Agni-V ICBM Operational Range Estimation
Alexander Levakov, Senior Research Fellow, Ph.D
June 4, 2018
Agni-V test. News photo
About Agni-V
According to BBC “India has successfully launched a long-range intercontinental ballistic missile able to carry a nuclear warhead, officials say. The Agni-V was launched from a site off India’s east coast and took about 20 minutes to hit its target somewhere near Indonesia in the Indian Ocean. The missile has a range of more than 5,000km (3,100 miles), potentially bringing targets in China within range.”
Research goal
We don’t believe any speculations about this ICBM. We just try estimate Agni-V operational range, applying linear regression with Bayesian model on SLBM data.
SLBM data
We use aggregated and transformed SLBM data to explore the relationship between M - Mass (kg), R - Range (km), P - Payload (kg), S - Stage (1,2,3), D - Diameter (m), L - Length (m) and W - Type of Warhead (Single - 1, MIRV - 2) of submarine launched ballistic missile.
load("slbm.dat")
library(DT)
datatable(slbm)Bayesian linear regression
Model and tests
fit.slbm.bs.4<-stan_glm(sqrt(R)~S+D+L+W+log(M)+log(P),data=slbm,chains=4,iter=10000,seed=12345)
fit.slbm.bs.4## stan_glm
## family: gaussian [identity]
## formula: sqrt(R) ~ S + D + L + W + log(M) + log(P)
## observations: 26
## predictors: 7
## ------
## Median MAD_SD
## (Intercept) -40.6 106.7
## S 9.4 5.1
## D 37.4 19.8
## L 0.9 1.7
## W 3.3 5.6
## log(M) 6.5 15.0
## log(P) -7.3 6.0
## sigma 10.2 1.7
##
## Sample avg. posterior predictive distribution of y:
## Median MAD_SD
## mean_PPD 69.0 2.8
##
## ------
## For info on the priors used see help('prior_summary.stanreg').par(mfrow=c(1,1))
plot(fit.slbm.bs.4)
posterior_vs_prior(fit.slbm.bs.4)##
## Drawing from prior...
fit.slbm.bs42<-as.array(fit.slbm.bs.4)
mcmc_hist(fit.slbm.bs42)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
mcmc_trace(fit.slbm.bs42)
summary(fit.slbm.bs.4)##
## 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: 26
## predictors: 7
##
## Estimates:
## mean sd 2.5% 25% 50% 75% 97.5%
## (Intercept) -40.0 109.1 -254.9 -112.3 -40.6 31.7 175.7
## S 9.4 5.4 -1.2 5.9 9.4 12.9 20.2
## D 37.4 20.3 -2.6 24.1 37.4 50.9 77.4
## L 0.9 1.8 -2.7 -0.3 0.9 2.0 4.4
## W 3.2 5.8 -8.5 -0.5 3.3 7.1 14.8
## log(M) 6.4 15.6 -24.3 -3.6 6.5 16.6 37.0
## log(P) -7.3 6.2 -19.5 -11.3 -7.3 -3.3 5.0
## sigma 10.4 1.8 7.6 9.2 10.2 11.4 14.6
## mean_PPD 69.0 2.9 63.2 67.1 69.0 70.9 74.7
## log-posterior -110.5 2.4 -116.3 -111.8 -110.1 -108.8 -107.1
##
## Diagnostics:
## mcse Rhat n_eff
## (Intercept) 1.2 1.0 8809
## S 0.0 1.0 12972
## D 0.2 1.0 9063
## L 0.0 1.0 12118
## W 0.1 1.0 11991
## log(M) 0.2 1.0 8316
## log(P) 0.1 1.0 13099
## sigma 0.0 1.0 10055
## mean_PPD 0.0 1.0 19069
## log-posterior 0.0 1.0 6234
##
## 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).Predicting Range by posterior distribution
Here we use Agni-V open source data from Wiki - https://en.m.wikipedia.org/wiki/Agni-V.
Agni-V data
slbm.pp4 <- posterior_predict(fit.slbm.bs.4,
newdata = data.frame(L=17.5,D=2,S=3,W=2,M=50000,P=1500),
seed = 12345)
quantile(slbm.pp4^2,probs = c(0.1,0.5,0.9))## 10% 50% 90%
## 7071.534 10162.157 13828.099hist(slbm.pp4^2,breaks = 50,col="blue",
main = "Posterior distribution for R~f(L=17.5,D=2,S=3,W=2,M=50000,P=1500)",
xlab = "R,km")
RR <- median(slbm.pp4^2)
abline(v = RR,col="red")
Conclusions
1.Given historical SLBM data (M,P,D,L,S,W) and Bayesian linear regression model we can produce posterior distribution sample for Agni-V data with 80% credible interval \(P(7072\le Range\le13828)=0.8\) and the mean \(Range=10162\)
2.The Agni-V missile has operational Range compared to the existing ICBMs of to date.