Train fault detection primarily relies on the comparative analysis of collected images with standard reference images, making the accurate identification of the collected image types crucial for effective fault detection. Most current systems achieve indirect classification of carriage images by using Automatic Equipment Identification (AEI) devices to recognize carriage identification number information while capturing the carriage images. However, damaged RF tags or blurred characters can hinder these devices, obstructing further train fault analyses. The unique features of carriage linear array images, such as high resolution, extreme aspect ratios, and local non-linear distortions, pose significant challenges to recognition algorithms. This paper proposes a method specifically designed to recognize these types of images. First, we implement an object detection algorithm to locate the positions of key components in carriage linear array images. By leveraging the spatial layout mapping between these key components and the carriage type classification, we simplify the complex image recognition problem into a sparse point set alignment task. To ensure effective registration despite local distortions in the linear array images, we propose a weighted radial basis function. To address the issues of unknown matching relationships and quantity mismatches during point set alignment, the proposed objective function is designed to maximize the similarity between Gaussian mixtures of point sets, thereby determining the RBF weights. Extensive experiments have demonstrated that our algorithm achieves 100% recognition accuracy under local nonlinear scale distortions of less than 15%. The algorithm remains effective even in the presence of some false positives or missed detections in key component object detection results. It can accurately identify the target category from 79 image categories within 24 milliseconds on an i7 CPU without GPU support. It is of great significance to reduce system cost and promote automatic exterior fault detection for train rolling stock.