examples: Examples

In ipptoolbox: IPP Toolbox

Description

Two self-contained examples, see commented code.

Usage

dsfcruesexample()
dsexample()

Details

Please see the code of the examples.

Author(s)

Philipp Limbourg <[e-mail]>

References

Philipp Limbourg, Etienne de Rocquigny (2010). Uncertainty analysis using evidence theory - confronting level-1 and level-2 approaches with data availability and computational constraints. Rel. Eng. & Sys. Safety 95(5): 550-564

Philipp Limbourg, Robert Savic et al. (2007). Fault Tree Analysis in an Early Design Stage using the Dempster-Shafer Theory of Evidence. European Conference on Safety and Reliability - ESREL 2007, Stavanger, Norway, Taylor and Francis.

Examples

print("Example Fcrues")
print("See code")
print(dsfcruesexample)
print("Execute example")
dsfcruesexample()

Example output

Loading required package: AlgDesign
Loading required package: copula
Loading required package: evd
Loading required package: triangle
Loading required package: kolmim
[1] "Example Fcrues"
[1] "See code"
function () 
{
    Qdonnes = c(3854, 1256, 1649, 1605, 341, 1149, 868, 1148, 
        1227, 1991, 1255, 1366, 1100, 1837, 351, 1084, 1924, 
        843, 2647, 1248, 2417, 1125, 903, 1462, 378, 1230, 1149, 
        1400, 2078, 1433, 917, 1530, 2442, 2151, 1909, 630, 2435, 
        1920, 1512, 1377, 3330, 1858, 1359, 714, 1528, 1035, 
        1026, 1127, 1839, 771, 1730, 1889, 3320, 352, 885, 759, 
        731, 1711, 1906, 1543, 1307, 1275, 2706, 582, 1260, 1331, 
        1283, 1348, 1048, 1348, 383, 1526, 789, 811, 1073, 965, 
        619, 3361, 523, 493, 424, 2017, 1958, 3192, 1556, 1169, 
        1511, 1515, 2491, 881, 846, 856, 1036, 1830, 1391, 1334, 
        1512, 1792, 136, 891, 635, 733, 758, 1368, 935, 1173, 
        547, 669, 331, 227, 2037, 3224, 1525, 766, 1575, 1695, 
        1235, 1454, 2595, 706, 1837, 1629, 1421, 2204, 956, 971, 
        1383, 541, 703, 2090, 800, 651, 1153, 704, 1771, 1433, 
        238, 122, 1306, 733, 793, 856, 1903, 1594, 740, 3044, 
        1128, 522, 642)
    Zmdonnes = c(55.09, 55, 54.87, 54.28, 54.74, 55.48, 55.36, 
        55.39, 54.8, 55.18, 54.94, 54.42, 55.34, 55.3, 54.31, 
        55.57, 54.28, 55.49, 54.49, 55.11, 55.15, 54.4, 55.87, 
        55.63, 54.93, 55.61, 54.95, 55.38, 54.57)
    Zvdonnes = c(50.39, 50.28, 50.23, 49.92, 50.51, 50.42, 50.16, 
        50.16, 49.76, 50.17, 50.71, 50.08, 49.95, 50.63, 49.51, 
        50.77, 49.98, 50.3, 50.1, 50.12, 50.54, 49.21, 50.55, 
        50.67, 50, 50.7, 50.27, 50.06, 49.49)
    Qlimits = c(10, 10000)
    Kslimits = c(5, 60)
    Zvlimits = c(48, 52.8)
    Zmlimits = c(53.2, 58)
    a = dsstruct(c(1000, 1040, 1))
    b = 558
    Q = dsadf("qgumbel", 10000, a, b)
    QlimitsBPA = dsstruct(c(Qlimits, 1))
    Q = dsdempstersrule(Q, QlimitsBPA)
    dscdf(Q, xlab = "Q", ylab = "")
    dev.new()
    dsqqplot(Q, Qdonnes)
    p = dskstest(Qdonnes, Q)
    print("K-S probability is:")
    print(p)
    Ks1 = dsminmeanmax(1000, 5, 30, 60)
    Ks2 = dsstruct(rbind(c(5, 20, 0.05), c(20, 40, 0.9), c(40, 
        60, 0.05)))
    dev.new()
    dscdf(Ks1, xlab = "Ks")
    dev.new()
    dscdf(Ks2, xlab = "Ks")
    dev.new()
    Ks = dsintersect(Ks1, Ks2)
    dscdf(Ks, xlab = "Ks", ylab = "")
    Zv = dslapconf(Zvdonnes, Zvlimits)
    dev.new()
    dscdf(Zv, xlab = "Zv")
    Zm = dsksconf(Zmdonnes, conf = 0.5, Zmlimits)
    dev.new()
    dscdf(Zm, xlab = "Zm")
    fcrue = function(x, ...) {
        Q = x[, 1]
        Ks = x[, 2]
        Zm = x[, 3]
        Zv = x[, 4]
        const = 1
        length = 5000
        B = 300
        result = Zv + (pmax(Q, 0) * const/(pmax(Ks, 0) * B * 
            sqrt((Zm - Zv)/length)))^0.6
    }
    temp = dsevalmc(fcrue, list(Q, Ks, Zm, Zv), 10000, dsmonotonous)
    Zc = temp[[1]]
    dev.new()
    dscdf(Zc, xlab = "Zc", ylab = "", xrange = c(48, 65))
    print("Median")
    print(dsconf(Zc, 0.5))
    print("Q99 with 95% Wilks bounds")
    print(dsconf(Zc, 0.99, 0.95))
    print("Bel/Pl(Zc<=55.5)")
    print(dsbelpl(Zc, c(-Inf, 55.5)))
    print("Bel/Pl(Zc>=55.5)")
    print(dsbelpl(Zc, c(55.5, Inf)))
    print("Exp. value")
    print(dsexpect(Zc))
    print("Variance, standard deviation")
    print(dsvariance(Zc))
    print(sqrt(dsvariance(Zc)))
    print("Aggregated width")
    print(dsaggwidth(Zc))
    sens = (dssensitivity(list(Q, Ks, Zm, Zv), c(1, 2, 3, 4), 
        fcrue, dsaggwidth, mcIT = 20, pinch_samples = 20, pinch_type = "distribution"))
    dev.new()
    barplot(sens, beside = TRUE, names = list("Q", "Ks", "Zm", 
        "Zv"))
    title("Sensitivity on aggregated width")
    temp = dsevalmc(fcrue, list(Q, Ks, Zm, Zv), 10000, dsmonotonous, 
        corr = c(0, 0, 0, 0, 0, 0.66))
    Zccorr = temp[[1]]
    dev.new()
    dscdf(Zccorr, xlab = "Zccorr", ylab = "", xrange = c(48, 
        65))
}
<bytecode: 0x5639840b0ed8>
<environment: namespace:ipptoolbox>
[1] "Execute example"
[1] "K-S probability is:"
[1] 0.9998713
dev.new(): using pdf(file="Rplots1.pdf")
dev.new(): using pdf(file="Rplots2.pdf")
dev.new(): using pdf(file="Rplots3.pdf")
dev.new(): using pdf(file="Rplots4.pdf")
[1] 0.1483171
dev.new(): using pdf(file="Rplots5.pdf")
dev.new(): using pdf(file="Rplots6.pdf")
[1] "Median"
[1] 52.19120 53.38995
[1] "Q99 with 95% Wilks bounds"
             [,1]     [,2]
y        54.60330 60.32616
confup   54.68547 60.72992
confdown 54.50539 60.00968
[1] "Bel/Pl(Zc<=55.5)"
[1] 0.8954 0.9985
[1] "Bel/Pl(Zc>=55.5)"
[1] 0.0015 0.1046
[1] "Exp. value"
[1] 52.20070 53.69626
[1] "Variance, standard deviation"
[1] 0.3517785 4.5207843
[1] 0.5931092 2.1262136
[1] "Aggregated width"
[1] 1.495556
dev.new(): using pdf(file="Rplots7.pdf")
dev.new(): using pdf(file="Rplots8.pdf")

ipptoolbox documentation built on May 2, 2019, 2:09 a.m.