# Optimized Detection Algorithm for Vertical Irregularities in Vertical Curve Segments
## 5 Conclusions  
This study addresses the issue of significant long-wavelength irregularity detection errors during dynamic measurements of track vertical irregularities, which arise due to the spatial frequency characteristics of vertical curve segments being similar to those of certain long-wavelength irregularities. A comprehensive vehicle-track multibody dynamics simulation model was established to tackle this issue, and the model's validity was verified by applying excitation irregularities. Subsequently, the effects of variations in train speed and key vertical curve design parameters on irregularity detection errors were investigated. The reference cancellation method was proposed by analyzing the mechanisms behind the elevated detection errors in vertical curve segments to enhance the accuracy of vertical irregularity detection. Various experimental conditions were designed to compare virtual irregularities calculated using the reference cancellation method and the inertial reference method, thereby validating the effectiveness of the proposed approach. This research provides a theoretical basis for improving track irregularity detection accuracy and facilitating track maintenance operations. Notably, the core of the reference phase cancellation method lies in obtaining ideal pitch angle data. In practical applications, an inclinometer sensor with a low-frequency response range should be selected to measure the pitch angle of the detection system. Additionally, it is essential to ensure that the inclinometer's sensitive axis is aligned parallel to the direction of track movement to minimize detection errors caused by the rolling and yawing motions of the detection device. The main conclusions are as follows:  
1. Simulation analyses reveal that detection errors for track vertical irregularities significantly increase when trains pass through vertical curve segments, particularly at gradient transition points and their vicinity. The degree of impact from different vertical curve design parameters on detection accuracy varies. The detection errors at gradient transition points are primarily influenced by the vertical curve radius; smaller radii correlate with larger detection errors. The vertical curve length is the sole factor determining the location of peak detection errors, which begin to increase 100 m before the transition point, reach their maximum at the transition point, and decrease to levels comparable to those in straight sections within 100 m after the transition. 2. The proposed reference cancellation method effectively removes track alignment components from the acceleration integration results. This method achieves a detection accuracy comparable to the acceleration integration method in straight and gradient sections, while significantly enhancing the accuracy in vertical curve segments. By employing the reference cancellation method, detection errors in vertical curve segments can be reduced to levels equivalent to those in straight and gradient sections, and it does not alter the power spectral density of track irregularities. 3. Various experimental conditions were established to validate the effectiveness of the reference cancellation method compared to the acceleration integration method under different scenarios. Simulation results indicate that, in comparison to the acceleration integration method, the reference cancellation method can reduce the maximum detection error \(E_{\text{max}}\) and the root mean square error \(E_{\text{rmse}}\) by up to 71.77% and 86.61%, respectively. Conceptualization, C.C. ; methodology, C.C. and R.X. ; software, R.X. ; validation, R.X. ; formal analysis, C.C. and R.X. ; resources, C.C. ; writing--original draft preparation, C.C. and R.X. ; writing--review and editing, C.C. ; supervision, C.C. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (No. 52372402) and the National Natural Science Foundation of China (U2034210). Not applicable.