## 1 Introduction
exploited multi-layer restricted Boltzmann machines (RBMs) for learning the abstract features of an input image, and reported satisfactory detecting results in their experiments [29]. Generally, deep learning based crack damage feature extracting often contributes to better detecting performances than the traditional hand-crafted features. However, these methods have several parameters that must be iteratively fine-tuned. Therefore, most of the existing DL-based crack detecting frameworks face the slow learning problem, which may hinder their practical use in real-time detecting applications. Moreover, as for the DL-based crack detecting architecture, both the multi-layer feature learning networks and the following binary classification network are \"hard coded\" together. Thus, we have to retrain the whole neural network when dealing with new training samples, which is a time consuming task and not appropriate for sustainable crack damage detection. As seen from the above analysis, we found that a good crack damage detector should have several characteristics: (1) Feature representation should be discriminative enough for the background disturbances, while being processed efficiently. (2) Crack region identification should have a low computing burden and can be quickly updated incrementally. (3) Considering that there may be some background disturbances (e.g., handwriting, etc.) similar to cracks, how to minimize the relevance between cracks and those noises is an important quality of robust crack detection. In this work, we only place emphasis on the first two points, and present a new crack damage detecting model by using the excellent feature learning and classification capabilities of an extreme learning machine (ELM). Unlike the greedy, layer-wise training in general DL-based crack detection, the presented crack detection consists of two separate parts: Unsupervised multilayer crack region feature extracting and supervised crack region identification. For the first part, a sparse ELM-based auto-encoder (AE) is used for extracting the multi-layer sparse features of the input images; while for the second part, we derived the incrementally updated crack feature classification model using online sequential ELM. The main advantage of developed crack detection is that it has a faster training efficiency than the deep learning methodologies, while keeping a good performance at the same time. It should be mentioned that, although the ELM theories have been well established, our work focuses on developing an effective and efficient crack detector. To our knowledge, this is the first time the ELM theories have been used to construct a comprehensive framework, including feature extraction and crack region identification, for a concrete crack damage detecting application. The contributions are summed, as follows. (1) We propose an effective multilayer feature representation for learning the image features of crack or non-crack images. Unlike existing unsupervised feature learning strategies (i.e., BP-based NNs) for crack detection, an efficient ELM auto-encoder is used to build the hierarchical feature learning pipeline. Owing to its randomly-chosen input hidden parameters, the presented image region feature learning network can be quickly built. Moreover, to further enhance learning of informative features, a sparsity constraint for the ELM-AE output weights is imposed, and an accelerated proximal gradient (APG) algorithm is utilized for processing the feature learning task. (2) An efficient crack region binary classification has been developed. Compared with traditional learning algorithms (SVM or neural networks), the proposed feature classification network is free from the BP-based iterative parameter tuning and, thus, the corresponding final crack region detector can be efficiently calculated. Furthermore, we have derived the incremental updating expression of the presented crack region identification model, which can be trained with the chunk-by-chunk available training samples.