CURVATURE

1 Configuración y Carga de Datos

##### UNIVERSIDAD CENTRAL DEL ECUADOR #####
#### AUTOR: MARTIN SARMIENTO ####
### CARRERA: INGENIERÍA EN PETRÓLEOS #####


#### VARIABLE CURVATURA ####
## DATASET ##
setwd("~/R/CURVATURE")
# Cargar dataset
Datos <- read.csv("DataSet_prov.csv", sep = ";", dec = ",", fileEncoding = "latin1")
# Estructura de los datos
str(Datos)

## 'data.frame':    5075 obs. of  30 variables:
##  $ FID_                  : int  0 2 3 4 5 6 10 11 12 13 ...
##  $ OBJECTID              : int  127 129 130 131 132 133 137 138 139 140 ...
##  $ code                  : chr  "00127-ARG-P" "00129-ARG-G" "00130-ARG-P" "00131-ARG-P" ...
##  $ plant_name            : chr  "Aconcagua solar farm" "Altiplano 200 Solar Power Plant" "Altiplano 200 Solar Power Plant" "Anchoris solar farm" ...
##  $ country               : chr  "Argentina" "Argentina" "Argentina" "Argentina" ...
##  $ operational_status    : chr  "announced" "operating" "operating" "construction" ...
##  $ longitude             : num  -68.9 -66.9 -66.9 -68.9 -70.3 ...
##  $ latitude              : num  -33 -24.1 -24.1 -33.3 -37.4 ...
##  $ elevation             : int  929 4000 4000 937 865 858 570 1612 665 3989 ...
##  $ area                  : num  250 4397290 5774 645 241 ...
##  $ size                  : chr  "Pequeña" "Grande" "Pequeña" "Pequeña" ...
##  $ slope                 : num  0.574 1.603 6.243 0.903 1.791 ...
##  $ slope_type            : chr  "Plano o casi plano" "Plano o casi plano" "Moderado" "Plano o casi plano" ...
##  $ curvature             : num  0.000795 -0.002781 -0.043699 0.002781 -0.002384 ...
##  $ curvature_type        : chr  "Superficies planas o intermedias" "Superficies planas o intermedias" "Superficies cóncavas / Valles" "Superficies planas o intermedias" ...
##  $ aspect                : num  55.1 188.7 270.9 108.4 239.3 ...
##  $ aspect_type           : chr  "Northeast" "South" "West" "East" ...
##  $ dist_to_road          : num  127 56015 52697 336 34 ...
##  $ ambient_temperature   : num  12.6 6.8 6.8 13.1 11.4 ...
##  $ ghi                   : num  6.11 8.01 7.88 6.12 6.22 ...
##  $ humidity              : num  53.7 53.7 53.7 53.7 53.7 ...
##  $ wind_speed            : num  3.78 7.02 8.33 3.87 6.56 ...
##  $ wind_direction        : num  55.1 55.1 55.1 55.1 55.1 ...
##  $ dt_wind               : chr  "Northeast" "Northeast" "Northeast" "Northeast" ...
##  $ solar_aptitude        : num  0.746 0.8 0.727 0.595 0.657 ...
##  $ solar_aptitude_rounded: int  7 8 7 6 7 7 7 8 7 8 ...
##  $ solar_aptittude_class : chr  "Alta" "Alta" "Alta" "Media" ...
##  $ capacity              : num  25 101 107 180 20 ...
##  $ optimal_tilt          : int  31 26 26 31 33 30 31 29 31 27 ...
##  $ pv_potential          : num  4.98 6.39 6.39 4.97 5 ...

# Cargamos las librerias
library(dplyr)

## 
## Adjuntando el paquete: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(gt)
library(e1071)

2 Cálculo de Intervalos y Frecuencias

# Extraer variable
Variable <- na.omit(Datos$curvature)
N <- length(Variable)

# CÁLCULO LÍMITES DECIMALES
min_dec <- min(Variable)
max_dec <- max(Variable)
k_dec <- floor(1 + 3.322 * log10(N))
rango_dec <- max(Variable) - min(Variable)
amplitud_dec <- rango_dec / k_dec

# Cortes exactos
cortes_dec <- seq(min(Variable), max(Variable), length.out = k_dec + 1)
cortes_dec[length(cortes_dec)] <- max(Variable) + 0.0001

# Frecuencias
inter_dec <- cut(Variable, breaks = cortes_dec, include.lowest = TRUE, right = FALSE)
ni_dec <- as.vector(table(inter_dec))

# CÁLCULOS MATEMÁTICOS 
hi_dec <- (ni_dec / N) * 100
Ni_asc_dec <- cumsum(ni_dec)
Hi_asc_dec <- cumsum(hi_dec)
Ni_desc_dec <- rev(cumsum(rev(ni_dec)))
Hi_desc_dec <- rev(cumsum(rev(hi_dec)))

# Dataframe Decimal 
TDF_Decimal <- data.frame(
  Li = cortes_dec[1:k_dec],
  Ls = cortes_dec[2:(k_dec+1)],
  MC = (cortes_dec[1:k_dec] + cortes_dec[2:(k_dec+1)]) / 2,
  ni = ni_dec,
  hi = hi_dec,
  Ni_asc = Ni_asc_dec,
  Ni_desc = Ni_desc_dec,
  Hi_asc = Hi_asc_dec,
  Hi_desc = Hi_desc_dec)


# CÁLCULO LÍMITES ENTEROS
Amplitud_int <- 0.02
min_int <- floor(min(Variable) / Amplitud_int) * Amplitud_int

# Generamos la secuencia de cortes
cortes_int <- seq(from = min_int, by = Amplitud_int, length.out = 2)
while(max(cortes_int) < max(Variable)) {
  cortes_int <- seq(from = min_int, to = max(cortes_int) + Amplitud_int + 0.0001, by = Amplitud_int)
}

# Definimos los límites
K_real <- length(cortes_int) - 1
lim_inf_int <- cortes_int[1:K_real]
lim_sup_int <- cortes_int[2:(K_real+1)]

# Frecuencias
inter_int <- cut(Variable, breaks = cortes_int, include.lowest = TRUE, right = FALSE)
ni_int <- as.vector(table(inter_int))

# CÁLCULOS MATEMÁTICOS 
hi_int <- (ni_int / N) * 100
Ni_asc_int <- cumsum(ni_int)
Hi_asc_int <- cumsum(hi_int)
Ni_desc_int <- rev(cumsum(rev(ni_int)))
Hi_desc_int <- rev(cumsum(rev(hi_int)))

# Dataframe Entero
TDF_Enteros <- data.frame(
  Li = lim_inf_int,
  Ls = lim_sup_int,
  MC = (lim_inf_int + lim_sup_int) / 2,
  ni = ni_int,
  hi = hi_int,
  Ni_asc = Ni_asc_int,
  Ni_desc = Ni_desc_int,
  Hi_asc = Hi_asc_int,
  Hi_desc = Hi_desc_int)

3 Tabla de Distribución de Frecuencias

3.1 Tabla con Límites Decimales

# Crear Dataframe
TDF_Dec_Final <- data.frame(
  Li      = as.character(round(TDF_Decimal$Li, 2)),
  Ls      = as.character(round(TDF_Decimal$Ls, 2)),
  MC      = as.character(round(TDF_Decimal$MC, 2)),
  ni      = as.character(TDF_Decimal$ni),
  hi      = as.character(round(TDF_Decimal$hi, 2)),
  Ni_asc  = as.character(TDF_Decimal$Ni_asc),
  Ni_desc = as.character(TDF_Decimal$Ni_desc),
  Hi_asc  = as.character(round(TDF_Decimal$Hi_asc, 2)), 
  Hi_desc = as.character(round(TDF_Decimal$Hi_desc, 2))
)

# Calcular Totales 
total_ni <- sum(TDF_Decimal$ni)
total_hi <- round(sum(TDF_Decimal$hi), 2) 

fila_total_dec <- c("TOTAL", "-", "-", total_ni, total_hi, "-", "-", "-", "-")
TDF_Dec_Final <- rbind(TDF_Dec_Final, fila_total_dec)

# Generar GT
TDF_Dec_Final %>%
  gt() %>%
  tab_header(title = md("**Tabla N°1 de Distribución de Frecuencias de Curvatura de las Plantas Solares**")) %>%
  cols_label(
    Li = "Lim. Inf", 
    Ls = "Lim. Sup", 
    MC = "Marca Clase", 
    ni = "Frec. Abs (ni)", 
    hi = "Frec. Rel (%)", 
    Ni_asc = "Ni (Asc)", 
    Ni_desc = "Ni (Desc)", 
    Hi_asc = "Hi Asc (%)", 
    Hi_desc = "Hi Desc (%)"
  ) %>%
  cols_align(align = "center", columns = everything()) %>%
  tab_options(heading.title.font.size = px(14), column_labels.background.color = "#F0F0F0")

Tabla N°1 de Distribución de Frecuencias de Curvatura de las Plantas Solares
Lim. Inf	Lim. Sup	Marca Clase	Frec. Abs (ni)	Frec. Rel (%)	Ni (Asc)	Ni (Desc)	Hi Asc (%)	Hi Desc (%)
-0.17	-0.15	-0.16	2	0.04	2	5075	0.04	100
-0.15	-0.12	-0.13	0	0	2	5073	0.04	99.96
-0.12	-0.09	-0.1	4	0.08	6	5073	0.12	99.96
-0.09	-0.06	-0.08	14	0.28	20	5069	0.39	99.88
-0.06	-0.04	-0.05	47	0.93	67	5055	1.32	99.61
-0.04	-0.01	-0.02	406	8	473	5008	9.32	98.68
-0.01	0.02	0	4453	87.74	4926	4602	97.06	90.68
0.02	0.05	0.03	121	2.38	5047	149	99.45	2.94
0.05	0.07	0.06	19	0.37	5066	28	99.82	0.55
0.07	0.1	0.09	7	0.14	5073	9	99.96	0.18
0.1	0.13	0.11	0	0	5073	2	99.96	0.04
0.13	0.16	0.14	1	0.02	5074	2	99.98	0.04
0.16	0.18	0.17	1	0.02	5075	1	100	0.02
TOTAL	-	-	5075	100	-	-	-	-

3.2 Tabla con Límites Enteros

# Crear Dataframe 
TDF_Int_Final <- data.frame(
  Li      = as.character(round(TDF_Enteros$Li, 2)), 
  Ls      = as.character(round(TDF_Enteros$Ls, 2)),
  MC      = as.character(round(TDF_Enteros$MC, 2)),
  ni      = as.character(TDF_Enteros$ni),
  hi      = as.character(round(TDF_Enteros$hi, 2)),
  Ni_asc  = as.character(TDF_Enteros$Ni_asc),
  Ni_desc = as.character(TDF_Enteros$Ni_desc),
  Hi_asc  = as.character(round(TDF_Enteros$Hi_asc, 2)),
  Hi_desc = as.character(round(TDF_Enteros$Hi_desc, 2))
)

# Calcular Totales 
total_ni_int <- sum(TDF_Enteros$ni)
total_hi_int <- round(sum(TDF_Enteros$hi), 2)

fila_total_int <- c("TOTAL", "-", "-", total_ni_int, total_hi_int, "-", "-", "-", "-")
TDF_Int_Final <- rbind(TDF_Int_Final, fila_total_int)

# Generar GT
TDF_Int_Final %>%
  gt() %>%
  tab_header(title = md("**Tabla N°2 de Distribución de Frecuencias de Curvatura (Intervalos 0.02)**")) %>%
  cols_label(
    Li = "Lim. Inf", 
    Ls = "Lim. Sup", 
    MC = "Marca Clase", 
    ni = "Frec. Abs (ni)", 
    hi = "Frec. Rel (%)", 
    Ni_asc = "Ni (Asc)",
    Ni_desc = "Ni (Desc)", 
    Hi_asc = "Hi Asc (%)", 
    Hi_desc = "Hi Desc (%)"
  ) %>%
  cols_align(align = "center", columns = everything()) %>%
  tab_options(heading.title.font.size = px(14), column_labels.background.color = "#F0F0F0")

Tabla N°2 de Distribución de Frecuencias de Curvatura (Intervalos 0.02)
Lim. Inf	Lim. Sup	Marca Clase	Frec. Abs (ni)	Frec. Rel (%)	Ni (Asc)	Ni (Desc)	Hi Asc (%)	Hi Desc (%)
-0.18	-0.16	-0.17	1	0.02	1	5075	0.02	100
-0.16	-0.14	-0.15	1	0.02	2	5074	0.04	99.98
-0.14	-0.12	-0.13	0	0	2	5073	0.04	99.96
-0.12	-0.1	-0.11	3	0.06	5	5073	0.1	99.96
-0.1	-0.08	-0.09	4	0.08	9	5070	0.18	99.9
-0.08	-0.06	-0.07	15	0.3	24	5066	0.47	99.82
-0.06	-0.04	-0.05	31	0.61	55	5051	1.08	99.53
-0.04	-0.02	-0.03	102	2.01	157	5020	3.09	98.92
-0.02	0	-0.01	2029	39.98	2186	4918	43.07	96.91
0	0.02	0.01	2759	54.36	4945	2889	97.44	56.93
0.02	0.04	0.03	98	1.93	5043	130	99.37	2.56
0.04	0.06	0.05	19	0.37	5062	32	99.74	0.63
0.06	0.08	0.07	7	0.14	5069	13	99.88	0.26
0.08	0.1	0.09	4	0.08	5073	6	99.96	0.12
0.1	0.12	0.11	0	0	5073	2	99.96	0.04
0.12	0.14	0.13	1	0.02	5074	2	99.98	0.04
0.14	0.16	0.15	0	0	5074	1	99.98	0.02
0.16	0.18	0.17	0	0	5074	1	99.98	0.02
0.18	0.2	0.19	1	0.02	5075	1	100	0.02
TOTAL	-	-	5075	100	-	-	-	-

4 Análisis Gráfico

4.1 Histogramas de Cantidad

par(mar = c(8, 5, 5, 2)) 
barplot(TDF_Enteros$ni, 
        names.arg = round(TDF_Enteros$MC, 2), 
        main = "", 
        xlab = "", 
        ylab = "Cantidad",
        col = "#778899",
        space = 0, 
        las = 2, 
        cex.names = 0.7)
mtext("Curvatura", side = 1, line = 4)

mtext("Gráfica N°1: Distribución de Cantidad de Plantas Solares por Curvatura", 
      side = 3, 
      line = 2, 
      adj = 0.5, 
      cex = 0.9, 
      font = 2)

par(mar = c(8, 5, 5, 2))
barplot(TDF_Enteros$ni, 
        main = "",
        xlab = "",
        ylab = "Cantidad",
        names.arg = round(TDF_Enteros$MC, 2),
        col = "#778899",
        space = 0,
        cex.names = 0.7,
        las = 2,
        ylim = c(0, sum(TDF_Enteros$ni))) 
mtext("Curvatura", side = 1, line = 4)

mtext("Gráfica N°2: Distribución de Cantidad de Plantas Solares por Curvatura", 
      side = 3, 
      line = 2, 
      adj = 0.5, 
      cex = 0.9, 
      font = 2)

4.2 Histogramas Porcentuales

par(mar = c(8, 5, 5, 2))
bp3 <- barplot(TDF_Enteros$hi, 
        main = "",
        xlab = "",
        ylab = "Porcentaje (%)",
        col = "#778899",
        space = 0,
        names.arg = round(TDF_Enteros$MC, 2),
        cex.names = 0.7,
        las = 2,
        ylim = c(0, max(TDF_Enteros$hi) * 1.2))
mtext("Curvatura", side = 1, line = 4)

mtext("Gráfica N°3: Distribución Porcentual de las Plantas Solares por Curvatura", 
      side = 3, 
      line = 2, 
      adj = 0.5, 
      cex = 0.9, 
      font = 2)

text(x = bp3, 
     y = TDF_Enteros$hi, 
     labels = paste0(round(TDF_Enteros$hi, 1), "%"), 
     pos = 3, cex = 0.6, col = "black")

par(mar = c(8, 5, 5, 2))
bp4 <- barplot(TDF_Enteros$hi, 
        main = "",
        xlab = "",
        ylab = "Porcentaje (%)",
        col = "#778899",
        space = 0,
        names.arg = round(TDF_Enteros$MC, 2),
        las = 2,
        cex.names = 0.7,
        ylim = c(0, 100)) 
mtext("Curvatura", side = 1, line = 4)

mtext("Gráfica N°4: Distribución Porcentual de las Plantas Solares por Curvatura", 
      side = 3, 
      line = 2, 
      adj = 0.5, 
      cex = 0.9, 
      font = 2)

text(x = bp4, 
     y = TDF_Enteros$hi, 
     labels = paste0(round(TDF_Enteros$hi, 1), "%"), 
     pos = 3, cex = 0.6, col = "black")

4.3 Diagrama de Cajas (Boxplot)

par(mar = c(5, 5, 4, 2))
boxplot(Variable, 
        horizontal = TRUE,
        col = "#778899",
        xlab = "Curvatura",
        cex.main = 0.9,
        main = "Gráfica N°5: Distribución de la Curvatura en las Plantas Solares")

4.4 Ojivas

par(mar = c(5, 5, 7, 10), xpd = TRUE)

# Coordenadas
x_asc <- TDF_Enteros$Ls
x_desc <- TDF_Enteros$Li
y_asc <- TDF_Enteros$Ni_asc
y_desc <- TDF_Enteros$Ni_desc

# 1. Dibujar la Ascendente 
plot(x_asc, y_asc,
     type = "b", 
     main = "",
     xlab = "Curvatura",
     ylab = "Frecuencia acumulada",
     col = "black",
     pch = 19, 
     xlim = c(min(TDF_Enteros$Li), max(x_asc)), 
     ylim = c(0, sum(TDF_Enteros$ni)),
     bty = "l"
)

# 2. Agregar la Descendente 
lines(x_desc, y_desc, col = "#A8A8A8", type = "b", pch = 19)

grid()
mtext("Gráfica N°6: Ojivas Ascendentes y Descendentes de la\nDistribución de la Curvatura en las Plantas Solares",
      side = 3, 
      line = 3, 
      adj = 0.5, 
      cex = 0.9, 
      font = 2)

legend("left", 
       legend = c("Ascendente", "Descendente"), 
       col = c("black", "#A8A8A8"), 
       lty = 1, 
       pch = 1, 
       cex = 0.6, 
       inset = c(0.05, 0.05),
       bty = "n")

5 Indicadores Estadísticos

## INDICADORES DE TENDENCIA CENTRAL
# Media aritmética
media <- round(mean(Variable), 2)

# Mediana
mediana <- round(median(Variable), 2)

# Moda
max_frecuencia <- max(TDF_Enteros$ni)
moda_vals <- TDF_Enteros$MC[TDF_Enteros$ni == max_frecuencia]
moda_txt <- paste(round(moda_vals, 2), collapse = ", ")

## INDICADORES DE DISPERSIÓN
# Varianza
varianza <- var(Variable)

# Desviación Estándar
sd_val <- sd(Variable)

# Coeficiente de Variación
cv <- round((sd_val / abs(media)) * 100, 2)

## INDICADORES DE FORMA
# Coeficiente de Asimetría
asimetria <- skewness(Variable, type = 2)

# Curtosis
curtosis <- kurtosis(Variable)

# Outliers
Q1 <- quantile(Variable, 0.25)
Q3 <- quantile(Variable, 0.75)
IQR_val <- Q3 - Q1
lim_inf <- Q1 - 1.5 * IQR_val
lim_sup <- Q3 + 1.5 * IQR_val

outliers_data <- Variable[Variable < lim_inf | Variable > lim_sup]
num_outliers <- length(outliers_data)

if(num_outliers > 0){
  rango_outliers <- paste0(num_outliers, " [", round(min(outliers_data), 2), "; ", round(max(outliers_data), 2), "]")
} else {
  rango_outliers <- "0 [Sin Outliers]"
}


tabla_indicadores <- data.frame(
 "Variable" = c("Curvatura"),
 "Rango_MinMax" = paste0("[", round(min(Variable), 2), "; ", round(max(Variable), 2), "]"),
 "X" = c(media),
 "Me" = c(mediana),
 "Mo" = c(moda_txt),
 "V" = c(varianza),
 "Sd" = c(sd_val),
 "Cv" = c(cv),
 "As" = c(asimetria),
 "K" = c(curtosis),
 "Outliers" = rango_outliers)

# Generar Tabla GT
tabla_conclusiones_gt <- tabla_indicadores %>%
 gt() %>%
 tab_header(title = md("**Tabla N°3 de Conclusiones de Curvatura de las Plantas Solares**")) %>%
 tab_source_note(source_note = "Autor: Martin Sarmiento") %>%
 cols_label(
  Variable = "Variable",
  Rango_MinMax = "Rango",
  X = "Media (X)",
  Me = "Mediana (Me)",
  Mo = "Moda (Mo)",
  V = "Varianza (V)",
  Sd = "Desv. Est. (Sd)",
  Cv = "C.V. (%)",
  As = "Asimetría (As)",
  K = "Curtosis (K)",
  Outliers = "Outliers [Intervalo]"
 ) %>%
 tab_options(
  heading.title.font.size = px(16),
  column_labels.background.color = "#F0F0F0"
 )

tabla_conclusiones_gt

Tabla N°3 de Conclusiones de Curvatura de las Plantas Solares
Variable	Rango	Media (X)	Mediana (Me)	Moda (Mo)	Varianza (V)	Desv. Est. (Sd)	C.V. (%)	Asimetría (As)	Curtosis (K)	Outliers [Intervalo]
Curvatura	[-0.17; 0.18]	0	0	0.01	0.0001479381	0.01216298	Inf	-0.8041808	41.29933	645 [-0.17; 0.18]
Autor: Martin Sarmiento

6 Conclusiones

La variable “Curvatura” fluctúa entre -0.17 y 0.18 y sus valores se encuentran alrededor de 0, con una desviación estándar de 0.01216298, siendo una variable muy heterogénea, cuyos valores se concentran en la parte media baja de la variable con la agregación de valores atípicos de 645 outliers; por todo lo anterior, el comportamiento de la variable es muy perjudicial.