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02 Analysis.R
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02 Analysis.R
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pacman::p_load(tidyverse, magrittr, ggthemr, hrbrthemes, stringr)
apply_partition_curve = function(float_sink_table, ep = 0.005, cutpoint = 1.5, t_0 = 0, t_100 = 100){
# Requires a tibble with a floats column <dbl>
float_sink_table %>%
mutate(recovery_to_product = (100 - (t_0 + (t_100 - t_0) / (1 + exp((1.0986 * (cutpoint - floats) / ep))))) / 100,
recovery_to_reject = 1 - recovery_to_product,
cutpoint = cutpoint,
ep = ep,
t_0 = t_0,
t_100 = t_100)
}
source("02 Apply Partition Curve.R")
#Demonstrate Apply Partition Curve
df = data.frame(floats = seq(from = 1, to = 2.2, by = 0.005))
partition_curve = df %>%
apply_partition_curve(ep = 0.05)
## Plot partition Curve
partition_curve %>% ggplot(aes(floats, recovery_to_product)) +
theme_ipsum()+
geom_line()+
scale_y_continuous(labels = scales::percent_format())+
labs(title = "JKMRC Partition Curve",
subtitle = "D50 = 1.5 SG, Ep = 0.05",
x = "SG",
y = "Recovery to Product (%)")
ggsave(
"plot/04 Partition Curve.png",
width = 7.5,
height = 5,
units = "cm",
scale = 3
)
## Demonstrate Mapping
Eps = seq(0.005, 0.2, 0.02)
partition_curves = Eps %>% map_df(~ apply_partition_curve(df, ep=.), .id = "Ep")
head(partition_curves)
# Note Ep column is just an identifier, not value used
partition_curves = Eps %>% map_df(~mutate(apply_partition_curve(df, ep=.),Ep = .))
head(partition_curves)
partition_curves %>% ggplot(aes(x = floats,
y = recovery_to_product,
colour = Ep,
group = Ep)) +
theme_ipsum()+
geom_line()+
scale_y_continuous(labels = scales::percent_format())+
labs(title = "JKMRC Partition Curves",
subtitle = "D50 = 1.5 SG",
x = "SG",
y = "Recovery to Product (%)")+
theme(
legend.position = c(.95, .95),
legend.direction = "horizontal",
legend.justification = c("right", "top"),
legend.box.just = "right",
legend.margin = margin(6, 6, 6, 6),
legend.box.background = element_rect(colour = "white")
)
ggsave(
"plot/05 Partition Curves.png",
width = 7.5,
height = 5,
units = "cm",
scale = 3
)
float_sink = read_csv("data/02 float sink.csv") %>%
mutate(float_sink_fraction = str_replace_all(float_sink_fraction," - ","\n"))
float_sink %>%
ggplot(aes(x = float_sink_fraction, y = fraction_mass/100))+
geom_col(fill="black")+
theme_ipsum()+
scale_y_continuous(labels = scales::percent_format())+
labs(title = "Float Sink Mass Fractions",
x = "SG",
y = "Mass Fraction (%)")
ggsave(
"plot/06 Float Sinks.png",
width = 7.5,
height = 5,
units = "cm",
scale = 3
)
partition_results = float_sink %>% apply_partition_curve(cutpoint = 1.6, ep = 0.05) %>%
mutate(Product = fraction_mass * recovery_to_product,
Reject = fraction_mass * recovery_to_reject)
partition_results %>%
gather(key,value, -(1:11)) %>%
mutate(key = factor(key, c("Reject","Product"))) %>%
ggplot(aes(x = float_sink_fraction,
y = value/100,
fill = key))+
geom_col()+
scale_fill_ipsum()+
theme_ipsum()+
scale_y_continuous(labels = scales::percent_format())+
labs(title = "Partition of Float Sinks",
x = "SG",
y = "Mass Fraction (%)")+
no_legend_title()+
theme(
legend.position = c(.95, .95),
legend.direction = "horizontal",
legend.justification = c("right", "top"),
legend.box.just = "right",
legend.margin = margin(6, 6, 6, 6),
legend.box.background = element_rect(colour = "white")
)
ggsave(
"plot/07 Float Sinks Partitioned.png",
width = 7.5,
height = 5,
units = "cm",
scale = 3
)
# Write a summary function
partition_yields = function(tbl){
tbl %>% mutate(product_mass = fraction_mass * recovery_to_product,
product_ash = fraction_ash * product_mass,
reject_mass = fraction_mass * recovery_to_reject,
reject_ash = fraction_ash * reject_mass) %>%
select(product_mass, product_ash, reject_mass, reject_ash) %>%
summarise_all(sum) %>%
mutate(product_ash = product_ash / product_mass,
reject_ash = reject_ash / reject_mass) %>%
bind_cols(tbl %>% select(cutpoint:t_100) %>% unique())
}
# works for one cutpoint
partition_results %>% partition_yields()
# Now try for many cutpoints
cutpoints = seq(1.2, 1.8, 0.01)
# Use map from purrr to run with various inputs
# use an anonymous function because the argument we want to change
# isn't the first one, otherwise we'd just call the function.
# last line outputs a dataframe and the map_df call binds them
df_partition_yields = cutpoints %>%
map(~ apply_partition_curve(
float_sink_table = float_sink,
cutpoint = .,
ep = 0.05
)) %>%
map_df(partition_yields)
head(df_partition_yields)
# now we are plotting the summaries of many simulations
df_partition_yields %>%
ggplot(aes(x = cutpoint,
y = product_mass/100)) +
geom_line() +
theme_ipsum()+
scale_y_continuous(labels = scales::percent_format(),
limits = c(0,1))+
labs(title = "Model Yield",
subtitle = "Ep = 0.05",
x = "Cutpoint",
y = "Product Yield")
ggsave(
"plot/08 Model Yields.png",
width = 7.5,
height = 5,
units = "cm",
scale = 3
)
df_partition_yields %>%
ggplot(aes(x = product_ash/100,
y = product_mass/100)) +
geom_line() +
theme_ipsum()+
scale_x_continuous(labels = scales::percent_format(),
limits = c(0,0.15))+
scale_y_continuous(labels = scales::percent_format(),
limits = c(0,1))+
labs(title = "Model Ash-Yield Curve",
subtitle = "Ep = 0.05",
x = "Product Ash",
y = "Product Yield")
ggsave(
"plot/09 Model Ash-Yields.png",
width = 7.5,
height = 5,
units = "cm",
scale = 3
)
# Now lets try not just different cutpoints but also Eps
# To do this we will modify our functions for clarities sake.
# We will make a list with individual elements 'cutpoint' and 'Ep'
# We take advantage of the 'cross' function from purrr
conditions = list(cutpoint = seq(1.2, 1.8, 0.01),
ep = c(0.025,0.05,0.1)) %>%
cross()
# because the object we are now passing is a list with sub vectors of length 1
# we can now address them by using the .$ method
# Alternative methods could use pmap or map2 however you need even length
# lists / vectors which means mucking around with rep
df_yields_ep = conditions %>%
map(~ apply_partition_curve(
float_sink_table = float_sink,
cutpoint = .$cutpoint,
ep = .$ep
)) %>%
map_df(partition_yields)
df_yields_ep %>%
mutate(ep = as.factor(ep)) %>%
ggplot(aes(x = product_ash/100,
y = product_mass/100,
group = ep,
colour = ep)) +
geom_line() +
scale_colour_ipsum()+
theme_ipsum()+
scale_x_continuous(labels = scales::percent_format(),
limits = c(0, 0.15))+
scale_y_continuous(labels = scales::percent_format(),
limits = c(0,1))+
labs(title = "Model Ash-Yield Curves",
subtitle = "Sensitivity Analysis on Ep",
x = "Product Ash",
y = "Product Yield")+
theme(
legend.position = c(.95, .95),
legend.direction = "vertical",
legend.justification = c("right", "top"),
legend.box.just = "right",
legend.margin = margin(6, 6, 6, 6),
legend.box.background = element_rect(colour = "white")
)+
no_legend_title()
ggsave(
"plot/10 Sensitivity Ash-Yields.png",
width = 7.5,
height = 5,
units = "cm",
scale = 3
)
df_yields_ep %>%
mutate(ep = as.factor(ep)) %>%
ggplot(aes(x = cutpoint,
y = product_mass/100,
group = ep,
colour = ep)) +
geom_line() +
scale_colour_ipsum()+
theme_ipsum()+
no_legend()+
scale_y_continuous(labels = scales::percent_format())+
labs(title = "Recovery Curves",
subtitle = "Sensitivity Analysis on Ep",
x = "Cutpoint",
y = "Product Yield")+
theme(
legend.position = c(.95, 0.05),
legend.direction = "vertical",
legend.justification = c("right", "bottom"),
legend.box.just = "right",
legend.margin = margin(6, 6, 6, 6),
legend.box.background = element_rect(colour = "white")
)+
no_legend_title()
ggsave(
"plot/11 Recovery Curves.png",
width = 7.5,
height = 5,
units = "cm",
scale = 3
)