Demystifying DF-26
Alexander Levakov, Senior Research Fellow, Ph.D
January, 2019
DF-26
DF-26
The DF-26 is a road-mobile, two-stage solid-fueled IRBM with an antiship variant possibly also in development. According to Chinese sources, the missile measures 14 m in length, 1.4 m in diameter, and has a launch weight of 20,000 kg. The missile has a range of 3,000-4,000 km, putting major U.S. military facilities, including those in Guam, within striking distance. The DF-26 comes with a “modular design,” meaning that the launch vehicle can accommodate two types of nuclear warheads and several types of conventional warheads. The accuracy of the DF-26 is uncertain, with speculators estimating the CEP at intermediate range between 150-450 meters.
For more see:
1.https://missilethreat.csis.org/missile/dong-feng-26-df-26/
2.https://en.wikipedia.org/wiki/DF-26
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
library(rstanarm)
library(bayesplot)
options(mc.cores = parallel::detectCores())
fit.slbm.bs<-stan_glm(sqrt(R)~S+D+L+W+log(M)+log(P),
data=slbm,chains=2,iter=10000,seed=12345)
fit.slbm.bs## stan_glm
## family: gaussian [identity]
## formula: sqrt(R) ~ S + D + L + W + log(M) + log(P)
## observations: 26
## predictors: 7
## ------
## Median MAD_SD
## (Intercept) -39.9 105.5
## S 9.4 5.1
## D 37.5 19.8
## L 0.9 1.7
## W 3.3 5.7
## log(M) 6.3 15.0
## log(P) -7.4 6.0
## sigma 10.2 1.7
##
## Sample avg. posterior predictive distribution of y:
## Median MAD_SD
## mean_PPD 69.0 2.9
##
## ------
## 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: 10000 (posterior sample size)
## observations: 26
## predictors: 7
##
## Estimates:
## mean sd 2.5% 25% 50% 75% 97.5%
## (Intercept) -40.2 108.7 -253.0 -112.2 -39.9 30.1 174.2
## S 9.4 5.4 -1.6 5.9 9.4 12.8 20.3
## D 37.4 20.2 -1.8 24.0 37.5 50.7 77.8
## L 0.9 1.8 -2.7 -0.3 0.9 2.0 4.3
## W 3.2 5.9 -8.6 -0.6 3.3 7.1 14.8
## log(M) 6.5 15.5 -24.4 -3.5 6.3 16.8 36.5
## log(P) -7.3 6.2 -19.5 -11.3 -7.4 -3.3 4.9
## sigma 10.4 1.8 7.6 9.1 10.2 11.5 14.7
## mean_PPD 69.0 3.0 63.1 67.1 69.0 70.9 74.8
## log-posterior -110.6 2.4 -116.3 -111.9 -110.2 -108.8 -107.1
##
## Diagnostics:
## mcse Rhat n_eff
## (Intercept) 1.6 1.0 4702
## S 0.1 1.0 6313
## D 0.3 1.0 4814
## L 0.0 1.0 6093
## W 0.1 1.0 6133
## log(M) 0.2 1.0 4466
## log(P) 0.1 1.0 6369
## sigma 0.0 1.0 4220
## mean_PPD 0.0 1.0 9422
## log-posterior 0.0 1.0 3065
##
## 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).DF-26 Operational Range
Here we use open source data (see above) for the Bayesian linear regression model.
slbm.pp <- rstanarm::posterior_predict(fit.slbm.bs,
newdata = data.frame(L=14,D=1.4,S=2,W=1,
M=20000,P=1800),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%
## 1629.949 3089.265 4953.897mean(Range.km<5000)## [1] 0.9044ggplot(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 DF-26 Range")
Conclusions
1.Applying Bayesian linear regression model for SLBM data (M,P,D,L,S,W) we can produce posterior distribution sample given DF-26 data (M=20000 kg,P=1800 kg,D=1.4 m,L=14 m,S=2,W=1) with 80% credible interval \(P(1630\le Range\le4954)=0.8\) and the mean \(Range=3089\).
2.DF-26 has operational Range corresponding to IRBM which could hit any possible target in the Pacific Ocean region including Guam.