Scope. Add a bounded confidence lane beside classical per-file RMS derived from run-to-failure vibration snapshots; values remain unchanged (phi((m,a)) = m).
Dataset acknowledgment (high-level). IMS Bearings run-to-failure experiments (University of Cincinnati / IMS), with multiple test campaigns and ASCII snapshots at regular intervals. This blog does not embed third-party data or CSVs. Use the repository link on this site for scripts, stamped runs, sample CSVs, and dataset license/citation details.
Knobs (this run, generic). eps_a = 1e-6, eps_w = 1e-12, BINS = 32, WIN = 128 (files-as-samples), K_GAIN = 2.0, GAMMA = 1.0 (weights w := |m|^GAMMA).
Sanitization note. We removed an internal path column from the processed CSV. Semantics remain identical: phi((m,a)) = m, u := atanh(a), {U,W} streaming (U += w*atanh(a), W += w), a_out := tanh(U/max(W,eps_w)).
Value KPI (explicit RMS definition, normative).
Let a snapshot file contain a numeric matrix X of shape [T x D] after dropping non-numeric columns. Definem := sqrt( (1/(T*D)) * sum_{t=1..T} sum_{d=1..D} X[t,d]^2 ).
Lane math (entropy on changes, with explicit conventions).
Over a rolling window of WIN files:
• s := { m[k - WIN + 1], ..., m[k] }
• z := |diff(s)| (absolute first differences)
• Binning policy: equal-width bins over min(z)..max(z)
• Log base: natural log (ln)
• Zero-probability convention: 0*log(0) := 0
• p_i := count(z in bin_i) / len(z)
• H := -sum_i p_i*log(p_i) ; Hn := H / log(BINS)
• a_raw := tanh( K_GAIN * (1 - Hn) ) ; a := clamp(a_raw, -1+eps_a, +1-eps_a)
Streaming fusion (order-invariant proof path).
Maintain U += w*atanh(a), W += w, and publish a_out := tanh( U / max(W, eps_w) ) with w := |m|^GAMMA.
This equals the closed form a_out := tanh( sum_i(w_i*u_i) / max(sum_i w_i, eps_w) ) and is order-invariant (batch == stream == shuffled).
Conformance (executive summary, dataset-neutral).
• Collapse parity: True (the RMS value lane m is never altered).
• Lane bounded/finite: True (a_out in (-1,+1), no NaN/Inf).
• Order-invariance: Streamed a_out matches the closed form within floating-point tolerance.
• Band posture: Long calm spans appear as higher bands (often A+), with occasional low-band intervals early in runs when history is minimal.
Reproduce (concept steps, paths generic).
- Arrange the dataset tree with the three test folders.
- Compute per-file RMS for
m; maintain(time,kpi,m,a,band,knobs_hash,build_id,site_id,unit_id,note). - Apply the entropy mapper to
|diff(m)|with the conventions above; clamp before anyatanh. - (Optional) Weight by magnitude with
w := |m|^GAMMAand stream-fuse via{U,W}. - Verify: collapse parity, bounded
a, order-invariant{U,W}, and a plausible band distribution.
Integrity & manifest (copy-ready skeleton).
[SSMH_MANIFEST]
profile = ims.rms_entropy
build_id = <build_id>
date_utc = <YYYY-MM-DD>
dataset = IMS_Bearings_UC
subsets = <1st_test;2nd_test;3rd_test>
selection = <describe subset/stride>
kpi = rms_per_file
# Knobs
eps_a = 1e-6
eps_w = 1e-12
entropy_bins = 32
entropy_win = 128
k_gain = 2.0
w_gamma = 1.0
# Mapper conventions (normative)
entropy_log_base = e
binning_policy = equal_width_minmax
zero_prob_convention = 0*log(0)=0
diff_mode = abs
fusion = U/W (w = |m|^1.0)
# Bands (alias note: App==A++, Ap==A+, Amm==A--)
bands = {App=0.75, Ap=0.50, A0=0.25, Am=0.10, Amm=-inf}
notes = Values unchanged; order-invariant U/W parity holds
manifest_checksum = <sha256>
conformance_checksum = <sha256>
[/SSMH_MANIFEST]
Why this works (one line).phi((m,a)) = m keeps numbers identical while {U,W} fusion (U += w*atanh(a), W += w, a_out := tanh(U/max(W,eps_w))) with atanh/tanh composition yields bounded, order-invariant evidence that highlights fragile intervals without hiding the KPI.
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The contents in the Shunyaya Symbolic Mathematical Hardware (SSMH) materials are research/observation material. They are not engineering advice, not a safety standard or certification, and not operational guidance. Do not use for safety-critical, medical, legal, or financial decisions. Use at your own discretion; no warranties are provided; results depend on correct implementation and inputs.
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