Structural Parameter Identification Using Multi-Objective Modified Directional Bat Algorithm - LIU Li-jun; LIN Ying-hai; SU Yong-hui; LEI Ying (工程科学与技术)
ObjectiveStructural parameter identification based on swarm intelligent optimization methods has become one of the popular methods for finite element model modification. The swarm intelligent optimization methods transform a complex problem of structural parameter identification into a constrained optimization problem. However， traditional single-objective optimization methods， which aggregate multiple evaluation indices into a single weighted objective function， often face challenges. The manual determination of weight factors introduces subjectivity， which can significantly affect the accuracy of the results. Improper weights may lead to suboptimal solutions， rendering the method less effective in practical applications. To address these challenges， a novel Multi-Objective Modified Directional Bat Algorithm （MOMDBA） was proposed for the structural parameters identification. Unlike traditional methods， MOMDBA independently explored each objective without the requirement for predefined weight factors. In this method， subjectivity was eliminated by constructing the Pareto frontier of the optimal solutions， and the optimal solution was identified according to the minimum of the maximum residual. This approach improved the accuracy and robustness of structural parameter identification while maintaining computational efficiency.MethodsMOMDBA is an enhanced version of the Directional Bat Algorithm （DBA）， a swarm intelligence optimization technique inspired by the echolocation behavior of bats. While DBA has been effective for various optimization problems， it is prone to issues such as premature convergence and suboptimal exploration of the solution space. MOMDBA addressed these limitations through three key improvements： 1） Individual Historical Best Position Tracking： This feature allowed the algorithm to retain and utilize the best individual solutions encountered during the search process， improving its ability to explore the solution space effectively. 2） Hybrid Global-Local Search Strategy： By combining global exploration with local exploitation， MOMDBA enhanced its ability to converge towards optimal solutions while avoiding local optima. 3） Elimination Mechanism： To maintain population diversity and prevent stagnation， low-performing individuals were periodically replaced with new solutions. The algorithm began with the initialization of optimization variables， constraints， Pareto front size， and key parameters such as frequency， loudness， and pulse rates. During each iteration， solutions were evaluated based on multiple objectives， and a Pareto frontier was constructed by assigning random weights to these objectives. Each solution on the frontier was assessed for its maximum residual across all objectives. The solution with the smallest maximum residual was selected as the global optimum. The approach was validated through two applications. In the first case， a 12-node， 26-element truss structure was analyzed for damage identification. Damage was simulated by reducing the Young’s modulus of specific elements. To simulate real-world conditions， noise was added to modal parameters. Dynamic features， such as natural frequencies and mode shapes， were used for damage detection. In the second application， MOMDBA was applied to update the finite element model of the Haiwen Bridge， a single-tower cable-stayed bridge with 236 girder elements and 60 tower elements. Static and dynamic features were combined， including natural frequencies， mode shapes， and strain influence lines. Fourteen structural parameters， such as elastic modulus， material density， and sectional properties， were optimized. Initial parameter values were intentionally perturbed from true values to test the robustness of the algorithm.Results and DiscussionsThe effectiveness of MOMDBA was demonstrated through two case studies： damage identification in a truss structure and finite element model updating of the Haiwen Bridge. In the truss damage identification case， MOMDBA demonstrated superior performance under challenging conditions， including 3% noise in the input data. The algorithm successfully identified damage locations and severities， achieving a maximum relative error of 3.85% for damaged elements. Only one false positive was detected， with a minor error of 1.52%. These results highlight the algorithm’s robustness and precision in handling noisy data. Compared to Multi-Objective Particle Swarm Optimization （MOPSO） and the Non-Dominated Sorting Genetic Algorithm-II （NSGA-II）， MOMDBA outperformed its counterpart. MOPSO and NSGA-II exhibited higher relative errors， particularly for severely damaged elements， and generated multiple false positives. In the Haiwen Bridge application， MOMDBA successfully identified all 14 structural parameters with a maximum relative error of 2.59%. The identified modal frequencies across seven modes exhibited a maximum deviation of 0.252%， demonstrating the method’s capability to handle complex， large-scale structural systems. By integrating static and dynamic features， the algorithm ensured accurate model updating even under noisy conditions. Additionally， the elimination mechanism ensured population diversity， preventing premature convergence and improving the quality of the solutions. By eliminating subjective weight factors， MOMDBA provided more accurate and reliable results in both damage identification and parameter optimization. Its robustness to noise make it a practical choice for real-world applications， where data quality may be affected by environmental and operational conditions. These results demonstrated that MOMDBA offers a systematic approach to multi-objective optimization in structural health monitoring. Its versatility and reliability make it suitable for a wide range of engineering applications， from small-scale structures to large， complex systems.ConclusionsThis study presents a novel Multi-Objective Modified Directional Bat Algorithm （MOMDBA） for structural parameter identification， addressing limitations of traditional single-objective optimization methods. Key contributions of MOMDBA include independent exploration of multiple objectives， elimination of weight factor subjectivity， and enhanced optimization performance through historical best position tracking and elimination strategies. Applications to both truss damage identification and the finite element model updating of the Haiwen Bridge validate the method’s effectiveness and reliability. For the truss structure， MOMDBA accurately identified damage locations and severities under noisy conditions， outperforming MOPSO and NSGA-II in precision and robustness. For the Haiwen Bridge， the algorithm successfully optimized structural parameters， demonstrating its suitability for large-scale and complex structures. Future work will focus on experimental validation of MOMDBA under real-world conditions and its integration with advanced monitoring technologies. Further research may also explore adaptive extensions of the algorithm for real-time structural health monitoring. Overall， the proposed method offers a reliable， accurate， and versatile solution for multi-objective optimization in structural parameters identification.