Physics-Grounded Latent Inversion with Selective State-Space Learning for In-Line PCCP Inspection

In-line eddy-current testing (ECT) of buried prestressed concrete cylinder pipe (PCCP) produces long dual-frequency impedance records whose statistics shift between inspection campaigns, and learned diagnostic models that perform well on one campaign often fail silently on the next. This article presents a two-stage interpretation framework that treats campaign drift as physics to be inverted rather than noise to be normalized. A model-based latent inversion fits each chainage-indexed record against a closed-form Dodd–Deeds forward operator for the finite-thickness steel cylinder, jointly estimating an effective conductivity–permeability state, a per-sequence channel calibration, and a physics-normalized anomaly stream; boundary conditions are satisfied analytically, and no material constants are assumed. A bidirectional selective state-space network then performs joint boundary localization and severity classification on the inverted features, with abstention driven by dual-detector agreement.

本文提出一種兩階段架構,將埋地預應力鋼筒混凝土管(PCCP)渦流檢測中的跨批次漂移視為可反演的物理量:以Dodd–Deeds解析正演算子進行模型式潛變量反演(有效電導率–磁導率狀態、逐序列校準、物理歸一化異常流),再由選擇性狀態空間網路完成接頭定位.

Contributions:

• First physics-informed, velocity-normalized multi-channel selective-SSM for long-range NDT.
• Learned low-rank common-mode baseline as the drift-robust, label-free substitute for physics.
• Spatial×spectral×detector fusion justified by measured complementarity/contrast.
• Genuine linear-complexity long-range inference where prior work used quadratic Transformers or fabricated state-space models.

Experiment Plan — SST-SSM for ECT Pipe Inspection

Claims

ID	Claim	Hypothesis	Primary metric	Pass bar
C1	PISSM jointly segments + classifies better than the existing baselines end-to-end	coupling + long-range SSM reduces error propagation	Propagated Precision (PP)	PP ≥ best baseline + 0.03
C2	Low-rank common-mode removal improves drift/OOD robustness	drift is common-mode; removing it yields drift-invariant signal	ΔF1 = F1_ID − F1_OOD (lower better)	Δ smaller than "w/o common-mode" by ≥0.03
C3	Dual-frequency fusion beats single-frequency	32/100 Hz are complementary (corr 0.4–0.77)	weighted F1	F1w(both) > F1w(best single)
C4	Selective SSM gives linear-complexity long-range modeling vs Transformer	O(L) vs O(L²)	wall-clock + peak mem vs seq len	linear scaling to ≥100k; < Transformer mem
C5	Cross-detector contrast |D1−D2| adds classification signal	measured discriminative	per-class F1 (rare classes)	F1(with contrast) > F1(without) on minority
C6	Velocity normalization improves boundary localization	removes 18±16mm spatial jitter	Boundary MAD (m)	MAD(resampled) < MAD(raw index)

Ablation matrix (each row = one trained model, same data/splits/seeds)

Config	Velocity norm	Common-mode removal	Dual-freq	|D1−D2| contrast	SSM backbone	Coupled heads
Full (SST-SSM)	✓	✓	✓	✓	bi-SSM	✓
w/o velocity norm	✗	✓	✓	✓	bi-SSM	✓
w/o common-mode	✓	✗	✓	✓	bi-SSM	✓
single-freq (32)	✓	✓	32-only	✓	bi-SSM	✓
w/o contrast	✓	✓	✓	✗	bi-SSM	✓
SSM→GRU	✓	✓	✓	✓	biGRU	✓
SSM→Transformer	✓	✓	✓	✓	attn	✓
decoupled heads	✓	✓	✓	✓	bi-SSM	✗

Each cell reports MAD(m), Seg-Acc@tol, F1w, PP. Maps directly to C1–C6.

Baselines (existing real code, same protocol)

CNN-LSTM (multiclass_final.py), TCN (segment_detector_TCN.py), MTF-CNN (mtf_binary_classifier_fixed.py), CPD (segment_detector_cpd.py), GaussianHMM (SSSM_v2.py).

Data splits

• ID: train/val/test split within a campaign pool {102, 88003, ...}.
• OOD (cross-campaign): train on a set of contracts, test on held-out contracts (files differ in class balance: 102=27% fault, 88003=1.8%, 86002=2%, 815002=0%).
• Report ID and OOD for every model. Seeds: {42, 123, 2024} → mean ± std.

Metrics (all in ssm_ndt/metrics.py, computed from committed predictions)

• Boundary MAD (m): greedy-match predicted boundary peaks to true, mean |Δ| × grid spacing.
• Seg-Acc@tol: fraction of true boundaries matched within tolerance τ (default 0.5 m).
• F1 / weighted F1: per-class and class-frequency-weighted.
• Propagated Precision: class-correct only where boundary localized within τ.
• Throughput/mem (C4): samples/s and peak memory vs sequence length.

Imbalance handling

Existing GAN augmentation (synthetic_GAN.py) + class-weighted CE + minority-focused F1 reporting.

Definition of done

A results table + ablation table generated entirely by ssm_ndt/train.py → results/*.json, plus figures, with seeds and OOD columns. Then and only then, claims are written.

Run order

1. ssm_ndt/data.py smoke (load + resample + decompose) ✅ first.
2. Train Full on one campaign (overfit sanity) → metrics sane.
3. Ablation rows on the campaign pool (ID).
4. Cross-campaign OOD for Full + key ablations.
5. C4 complexity benchmark.
6. Baseline re-evaluation under same metrics.