Digital Image Correlation + Bayesian Inference

Full-field optical strain measurement combined with probabilistic uncertainty quantification for structural material characterization.

Juan Manuel Orozco Henao — Civil Engineer, Universidad del Valle · Cali, Colombia
2.5 years of research · Research Monitor (G-7 Group) + Undergraduate Thesis

Overview

This research applies Digital Image Correlation (DIC) — a non-contact, full-field optical measurement technique — to characterize the mechanical behavior of structural materials: reinforced concrete and structural steel. The work spans two overlapping projects:

› G-7 Research Group (Universidad del Valle): 2D DIC on full-scale concrete beams as part of a structural monitoring research initiative. Role: research monitor — responsible for DIC implementation, sensor installation, and beam fabrication up to 5.5 m in length.
› Undergraduate Thesis: 3D DIC on concrete cylinders combined with Bayesian inference to produce probabilistic estimates of the Modulus of Elasticity of Concrete.

A manuscript based on the thesis is currently under review at the ACI Structural Journal, and the work was presented at the XI National Congress of Seismic Engineering (CNIS XI, 2024), Bucaramanga, Colombia.

Juan Manuel Orozco at the Structures Lab — Structures and Materials Laboratory, Universidad del Valle.

Why this matters: Traditional methods for estimating material properties like the Modulus of Elasticity rely on point measurements and code-defined formulas. DIC provides spatially distributed, full-field strain data that reveals local behavior invisible to conventional sensors — making it a foundational technology for AI-driven structural monitoring, inspection, and digital twins.

Specimen	Project	DIC Method	Software	Additional Instrumentation
Concrete beams (up to 5.5 m)	G-7 Research Monitor	2D DIC	Ncorr (MATLAB)	Strain gauges, LVDTs
Concrete cylinders (150×300 mm)	Undergraduate Thesis	3D DIC (stereo)	DuoDIC (MATLAB)	Strain gauges, LVDTs
Steel reinforcing bars	Undergraduate Thesis	— (no DIC)	—	LVDTs, strain gauges

Part 1 — Beam Tests

G-7 Research Group · 2D DIC

The G-7 Structural Engineering Research Group investigates the behavior of reinforced concrete structural elements. As a research monitor, I contributed to the fabrication, instrumentation, and DIC-based measurement of full-scale concrete beams.

Beam Fabrication

Concrete beams of up to 5.5 meters in length were designed, reinforced, and cast in-house at the Structures Laboratory. This included cutting and assembling the steel rebar cages, placing strain gauges on the internal reinforcement before casting, and preparing the wooden formwork.

Concrete beam molds being prepared — Reinforced concrete beam molds at the Structures Laboratory. Multiple beams prepared for the experimental campaign.

Strain gauges installed on reinforcing bars — Strain gauges bonded to internal steel reinforcement inside the beam formwork, prior to concrete casting.

Beam fabrication work at night — Preparing the steel elements for the structural test frames — welding and assembly at the Structures Laboratory.

2D DIC Setup

For beam tests, 2D DIC was selected because the monitored face of the beam is planar, and under the applied loading conditions the out-of-plane rotation is negligible. A single camera was positioned perpendicular to the beam face to capture a high-resolution image sequence throughout the loading process. The speckle pattern (random black dots on a white painted surface) was hand-applied to ensure high-contrast texture for the correlation algorithm.

Concrete beam with speckle pattern — Concrete beam with hand-applied stochastic speckle pattern. An LVDT extensometer is visible at the bottom.

Beam test setup in the laboratory — Full experimental setup: speckled beam on supports, Nikon camera, hydraulic loading frame, and DAQ system.

Processing with Ncorr

Processing was done in Ncorr (MATLAB), an open-source 2D DIC toolbox implementing the Reliable Region DIC (RO-DIC) algorithm. A Region of Interest (ROI) was defined on the reference image, and the correlation algorithm tracked displacement of each subset across all subsequent load-step images.

Ncorr reference image setup — Reference image loaded in Ncorr with ROI defined on the speckled beam surface.

Ncorr DIC analysis running — Ncorr processing 47 images during a beam bending test. Seed point propagation ensures spatial continuity.

Strain Field Results

The DIC output produces a spatially continuous map of surface strains — enabling identification of strain gradients, neutral axis location, and comparison with analytical beam theory predictions.

Full-field DIC strain map on concrete beam — Full-field axial strain map (εyy) on a concrete beam under three-point bending, obtained with Ncorr. Color scale: compression (blue) to tension (red). Field of view: 244 mm. Subset radius 20 px, strain radius 15 px.

DIC applied to pure bending simulation — MATLAB simulation of a beam under pure bending (left: speckle-textured beam; right: vertical displacement field). The gradient matches Euler-Bernoulli beam theory. Presented at a structural engineering congress in Armenia, Colombia.

Part 2 — Cylinder Tests & Thesis

3D DIC + Multi-Sensor Instrumentation

The undergraduate thesis focused on quantifying the uncertainty in the Modulus of Elasticity of Concrete by combining multiple measurement sources — 3D DIC, strain gauges, and LVDTs — within a Bayesian probabilistic framework.

Cylinder Instrumentation

Standard concrete cylinders (150 mm × 300 mm) were instrumented with electrical resistance strain gauges bonded directly to the cylinder surface, complemented by LVDTs for displacement measurement. Three independent measurement channels were available for each specimen: DIC, strain gauges, and LVDTs.

Concrete cylinders with strain gauges installed — Concrete cylinders instrumented with surface strain gauges, ready for uniaxial compression testing.

Concrete cylinder in compression machine — Concrete cylinder in the universal testing machine, with strain gauges and LVDTs. Test follows ASTM C469.

3D DIC with DuoDIC

For concrete cylinders, the curved geometry made 2D DIC unsuitable — a stereoscopic (3D) DIC setup was used instead. The software DuoDIC (open-source, developed by Dana Solav) implements a full stereo DIC pipeline in MATLAB: stereo camera calibration, 2D DIC on each camera independently (via Ncorr), and 3D reconstruction of the full displacement field.

Natural concrete surface texture — Close-up of concrete cylinder surface. Natural aggregate texture enhanced by an applied black-dot speckle pattern.

Checkerboard calibration target for stereo DIC — Checkerboard calibration target for stereo camera calibration (8×11 grid, 7 mm squares). Used by Zhang's method.

3D DIC displacement field on concrete cylinder — 3D DIC result on a concrete cylinder under uniaxial compression. Color map shows vertical displacement field within the Region of Interest (ROI).

Part 3 — Bayesian Uncertainty Quantification

Probabilistic material characterization

The central thesis contribution is a Bayesian framework for uncertainty quantification of material properties, applied separately to concrete and steel.

Concrete: Modulus of Elasticity

For concrete cylinders, DIC strains, strain gauge readings, and LVDT displacements provided three independent estimates of the compressive strain at each load step. A Bayesian model was built in PyMC to fuse these sources, producing a posterior probability distribution of E rather than a single deterministic value. The posterior reflects both the measurement variability across sensor types and the scatter between specimens.

Histogram of DIC strain values from a single image — Histogram of strain values from all correlation points in a single DIC image. The near-Gaussian distribution reflects the measurement noise floor and forms the basis for the Bayesian likelihood function.

Posterior Predictive Check for LVDT data — Posterior Predictive Check (LVDT channel). Red dots: observed data. Blue line: mean prediction. Blue band: 95% credible interval.

Posterior distribution of E from DIC data. Mean: 13,485 MPa · Std Dev: 46 MPa · 95% CI: [13,394 – 13,576 MPa].

Steel: GMP Constitutive Model Calibration

For structural steel reinforcing bars, instrumentation consisted of LVDTs and electrical strain gauges under cyclic loading — reproducing seismic demand on rebar. The measured stress-strain hysteresis curves were used to calibrate the Giuffré-Menegotto-Pinto (GMP) constitutive model in OpenSees, with Bayesian calibration implemented using Emcee (an affine-invariant MCMC ensemble sampler in Python).

Steel hysteresis curves under cyclic loading — Experimental stress-strain hysteresis curves for structural steel reinforcing bars under cyclic loading.

MCMC Sampling

Both calibrations use Markov Chain Monte Carlo (MCMC) sampling to explore the posterior distribution. The algorithm proposes parameter values iteratively, accepting or rejecting each proposal based on its likelihood given the observed data.

MCMC algorithm conceptual diagram — Conceptual diagram of MCMC: at each step, a candidate parameter θ is proposed and accepted or rejected based on data likelihood. Accepted samples form the posterior distribution.

Posterior distribution of elastic modulus for steel — Posterior of E for steel. Mean: 211,024 MPa · 95% CI: [177,868 – 244,701 MPa]. From Emcee MCMC sampling.

Posterior Predictive Check for steel GMP model — PPC: 200 simulated curves (orange) from GMP model with posterior-sampled parameters, overlaid on experimental data (black).

Key Results

Concrete E posterior distribution obtained by fusing three independent sensor types (3D DIC, strain gauges, LVDTs) — revealing systematic biases between measurement methods not visible with deterministic analysis.

Steel GMP model fully calibrated probabilistically from cyclic data — posterior predictive checks confirm excellent agreement with experimental hysteresis.

2D DIC on beams validated against strain gauge measurements at multiple cross-sections, demonstrating consistency of full-field and point measurements across 5.5 m specimens.

3D stress-strain curves DIC vs strain gauge — 3D stress-strain curves comparing DIC (red) and strain gauge (blue) measurements across multiple cylinder tests. Systematic differences in the elastic slope motivated the multi-source Bayesian fusion.

Juan Manuel analyzing data at workstation — Data analysis and model calibration at the Structures Laboratory. Left screen: Python code (PyMC / Emcee). Right screen: structural analysis output.

Tools & Stack

Category	Tools
DIC (2D)	Ncorr (MATLAB, open-source)
DIC (3D stereo)	DuoDIC (MATLAB, open-source — Dana Solav)
Bayesian inference — concrete	PyMC (Python)
Bayesian inference — steel	Emcee (Python affine-invariant MCMC)
Structural simulation	OpenSees (GMP model verification)
Data acquisition	Electrical resistance strain gauges, LVDTs, DAQ system
CAD / Test design	Autodesk Inventor

Ncorr DuoDIC PyMC Emcee OpenSees MATLAB Python MCMC Bayesian Inference DIC

Publications & Presentations

Journal — Under Review

Uncertainty Quantification of Experimental Characterization for Concrete's Modulus of Elasticity

J. Orozco, A. R. Ortiz, P. Thomson · Universidad del Valle

ACI Structural Journal (American Concrete Institute), 2025

Conference

Bayesian Quantification of Structural Material Properties Using DIC

XI Congreso Nacional de Ingeniería Sísmica (CNIS XI, 2024)

Bucaramanga, Colombia

Connection to AI & Structural Engineering

› DIC as computer vision: The correlation algorithm tracks image texture patterns frame-by-frame, analogous to optical flow used in video-based structural health monitoring and AI-driven inspection platforms.
› Bayesian inference as probabilistic ML: The PyMC / Emcee pipelines are functionally equivalent to probabilistic programming models used in Bayesian neural networks and physics-informed ML for engineering.
› Full-field data as the bridge to digital twins: Spatially distributed DIC measurements are precisely the sensor data format that feeds structural health monitoring systems and digital twin platforms.

For code samples, data, and additional figures: orozco.juan@correounivalle.edu.co

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