rm (list = ls())
\nlibrary(timelineS)
\nlibrary(lubridate)
\nlibrary(ggplot2)
\nlibrary(dplyr)
\nlibrary(reshape2)
\nlibrary(rPref)
\nlibrary(mco)
\nlibrary(MASS)
\nplot.timeline <- function(lifetime, events.name, start.Date, plot.Name) {
\ndataP <- data.frame(Events = events.name, Event_Dates = ymd(start.Date) +
\nyears(lifetime))
\ntimelineS(dataP, main = plot.Name,
\nlabels = events.name, label.direction = “up”, label.position = 3)
\n}
\ndist.Events <- function (lifetime, events, start.Date, option.Name) {
\n#sort the events
\nevents <- sort(events, decreasing = T)
\n#create the distribution of the events
\ndistribution.events <- sapply(events, seq, from = 0, to = lifetime)<\/p>\n
#all events unlisted
\nall.events <- melt(distribution.events)
\ncolnames(all.events) <- c(“frequency”, “event”)
\n#sort the events ascending
\nall.events <- all.events[order(all.events$frequency),]
\n#get the unique sequence of events
\nunique.events <- all.events[!duplicated(all.events$frequency),]
\nunique.events$event[which(unique.events$frequency == 0)] <- “DC”
\n#plot the timeline
\nplot.timeline(unique.events$frequency, unique.events$event, start.Date, option.Name)
\nreturn(unique.events)
\n}
\ncombine.lifeTimelines <- function(product.1, product.2, p1.dur, p2.dur) {
\n#function body
\nbase <- list(Names = c(), frequency = c(), duration = c())
\nbase$frequency <- sort(unique(c(product.1$frequency,
\nproduct.2$frequency)),
\ndecreasing = FALSE)
\nbase$Names[1] <- “DC”
\nbase$duration[1] <- 0
\nbase$Names[length(base$frequency)] <- “END”
\nbase$duration[length(base$frequency)] <- 0
\nfor(index in 2:(length(base$frequency) – 1)) {
\nphase.1 <- product.1$event[which(product.1$frequency ==
\nbase$frequency[index])]
\nphase.2 <- product.2$event[which(product.2$frequency ==
\nbase$frequency[index])]
\nif(length(phase.1) != 0 && length(phase.2) != 0) {
\nbase$Names[index] <- paste(phase.1, phase.2)
\nbase$duration[index] <- max(p1.dur[which(names(p1.dur) == phase.1)],
\np2.dur[which(names(p2.dur) == phase.2)])
\n} else if(length(phase.1) != 0 && length(phase.2) == 0) {
\nbase$Names[index] <- phase.1
\nbase$duration[index] <- p1.dur[which(names(p1.dur) == phase.1)]
\n} else if (length(phase.1) == 0 && length(phase.2) != 0) {
\nbase$Names[index] <- phase.2
\nbase$duration[index] <- p2.dur[which(names(p2.dur) == phase.2)]
\n} else {
\nbase$duration[index] <- 0
\n}
\n}
\nreturn(base)
\n}
\npar(mfrow = c(2, 1))
\nstart.Date = “2020-01-01”
\nlifetime <- 100
\nevents.Op1.Bridge = c(SDO = 15, M = 5, DR = 30, END = lifetime)
\nduration.ev.Bridge <- c(SDO = 7, M = 2, DR = 21)
\nevents.Op1.Tunnel <- c(BR = 15, M.r = 7, AACL = 15, END = lifetime)
\nduration.ev.Tunnel <- c(BR = 21, M.r = 2, AACL = 14)
\ndesign.Options.Bridge <- list(desing.Op1 <- “1.Cast in place deck and steel girders”)
\ndesign.Options.Tunnel <- list(desing.Op1.Tunnel <- “Tunnel”)
\nmaintenance.Bridge <- dist.Events(lifetime, events.Op1.Bridge, start.Date, design.Options.Bridge)
\nmaintenance.Tunnel <- dist.Events(lifetime, events.Op1.Tunnel, start.Date, design.Options.Tunnel)
\nintegrated.interv <- combine.lifeTimelines(maintenance.Bridge, maintenance.Tunnel,
\nduration.ev.Bridge, duration.ev.Tunnel)
\nsum(integrated.interv$duration)
\nevents.Op1.Bridge = c(SDO = 15, M = 5, DR = 30, END = lifetime)
\nduration.ev.Bridge <- c(SDO = 7, M = 2, DR = 21)
\nevents.Op1.Tunnel <- c(BR = 17, M.r = 6, AACL = 15, END = lifetime)
\nduration.ev.Tunnel <- c(BR = 21, M.r = 2, AACL = 14)
\ndesign.Options.Bridge <- list(desing.Op1.Bridge <- “1.Cast in place deck and steel girders”)
\ndesign.Options.Tunnel <- list(desing.Op1.Tunnel <- “Tunnel”)
\nmaintenance.Bridge <- dist.Events(lifetime, events.Op1.Bridge, start.Date,
\ndesign.Options.Bridge)
\nmaintenance.Tunnel <- dist.Events(lifetime, events.Op1.Tunnel, start.Date,
\ndesign.Options.Tunnel)
\nintegrated.interv <- combine.lifeTimelines(maintenance.Bridge, maintenance.Tunnel,
\nduration.ev.Bridge, duration.ev.Tunnel)
\nsum(integrated.interv$duration)
\ndesign.explore <- function(events1, events2) {
\nresults <- c()
\nfor(i in 1: dim(events1)[1]) {
\nev1 <- unlist(events1[i, ])
\ndist.1 <- dist.Events(lifetime, ev1, start.Date, desing.Op1)
\ndur.ev1 <- ev1\/2
\nfor (j in 1: dim(events1)[1]) {
\nev2 <- unlist(events2[j, ])
\ndist.2 <- dist.Events(lifetime, ev2, start.Date, design.Options.Tunnel)
\ndur.ev2 <- ev2\/2
\ncombined.lifetime <- combine.lifeTimelines(dist.1, dist.2,
\ndur.ev1, dur.ev2)
\nmin.dist.int <- min(abs(combined.lifetime$frequency[1:(length(combined.lifetime$frequency) – 1)] –
\ncombined.lifetime$frequency[2:length(combined.lifetime$frequency)]))
\nresults <- rbind(results, c(ev1, ev2, dur = sum(combined.lifetime$duration), dist.inter = min.dist.int))
\n}
\n}
\nreturn(as.data.frame(results))
\n}
\nn.grid <- 5
\nevents.grid.bridge <- expand.grid(SDO = sample(seq(10,20, by = 1), n.grid),
\nM = sample(seq(3,8,1), n.grid),
\nDR = sample(seq(20, 35, 1), n.grid))
\nevents.grid.Tunnel <- expand.grid(BR = sample(seq(10, 20, by = 1), n.grid),
\nM.r = sample(seq(3,8,1), n.grid),
\nR.r = sample(seq(10, 20, 1), n.grid))
\nresponse.space <- design.explore(events.grid.bridge, events.grid.Tunnel)
\np <- low(dur)* high(dist.inter)
\nsky <- psel(response.space, p)
\npareto2 <- psel(response.space, p, top = nrow(response.space))
\nggplot(response.space, aes(x = dur, y = dist.inter)) +
\ngeom_point(shape = 21) +
\ngeom_point(data = pareto2, size = 3, aes(color = factor(pareto2$.level)))
\nshow_front <- function(pref) {
\nplot(response.space$dur, response.space$dist.inter)
\nsky <- psel(response.space, pref)
\nplot_front(response.space, pref, col = rgb(0, 0, 1))
\npoints(sky$dur, sky$dist.inter, lwd = 3)
\n}
\nshow_front(p)
\np <- high(dur) * low(dist.inter)
\nshow_front(p)
\nLCI.materials <- read.csv(“LCImaterials.csv”)
\nLCA.bridge <- function(length, width, height, thickness, girder.Option,
\ndeck.Option, materials, dist.event) {
\nprefab.girder.Section <- 0.78
\nsteel.girders.unitWeight <- 317
\nasphalt.Q <- length * width * thickness
\n#based on the use of each material, we will split the data frame
\nmaterials.split <- split(materials, materials$scope)<\/p>\n
#new line to get the interventions
\ns <- summary(as.factor(dist.event$event))
\ns2 <- as.data.frame(rbind(Freq = s), stringsAsFactors=F, row.names = 1:length(s))<\/p>\n
# calculate the volume of the deck based on different materials strategies
\nif(deck.Option == “RC”) {
\ndeck.volume <- length * width * height
\ninterventions.deck <- s2$DC + s2$DR + 0.25 * s2$SDO + 0.35 * (if (!is.null(s2$PR)) {s2$PR}
\nelse {0})
\n} else if (deck.Option == “PC”) {
\ndeck.volume <- 10.2*length
\ninterventions.deck <- s2$DC + s2$BR + 0.25 * s2$AACL + 0.35 * (if (!is.null(s2$PF))
\n{s2$PF} else {0})<\/p>\n
}
\n#girder options
\nif (girder.Option == “steel”) {
\n#get the numbers of girders
\nn <-round(width \/ 3, 0)
\ninterventions.girders <- s2$DC + if (!is.null(s2$DR)) {s2$DR} else{ 0 } + 0.55 * (if(!is.null(s2$PR)) {s2$PR} else {0})<\/p>\n
#get the volume of the concrete for the prefab girders
\ngirders.V <- n * steel.girders.unitWeight * length
\n} else if (girder.Option == “C”) {
\nn <- 0
\ngirders.V <- 7.85*0.05*0.65*(11.3-10)*6*666
\ninterventions.girders <- s2$DC + if (!is.null(s2$BR)) {s2$BR} else{ 0 } + 0.55 * (if(!is.null(s2$AACL)) {s2$AACL} else {0})<\/p>\n
}<\/p>\n
asph.interventions = length(dist.event$event)-1
\nasphalt <- mutate(materials.split$asphalt, bridge.Q = asphalt.Q, interventions =
\nasph.interventions)
\ndeck <- mutate(materials.split[[deck.Option]], bridge.Q = deck.volume, interventions =
\ninterventions.deck)<\/p>\n
girders <- mutate(materials.split[[girder.Option]], bridge.Q = girders.V, interventions =
\ninterventions.girders)
\nLCA.matrix <- rbind(deck, girders, asphalt)
\nLCA.matrix <- mutate(LCA.matrix, TotalMaterials.Q = quantities * bridge.Q \/ 1000,
\nmaterials.LC = TotalMaterials.Q * interventions,
\nEnergy.LC = materials.LC * energy,
\nCO2.LC = materials.LC * CO2 * 1000,
\nNOx.LC = materials.LC * NOx * 1000,
\nSO2.LC = materials.LC * SO2 * 1000)
\nLCA.results <- list(Energy = sum(LCA.matrix$Energy.LC),
\nCO2 = sum(LCA.matrix$CO2.LC),
\nNOx = sum(LCA.matrix$NOx.LC),
\nSO2 = sum(LCA.matrix$SO2.LC))<\/p>\n
return(LCA.results)
\n}
\nb.length <- 500 # units: m
\nb.width <- 15 #units: m
\nbd.depth <- 0.35 #units: m
\nasphalt.tk <- 0.12 #units: m
\nt.depth <- 0.35 #units: m
\nt.lenght <- 1000 #m 100 meters on each side of the bridge
\ngirder.Options <- c(“steel”, “C”)
\ndeck.options <- c(“RC”, “PC”)
\nOption.bridge <- LCA.bridge(b.length, b.width, bd.depth, asphalt.tk,
\ngirder.Options[1], deck.options[1], LCI.materials, maintenance.Bridge)
\nOption.Tunnel <- LCA.bridge(t.lenght, b.width, t.depth, asphalt.tk,
\ngirder.Options[2], deck.options[2], LCI.materials, maintenance.Tunnel)
\nintegrated.Design <- as.data.frame(list(Energy = Option.bridge$Energy + Option.Tunnel$Energy,
\nCO2 = Option.bridge$CO2 + Option.Tunnel$CO2,
\nNOx = Option.bridge$NOx + Option.Tunnel$NOx,
\nSO2 = Option.bridge$SO2 + Option.Tunnel$SO2))
\nEnergy.costs <- 0.128
\nCO2.unitcost <- 26 # per metric tone
\nNOx.unitCost <- 42 # per metric tone
\nSO2.unitCosts <- 85 # per metric tone
\nintegrated.Design <- mutate(integrated.Design,
\nCosts = (Energy * Energy.costs +
\nCO2*CO2.unitcost +
\nNOx * NOx.unitCost +
\nSO2 * SO2.unitCosts)\/10^9)
\nfitness <- function(x) {
\n#define the output dimension
\nz <- numeric(7)
\n#function body
\nx <- round(x, 0)
\ny <- expand.grid(SDO = x[1], M = x[2], DR = x[3], BR = x[4], M.r = x[5], AACL = x[6])<\/p>\n
dur.ev1 <- unlist(y[1:3] \/ 2)
\ndur.ev2 <- unlist(y[4:6] \/ 2)<\/p>\n
dist.1 <- apply(y[1:3], 1, FUN = dist.Events, lifetime = lifetime, start.Date = start.Date,design.Options.Bridge)
\ndist.2 <- apply(y[4:6], 1, FUN = dist.Events, lifetime = lifetime, start.Date = start.Date,design.Options.Tunnel)
\nresults <- combine.lifeTimelines(dist.1[[1]], dist.2[[1]], dur.ev1, dur.ev2)
\nz[1] <- sum(results[[“duration”]])
\nz[2] <- -min(abs(results$frequency[1:(length(results$frequency) – 1)] –
\nresults$frequency[2:length(results$frequency)]))
\nb.width <- x[7]
\nb.length <- 25 # units: m
\nbd.depth <- 0.35 #units m
\nasphalt.tk <- 0.12 #units m
\nt.depth <- 0.35 #units: m
\nt.lenght <- 1000 #m 100 meters on each side of the bridge
\nmaterials <- LCI.materials
\ngirder.Options <- c(“steel”, “C”)
\ndeck.options <- c(“RC”, “PC”)
\nEnergy.costs <- 0.128
\nCO2.unitcost <- 26
\nNOx.unitCost <- 42
\nSO2.unitCosts <- 85
\nproduct.1.bridge <- LCA.bridge(b.length, b.width, bd.depth, asphalt.tk,
\ngirder.Options[1], deck.options[1], LCI.materials, dist.1[[1]])<\/p>\n
product.2.Tunnel <- LCA.bridge(t.lenght, b.width, t.depth, asphalt.tk,
\ngirder.Options[2], deck.options[2], LCI.materials, dist.2[[1]])<\/p>\n
integrated.system <- as.data.frame(list(Energy = product.1.bridge$Energy +
\nproduct.2.Tunnel$Energy,
\nCO2 = product.1.bridge$CO2 + product.2.Tunnel$CO2,
\nNOx = product.1.bridge$NOx + product.2.Tunnel$NOx,
\nSO2 = product.1.bridge$SO2 + product.2.Tunnel$SO2))
\nintegrated.system <- mutate(integrated.system,
\nCosts = (Energy * Energy.costs +
\nCO2*CO2.unitcost +
\nNOx * NOx.unitCost +
\nSO2 * SO2.unitCosts)\/10^9)
\nz[3] <- integrated.system$Energy
\nz[4] <- integrated.system$CO2
\nz[5] <- integrated.system$NOx
\nz[6] <- integrated.system$SO2
\nz[7] <- integrated.system$Costs
\nreturn(z)
\n}
\nr2 <- nsga2(fitness, idim = 7, odim = 7,
\ngenerations=5, popsize=4,
\nlower.bounds=c(10, 3, 20, 10, 10, 3, 25),
\nupper.bounds= c(20, 8, 35, 20, 20, 8, 45))
\nr2 <- nsga2(fitness, idim = 7, odim = 7,
\ngenerations=10, popsize=100,
\nlower.bounds=c(10, 3, 20, 12, 4, 27, 25),
\nupper.bounds= c(20, 8, 35, 25, 10, 37, 45))
\nr2Results <- as.data.frame(r2$value)
\noutNames <- c(“duration”, “interv.dist”, “energy”, “co2”, “nox”, “so2”, “cost” )
\ncolnames(r2Results) <- outNames
\npareto3 <- as.data.frame(paretoFront(r2))
\ncolnames(pareto3) <- outNames
\nggplot(r2Results, aes(x = duration, y = cost)) + geom_point(shape = 21) +
\ngeom_point(data = pareto3, size = 3, color=”red”) +
\ngeom_line(data = pareto3, color=”blue”)
\ninput.params <- round(r2$par, 0)
\nall.results <- cbind(input.params, r2Results, r2$pareto.optimal)
\ncolnames(all.results) <- c(“SDO”, “M”, “DR”,
\n“BR”, “M.r”, “AACL”,
\n“b.width”, “duration”, “interv.dist”,
\n“energy”, “co2”, “nox”, “so2”, “cost”,
\n“pareto”)
\npar(mfrow = c(1,1))
\nparcoord(all.results[, 1:14], var.label = T,
\ncol = ifelse(all.results$pareto == TRUE, “indianred”, “skyblue2”),
\nlty = ifelse(all.results$pareto == TRUE, 1, 3),
\nlwd = ifelse(all.results$pareto == TRUE, 3, 1))<\/p>\n","protected":false},"excerpt":{"rendered":"
rm (list = ls()) library(timelineS) library(lubridate) library(ggplot2) library(dplyr) library(reshape2) library(rPref) library(mco) library(MASS) plot.timeline <- function(lifetime, events.name, start.Date, plot.Name) { dataP <- data.frame(Events = events.name, Event_Dates = ymd(start.Date) + years(lifetime)) timelineS(dataP, main = plot.Name, labels =Continue reading<\/a><\/p>\n","protected":false},"author":148,"featured_media":0,"parent":9274,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-10118","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/10118","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/users\/148"}],"replies":[{"embeddable":true,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=10118"}],"version-history":[{"count":1,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/10118\/revisions"}],"predecessor-version":[{"id":10120,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/10118\/revisions\/10120"}],"up":[{"embeddable":true,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/9274"}],"wp:attachment":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10118"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}