PSI - Issue 84

Andrea Mileto et al. / Procedia Structural Integrity 84 (2026) 829–836 835 For configurations with =0 (graphs at the top), that is, for straight bridges, the flexural-torsional dynamic behaviour of the structure remains uncoupled. Under this condition, the adoption of the Truncation Method does not compromise the identification accuracy, provided that a sufficiently rich modal basis is retained. In particular, the use of a modal basis of the order of 12 modes allows preserving an objective function characterized by a well-defined and unique minimum, enabling the correct convergence of the DE algorithm while significantly reducing the computational cost. A different behaviour is however observed for configurations with ≠0 (graphs at the bottom), that is, for skew bridges. For these, the dynamic problem becomes coupled and the introduction of modal truncation leads to a loss of essential dynamic information, which directly affects the shape of the objective function, whose minimum moves away from the correct position (abscissa and ordinate both equal to zero).

Fig. 3. Results of the sensitivity analysis for case 3.

4. Conclusions This paper has presented an improved and extended validation of a response-based Moving Load Identification (MLI) technique for skew bridges, combining a reduced-order analytical beam model with a Differential Evolution (DE) optimization algorithm. The proposed approach is specifically tailored to skewed bridge configurations, where flexural-torsional coupling plays a fundamental role and may significantly affect the accuracy of load identification if neglected. By adopting a one-dimensional Euler–Bernoulli beam formulation with bending–torsional coupling, the method achieves a favorable balance between mechanical representativeness and computational efficiency, making it suitable for iterative inverse analyses within structural monitoring frameworks (as for the adopted DE algorithm). The numerical investigations here performed under generalized conditions have highlighted several key aspects of the identification problem. Sensitivity analyses conducted for different load configurations have shown that multiple combinations of axle loads and transverse eccentricities may produce comparable dynamic responses, especially in skew bridges, leading to non-uniqueness regions in the objective function landscape. In this respect, the comparison between alternative objective functions has demonstrated that the inclusion of additional response features, such as