From multimodal magnetic and ultrasonic measurements to mechanical and physical properties of steels

This research takes place in a collaborative project between a small-size industrial company (CMPHy) and a Vision and Artificial Intelligence academic research laboratory ImViA at Université Bourgogne Europe.

The challenge is to bridge the gap between raw sensor data and mechanical properties while accounting for uncertainties, noise, and variability in industrial environments. The PhD will focus on modelling, optimization, and uncertainty quantification, with the goal of delivering a robust and transferable solution for industrial applications.

The PhD will focus on:

• Developing predictive models (AI-based, Bayesian, or hybrid) to correlate magnetic/ultrasonic signals with mechanical properties.
• Optimizing input acquisition (signal types, parameters) to minimize uncertainty.
• Quantifying uncertainties in predictions, accounting for measurement noise, material variability, and model limitations.

A preliminary dataset will be built before the beginning of the PhD, and will be updated during the project using CMPhy’s 4-methods probe (BN, EC, IP, HA), an ultrasound sensor and tensile testing machines. The candidate will collaborate with industrial partners to design experiments and validate models on real-world steel samples.

1 Development of Predictive Models:

Objective: Design and implement models to predict mechanical properties (e.g., hardness, residual stress) from multimodal magnetic and ultrasonic signals. First, applied strain will be studied as mechanical properties, then mechanical hardness will be estimated.

This will need to explore a range of modelling techniques, including:

• AI-based models (e.g., neural networks, transformer architectures).
• Physics-informed models (e.g., hybrid models combining domain knowledge with machine learning).
• Bayesian models (e.g., Gaussian processes for uncertainty-aware predictions).

Then, the work will use the pre-existing database of calibrated measurements to train and validate models. A collaboration with CMPhy to refine the understanding of signal-property relationships is planned.

2 Optimization of Input Acquisition:

Objective: Identify the most informative signals and acquisition parameters to minimize uncertainty in predictions.

To that end, it is expected to perform sensitivity analysis (e.g., Sobol indices, Morris method) to determine which signals (e.g., Barkhausen noise, incremental permeability, Eddy current, harmonic analysis of tangential magnetic field and ultrasound) and parameters (e.g., frequency, amplitude) contribute most to prediction accuracy.

Then, the protocol will ve validated through experiments on steel samples with known properties.

3 Quantification of input signals Impact on Model Accuracy

Objective: Establish a quantitative link between input signals (type, number, acquisition parameters) and the accuracy of model predictions (precision, robustness, uncertainty). The goal is to develop a methodology for selecting which signals to acquire based on a desired prediction accuracy, while optimizing cost and acquisition complexity.

Several appraches can be studied :

• Sensitivity Analysis of Input Signals: Assess the impact of each type of signal (e.g., Barkhausen Noise, Eddy Currents, Incremental Permeability, Ultrasonic Signals) on prediction accuracy.
• Quantify quantify the contribution of each signal to model accuracy using sensitivity analysis methods.
• Evaluate the influence of acquisition parameters (e.g., frequency, magnetic field amplitude, probe orientation) on prediction quality.
• Estimate prediction uncertainty based on the signals used: Use Bayesian methods or Monte Carlo simulations to propagate uncertainties related to input signals (e.g., measurement noise, material variability).
• Map uncertainty as a function of signal combinations and their acquisition parameters. (Example: If only Barkhausen Noise is used, the uncertainty in hardness prediction is ±10%. By adding Incremental Permeability, this uncertainty drops to ±4%.)

Timeline for the 3-year PhD:

Year 1

- Literature review (state-of-the-art in multimodal NDT, uncertainty quantification, and predictive modeling).
- Preliminary modeling: Test simple models to establish baselines. First, for applied stress estimation then for mechanical hardeness estimation

Year 2

- Advanced model development: Implement and compare AI-based (e.g., neural networks), Bayesian, or hybrid models.

- Uncertainty analysis: Begin integrating uncertainty quantification (e.g., Monte Carlo, Bayesian inference).

Year 3

- Uncertainty quantification: Finalize framework for estimating prediction confidence intervals.
- Optimization: Select optimal input signals/parameters to minimize uncertainty.
- Validation: Test models on industrial steel samples and compare with ground truth (e.g., tensile tests, hardness measurements).

Imagerie et Vision Artificielle

Conception de systèmes de vision, analyse d'images temps réel, aide au diagnostic médical, IA pour l'analyse de signaux et d'images, systèmes d'imagerie multi-modale et non conventionnelle, modélisation de l'apparence, perception pour/par la robotique, commande robotique.

CMPhy is a company located in Chalon-sur-Saone, which specialized itself in developing advanced Non-Destructive Testing (NDT) machines based on (but not limited to) electromagnetic field effect. ImViA is based in Dijon and Le Creusot and is developing academic research on non-conventional imaging and image processing associated (ML and IA models).

The OPTEND project aims to develop a non-destructive testing (NDT) tool (a hardware and a software) capable of predicting mechanical and physical properties of high-value steels (e.g., hardness, residual stress, carbon profile, magnetic permeability) from multimodal magnetic and ultrasonic measurements. This PhD is a collaboration between ImViA (academic laboratory) and CMPhy (industrial partner), with access to a pre-existing database of multimodal measurements (Barkhausen noise, Eddy currents, harmonic analysis of tangential magnetic field, incremental permeability, ultrasonic signals) collected on steel samples with various surface treatments (e.g., shot peening, nitriding, grinding) or applied mechanical constraints.

The ideal candidate has a Master degree and/or an Engineering degree in Physics, Signal processing or Materials. Candidates with majors in AI are welcome to apply.

The candidate must have:

• Good understanding of materials and instrumentation.
• Good understanding of Modelization techniques, Machine-Learning and Deep-Learning
• Knowledge in NDT techniques.

Required skills:

• Background in data analysis, modeling, or NDT techniques.
• Proficiency in Python.
• Good written and oral English.

Preferred skills:

• Knowledge of machine learning, Bayesian methods, or optimization.
• Experience with experimental design or instrumentation.
• Familiarity with uncertainty quantification.
• Knowledge in:  Experimental design, Design of Experiment

Personal qualities:

• Autonomous, rigorous, and team-oriented.
• High motivation for applied research and industrial collaboration.
• Enthusiasm for experimentation, instrumentation, teamwork, and capability of independent problem-solving.
• Eager to disseminate research results through publications and presentations at both academic and industrial international conferences.