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J2 Results — Seven-Phase Claim-Driven Prototype

Date: 2026-04-18 Status: Fifth prototype; companion to the J2 methodology prototype. Applied retrospectively to J2 results sections (§3 Validation + §4 Results and Discussion) ahead of R2 submission 2026-04-29.

Results sections have a different claim structure than methodology sections: headline finding / sensitivity / comparison against prior work / edge cases rather than framework / assumptions / setup / V&V. Running the workflow on J2's results surfaces a different class of defect than the methodology pass did.

Phase 1 — Thesis statement

The 3D-FE-calibrated Winkler model predicts the baseline natural frequency of the 4.2 MW Gunsan tripod within −3.9 % of 32 months of field data, establishes a power-law \(|\Delta f / f_0| = 0.167 (S/D)^{1.47}\) across 11 scour depths, and — across a four-representation comparison — is the only model that simultaneously preserves depth-resolved stiffness evolution and runs five orders of magnitude faster than direct 3D analysis.

Phase 2 — Claim list

  • R1 — Baseline field match. Predicted \(f_1\) within −3.9 % of 32-month Gunsan field data; prediction and measurement overlaid with scoured-frequency evolution annotated.
  • R2 — Power-law across 11 scour depths. Monotone, well-fit by \(|\Delta f / f_0| = 0.167 (S/D)^{1.47}\); residual plot confirms no systematic departure.
  • R3 — Four-representation comparison. Fixed-base, macro-element, standard BNWF, distributed BNWF on identical cases. Only distributed BNWF captures the depth-resolved evolution; fixed-base predicts zero response; macro-element misses scour-depth localisation.
  • R4 — Five-orders-of-magnitude speed-up. Wall-clock runtime of distributed BNWF eigenvalue analysis vs. direct 3D FE eigenvalue analysis; averaged over 11 scenarios with per-case timing table.
  • R5 — Per-bucket load-sharing and lid contribution. Load-share ratio per bucket at \(S/D \in \{0, 0.2, 0.4, 0.6\}\); lid-bearing vs skirt-friction breakdown as scour progresses.
  • R6 — SHM threshold alignment. 1P-resonance boundary crossed at \(S/D = 0.43\); mapped against DNV-RP-C212 and IEC 61400-3 fatigue DEL thresholds.

Phase 3 — Claim → evidence map

flowchart TD
    T["<b>Thesis (results)</b><br/>−3.9% field match · PL-1 power-law ·<br/>10⁵× speedup · depth-resolved BNWF wins"]
    T --> R1["R1 · Baseline field match"]
    T --> R2["R2 · Power-law across 11 depths"]
    T --> R3["R3 · Four-representation comparison"]
    T --> R4["R4 · 5-orders speedup"]
    T --> R5["R5 · Per-bucket load-sharing"]
    T --> R6["R6 · SHM threshold alignment"]
    R1 --> E1["Fig · predicted vs field f1 time series (32 months)<br/>Stat · relative error = −3.9%"]
    R2 --> E2["Fig · PL-1 fit across 11 scour depths + residual panel<br/>Table · power-law coefficients with 95% CI"]
    R3 --> E3["Fig · four-representation f1 vs S/D overlay<br/>Table · per-representation error + computational cost"]
    R4 --> E4["Table · wall-clock benchmark (single case + batch of 100)"]
    R5 --> E5["Fig · per-bucket reactions at 4 scour depths<br/>Fig · lid vs skirt contribution as S/D progresses"]
    R6 --> E6["Fig · f1(S/D) vs DNV-RP-C212 + IEC fatigue DEL thresholds"]
    E1 --> S1["spec · fig-field-match-32month"]
    E2 --> S2["spec · fig-powerlaw-fit<br/>table · pl1-coefficients"]
    E3 --> S3["spec · fig-four-representation<br/>table · representation-comparison"]
    E4 --> S4["table · runtime-benchmark"]
    E5 --> S5["spec · fig-per-bucket-share<br/>spec · fig-lid-vs-skirt"]
    E6 --> S6["spec · fig-shm-thresholds"]

Seven figures, three tables.

Phase 4 — Figure specs

fig-field-match-32month (R1). 32-month Gunsan field \(f_1\) time series (grey) overlaid with the Winkler model's predicted \(f_1\) (blue). Annotation: relative error −3.9 %. Shaded region for the calibration window vs. post-calibration prediction. Residual panel below.

fig-powerlaw-fit (R2). 11 scour depths' \(|\Delta f / f_0|\) vs. \(S/D\) on log-log axes with PL-1 fit line \(|\Delta f / f_0| = 0.167 (S/D)^{1.47}\). Residual panel below shows deviation from fit, confirming no systematic departure. \(R^2\) annotated.

table-pl1-coefficients (R2). Row: coefficient \(a\), exponent \(b\), \(R^2\), RMSE, per-depth max residual. 95 % CI on \(a\) and \(b\) from bootstrap.

fig-four-representation (R3). Four curves (fixed-base, macro-element, standard BNWF, distributed BNWF) of \(f_1/f_{1,0}\) vs \(S/D\) on the same axes. Field data point overlay. Annotation: only distributed BNWF matches the observed trend.

table-representation-comparison (R3). Columns: representation, relative error at \(S/D = 0\), \(S/D = 0.25\), \(S/D = 0.5\); computational cost per case; verdict (✓ or specific-failure-mode note).

table-runtime-benchmark (R4). Rows: 3D FE (OptumGX), Mode A fixed-base, Mode B 6×6, Mode C distributed BNWF, Mode D dissipation-weighted. Columns: single-case wall-clock, batch of 100, speedup ratio vs 3D FE, hardware spec. Matches reviewer comment R2.4 from the J2 R2 response.

fig-per-bucket-share (R5). Stacked bar chart at \(S/D \in \{0, 0.2, 0.4, 0.6\}\) showing load-share fraction across bucket A, B, C. Annotation: as scour progresses asymmetrically, load redistributes by 20–40 %.

fig-lid-vs-skirt (R5). Dual-axis line plot: lid-bearing capacity contribution (%) vs scour depth (left axis); skirt-friction contribution (%) vs scour depth (right axis). Annotation: at \(S/D = 0.5\), lid contributes ~30 % of lateral resistance — a mechanism absent in monopile theory.

fig-shm-thresholds (R6). \(f_1/f_{1,0}\) vs \(S/D\) with four horizontal threshold bands coloured green / yellow / orange / red; 1P-resonance boundary annotated at \(S/D = 0.43\); DNV-RP-C212 and IEC 61400-3 fatigue-DEL thresholds overlaid as dashed lines.

Phase 5 — Paragraph skeletons

§3 Validation. ¶1 (field baseline) [→ fig-field-match-32month]. Predicted \(f_1\) within −3.9 % of 32 months of Gunsan field data. Framing: baseline match is a necessary condition for the Winkler model's credibility; it is the first number a reviewer wants. ¶2 (centrifuge cross-check). Reference the J3 centrifuge power-law (|a| = 0.044–0.086 in saturated sand) vs the numerical |a| = 0.167; disparity attributed to the centrifuge-protocol OCR artefact (J3 §2.4.1), directionally conservative. ¶3 (validation coverage). Baseline-field + centrifuge-cross-check + benchmark-against-literature = three independent validation anchors. Stress that further scour-history validation requires bathymetric ground truth, flagged in limitations.

§4 Results and discussion. ¶1 (power-law extraction) [→ fig-powerlaw-fit, table-pl1-coefficients]. PL-1 fit across 11 scour depths; well-constrained power-law. ¶2 (four-representation comparison) [→ fig-four-representation, table-representation-comparison]. Only distributed BNWF captures both magnitude and depth-resolved evolution. Fixed-base ≡ 0 (no scour sensitivity by construction). Macro-element misses the scour-depth localisation because it condenses to a single node. ¶3 (computational cost) [→ table-runtime-benchmark]. Five-orders-of-magnitude speedup. Critical for real-time digital-twin updating (Paper A) and population-scale Monte Carlo (Paper J5). ¶4 (per-bucket load-sharing) [→ fig-per-bucket-share, fig-lid-vs-skirt]. Three-bucket load redistribution and lid-bearing contribution quantified — the mechanism-level answer to why tripods are less scour-sensitive than monopiles. Addresses reviewer R2.5. ¶5 (SHM thresholds) [→ fig-shm-thresholds]. 1P-resonance boundary at \(S/D = 0.43\) (\(\approx 3.4\) m scour); mapped against DNV-RP-C212 + IEC 61400-3 fatigue DEL. Addresses reviewer R2.2.

Phase 6 — Generate figures (figure_generator integration)

Seven figure_generator sessions + three tables. fig-field-match-32month and fig-powerlaw-fit are the hero pair — if either fails, the paper's headline fails.

Highest priorities before R2 submission (2026-04-29):

  • fig-per-bucket-share + fig-lid-vs-skirt are NEW figures for R2, addressing reviewer R2.5. Without them, the reviewer response to R2.5 is narrative only.
  • table-runtime-benchmark is NEW, addresses R2.4.
  • fig-shm-thresholds needs the DNV-RP-C212 + IEC 61400-3 overlay added for R2.2.

Each is one figure_generator session.

Phase 7 — Coherence passes

Pass A — paragraphs only. - §3 (validation) currently narrates the baseline match before showing the figure. Fix: hero figure goes first (¶1 sentence: "figure X shows field match within −3.9 %"), then narrative. - §4 ¶4 (load-sharing) currently claims the mechanism but does not derive it from the figures. Fix: the paragraph must walk the reader from the per-bucket reaction plot to the lid-vs-skirt decomposition and then to the mechanism conclusion. Three sentences, each tied to a figure element. - §4 ¶5 (SHM thresholds) frames the result as operational guidance but does not say who is the intended user. Fix: one sentence naming the audience ("an asset manager setting inspection intervals under DNV-RP-C212 compliance").

Pass B — figures only. - Seven figures is borderline dense for a 9,000-word paper. Consider: combine fig-per-bucket-share + fig-lid-vs-skirt into a single two-panel figure (panel a = bucket shares, panel b = lid vs skirt). Saves one figure slot; the mechanism argument still reads. - fig-powerlaw-fit with a residual panel underneath is visually heavy. Decide: split into main figure (top panel) + supplementary residual, or keep combined with a smaller residual panel height. Either works.

Reviewer objection rehearsal (results-specific):

  1. "How do you know the 32-month baseline match is not overfit?" — answered by ¶2 centrifuge cross-check + ¶3 three-anchor validation narrative. Strengthen: cite the hold-out window (if any) where the model was not calibrated; if no hold-out, acknowledge and frame the −3.9 % as a single-anchor match.
  2. "Why 11 scour depths rather than a coarser set?" — answered by convergence rationale in methodology §2.2.3. Pointer needed in results §4 ¶1.
  3. "Is the power-law exponent 1.47 stable across soils?" — currently not addressed. Add one sentence on the coefficient's soil-dependence expected behaviour + citation to Paper B's Buckingham-Pi framework, or flag as future work if out of scope.

Actionable items before R2 submission:

# Item Driving reviewer comment Cost
1 Build fig-per-bucket-share + fig-lid-vs-skirt (or combined) R2.5 1–2 sessions
2 Build table-runtime-benchmark with actual wall-clock measurements R2.4 1 session
3 Overlay DNV-RP-C212 + IEC fatigue DEL on SHM threshold figure R2.2 30 min
4 Add one-sentence pointer to soil-dependence of power-law exponent new 5 min
5 Coherence edit on §4 ¶4 walking figure → figure → mechanism new 15 min

Four new figures/edits, total ~4 sessions. Completable in the first two days of the R2 work plan.

What this pass surfaces that the methodology pass did not

  • Three of the five R2 reviewer items (R2.2, R2.4, R2.5) are results-section figures, not methodology-section figures. The methodology prototype flagged R2.4 and R3.1 as missing evidence; this results-prototype pass catches R2.5 and R2.2 additionally.
  • The paragraph-level coherence fixes are different between methodology and results. Methodology fixes tend to be framing sentences (claim-to-section links). Results fixes tend to be mechanism walk-throughs tying figures together.
  • The "who is the intended user" sentence on the SHM thresholds slide is a results-section-specific fix — in methodology sections the reader is the peer reviewer; in results sections it is the engineer or asset manager. This distinction should propagate into other papers' results-section prototypes (J3 results comes next).