1.5)
#################################################
#### EXAMPLE 2 of Schobi & Sudret (2016)
#### Imprecise Probability distributions
#################################################
#### Model function
FUN<-function(X){
A=X[1]
B=X[2]
return(100*(B-A^2)^2+(1-A)^2)
}
ninput<-6 #Number of input parameters
input<-vector(mode="list", length=ninput) # Initialisation
# Imprecise normal probability
# whose parameters are described by the 3rd and 5th parameters
input[[1]]=CREATE_INPUT(
name="A",
type="impr proba",
distr="normal",
param=c(3,5),
monoton="dunno"
)
# Imprecise normal probability
# whose parameters are described by the 4th and 6th parameters
input[[2]]=CREATE_INPUT(
name="B",
type="impr proba",
distr="normal",
param=c(4,6),
monoton="dunno"
)
# imprecise paramters of afore-described probability distribution
# mean of input number 1 as an interval
input[[3]]=CREATE_INPUT(
name="mu_A",
type="possi",
distr="interval",
param=c(-0.5,0.5)
)
# mean of input number 2 as an interval
input[[4]]=CREATE_INPUT(
name="mu_B",
type="possi",
distr="interval",
param=c(-0.5,0.5)
)
# standard deviation of input number 1 as an interval
input[[5]]=CREATE_INPUT(
name="s_A",
type="possi",
distr="interval",
param=c(0.7,1)
)
# standard deviation of input number 2 as an interval
input[[6]]=CREATE_INPUT(
name="s_B",
type="possi",
distr="interval",
param=c(0.7,1)
)
####CREATION OF THE DISTRIBUTIONS ASSOCIATED TO THE PARAMETERS
input=CREATE_DISTR(input)
####VISU INPUT (needs propagation parameters to plot impr proba distributions)
PLOT_INPUT(input)
#################################################
### PROPAGATION
# OPTIMZATION CHOICES (could take some time)
choice_opt="GENOUD"
param_opt=c(50,3,1.e-1)
#PROPAGATION RUN
Z0_IRS<-PROPAG(N=1000,input,FUN,choice_opt,param_opt,mode="IRS")
#################################################
### VISU - PROPAGATION
PLOT_CDF(Z0_IRS,xlab="Z",ylab="CDF",main="EX 2",lwd=1.5)
## End(Not run)
HYRISK documentation built on May 2, 2019, 12:54 p.m.
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Description Usage Arguments Details Value References See Also Examples
Description
Function for conducting joint propagation of probability, imprecise probability and possibilisty distributions (or intervals) using IRS (Baudrit et al., 2006) or hybrid method (Guyonnet et al., 2003).
Usage
1 2 |
Arguments
N |
Integer corresponding to the number of random samples. |
input |
List of inputs as provided by the function CREATE_INPUT(). |
FUN |
Model assessment function. |
choice_opt |
Option for the constrainted optimization algorithm:
|
param_opt |
Parameters needed by the optimization algorithm:
|
mode |
Type of hybrid uncertainty propagation:
|
corr |
Tolerance to avoid empty alpha-cuts. By default, corr=0.01. |
NL |
Integer to specify the number of alpha-cuts needed for hybrid propagation described by Baudrit et al. (2006). By default, NL=10. |
Details
Details of the theory and example 1 in Dubois & Guyonnet (2011), available at: https://hal-brgm.archives-ouvertes.fr/file/index/docid/578821/filename/Uncertainties_RA_09_l_dg.pdf
Details on the representation via imprecise probability distributions in Pedroni et al. (2013).
Details on example 2 in Sch\"obi & Sudret (2016), available at: https://arxiv.org/pdf/1608.05565.pdf
Value
Matrix Z0 of 2 rows and N columns (for IRS mode) or NxNL (for HYBRID mode). This corresponds to the set of random intervals (row Number 1: lower bound; row Number 2: upper bound), which can be summarized in different forms, see Baudrit et al. (2006).
References
Baudrit, C., Dubois, D., & Guyonnet, D. 2006. Joint propagation and exploitation of probabilistic and possibilistic information in risk assessment. IEEE transactions on fuzzy systems, 14(5), 593-608.
Baudrit, C., Guyonnet, D., Dubois, D. 2007. Joint propagation of variability and partial ignorance in a groundwater risk assessment. Journal of Contaminant Hydrology, 93: 72-84.
Mebane, W., Jr. and Sekhon, J. S. 2011. Genetic Optimization Using Derivatives: The rgenoud package for R. Journal of Statistical Software, 42(11): 1-26.
Pedroni, N., Zio, E., Ferrario, E., Pasanisi, A., & Couplet, M. 2013. Hierarchical propagation of probabilistic and non-probabilistic uncertainty in the parameters of a risk model. Computers & Structures, 126, 199-213.
Sch\"obi, R., Sudret, B. 2016. Uncertainty propagation of p-boxes using sparse polynomial chaos expansions, https://arxiv.org/pdf/1608.05565.pdf
See Also
CREATE_INPUT
CREATE_DISTR
PLOT_CDF
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 | ## Not run:
#################################################
#### EXAMPLE 1 of Dubois & Guyonnet (2011)
#### Probability and Possibility distributions
#################################################
#### Model function
FUN<-function(X){
UER=X[1]
EF=X[2]
I=X[3]
C=X[4]
ED=X[5]
return(UER*I*C*EF*ED/(70*70*365))
}
ninput<-5 #Number of input parameters
input<-vector(mode="list", length=ninput) # Initialisation
input[[1]]=CREATE_INPUT(
name="UER",
type="possi",
distr="triangle",
param=c(2.e-2, 5.7e-2, 1.e-1),
monoton="incr"
)
input[[2]]=CREATE_INPUT(
name="EF",
type="possi",
distr="triangle",
param=c(200,250,350),
monoton="incr"
)
input[[3]]=CREATE_INPUT(
name="I",
type="possi",
distr="triangle",
param=c(1,1.5,2.5),
monoton="incr"
)
input[[4]]=CREATE_INPUT(
name="C",
type="proba",
distr="triangle",
param=c(5e-3,20e-3,10e-3)
)
input[[5]]=CREATE_INPUT(
name="ED",
type="proba",
distr="triangle",
param=c(10,50,30)
)
####CREATION OF THE DISTRIBUTIONS ASSOCIATED TO THE PARAMETERS
input=CREATE_DISTR(input)
####VISU INPUT
PLOT_INPUT(input)
#################################################
#### PROPAGATION
#OPTIMZATION CHOICES
choice_opt=NULL #no optimization needed
param_opt=NULL
#PROPAGATION RUN
Z0_IRS<-PROPAG(N=1000,input,FUN,choice_opt,param_opt,mode="IRS")
Z0_HYBRID<-PROPAG(N=250,input,FUN,choice_opt,param_opt,mode="HYBRID")
#################################################
#### POST-PROCESSING
# VISU - PROPAGATION
PLOT_CDF(Z0_IRS,xlab="Z",ylab="CDF",main="EX 1",lwd=1.5)
PLOT_CDF(Z0_HYBRID,new=FALSE,color1=3,color2=4,lwd=1.5)
#################################################
#### EXAMPLE 2 of Schobi & Sudret (2016)
#### Imprecise Probability distributions
#################################################
#### Model function
FUN<-function(X){
A=X[1]
B=X[2]
return(100*(B-A^2)^2+(1-A)^2)
}
ninput<-6 #Number of input parameters
input<-vector(mode="list", length=ninput) # Initialisation
# Imprecise normal probability
# whose parameters are described by the 3rd and 5th parameters
input[[1]]=CREATE_INPUT(
name="A",
type="impr proba",
distr="normal",
param=c(3,5),
monoton="dunno"
)
# Imprecise normal probability
# whose parameters are described by the 4th and 6th parameters
input[[2]]=CREATE_INPUT(
name="B",
type="impr proba",
distr="normal",
param=c(4,6),
monoton="dunno"
)
# imprecise paramters of afore-described probability distribution
# mean of input number 1 as an interval
input[[3]]=CREATE_INPUT(
name="mu_A",
type="possi",
distr="interval",
param=c(-0.5,0.5)
)
# mean of input number 2 as an interval
input[[4]]=CREATE_INPUT(
name="mu_B",
type="possi",
distr="interval",
param=c(-0.5,0.5)
)
# standard deviation of input number 1 as an interval
input[[5]]=CREATE_INPUT(
name="s_A",
type="possi",
distr="interval",
param=c(0.7,1)
)
# standard deviation of input number 2 as an interval
input[[6]]=CREATE_INPUT(
name="s_B",
type="possi",
distr="interval",
param=c(0.7,1)
)
####CREATION OF THE DISTRIBUTIONS ASSOCIATED TO THE PARAMETERS
input=CREATE_DISTR(input)
####VISU INPUT (needs propagation parameters to plot impr proba distributions)
PLOT_INPUT(input)
#################################################
### PROPAGATION
# OPTIMZATION CHOICES (could take some time)
choice_opt="GENOUD"
param_opt=c(50,3,1.e-1)
#PROPAGATION RUN
Z0_IRS<-PROPAG(N=1000,input,FUN,choice_opt,param_opt,mode="IRS")
#################################################
### VISU - PROPAGATION
PLOT_CDF(Z0_IRS,xlab="Z",ylab="CDF",main="EX 2",lwd=1.5)
## End(Not run)
|
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