**1. Introduction**

The parameter identification of the materials used in historic structures demands the application of non-destructive means. The need to preserve structural safety and integrity is usually superior to any goal of structural testing. However, recognizing the properties of materials used in historic structures helps to select modern materials for some restoration works. The properties may be identified in the inverse analysis, in which the structural parameters are determined based on the measured structural response to a known, or unknown, action. The present paper discusses the identification of the material parameters of a slender masonry lighthouse. A fully non-invasive method was selected, in which the material properties were determined by the numerical model validation applied to the first pair of natural frequencies and the related mode shapes that were experimentally determined.

To obtain experimental data for the inverse analysis, operational modal analysis (OMA) was applied to the structure. OMA is widely discussed in the literature concerning structural health monitoring (SHM). Numerous OMA methods have been developed [1,2], and they are dedicated to certain vibration cases, i.e., free-decay or ambient. Their efficiency depends on the quality of the vibration signals. Subsequently, the quality of the OMA results determine the possibility of its further usage. Natural frequencies or modal forms, when identified with a considerable error, will induce untrue results or conclusions. Therefore, the quality of the OMA results must be treated with care.

In the present paper, the modal identification (MID) of the lighthouse is discussed considering three kinds of structural excitation. The following MID techniques are applied herein: the eigensystem realization algorithm (ERA), the peak picking technique based on correlation analysis (PP-CA), and the natural excitation technique with ERA (NExT-ERA). The application of these three techniques increases the chance of true results being obtained.

The considered tower is a historic lighthouse situated in Gda ´nsk (Poland). The brick construction is massive and rigid due to the spiral granite staircase filling the whole tower interior. The modal identification of similar structures is described in the literature [3]. Examples for masonry bell towers are presented in [4,5]. The SHM systems built for such structures are described in [6,7]. The systems monitor natural frequencies, and correlate them with temperature changes or with a day's anthropogenic activity in the city. Ref. [8] concerns the identification of the foundation stiffness of the masonry tower, based on experimentally identified modal data.

The aim of this paper is to determine reasonable MID results for the lighthouse, in order to use these in the material parameter identification of the structural FEM model. The outcomes of three OMA methods under various excitations were compared, whereby the excitation caused by sheet piling hammering was a unique one. The opportunity to measure the lighthouse's vibrations under such conditions arose during the modernization of the port quay in Gda ´nsk. The basic excitation was the environmental impact most affected by wind and river influences. The study presents the results of the PP-CA technique in the three following excitation cases: ambient, ambient enhanced by the ground vibrations enforced by the hammer action, and the two combined, i.e., ambient enhanced by the hammer action in selected time periods. The NExT-ERA results relate to the first and the third above-mentioned excitation kinds. The ERA technique was applied to the short-term free-decay parts of the ambient signals, as well as to the steady-state vibrations generated by the sheet piling hammering. In the first case, natural frequencies and related mode shapes and damping ratios were identified. In the second case, forced vibration frequencies and related response shapes were obtained.

The provided results prove that in the case of a broad spectrum of excitations acting on a real structure, the OMA results obtained using different techniques may not be repeatable. To approach the true results, the analysis should be performed with care and skepticism. Furthermore, the application of a few OMA methods should be considered to ensure more objective inferences. Such an approach accepted in the described study provided reasonable MID results, which were further applied in the numerical model of validation for the lighthouse so as to finally determine the mechanical properties of the materials used in the construction, as well as their elastic support.
