L1 ⚛ L1-124 ⊙ Testnet

Vibration-Based Damage Detection (modal analysis NDT)

Industrial Inspection · Modal / operational deflection shape damage ID

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⬇ L1-124.md

# ⚛ L1 Principle — Vibration-Based Damage Detection (modal analysis NDT) **ID:** `L1-124` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Industrial Inspection — *Modal / operational deflection shape damage ID* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** damage location severity > **📡 Carrier:** acoustic · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554212 --- ## 🧠 1. Introduction **Vibration-Based Damage Detection (modal analysis NDT)** is a **nonlinear inverse problem** whose unknown lives in **damage location severity** space, within the **Modal / operational deflection shape damage ID** sub-domain of **Industrial Inspection**. Measurements consist of acoustic pressure waves recorded by transducers via a **modal vibration analysis** sensing mechanism. The forward operator applies, in order: L · excite · broadband operator; D · accelerometer array operator; L · modal extract operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Existence of the recovered damage location severity is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 12); environmental_variability dominates the stability cliff; operational_load_variation and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. ## ⚙ 2. Forward Model Physical chain: **x** → L · excite · broadband → D · accelerometer array → L · modal extract → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.modal_extract` `D.accelerometer_array` `L.excite.broadband` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.excite.broadband` | L · excite · broadband operator | | `D.accelerometer_array` | D · accelerometer array operator | | `L.modal_extract` | L · modal extract operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Industrial Inspection | | Sub domain | Modal / operational deflection shape damage ID | | Carrier | acoustic | | Problem class | nonlinear_inverse | | Solution space | damage_location_severity | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered damage location severity is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 12); environmental_variability dominates the stability cliff; operational_load_variation and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `vibration_damage` · **Forward operator:** `vibration_damage_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 25 | | N modes | — | 10 | | N sensors | — | 32 | | F range hz | Hz | 0.1 – 200 | | T acquire s | s | 60 | | Mode truncation | — | 0 | | Environmental variability | — | 0 | | Operational load variation | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0.0 – 40.0 | | N modes | — | 3 – 50 | | N sensors | — | 4 – 500 | | T acquire s | s | 5 – 3600 | | Sensor noise | — | 0.0 – 0.2 | | Mode truncation | — | 0.0 – 0.5 | | Environmental variability | — | 0.0 – 0.2 | | Operational load variation | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 20.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 40.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x7c2f432e98c71305c202164d4f77c98396401aa481b79fbfc4a16a9716430b14` - **Chain tx hash:** `0xda465af1a2a3a051daef3e32cca2720f01adf98be5d445fcd5ac952325f916ea` - **Chain block:** `41554212` --- ## File Mapping This bundle consists of: `L1-124.md`, `L1-124.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-124.md` | Source of truth — edit this | Human or LLM | | `L1-124.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-124`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-124.md).
Regenerate L1-124.json so every field matches the Markdown.
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L2-124-001 Vibration-Based Damage Detection (modal analysis NDT) Mismatch-Only Spec

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📋 JSON metadata

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  "domain": "Industrial Inspection",
  "hardness_fn": {
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    "kappa": 240,
    "metric": "PSNR_dB",
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    "regime": "Existence of the recovered damage location severity is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 12); environmental_variability dominates the stability cliff; operational_load_variation and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
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    "carrier": "acoustic",
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    "integration_axis": "temporal",
    "noise_model": "gaussian",
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      "D.accelerometer_array",
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    "sensing_mechanism": "modal_vibration_analysis",
    "solution_space": "damage_location_severity",
    "sub_domain": "Modal / operational deflection shape damage ID",
    "title": "Vibration-Based Damage Detection (modal analysis NDT)"
  },
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      "operational_load_variation",
      "mode_truncation",
      "environmental_variability",
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    "allowed_problem_classes": [
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        "operational_load_variation": 0.0
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      "N_sensors": [
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      ],
      "sensor_noise": [
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        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Modal / operational deflection shape damage ID",
  "title": "Vibration-Based Damage Detection (modal analysis NDT)"
}

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