⚡ electrical engineering

Physics-Integrated Machine Learning Framework for Predicting the Load Capacity of Single Row Bolted Steel to Timber Connections in Tropical Hardwoods

This study presents a physics-integrated machine learning framework that successfully predicts the lateral load capacity of single-row bolted steel-to-timber connections in Malaysian tropical hardwoods (Balau and Bitis) by training models to correct discrepancies between experimental results and existing design codes, thereby offering a reliable pathway for extending timber design standards to tropical species.

Original authors: Md. Abdul Kaium Mia, Abdul Razak Abdul Karim, Norazzlina M. Sa’don, Md. Habibur Rahman Sobuz, Borsha Podder, Siti Hanim Sahari, Teng Xin Yao, Nur Liza Rahim, Pierre Quenneville

Published 2026-07-01

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Md. Abdul Kaium Mia, Abdul Razak Abdul Karim, Norazzlina M. Sa’don, Md. Habibur Rahman Sobuz, Borsha Podder, Siti Hanim Sahari, Teng Xin Yao, Nur Liza Rahim, Pierre Quenneville

Original paper licensed under CC BY 4.0 (https://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

The Big Picture: Building a Better Safety Net for Wooden Bridges

Imagine you are building a bridge out of wood and steel, held together by giant bolts. You need to know exactly how much weight that bridge can hold before it breaks.

For decades, engineers have used a "rulebook" (mathematical formulas) to guess this weight. However, these rulebooks were written for softwoods like pine and spruce (the kind found in cold climates). The researchers in this paper are working with tropical hardwoods (like Balau and Bitis) from Malaysia. These woods are denser, harder, and behave differently. Using the old rulebooks on these new woods is like trying to drive a Formula 1 car using a manual written for a bicycle; it might work, but it's not precise, and it might be unsafe.

This study tries to fix that by building a "Smart Co-Pilot" for engineers. It combines the old, trusted rulebooks with a new, data-smart computer brain to predict exactly how strong these tropical wood connections are.

The Problem: The "Copy-Paste" Trap

The researchers faced a tricky problem with their data. They tested 36 different groups of wood connections. Each group had 10 identical pieces of wood.

If you teach a computer to learn from this data by shuffling the pieces randomly, the computer gets a cheat code. It sees 9 pieces of a specific group in its "training" and then has to guess the 10th piece. Since the 10th piece is identical to the other 9, the computer isn't really learning physics; it's just memorizing the answer. This is called data leakage. It's like a student memorizing the answer key for a specific test question rather than learning the subject.

The Fix: The researchers made the computer learn by "group." They hid one entire group of 10 pieces from the computer, trained it on the other 35 groups, and then asked it to guess the hidden group. They repeated this 36 times. This ensures the computer is learning the rules of the wood, not just memorizing specific answers.

The Solution: The "Physics-Residual" Strategy

Instead of asking the computer to predict the weight from scratch (which is hard and prone to wild guesses), they used a clever two-step strategy called Physics-Residual Learning.

Think of it like this:

The Old Rulebook (The Anchor): First, the computer calculates the weight using the standard engineering formulas (EYM, RSM, and MS544). Let's say the rulebook says the bridge can hold 50 tons.
The Real World (The Gap): In the lab, the bridge actually held 65 tons. There is a gap of 15 tons.
The Smart Co-Pilot (The Correction): The computer's only job is to learn how to fix that 15-ton gap. It doesn't try to reinvent the wheel; it just learns the "correction factor" needed to make the old rulebook match reality.

This keeps the prediction grounded in real physics. Even if the computer gets confused, it won't suggest the bridge can hold 1,000 tons or -50 tons; it stays close to the safe, logical baseline.

The Results: Who Won the Race?

The researchers tested six different types of computer "brains" (algorithms) to see which one was best at fixing the gap.

The Winner: Support Vector Regression (SVR). It was the most accurate, with an error rate of only about 8.6%. It was like the most reliable mechanic in the shop.
The Runners-Up: CatBoost and XGBoost were also very good, almost as accurate as the winner.
The Losers: Some other methods (like simple decision trees) were too shaky and made bigger mistakes.

What Did the Computer Learn? (The "Why")

The researchers used a special tool called SHAP to ask the computer, "Which factors mattered most?"

Wood Type is King: The most important factor was simply what kind of wood it was. The "Bitis" wood was consistently stronger than the "Balau" wood. The computer learned this immediately.
Spacing Matters: How far apart the bolts were placed (bolt spacing) was the second most important thing.
The Rulebook Still Counts: Interestingly, the best models (SVR and CatBoost) actually listened to the old rulebook numbers. The "XGBoost" model, however, mostly ignored the rulebook and relied only on geometry. The researchers prefer the models that listen to the rulebook because it makes the predictions safer and more logical.

The Final Product: A Safe Design Tool

The goal wasn't just to predict the average weight; it was to find a safe, conservative limit for engineers to use in real life.

They calculated a "Safety Factor" (a number less than 1).

For the best model (SVR), this factor was 0.842.
How it works: If the computer predicts a bridge can hold 100 tons, the engineer multiplies that by 0.842. The design limit becomes 84.2 tons.
Why? This ensures that in 95 out of 100 cases, the actual wood will be stronger than the design limit. It's a safety buffer that accounts for the fact that wood is a natural material and can vary.

Summary

This paper created a new, smarter way to design bolted connections for tropical hardwoods.

It avoided cheating by testing the computer on whole groups of wood, not just individual pieces.
It didn't throw away old engineering rules; it used them as a base and let the computer learn the "corrections."
It found that the type of wood and bolt spacing are the most critical factors.
It produced a simple formula (Prediction × 0.842) that engineers can use to safely design structures using Malaysian tropical hardwoods, ensuring they are strong enough to hold the load without being overly wasteful.

Note: The study is currently limited to two specific types of wood (Balau and Bitis) and specific bolt sizes. The researchers are careful to say this tool is for these specific cases and shouldn't be used for other woods or bolt types until more testing is done.

Technical Summary: Physics-Integrated Machine Learning Framework for Predicting Load Capacity of Bolted Steel-to-Timber Connections in Tropical Hardwoods

1. Problem Statement

Predicting the lateral load capacity of bolted steel-to-timber connections remains a significant challenge in timber engineering, particularly for tropical hardwoods. Existing design standards, such as the European Yield Model (EYM) and Row Shear Model (RSM), were primarily calibrated using temperate softwood species (e.g., spruce, pine, fir). These models often lack accuracy when applied to Malaysian tropical hardwoods like Balau (Shorea spp.) and Bitis (Madhuca spp.), which possess higher densities, different grain structures, and distinct failure mechanisms.

Furthermore, the application of machine learning (ML) to this domain faces three specific methodological hurdles:

Data Scarcity and Structure: Experimental datasets for connection testing are typically small and highly structured, with multiple specimens sharing identical geometric inputs within a single connection group.
Data Leakage: Standard random cross-validation at the specimen level leads to data leakage, where models "memorize" group responses rather than learning generalizable mappings, resulting in overly optimistic performance estimates.
Lack of Physical Grounding: Purely data-driven models may produce predictions that violate established engineering principles, especially when extrapolating beyond the training domain.

2. Methodology

2.1 Experimental Dataset

The study utilized a dataset comprising 36 connection groups (360 individual specimens) derived from systematic testing of single-shear, single-row, steel-plate-to-timber bolted connections.

Species: Balau and Bitis (Malaysian Strength Group 1).
Configuration: M13 Grade 4.6 bolts, 6 mm mild steel plates, loaded parallel to the grain.
Variables: Number of fasteners ( $N$ ), end distance ratio ( $e/d$ ), and bolt spacing ratio ( $s_b/d$ ).
Target: The mean load capacity of each group was used as the data point for modeling.

2.2 Physics-Integrated Framework

The study adopted a physics-residual learning strategy rather than training models to predict load capacity from scratch.

Physics Anchor: Three established design equations (EYM, RSM, and MS544-5) were computed for each group. The minimum of these three predictions ( $R_{min}$ ) served as the physics baseline.
Residual Learning: The ML models were trained to predict the residual error ( $\varepsilon = R_{exp} - R_{min}$ ) rather than the absolute load capacity. The final prediction ( $R_{ml}$ ) is calculated as $R_{min} + \hat{y}(\varepsilon)$ . This ensures predictions remain anchored to physical theory.

2.3 Validation and Explainability

Group-Level Leave-One-Out Cross-Validation (Group-LOO-CV): To prevent data leakage, the study employed a 36-fold cross-validation scheme where entire connection groups (not individual specimens) were withheld as test sets. This ensures the model is tested on unseen geometric configurations.
Algorithms: Six algorithms were evaluated: Support Vector Regression (SVR), CatBoost, XGBoost, Random Forest, K-Nearest Neighbors (KNN), and Gradient Boosting.
Explainability: SHAP (SHapley Additive exPlanations) and permutation importance were used to quantify feature contributions and ensure physical interpretability.
Calibration: A calibration factor ( $\phi$ ) was derived as the 5th percentile of the ratio of experimental to predicted values to generate conservative design strengths ( $R_{5th}$ ).

3. Key Results

3.1 Predictive Performance

All models outperformed the code-based baseline ( $R_{min}$ ). Support Vector Regression (SVR) emerged as the best-performing model:

$R^2$ : 0.876 (±0.043)
RMSE: 6.09 kN
MAE: 4.80 kN
Bias: -0.783 kN (slightly conservative)

CatBoost ( $R^2$ = 0.846) and XGBoost ( $R^2$ = 0.842) followed closely. Statistical tests (Wilcoxon signed-rank) indicated that while SVR was the top performer, the differences between the top three models were not statistically significant at the 95% confidence level. However, SVR demonstrated the most consistent performance across folds.

3.2 Feature Importance

SHAP analysis revealed that Wood Species, Bolt Spacing Ratio, and Edge Distance Ratio were the most influential predictors.

Wood Species: Identified as the dominant feature, reflecting the 6.9 kN difference in mean capacity between Bitis and Balau.
Physics Anchor Utilization: SVR and CatBoost assigned significant importance to the physics anchor ( $R_{min}$ ), ensuring physical consistency. In contrast, XGBoost largely ignored the physics anchor (SHAP value ~0.19 kN), relying instead on geometric inputs, which may limit its extrapolation reliability.

3.3 Calibration and Design Application

The study derived calibration factors ( $\phi$ ) to convert raw predictions into conservative design values.

SVR Calibration Factor: $\phi$ = 0.842.
Characteristic Strength ( $R_{5th}$ ): The calibrated SVR prediction yielded an $R_{5th}$ of 26.27 kN, which is slightly below the experimental benchmark of 27.45 kN. This confirms the framework produces conservative, safe design values comparable to existing standards like MS544-5.

4. Key Contributions

Methodological Rigor: The study addresses the critical issue of data leakage in small, structured experimental datasets by implementing Group-LOO-CV, a necessary step often overlooked in structural ML applications.
Physics-Residual Strategy: It demonstrates that training models to correct the gap between code predictions and experimental results (rather than predicting from scratch) yields higher accuracy and physical consistency for tropical hardwoods.
Explainability in Design: By integrating SHAP analysis, the study validates that ML models learn physically meaningful relationships (e.g., the dominance of species and spacing ratios) rather than spurious correlations.
Practical Calibration: The derivation of a specific calibration factor provides a direct pathway for integrating ML predictions into conservative structural design frameworks, bridging the gap between data-driven accuracy and engineering safety requirements.

5. Significance and Claims

The paper claims to represent one of the earliest physics-integrated machine learning frameworks specifically developed for predicting the load capacity of bolted steel-to-timber connections in Malaysian Strength Group 1 tropical hardwoods.

The significance of the work lies in its ability to:

Extend design guidance to tropical hardwoods where existing standards are less accurate.
Provide a "clear, physically grounded pathway" for extending design guidance without replacing established mechanics-based theories.
Offer a robust, leakage-resistant validation protocol that can serve as a template for other structural engineering problems with limited, structured data.

The authors maintain a modest stance, acknowledging that the framework is currently limited to Balau and Bitis species and single-row configurations. They emphasize that the model is intended as a decision-support tool to complement, not replace, existing design standards, and that future work requires validation on external datasets and broader species ranges.