PSI - Issue 78

Livia Fabbretti et al. / Procedia Structural Integrity 78 (2026) 823–830

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4. Computational implementation and MATLAB-SAP2000 integration 4.1. Optimization code architecture in MATLAB and genetic algorithms for parametric optimization The optimization procedure uses the same simplified model, but with the assumption that the isolator parameters are the unknown quantities to be identified, while the ground accelerogram and the displacements and accelerations at the control points are known (Table 3). Indeed, in the future, these will derive from monitoring system recordings. Thus, given known inputs and outputs in the model used for optimization, the problem consists of identifying the isolator parameters so as to accurately reproduce the input/output transformation observed in the reference model. The adopted methodology integrates MATLAB, version R2023b, with SAP2000 through the Application Programming Interface (API) by Computers & Structures, Inc., enabling fully automated control of simulations, dynamic updating of isolator parameters, and systematic extraction of the outputs required for the cost function evaluation. Parametric identification is based on genetic algorithms, ideal for tackling nonlinear and multidimensional problems where the objective is to minimize the difference between simulated signals and reference signals. The algorithm is implemented using the MATLAB “GA” function. It begins with a population of 50 individuals and it can run for up to 300 generations. Each individual in the population represents a possible triplet of the key isolator parameters. The search ranges are defined based on construction specifications and main literature evidence: μ fast is searched within 0.01-0.20, rp within 0.01-0.10, and a K within 15-650. Algorithm convergence is guided by minimizing the cost function through successive generations until the optimal parameter combination is identified. In the numerical calculations, the equivalent stiffness K eff is also automatically updated by the code for each parameter set evaluated, calculating d max as the maximum absolute displacement associated with the inputs. To consider the real working conditions of the monitoring system, the analysis was conducted with the introduction of synthetic Gaussian noise on reference data, calibrated with an intensity of 10% on acceleration measurements and 4% on displacements, consistent with the sensor specifications. 4.2. Formulation of the cost function and strategy for convergence The definition of an effective cost function represents the crucial element for the success of the parametric identification procedure. It quantifies the discrepancy between the responses simulated by the numerical model with variable parameters and those considered as reference experimental recordings. The implemented formulation simultaneously considers differences in the relative displacements of the isolators and in the accelerations measured at the control points, applying normalization factors to balance the relative influence of the different physical quantities, which have different orders of magnitude and units of measurement: = 6 1 ∑ ∑ [ ( )] 2 6 =1 =1 (4) where ( ) = , ( ) − , ( ) represents the instantaneous error between the real and simulated signal for the i-th signal at the k-th time sample. The normalization accounts for both the number of monitored signals (two relative displacements and four accelerations at control points) and the total number of time samples ( N ≈ 7471 ), ensuring a balanced comparison among different physical quantities. 5. Dynamic identification results and computational validation 5.1. Accuracy in parameter identification The analysis of the results shows that the genetic algorithm exactly identifies the friction coefficient μ fast and the initial stiffness parameter a K , which coincide with the target values set in the reference data, with a relative deviation of zero on μ fast and only +0.02% on a K . Conversely, the rate parameter rp is identified with a significant deviation