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NAAS Journal 2026

International Journal Of Engineering, Business And Management(IJEBM)

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  3. Vol-10,Issue-2, April - June 2026
  4. A Lightweight Digital Twin Framework for Structural Dynamic Model Updating Using Natural Frequencies and Mode Shapes

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A Lightweight Digital Twin Framework for Structural Dynamic Model Updating Using Natural Frequencies and Mode Shapes

Sultan Mahamdnur Ibrahim


International Journal of Engineering, Business And Management(IJEBM), Vol-10,Issue-2, April - June 2026, Pages 66-80 , Received: 22 May 2026; Received in revised form: 19 Jun 2026; Accepted: 22 Jun 2026; Available online: 27 Jun 2026

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Article Info: Received: 22 May 2026; Received in revised form: 19 Jun 2026; Accepted: 22 Jun 2026; Available online: 27 Jun 2026

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Digital twins require numerical models that can be reconciled repeatedly with the changing dynamic behaviour of physical structures. Conventional finite element model updating, however, often depends on repeated eigensolutions, finite-difference gradients, or large stochastic sample sets, which limits its suitability for frequent execution on resource-constrained hardware. This study presents a lightweight digital-twin framework for structural dynamic model updating using measured natural frequencies and mode shapes. The method reduces computational demand through three coordinated measures. Candidate parameters are first screened using normalized modal sensitivities so that weakly influential and poorly identifiable variables are excluded before inversion. Eigenvalue derivatives are then evaluated analytically, while eigenvector derivatives are obtained through Nelson’s method, avoiding the repeated perturbed eigensolutions required by finite-difference schemes. A regularized Levenberg–Marquardt procedure updates the retained parameters, and a sparse polynomial surrogate is available when direct eigensolutions remain costly. Spatially incomplete mode shapes are reconciled through the System Equivalent Reduction–Expansion Process, and modal correspondence is enforced using the Modal Assurance Criterion. The framework is verified on a cantilever beam with localized stiffness changes and a planar truss with uncertain member and support stiffnesses. In both cases, the prescribed parameters are recovered within six to seven iterations, final natural-frequency errors fall below 10⁻³%, and the updated mode shapes achieve MAC values of 1.000 under noise-free conditions. Monte Carlo simulations with modal noise levels up to 3% show stable estimation, with median mean-frequency errors remaining below the imposed noise level. Computational benchmarking further shows that the analytical formulation requires six eigensolutions, compared with thirty for finite-difference updating and 15,001 forward evaluations for the MCMC reference. These results demonstrate that accurate modal reconciliation can be achieved without repeated parameter-wise eigensolutions or extensive stochastic sampling. The proposed framework therefore provides a computationally compact basis for repeated structural model updating, although experimental validation and implementation on embedded edge hardware remain necessary before operational deployment.

Digital twin, finite element model updating, modal analysis, mode shapes, natural frequencies, sensitivity method, structural health monitoring

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