## 1 Introduction  
Damage identification for steel box beams and orthotropic plates in bridges is critical for ensuring structural integrity, safety, and longevity. Early detection of defects through Structure Health Monitoring (SHM) techniques prevents catastrophic failures [1], optimizes maintenance strategies [2], and leads to significant cost savings over the bridge's lifespan [3]. By addressing damage promptly, engineers can enhance structural performance, minimize risks, and ensure the continued functionality of bridge infrastructure, ultimately benefiting society by maintaining safe and reliable transportation networks. Nondestructive testing (NDT) technology offers several advantages over traditional testing methods in bridge engineering, particularly for steel box beams and orthotropic plate structures. NDT preserves structural integrity by allowing an assessment without causing harm, thus minimizing downtime and disruption to transportation networks. Unlike traditional methods, NDT can be performed efficiently and non-invasively, often without the need for bridge closures or interruptions [4]. Additionally, NDT provides real-time results and immediate feedback, facilitating timely decision making regarding maintenance and repair interventions [5]. With comprehensive inspection coverage, NDT identifies potential issues that may be overlooked by traditional methods, ensuring the thorough assessment of defects. Moreover, NDT is cost-effective and efficient, requiringfewer resources and enabling optimization of maintenance budgets, ultimately contributing to the safety, durability, and longevity of bridge infrastructure [6]. The Wavelet Packet Permutation Entropy (WPPE) technique offers several advantages for damage identification in steel box beams and orthotropic plates compared to other nondestructive testing techniques (such as using natural frequency [7], mode shape [8], and mode curvature [9] to establish the damage characteristics.). By enabling a multiscale analysis, sensitivity to complex dynamics, and nonlinear assessment, WPPE can detect subtle changes indicative of damage, even in noisy environments [10; 11]. Its data-driven approach and complementary nature to other techniques enhance its versatility and effectiveness in identifying defects [10; 12]. Overall, WPPE provides a powerful tool for comprehensive damage assessment, making it a valuable addition to the arsenal of nondestructive testing methods for ensuring the structural integrity and safety of bridges. While the WPPE technique offers significant advantages for damage identification, there are potential downsides to consider [13]. These include computational complexity due to intensive signal processing, parameter sensitivity requiring careful tuning, challenges in interpreting results, and limited validation in real-world bridge inspection scenarios. Additionally, the technique's resilience to noise may vary depending on the signal-to-noise ratio and the specific characteristics of the noise present in the data. Addressing these limitations, including enhancing noise resistance, will be essential to ensure the practical effectiveness and reliability of WPPE in nondestructive testing applications for steel box beams and orthotropic plates. The WPPE method was found to be useful in an experimental study on a steel box girder to identify the damage location when sinusoidally excited at 10 Hz [10]. This study addresses the challenges associated with the WPPE technique by considering the finite element model of a steel box girder and analyzing the vibration acceleration responses under sinusoidal excitation at frequencies such as any frequencies or at the natural frequencies. The study further verifies the validity of WPPE for damage identification in steel box beams and orthotropic plates. Additionally, the robustness of the methodology is tested under various white noise interference conditions, providing insights into its effectiveness in real-world scenarios.