## 1 Introduction
Detecting voids that arise inside the ducts of PSC bridges is a particularly significant issue; however, it has only been investigated using a signal processing-based method, and machine learning is rarely applied. Therefore, by utilizing IE data and LSTM, supervised learning was attempted to detect defects inside ducts in previous studies [26; 27; 28]. Utilizing IE data and structural information (concrete thickness, depth of duct, distance between the measured point and impact point), [26] used LSTM to classify the duct's voids. However, we determined that the structural information affects the scalability of the deep learning-based approach. Therefore, [27; 28] developed an LSTM-based model that can use a frequency spectrum with IE data. These experiments demonstrated good performance; however, a significant issue was found: the pattern of the IE data appears irregular. For example, the pattern of the IE data of the specimen used for training and the IE data of the new specimen or PSC bridge appear different. This phenomenon was found even for the new specimen, in the same conditions. In addition, if there are voids on the opposite side of the measurement point, another pattern appears, making it difficult to detect. Consequently, it is required to provide training data with a variety of patterns, but doing so is actually a challenging undertaking. As a result, the supervised learning models trained to the specimen's IE data found only part of the voids in real-world PSC bridges. To minimize these issues, a deep learning approach that can flexibly utilize both the data used for training and the data measured elsewhere is required. In particular, cases where voids occur in industrial sites are extremely rare (i.e., class imbalance issue). In this paper, we used deep support vector data description (Deep SVDD) [29] to solve the limitations of supervised learning due to the characteristics of the IE method. Basically, Deep SVDD, which is a semi-supervised learning approach, establishes a hypersphere around normal data, reduces the size of this boundary, and classifies all data outside the hypersphere as abnormal. In other words, Deep SVDD assumes that the distribution of normal and abnormal data is different. Due to these characteristics, we considered it suitable for solving the class imbalance issue and the limitation of the IE method that appears in irregular patterns (or distributions), whether they are normal or voids. At this time, Deep SVDD utilizes a pre-trained autoencoder that can represent the normal data and defect the data distribution differently for the inputs. So, it is important to design a suitable autoencoder structure that can represent the distribution of input data (normal data and void data) differently. Therefore, we developed the autoencoder based on an ELMo (embeddings from language model)-like LSTM architecture [30] because ELMo represents the context well. It trains in both the forward and backward directions, unlike bidirectional LSTM (Bi-LSTM). Then, Deep SVDD trains a minimized hypersphere surrounding the feature space (i.e., latent vector in autoencoder) for the IE data, which are normal data, and determines the IE data outside of this hypersphere as a void. For the experiment, we evaluated the performance of our proposed model using IE data collected from two different specimens and compared it with the supervised learning models which were developed in previous studies. The format of this paper is as follows. Section 2 describes the IE data collected for the experiment as well as the issues we discovered with the IE data. Our proposed method is described in Section 3, and the experimental results are provided in Section 4. Finally, Section 5 concludes with a summary of our findings.