Gopalkrishna Advanced Rural Research Foundation (GARRF)
Advanced Virtual EMI Laboratory • Quantum AI Inversion
Formulation-Specific Quantum Ansatz • Decoupled 5-State Inversion Pipeline
1. Specimen & Transducer Configuration
Specimen Geometry (Aspect Ratio Constrained)
🧪 Interfacial Adhesive Shear-Lag Parameters
🌡 Environmental Temperature Drift & Decoupling
⚙ Temperature Compensation Filter (EOM):
⚛ Formulation-Adaptive Quantum AI Ansatz
• Physical Crack Geometry Progression (t_s = Specimen Thickness)
| State | Length (a) | Depth (d) | Remaining t_s | ΔK Loss |
|---|
2. Spectral Measurement Sequence (Active When Locked)
Screen 1: Specimen Support, Bond Layer & Dynamic Crack Kinematics
Setup Unlocked • Configure parameters & click 'Lock Parameters'
Screen 2: Real Conductance Spectrum G(ω) [10 kHz – 1 MHz]
Pristine
Crack 1
Crack 2
Crack 3
Crack 4
Screen 3: Imaginary Susceptance Spectrum B(ω) [10 kHz – 1 MHz]
Pristine
Crack 1
Crack 2
Crack 3
Crack 4
Screen 4: Statistical Damage Indices (Classical Metrology)
Relative to Pristine Baseline
| Damage State | RMSD (%) | MAPD (%) | CCD (1 - r) | Status |
|---|---|---|---|---|
| Pristine | 0.00 % | 0.00 % | 0.0000 | Reference |
| Crack 1 | -- | -- | -- | Unmeasured |
| Crack 2 | -- | -- | -- | Unmeasured |
| Crack 3 | -- | -- | -- | Unmeasured |
| Crack 4 | -- | -- | -- | Unmeasured |
Screen 5: Quantum AI Inversion & Formulation Error Approximation (PI-QNN)
Quantum Engine: Idle (Awaiting Inversion)
Inspect Quantum State:
Decoupled Formulation Parameters for Pristine (State 0)
True Predicted Stiffness Loss (ΔKQuantum):
-- %
Adhesive Boundary Attenuation Error (εbond):
-- %
Thermal Elasticity Softening Error (εΔT):
-- %
Quantum State Fidelity (|⟨ψ0|ψopt⟩|2):
--
Convergence Optimization Loss (PI-QNN ƒ):
--
1. Why Quantum AI Architecture Must Differ for 1D, 2D, and 3D Mechanics
In physical electromechanical impedance (EMI) problems, applying a single generic quantum neural network across 1D beams, 2D plates, and 3D solids is physically invalid. The complexity of dynamic stress tensors and wave reflections differs fundamentally across dimensions, requiring tailor-made quantum ansatzes:
| Mechanics Formulation | Governing Wave Physics & Tensor | Optimal Quantum AI Ansatz | Hilbert Space Dimension | Physical Decoupling Justification |
|---|---|---|---|---|
| 1D Beam (Liang et al.) | Uniaxial wave propagation ($T_2 = T_3 = 0$); single axial reflection path. | 2-Qubit Variational Quantum Circuit (VQC) with Pauli-Z feature map. | $\mathcal{H} = 2^2 = 4$ Basis States | 4 basis states ($\Vert{}00\rangle, \Vert{}01\rangle, \Vert{}10\rangle, \Vert{}11\rangle$) are mathematically optimal to decouple 1D crack stiffness from thermal drift without barren plateaus. |
| 2D Plate (Zhou / Bhalla & Soh) | Biaxial plane stress ($T_3 = 0$) with Poisson ratio contraction ($\nu$) and radial modal reflections. | 3-Qubit Quantum Convolutional Neural Network (QCNN) with Circular Entanglement ($CZ$). | $\mathcal{H} = 2^3 = 8$ Basis States | 8 basis states capture orthogonal wave vector interactions ($k_x, k_y$) and non-linear boundary reflections across four edges. |
| 3D Continuum (Annamdas & Soh) | Full 3D stress tensor ($T_1, T_2, T_3 \ne 0$), Rayleigh surface waves, and thickness dilatation mode (600–900 kHz). | 4-Qubit Physics-Informed Quantum Neural Network (PI-QNN) with All-to-All Entanglement. | $\mathcal{H} = 2^4 = 16$ Basis States | 16 basis states are strictly required to resolve directional sum impedances across all 6 faces and decouple internal aggregate confinement from surface defects. |
2. Mathematical Definition of Crack Geometry ($t_s = \text{Specimen Thickness}$)
In fracture mechanics and non-destructive evaluation, crack severity is non-dimensionalized with respect to the substrate thickness $t_s$:
- Baseline ($S_0$): Pristine uncracked specimen ($d = 0.0\text{ mm}$, remaining thickness $100\%$).
- Crack 1 ($S_1$): Incipient surface microcrack ($d = 0.10 \cdot t_s$, length $a = 2.0\text{ mm}$).
- Crack 2 ($S_2$): Minor fatigue crack ($d = 0.30 \cdot t_s$, length $a = 5.0\text{ mm}$).
- Crack 3 ($S_3$): Moderate structural fracture ($d = 0.50 \cdot t_s$, length $a = 10.0\text{ mm}$).
- Crack 4 ($S_4$): Critical through-thickness crack ($d = 0.80 \cdot t_s$, length $a = 18.0\text{ mm}$).
3. Exact Quantitative PZT Placement Coordinates
Transducer positions are calculated on normalized spatial coordinates:
- 1D Beam: $x = 0.15 L$ (Near Clamped Root), $x = 0.50 L$ (Mid-Span Center), $x = 0.85 L$ (Near Free Tip End).
- 2D Plate: $(x = 0.50 L, y = 0.50 W)$ (Plate Center), $(x = 0.35 L, y = 0.20 W)$ (Plate Edge), $(x = 0.20 L, y = 0.20 W)$ (Plate Corner).
- 3D Solid: $(0.50 L, 0.50 W, t_s)$ (Surface Center), $(0.25 L, 0.25 W, t_s)$ (Offset Edge), $(0.50 L, 0.50 W, 0.50 t_s)$ (Centrally Embedded).
4. Peer-Reviewed Scholarly References
- Havlíček, V., et al. (2019). "Supervised learning with quantum-enhanced feature spaces." Nature, 567(7747), pp. 209–212.
- Cong, I., Choi, S., & Lukin, M. D. (2019). "Quantum convolutional neural networks." Nature Physics, 15(12), pp. 1273–1278.
- Bhalla, S., & Soh, C. K. (2004). "Electromechanical Impedance Modeling for Adhesively Bonded Piezo-Transducers." Journal of Aerospace Engineering (ASCE), 17(4), pp. 154–165.
- Annamdas, V. G. M., & Soh, C. K. (2007). "Three-dimensional electromechanical impedance model for piezoceramic transducer–structure interaction, Part I: Formulation of directional sum impedance." Smart Materials and Structures, 16(5), pp. 1801–1813.
- Annamdas, V. G. M., & Soh, C. K. (2008). "Three-dimensional electromechanical impedance model for multiple piezoceramic transducers-structure interaction." Smart Materials and Structures, 17(5), p. 055009.