A Comparative Machine Learning (ML) Metaheuristic Framework for Bolt Pitch Optimization under IS 800, Eurocode 3, and AISC

Technical Summary: A Comparative Machine Learning (ML) Metaheuristic Framework for Bolt Pitch Optimization under IS 800, Eurocode 3, and AISC

Problem Statement
The design of bolted connections in steel structures requires a critical balance between structural safety, material efficiency, and constructability. Traditionally, engineers rely on the minimum and maximum allowable pitch distances prescribed by design codes (IS 800:2007, Eurocode 3, and AISC 360-16). However, these code-prescribed limits often lead to conservative designs that increase material costs without providing commensurate safety advantages. Furthermore, existing literature frequently addresses optimization within a single code or relies on simplified case studies, lacking a unified framework that integrates predictive modeling with metaheuristic optimization across multiple international standards. There is a distinct gap in understanding how bolt spacing interacts with failure modes and material characteristics to produce optimal, code-compliant designs that minimize material usage while ensuring safety.

Methodology
The study proposes an integrated framework combining data-driven machine learning (ML) and metaheuristic optimization to determine optimal bolt pitch distances. The methodology proceeds through four distinct phases:

1. Data Generation: A comprehensive synthetic dataset of 4,500 bolted connection configurations was generated. This dataset was derived from the specific limits and requirements of IS 800, Eurocode 3, and AISC. It includes 1,500 configurations per code, incorporating variables such as material properties (yield and ultimate strength), geometric parameters (bolt diameter, plate thickness, edge distances), loading conditions (shear, tension, moment), and connection types. A weighted efficiency metric was established, prioritizing safety (70%) and material efficiency (30%), to classify configurations as "Optimal" or "Non-Optimal."
2. Machine Learning Classification: Six ML algorithms—Random Forest (RF), XGBoost, Support Vector Machine (SVM), Neural Networks (NN), Gradient Boosting (GB), and Logistic Regression (LR)—were trained to predict optimal pitch classifications. Model performance was evaluated based on accuracy, ROC AUC, and training time. Feature importance analysis was conducted to identify key influencing parameters.
3. Metaheuristic Optimization: Two optimization algorithms, Genetic Algorithm (GA) and Simulated Annealing (SA), were implemented to identify the precise pitch values that maximize the efficiency metric while adhering to code constraints. Both algorithms were configured to minimize the negative of the efficiency metric.
4. Validation and Sensitivity Analysis: The optimized results were validated against experimental data from recent studies to calculate prediction errors. Additionally, a sensitivity analysis was performed by varying key parameters (bolt diameter, plate thickness, number of bolts, shear load, tension load) by ±30% to determine their influence on the optimal pitch.

Key Results

• Machine Learning Performance: The Random Forest classifier emerged as the most effective model, achieving an accuracy of 0.923 and a ROC AUC of 0.941. XGBoost followed closely with an accuracy of 0.917 and a ROC AUC of 0.938. Feature importance analysis revealed that bolt diameter is the most critical parameter influencing pitch distance (importance value ~0.217), followed by shear load, plate thickness, and the number of bolts.
• Optimization Outcomes: Both GA and SA converged to identical optimal solutions for each code, demonstrating consistency. The Genetic Algorithm (GA) demonstrated superior reliability and lower error rates compared to Simulated Annealing (SA) when validated against experimental data. The average error for GA was 8.7%, whereas SA yielded an average error of 9.3%. GA showed a narrow error distribution, while SA exhibited higher variance and significant outliers.
• Code-Specific Optimal Ratios: The study identified distinct optimal pitch-to-diameter (P/D) ratios for each code:
  • IS 800: 2.8–3.2
  • Eurocode 3: 2.5–2.9
  • AISC: 2.9–3.3
• Sensitivity Findings: Bolt diameter, shear load, and the number of bolts were found to have the most significant impact on optimal pitch. Conversely, plate thickness and tension load had minimal influence within the tested ranges. The analysis confirmed that the optimization framework remains robust across different design codes.

Significance and Contributions
The paper claims to address a significant research gap by providing a comprehensive framework that integrates ML-based classification with metaheuristic optimization specifically for bolted connection pitch design across three major international codes. The primary contributions include:

1. Unified Framework: The ability to operate across IS 800, Eurocode 3, and AISC, enabling comparative analysis and code-specific optimization in a single system.
2. Practical Design Recommendations: The study provides actionable guidelines for engineers, suggesting target pitch values (e.g., ~3.0d for IS 800, ~2.7d for Eurocode 3, ~3.1d for AISC) that balance safety and material economy.
3. Validation of Computational Methods: By validating the framework against experimental data, the study demonstrates that combining predictive ML models with GA can produce reliable, code-compliant designs that reduce material usage without compromising structural integrity.
4. Efficiency Improvement: The proposed approach offers a systematic alternative to traditional manual design, potentially reducing the conservatism inherent in code-prescribed limits and improving the efficiency of steel structure design.

The authors conclude that while the framework significantly improves the design process, future work should aim to broaden the model to include more variables, different failure mechanisms, and complex loading conditions to further enhance accuracy and applicability.