🔬 applied physics

Physics-Informed Framework for Impact Identification in Aerospace Composites

This paper presents a novel physics-informed framework (Phy-ID) that integrates physical laws with data-driven inference to achieve robust, stable, and accurate identification of impact parameters in aerospace composites, even under noisy conditions and limited data availability.

Original authors: Natália Ribeiro Marinho, Richard Loendersloot, Jan Willem Wiegman, Frank Grooteman, Tiedo Tinga

Published 2026-03-31

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Natália Ribeiro Marinho, Richard Loendersloot, Jan Willem Wiegman, Frank Grooteman, Tiedo Tinga

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a detective trying to solve a crime, but you didn't see the crime happen. All you have are the ripples left in a pond after a stone was thrown in. Your job is to figure out: How big was the stone? How fast was it moving? And how hard did it hit?

This is exactly the challenge engineers face with airplane wings made of composite materials (like carbon fiber). These wings are incredibly strong and light, but if a bird hits them or a tool drops on them, the damage can be hidden deep inside, invisible to the naked eye. If they don't know the "force" of that hit, they can't tell if the plane is safe to fly.

This paper introduces a new "super-detective" tool called Phy-ID (Physics-Informed Impact Identification). Here is how it works, explained simply:

The Problem: The "Guessing Game" is Broken

Usually, engineers try to guess the impact force by looking at the vibrations (the ripples) recorded by sensors.

The Old Way (Pure Data): They used to feed the sensor data into a computer program and say, "Learn from this and guess." But this is like asking a student to solve a math problem without knowing the formula. If the data is noisy (like a bad phone connection) or if the student hasn't seen that specific type of problem before, they guess wildly wrong.
The Physics Way: They used to rely entirely on complex physics equations. But these are like trying to solve a puzzle with a map that has missing pieces. If the real world is messy (wind, temperature, weird shapes), the map doesn't fit, and the computer takes too long to calculate.

The Solution: The "Physics-Savvy" Detective

The authors created a new framework that combines the best of both worlds. They call it Physics-Informed Machine Learning. Think of it as hiring a detective who is both a brilliant data analyst and a certified physics professor.

They built this detective using three specific "biases" (or rules of thumb):

1. Observational Bias: "Looking at the Right Clues"

Instead of feeding the computer raw, messy sound waves, the team first translates the data into "physics-based energy indicators."

Analogy: Imagine trying to describe a storm. Instead of just recording the wind noise, you measure specific things: "How high were the waves?" "How fast was the rain falling?" "How much energy did the thunder carry?"
Result: The computer gets a clean, organized list of clues that actually matter, rather than a jumbled mess of noise.

2. Inductive Bias: "Building a Smart House"

They didn't just build a generic computer brain; they built a house with specific rooms designed for specific jobs.

The Split: They realized that guessing the weight of the object and guessing its speed are two different tasks. Speed is loud and obvious in the data; weight is quiet and hidden.
The Strategy: They used two separate "mini-detectives" (neural networks). One focuses only on speed, the other only on weight.
The Rule: They forced the "weight detective" to only give positive numbers (you can't have negative mass!). This prevents the computer from coming up with impossible answers.

3. Learning Bias: "The Strict Teacher"

This is the most important part. When the computer makes a guess, the "teacher" checks it against the Law of Conservation of Energy.

The Rule: The computer knows a simple physics formula: Energy = ½ × Mass × Speed².
The Check: If the computer guesses a heavy weight but a slow speed, the teacher says, "Wait, that math doesn't add up to the energy we measured! Try again."
Result: The computer is constantly corrected to stay within the laws of physics. It can't just "hallucinate" a random answer; it must make physical sense.

The Results: A Reliable Detective

The team tested this new system on a real, complex airplane wing part in a lab. They dropped heavy weights on it from different heights to simulate crashes.

Accuracy: The system guessed the speed and weight with very high accuracy (less than 8% error).
Robustness: Even when they added "noise" to the data (simulating bad sensors) or gave the computer very little data to learn from, it still performed well. It didn't panic like the old methods.
Generalization: When the computer saw a crash it had never seen before, it could still make a good guess, provided it had seen some examples of damaged wings during its training.

Why This Matters

In the past, if a sensor was a little bit broken or the data was messy, the system might say, "The plane is fine," when it was actually broken. Or it might say, "The plane is doomed," when it was actually fine.

This new Phy-ID framework acts like a safety net. By forcing the computer to respect the laws of physics, it ensures that the answers are realistic, stable, and trustworthy. It turns a "black box" guessing game into a transparent, logical investigation that engineers can actually trust to keep airplanes safe.

In short: They taught the computer to do math and physics at the same time, so it never gives an answer that breaks the laws of nature.

1. Problem Statement

Aerospace composite structures are highly susceptible to low-velocity impact damage, which often causes severe internal delamination without visible surface signs. Effective Structural Health Monitoring (SHM) requires estimating impact energy to assess damage severity. However, this is a complex inverse problem characterized by:

Ill-posedness: Sparse and noisy sensor data often fail to uniquely determine impact parameters.
Missing Excitation Data: Direct measurements of impactor mass and velocity are frequently unavailable in operational settings.
Non-linearity: Structural responses become highly nonlinear, especially when damage occurs, complicating the relationship between sensor signals and impact severity.
Limitations of Existing Methods:
- Physics-based models are accurate but computationally expensive and require detailed material knowledge.
- Data-driven (ML) models are efficient but lack physical constraints, leading to poor interpretability, sensitivity to noise, and weak extrapolation capabilities.
- Probabilistic approaches often embed physics implicitly, failing to guarantee physically admissible solutions.

2. Methodology: The Phy-ID Framework

The authors propose Phy-ID (Physics-Informed Impact Identification), a unified framework that integrates observational, inductive, and learning biases to enforce physical consistency while leveraging data-driven inference.

A. Core Architecture

The framework utilizes a disjoint inference formulation using two decoupled Fully Connected Neural Networks (FCNNs) trained sequentially:

Displacement Network ( $w_\theta$ ): Maps input features to transverse displacement. Impact velocity ( $v_0$ ) is inferred by differentiating the displacement with respect to time at $t=0$ .
Mass Network ( $m_\phi$ ): Predicts the impactor mass ( $m$ ).
Coupling: The two networks are linked via the Kinetic Energy relation ( $E = \frac{1}{2}mv^2$ ). This ensures that the inferred mass and velocity are physically consistent with the measured impact energy.

B. Integration of Biases

Observational Bias (Input Space):
- Raw sensor signals are transformed into multi-domain features (time, frequency, and time-frequency).
- Selected features act as physics-based energy indicators (e.g., RMS, Peak Amplitude, Weighted Peak Frequency) to ensure the input space captures relevant structural dynamics.
Inductive Bias (Model Architecture):
- Surrogate Models: Separate networks for mass and velocity prevent optimization imbalance (where velocity dominates due to its quadratic effect on energy).
- Activation Functions: Smooth functions (e.g., Tanh, Softplus) are used to ensure stable differentiation for velocity calculation.
- Constraints: The mass network enforces a strictly positive output (via Softplus) to prevent non-physical negative mass.
Learning Bias (Loss Function):
- A hybrid loss function combines data-driven terms (MSE against measured targets) and physics-driven terms.
- Physics Loss Terms:
  - Initial Conditions: Enforces zero displacement at $t=0$ .
  - Kinetic Energy Consistency: Penalizes deviations between the predicted energy ( $\frac{1}{2}mv^2$ ) and the measured energy.
- Sequential Training: The networks are trained alternately. In each cycle, one network's parameters are fixed while the other is optimized, ensuring balanced convergence.

3. Key Contributions

Unified Framework: Introduction of Phy-ID, which systematically combines observational, inductive, and learning biases to solve the ill-posed impact identification problem.
Disjoint Inference Strategy: A novel approach to decouple mass and velocity estimation to avoid optimization bias, subsequently coupling them via kinetic energy conservation.
Physically Meaningful Parameters: Instead of predicting energy directly, the model infers latent physical parameters (mass and velocity), enhancing interpretability and event characterization.
Robustness to Real-World Conditions: Demonstrated performance under sparse data, high noise, and out-of-distribution (OOD) scenarios.

4. Experimental Results

The framework was validated using experimental data from a stiffened thermoplastic composite panel (1600 mm × 370 mm) with 73 impact events (3.74 J to 80.95 J).

Predictive Accuracy (Case P1):
- Impact Velocity: MAPE = 4.97%.
- Impactor Mass: MAPE = 7.75%.
- Impact Energy: MAPE = 9.85%.
- Comparison: A standard data-driven model (without physics constraints) yielded a higher MAPE (12.66%) and significantly fewer predictions within the $\pm10\%$ tolerance band (51.8% vs. 88.9% for Phy-ID).
Robustness (Cases R1–R3):
- Data Scarcity: Performance remained stable (MAPE $\approx$ 10–15%) even with only 25% of training data available.
- Noise: The model showed high tolerance to measurement noise (up to 5%), maintaining accuracy due to the robustness of the selected physics-based features.
- Combined Stress: Under the worst-case scenario (25% data + 5% noise), MAPE rose to 25.4%, indicating gradual degradation rather than catastrophic failure.
Generalization (Case G1):
- Linear Regime (Pristine): The model generalized well to OOD samples in the low-energy (linear) regime.
- Non-linear Regime (Damaged): Generalization to high-energy (damaged) impacts depended heavily on the inclusion of damaged samples in the training set. When >50% of damaged data was included, predictions aligned closely with ground truth, highlighting the need for representative damage data to capture non-linearities.

5. Significance and Conclusion

The Phy-ID framework represents a significant advancement in SHM for aerospace composites by bridging the gap between pure physics-based modeling and pure data-driven learning.

Reliability: By enforcing governing physical laws (kinetic energy conservation), the framework eliminates non-physical solutions, ensuring that inferred parameters are mechanically plausible.
Data Efficiency: The integration of physical priors allows for accurate estimation even with limited and noisy datasets, a critical requirement for real-world aerospace applications where data collection is expensive.
Interpretability: The ability to infer specific physical quantities (mass and velocity) rather than a black-box energy output supports better decision-making for maintenance and safety.
Future Outlook: The authors suggest extending the framework with transfer learning for scalability, multi-fidelity modeling (combining simulations and experiments), and uncertainty quantification to provide confidence bounds for safety-critical decisions.

In summary, Phy-ID offers a robust, interpretable, and data-efficient solution for impact identification, demonstrating that systematic integration of physics-informed biases is essential for reliable monitoring in complex, nonlinear structural environments.