A combined Kalman-fractional calculus method for the parameter identification of structures under arbitrarily correlated ambient noise K. Runtemund 1 , G. Cottone 2 , G. M ¨ uller 1 1 Technische Universit¨ at M ¨ unchen, Chair of Structural Mechanics, D-80333 M ¨ unchen, Germany e-mail: katrin.runtemund@bv.tum.de 2 Technische Universit¨ at M ¨ unchen, Engineering Risk Analysis Group, D-80333 M ¨ unchen, Germany Abstract In civil engineering forced vibration tests on structures such as bridges, long-span frame structures or build- ings are usual costly and time consuming as they require a specific excitation by impact hammers or heavy shakers in order to excite the modes of interest with sufficient energy. Therefore often ambient vibration tests based on the ’natural’ excitation of the structure due to wind or traffic loads are used, permitting to continuously measure the structural response without interruption of its use during large time intervals. In order to study the dynamic behavior of structures computational efficient methods are required for: (i) the simulation of the loads and (ii) the estimation of the structural response to these loads using output-only model identification. In this paper, we introduce a technique in which, first, the load is simulated by the recently proposed ’H- fractional spectral moments’ (H-FSM) decomposition, which allows to represent a stationary colored Gaus- sian process in closed form as output of a system of linear fractional differential equations. Then, the identi- fication of the model parameters and the system response is based on the H-fractional extended Kalman filter algorithm, a time domain approach which allows to consider uncertainties in the model of the structure as well as the autocorrelation of the process noise. The method is applied to a single degree of freedom system excited by different autocorrelated loads in order to estimate the stiffness and damping parameters. 1 Introduction In the last four decades ambient vibration tests gained great attention in civil engineering. A literature review can be found e.g. in [1]. The first use of the ambient vibration technique for the dynamic characterization of full-scale structures is reported in the ’70s. Since then the technique is extensively used in engineering in the scope of parameter identification (frequencies, damping ratios and modal shapes) [2, 3, 4, 5, 6, 7, 8], model updating [9, 8] as well as damage detection and health monitoring [10, 11, 12] of slender structures such as pedestrian bridges, chimneys, long-span frame structures or high-rise buildings. While forced vibration tests are in general costly, time consuming and often require a temporary out of service state of the structure, ambient vibration tests can be conducted using the excitation by natural and/or service loads as wind, traffic or humans. Such loads are caused by the superposition of multiple inputs and thus lead to a broad-band excitation of a significant number of vibration modes [13, 14]. Due to their inherent random nature, they have to be modeled as stochastic processes. In the last years, many experimental modal identification methods for output-only measurements, such as the the peak picking method, the stochastic subspace identification method, the natural excitation technique have 2705