SS-20/Pioneer

SS-20/Pioneer

SS-20

The RSD-10 Pioneer (Russian: ракета средней дальности (РСД) «Пионер» tr.: raketa sredney dalnosti (RSD) “Pioner”; English: Medium-Range Missile “Pioneer”) was an intermediate-range ballistic missile with a nuclear warhead, deployed by the Soviet Union from 1976 to 1988. It carried GRAU designation 15Zh45. Its NATO reporting name was SS-20 Saber.

For more see:

https://en.wikipedia.org/wiki/RSD-10_Pioneer

http://rbase.new-factoria.ru/missile/wobb/pioner/pioner.shtml

http://rvsn.ruzhany.info/ss_20.html

SLBM data

load("slbm.dat")
library(DT)
datatable(slbm)
library(ggplot2)
library(GGally)
#Here we use function from https://www.r-bloggers.com/multiple-regression-lines-in-ggpairs/
my_fn <- function(data, mapping, ...){
  p <- ggplot(data = data, mapping = mapping) + 
    geom_point() + 
    geom_smooth(method=loess, fill="red", color="red", ...) +
    geom_smooth(method=lm, fill="blue", color="blue", ...)
  p
}

g = ggpairs(slbm,columns = 2:6, lower = list(continuous = my_fn))
g

Bayesian Linear Regression Model

We apply SLBM data frame without SS-N-32 data for the purpose of model accuracy i.e to be free of noise in our data.

library(rstanarm)
## Loading required package: Rcpp
## rstanarm (Version 2.17.3, packaged: 2018-02-17 05:11:16 UTC)
## - Do not expect the default priors to remain the same in future rstanarm versions.
## Thus, R scripts should specify priors explicitly, even if they are just the defaults.
## - For execution on a local, multicore CPU with excess RAM we recommend calling
## options(mc.cores = parallel::detectCores())
## - Plotting theme set to bayesplot::theme_default().
library(bayesplot)
## This is bayesplot version 1.4.0
## - Plotting theme set to bayesplot::theme_default()
## - Online documentation at mc-stan.org/bayesplot
options(mc.cores = parallel::detectCores())

fit.slbm.bs<-stan_glm(sqrt(R)~S+D+L+W+log(M)+log(P),
                        data=slbm[-16,],chains=4,iter=10000,seed=12345)
fit.slbm.bs
## stan_glm
##  family:       gaussian [identity]
##  formula:      sqrt(R) ~ S + D + L + W + log(M) + log(P)
##  observations: 25
##  predictors:   7
## ------
##             Median MAD_SD
## (Intercept) -40.0  110.2 
## S             9.4    5.5 
## D            37.1   20.3 
## L             0.9    1.8 
## W             3.2    5.7 
## log(M)        6.5   15.7 
## log(P)       -7.4    6.1 
## sigma        10.5    1.8 
## 
## Sample avg. posterior predictive distribution of y:
##          Median MAD_SD
## mean_PPD 67.9    3.0  
## 
## ------
## For info on the priors used see help('prior_summary.stanreg').
plot(fit.slbm.bs)

posterior_vs_prior(fit.slbm.bs)
## 
## Drawing from prior...

fit.slbm.bs2<-as.array(fit.slbm.bs)
mcmc_hist(fit.slbm.bs2)
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

mcmc_trace(fit.slbm.bs2)

summary(fit.slbm.bs)
## 
## Model Info:
## 
##  function:     stan_glm
##  family:       gaussian [identity]
##  formula:      sqrt(R) ~ S + D + L + W + log(M) + log(P)
##  algorithm:    sampling
##  priors:       see help('prior_summary')
##  sample:       20000 (posterior sample size)
##  observations: 25
##  predictors:   7
## 
## Estimates:
##                 mean   sd     2.5%   25%    50%    75%    97.5%
## (Intercept)    -40.0  114.0 -265.1 -114.8  -40.0   33.7  189.6 
## S                9.4    5.6   -1.6    5.7    9.4   13.1   20.6 
## D               37.3   21.2   -4.7   23.6   37.1   50.9   79.8 
## L                0.9    1.9   -2.8   -0.3    0.9    2.1    4.5 
## W                3.1    6.0   -8.7   -0.7    3.2    7.0   15.1 
## log(M)           6.5   16.3  -26.7   -4.1    6.5   17.1   38.7 
## log(P)          -7.4    6.5  -20.3  -11.5   -7.4   -3.3    5.5 
## sigma           10.8    1.9    7.8    9.4   10.5   11.8   15.2 
## mean_PPD        68.0    3.1   61.8   65.9   67.9   70.0   74.1 
## log-posterior -107.5    2.4 -113.3 -108.8 -107.1 -105.7 -104.0 
## 
## Diagnostics:
##               mcse Rhat n_eff
## (Intercept)   1.2  1.0   9010
## S             0.0  1.0  14324
## D             0.2  1.0   9847
## L             0.0  1.0  12107
## W             0.1  1.0  14134
## log(M)        0.2  1.0   8580
## log(P)        0.1  1.0  14045
## sigma         0.0  1.0  10090
## mean_PPD      0.0  1.0  18807
## log-posterior 0.0  1.0   5926
## 
## For each parameter, mcse is Monte Carlo standard error, n_eff is a crude measure of effective sample size, and Rhat is the potential scale reduction factor on split chains (at convergence Rhat=1).

SS-20 Operational Range

Here we use open source data (see above) for the Bayesian linear regression model. The value for diameter is adopted for two stages as the mean \(D=(D_{1}+D_{2})/2\)

slbm.pp <- posterior_predict(fit.slbm.bs,
          newdata = data.frame(L=16.5,D=1.65,S=2,W=2,
                               M=37000,P=1740),seed=12345)

Range.km <- slbm.pp^2
Range.km <- Range.km[1:10000,]
quantile(Range.km,probs = c(0.1,0.5,0.9))
##      10%      50%      90% 
## 3314.406 5543.618 8325.102
mean(Range.km<7400)
## [1] 0.814
ggplot(data=as.data.frame(Range.km), aes(Range.km)) + 
  geom_histogram(bins = 30,col="black",fill="green") + 
  geom_vline(xintercept = mean(Range.km), color = "red") + 
  geom_errorbarh(aes(y=-5, xmin=quantile(Range.km,0.1),
                     xmax=quantile(Range.km,0.9)), 
                 data=as.data.frame(Range.km), col="#0094EA", size=3) +
  ggtitle(label="Probability density of SS-20 range")

Conclusions

1.Applying Bayesian linear regression model for SLBM data (M,P,D,L,S,W) we can produce posterior distribution sample given SS-20 data (M=37000 kg,P=1740 kg,D=1.65 m,L=16.5 m,S=2,W=2) with 80% credible interval \(P(3314\le Range\le8325)=0.8\) and the mean \(Range=5544\).

2.SS-20 had operational Range corresponding to IRBM which could hit any possible target Europe wide.

3.SS-20 Mod3 (SS-X-28) could reach the range of 7400 km with 81% probability according to the Bayesian model results.