The fundamental frequency of a historical monument like a masonry bridge or any other structure provides a better and detailed seismic assessment of its demand to provide protection against unexpected seismic ground motion. On this basis, this paper aims to develop an empirical formulation to fit the ambient vibration frequency of historical masonry bridges using a nonlinear regression model. For this purpose, data series were collected from the literature especially focused on both ambient vibration measurement and finite element models of historical masonry bridges modeled on a full scale to get the first global natural frequency. The first approach is to forecast the natural vibration frequency by using only physical characteristics of the historical masonry bridges obtained from the literature-based experimental ambient vibration frequency data. The second approach consists of forecasting the first natural vibration frequency considering the unit weight and elasticity modulus of the dominant construction material based on the homogenization approach. In addition to mechanical characteristics, physical properties of historical masonry bridges were used, such as the length, height, width, and Main Arch Span (MAS) length of the masonry bridge, to predict the first natural vibration frequency. Among the proposed equations, a maximum accuracy of 58% was reached with the literature-based experimental approach. Moreover, an empirical formulation with 81% accuracy was proposed by using both physical characteristics and mechanical properties of the bridges on the basis of finite element model results. Also, this study highlights that this accuracy decreases to 35% if the modulus of elasticity and unit weight are ignored. In addition, the developed formulations are compared with other empirical formulations using the Mean Square Error (MSE), as a measure of the average of the squares of the errors. Consequently, the smallest MSE value of 1.95 was obtained with the proposed equation, whose accuracy was 81% in this study.

诸如砌石桥或任何其他结构的历史古迹的基本频率可对其需求进行更好，更详细的地震评估，以提供针对意外地震地面运动的保护。在此基础上，本文旨在利用非线性回归模型开发经验公式，以拟合历史砌体桥梁的环境振动频率。为此，从文献中收集了数据系列，尤其侧重于环境振动测量和历史砌体桥梁的有限元模型，并对其进行了全面建模，以获得第一个全球自然频率。第一种方法是仅使用从基于文献的实验环境振动频率数据中获得的历史砌筑桥梁的物理特征来预测自然振动频率。第二种方法是在均质化方法的基础上，考虑主要建筑材料的单位重量和弹性模量来预测第一自然振动频率。除了机械特性外，还使用了历史性砖石桥梁的物理特性，例如砌体桥梁的长度，高度，宽度和主拱跨度（MAS）长度，以预测第一个自然振动频率。在提出的方程中，采用基于文献的实验方法可达到58％的最大精度。此外，在有限元模型结果的基础上，结合桥梁的物理特性和力学性能，提出了精度为81％的经验公式。此外，这项研究还强调，如果忽略弹性模量和单位重量，则精度会降低到35％。此外，使用均方误差（MSE）将开发的公式与其他经验公式进行比较，以衡量误差平方的平均值。因此，最小的MSE 所提出的方程得到的数值为1.95，在本研究中其准确度为81％。