**1. Introduction**

Bridges are key elements of the transportation system. Health monitoring and assessment of large-span bridges, mastering the evolution law of structural state, predicting structural performance changes and early warning of emergencies are effective means to ensure bridge operation safety, and are the priorities and research direction in bridge engineering. As a response parameter of the bridge structure, the bridge alignment can directly reflect the overall state and performance degradation of the structure (i.e., force change, material degradation, stiffness degradation, etc. all could cause the alignment change) and is an important parameter for assessment of the structure state. Structural state monitoring, analysis and assessment with bridge alignment as the key index is one of the important aspects of bridge health monitoring. Bridge alignment prediction is an area of intense research in academia and industry which has important theoretical significance and engineering application value.

SCCB are a new type of structure developed on the basis of steel and concrete. This structure can resist the lifting and opposite sliding at the interface of the steel beam and concrete bridge deck by setting shear connectors (shear nails, bending bars, etc.) between the steel beam and the concrete bridge deck, so as to make it work together as a whole. The SCCB bridge has the advantages of both steel and concrete structures, and is the main development direction of long-span bridges. The research on the alignment prediction of SCCB bridges is of great significance. Due to the influence of large traffic volume, narrow

**Citation:** Li, X.; Luo, H.; Ding, P.; Chen, X.; Tan, S. Prediction Study on the Alignment of a Steel-Concrete Composite Beam Track Cable-Stayed Bridge. *Buildings* **2023**, *13*, 882. https://doi.org/10.3390/ buildings13040882

Academic Editors: Humberto Varum and Ahmed Senouci

Received: 15 February 2023 Revised: 9 March 2023 Accepted: 21 March 2023 Published: 28 March 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

width, and high frequency of operation, the error between the predicted alignment and actual alignment of large-span SCCB track cable-stayed bridges can be large. The alignment state of such bridges directly impacts their safe construction and operation. If the error of alignment prediction is too large, it can cause a great threat to the safety of the whole bridge. Alignment analyses of large-span SCCB track cable-stayed bridges have been carried out in several studies, starting from the response surface method (RSM), and accurate alignment predictions were obtained.

Changes in bridge alignment are closely related to the bridge structure system, material characteristics, construction technology, etc. Researchers have carried out a large number of related studies and achieved fruitful research results. Ahad et al. [1,2] explored the role of bonding between ultra-high-performance concrete and reinforcement through experiments. Xiong [3] studied the influence of different influencing factors on the construction control of SCCB cable-stayed bridges through a geometric control method and identified the parameter sensitivity affecting the alignment of the main beam.

In order to reduce the influence of the construction process, several researchers have proposed different methods to improve the efficiency of alignment analysis for large-span bridges as bridge construction technology continues to mature. Xin et al. [4] proposed a new method based on improved variational mode decomposition (IVMD) and conditional kernel density estimation (CKDE) analysis data to obtain a high reliability bridge alignment prediction. Lu et al. [5] have proposed an agent model which is based on mind evolutionary computation-back propagation (MEC-BP) to improve the efficiency of the finite dimension analysis through the assistance of the model, using the model to study the alignment of a large span of waveform steel webs. Zhou et al. [6] proposed an optimized extreme learning machine algorithm to obtain the optimum extreme learning machine (ELM) data through an MEC search and then added in the ELM for the training so as to obtain a model with an average error of only 0.225 cm to generate a construction alignment prediction of large-span continuous rigid bridges. Chen et al. [7] established the multivariable grey model (MGM) (1,2) on the basis of grey system theory in order to combine the grey prediction model and the characteristics of the arch rib space of the shaped arch. They used the actual work for comparison to prove that the MGM(1,2) model is an accurate and reasonable method to predict the arch rib space of a shaped arch bridge alignment. Li and Zhu et al. [8] evaluated the long-term state of the Qingma Bridge under traffic load by a suspension cable monitoring system. Li and Wei et al. [9] proposed a cable state evaluation method based on machine learning, which showed that the cable tension ratio is only related to the properties of the cable and the transverse position of the vehicle on the deck. The model analysis showed that the tension ratio can be considered an effective feature reflecting the cable state which can be used effectively for cable state evaluation. Considering the inaccuracy of monitoring systems caused by temperature in some specific cases, Li et al. [10] proposed a method to extract bridge deformation under the influence of temperature and effectively analyzed the influence of temperature. Zhang et al. [11] established the dual defects magnetic dipole model with double defects in the cable and evaluated the state of the cable by quantifying the fracture width. Statistical methods are also becoming more widely used in the field of civil engineering. Among them, multiple linear regression is a statistical method that uses mathematical models to describe the relationship between one or more dependent variables. Yang et al. [12] analyzed eight parameters using the multiple linear regression method. In this way, the energy consumption of buildings could be analyzed and predicted. This statistical method is also applicable to the prediction research of bridge engineering. RSM is often used as a statistical method in engineering research. Li et al. [13] revised the model of cable-stayed bridges based on RSM. Using RSM, Ma et al. [14] performed synchronous revision of the structural parameters of the multiscale finite element model (FEM) for a concrete-filled steel tube bridge. Xin et al. [15] used RSM to predict the long-term deformation of track cable-stayed bridges in a probabilistic sense considering five main structural parameters. Liu et al. [16] combined the RSM

and equivalent normalization method (JC method) to analyze the reliability of large-span bridges.

However, the RSM has been applied less to the prediction of the alignment for largespan SCCB track cable-stayed bridges. There is less research on how to accurately predict the alignment for large-span SCCB track cable-stayed bridges. In this study, the RSM was used to conduct the alignment prediction based on environmental factors, actual situation on site, applicable standards and specifications, and other factors. It can supplement the alignment prediction research of entire large-span track bridges, and provide a reference for bridge health monitoring, assessment and reasonable alignment control during the operation period.
