**1. Introduction**

In recent years, deformation and strengthening of structures have been widely studied [1–4]; fiber-reinforced polymers (FRP) have been widely used to strengthen structures [5]. However, due to the linear elasticity of the material, debonding failure occurs in FRP-strengthened reinforced concrete (RC) beams before the FRP has reached its full performance, which largely limits its further application. [6–10]. PE and IC debonding are the two failure modes for FRP-strengthened RC beams (Figure 1). Generally, IC debonding occurs in beams with a relatively large shear-span-to-depth ratio, while for beams with a relatively small shear-span-to-depth ratio, since the bending moment is minor at this time, the beams are mainly subjected to shear strength, so PE debonding occurs [6]. Nevertheless, due to the complex mechanism of debonding failure of FRP-strengthened RC beams in flexure, it is not realistic to judge the failure modes in strengthened beams merely by shear-span-to-depth ratio [11,12].

**Figure 1.** Debonding modes.

Academic Editor: Krishanu Roy

Received: 29 January 2023 Revised: 21 February 2023 Accepted: 24 February 2023 Published: 25 February 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/).

To clarify the failure mechanism of FRP-strengthened RC beams, researchers have conducted a lot of experiments and proposed some models. For PE debonding, in 1992, Oehlers proposed a model for strength based on the forces of shear and flexural moments which act on the end of the plate [11]. In 1997, Jansze proposed a plate-end debonding strength model for steel-plated beams. The model focuses on PE debonding of the strengthened beams at the onset of shear cracking [13]. Ahmed and Van Germert, in 1999, modified Jansze's model to take into account the differences between FRP and steel properties and the effect of shear reinforcement [14]. In 2001, fib Bulletin adopted Blaschko's beam-based model for the shear strength of concrete [15]. In 2002, Smith and Teng proposed a concrete shear strength model for PE debonding [16]. Yao and Teng, in 2007, conducted tests on FRP-strengthened RC beams and modified the expressions proposed by Oehlers [17]. TR55 in 2012, ACI and AS in 2017 recommended an upper limit on the shear force in the plate end region to avoid PE debonding [18–20]. El-Sayed proposed a model for predicting PE debonding based on the beam's concrete shear strength, which considers the parameters that affect the opening of shear cracks in 2021 [21]. For IC debonding, in 2001, fib and JSCE proposed models which limit the tensile stress during debonding [15,22]. CECS 2003, CNR 2004, and TR55 2012 present FRP ultimate debonding strain models which are based on tests of shear at the interface between FRP and concrete. [18,23,24]. In 2013, Kim and Harries proposed a Monte Carlo prediction model for the effective strain of FRP based on the statistical approach [25]. Bilotta et al., in 2013, proposed standard and design values for the maximum tensile strain of FRP when IC debonding occurs based on flexural tests of RC beams strengthened with FRP [26]. In 2016, Lopez-Gonzalez characterized the FRP– concrete interface of the strengthened beams and proposed an interface fracture energy model [27]. ACI modified the model proposed by Teng in 2003 based on the maximum tensile strain of RC beams strengthened with FRP and proposed a model for calculating the allowable debonding strain of FRP in 2017 [20]. Li and Wu investigated the mechanism of IC debonding of FRP-strengthened beams using a finite element analysis model based on the smeared-crack method in 2018. They established a model for IC debonding based on the finite element analysis simulation results [28].

These models for predicting PE and IC debonding have facilitated the study of the debonding failure of FRP-strengthened RC beams. Still, they have significant coefficients of variation between the calculated and experimental values [21,29]. Therefore, it is necessary to conduct a deeper study on debonding failure to establish more accurate models for predicting PE and IC debonding. In recent years, machine learning has been widely used in structural engineering [30–32]. In this paper, a data-driven model was adopted, which reduces the cost of experiments and is scientific in the selection of indicators; 229 beams with debonding failure were collected as a database, of which 128 were PE debonding and 101 were IC debonding. Correlation analysis and grey correlation analysis were used to establish the indicator systems for predicting PE and IC debonding and to identify the important indicators among them. Five machine learning models, linear regression, ridge regression, decision trees, random forests, and BP neural networks, were used to build the two debonding prediction models. Optimization of the best prediction among the five machine learning models took place using the Dung Beetle Optimizer (DBO). Finally, the optimal prediction model was compared with the models suggested by codes.
