"""E13: survival / reliability model (runs on CPU, e.g. the local M4). From the per-bit catastrophe probability and the accumulated-dose sweep we model the probability that a rendered frame is catastrophic after k independent upsets as 1-(1-p_c)^k, validate it against the multi-upset measurements, and translate it into a mean time between catastrophic frames for a model of B stored bits under representative single-event-upset rates (ground, avionics, low-Earth orbit), with and without the support guard. """ import argparse import glob import json import math import os import numpy as np import matplotlib matplotlib.use("Agg") import matplotlib.pyplot as plt plt.rcParams.update({"font.family": "serif", "mathtext.fontset": "cm", "font.size": 12, "axes.labelsize": 12, "legend.fontsize": 10, "lines.linewidth": 1.9, "lines.markersize": 5.5, "axes.grid": True, "grid.alpha": 0.25, "savefig.dpi": 220, "savefig.bbox": "tight"}) # representative SEU rates (upsets per stored bit per hour), order-of-magnitude, # from terrestrial/avionic/space soft-error literature. SEU_RATE = {"ground": 1e-12, "avionics": 3e-10, "LEO": 1e-8} CAT_PSNR = 25.0 # a frame is catastrophic if global PSNR falls below this def per_bit_catastrophe(root): """p_c from the main campaign: fraction of uniform-random single-bit upsets that are catastrophic (footprint > 1% or non-finite), weighted over fields.""" import numpy as np shards = glob.glob(os.path.join(root, "campaign", "shard_*_fp32.npz")) shards = [s for s in shards if not s.endswith("_guard.npz")] fr, cat = [], [] for s in shards: d = np.load(s, allow_pickle=True); a = d["data"]; cols = list(d["cols"]) ci = {c: i for i, c in enumerate(cols)} fr.append(a[:, ci["fracchg"]]); cat.append(a[:, ci["cat"]]) if not fr: return None, None fr = np.concatenate(fr); cat = np.concatenate(cat) is_cat = (cat > 0.5) | (fr > 0.01) p_c = float(is_cat.mean()) # guarded residual, if present g = glob.glob(os.path.join(root, "campaign", "shard_*_fp32_guard.npz")) pg = None if g: frg, catg = [], [] for s in g: d = np.load(s, allow_pickle=True); a = d["data"]; cols = list(d["cols"]); ci = {c: i for i, c in enumerate(cols)} frg.append(a[:, ci["fracchg"]]); catg.append(a[:, ci["cat"]]) frg = np.concatenate(frg); catg = np.concatenate(catg) pg = float(((catg > 0.5) | (frg > 0.01)).mean()) return p_c, pg def multiupset_pcat(root): """empirical P(catastrophic frame) vs k from the no-guard multi-upset sweep.""" per_k = {} for fp in glob.glob(os.path.join(root, "multiupset", "multiupset_*_fp32.npz")): if fp.endswith("_guard.npz"): continue d = np.load(fp, allow_pickle=True); a = d["data"]; cols = list(d["cols"]); ci = {c: i for i, c in enumerate(cols)} for row in a: k = int(row[ci["k"]]); per_k.setdefault(k, []).append(row[ci["psnr"]]) ks = sorted(per_k) pcat = {k: float(np.mean(np.array(per_k[k]) < CAT_PSNR)) for k in ks} return ks, pcat def fmt_hours(h): if h <= 0: return "n/a" yr = h / 8760.0 if yr >= 1e5: e = int(math.floor(math.log10(yr))) m = yr / 10 ** e return f"$\\sim{m:.0f}\\times10^{{{e}}}$ yr" if yr >= 10: return f"{yr:,.0f} yr".replace(",", "{,}") if yr >= 1: return f"{yr:.1f} yr" d = h / 24.0 if d >= 1: return f"{d:.0f} d" return f"{h:.1f} h" def main(): ap = argparse.ArgumentParser() ap.add_argument("--root", default="data_local") ap.add_argument("--out", default="../generated") ap.add_argument("--bits", type=float, default=2.55e8, help="stored bits in the model") args = ap.parse_args() os.makedirs(args.out, exist_ok=True) p_c, p_g = per_bit_catastrophe(args.root) ks, pcat = multiupset_pcat(args.root) macros = {} if p_c is None: p_c = 1e-3 macros["pcUpset"] = f"{p_c*100:.3f}" macros["pcGuard"] = (f"{p_g*100:.4f}" if p_g is not None else "0.0000") B = args.bits macros["modelBits"] = f"{B/1e6:.0f}\\times10^6" # survival figure: empirical P(cat|k) vs the 1-(1-p_c)^k model plt.figure(figsize=(6.2, 4)) if ks: ke = np.array(ks) plt.plot(ke, [pcat[k] for k in ks], "o", label="measured") kk = np.logspace(0, np.log10(max(ks)), 100) plt.plot(kk, 1 - (1 - p_c) ** kk, "-", label=r"$1-(1-p_c)^k$ model") plt.xscale("log"); plt.xlabel("simultaneous single-bit upsets $k$") plt.ylabel("P(catastrophic frame)"); plt.legend(); plt.grid(alpha=0.3) plt.savefig(os.path.join(args.out, "fig_survival.pdf"), bbox_inches="tight"); plt.close() # reliability table -> macros (MTBF for first catastrophic frame). # LaTeX command names must be letters only, so use camelCase keys. NM = {"ground": "Ground", "avionics": "Avionics", "LEO": "Leo"} for env, rate in SEU_RATE.items(): ev_per_hr = rate * B * p_c mtbf = float("inf") if ev_per_hr <= 0 else 1.0 / ev_per_hr macros[f"mtbf{NM[env]}Ng"] = fmt_hours(mtbf) ev_g = rate * B * (p_g if p_g else 1e-9) mtbf_g = float("inf") if ev_g <= 0 else 1.0 / ev_g macros[f"mtbf{NM[env]}G"] = fmt_hours(mtbf_g) # emit a small table and macro file with open(os.path.join(args.out, "tab_survival.tex"), "w") as f: f.write("\\begin{table}[tbp]\n\\centering\n") f.write("\\caption{Estimated mean time between catastrophic frames for a " "model of $\\modelBits$ stored bits under representative single-event-upset " "rates, without and with the support guard. Rates are order-of-magnitude " "values from the soft-error literature.}\n\\label{tab:survival}\n") f.write("\\begin{tabular}{lrr}\n\\toprule\nEnvironment & no guard & support guard \\\\\n\\midrule\n") names = {"ground": "ground (sea level)", "avionics": "avionics ($\\sim$10 km)", "LEO": "low-Earth orbit"} NM = {"ground": "Ground", "avionics": "Avionics", "LEO": "Leo"} for env in ["ground", "avionics", "LEO"]: f.write(f"{names[env]} & {macros['mtbf'+NM[env]+'Ng']} & {macros['mtbf'+NM[env]+'G']} \\\\\n") f.write("\\bottomrule\n\\end{tabular}\n\\end{table}\n") with open(os.path.join(args.out, "survival_numbers.tex"), "w") as f: # provide safe defaults too defaults = {"pcUpset": "0.000", "pcGuard": "0.0000", "modelBits": "2.6\\times10^8"} for nm in ["Ground", "Avionics", "Leo"]: defaults[f"mtbf{nm}Ng"] = "n/a"; defaults[f"mtbf{nm}G"] = "n/a" for k, v in defaults.items(): macros.setdefault(k, v) for k, v in macros.items(): f.write(f"\\newcommand{{\\{k}}}{{{v}}}\n") print("SURVIVAL macros:", macros) if __name__ == "__main__": main()