Porous media are ubiquitous in both nature and engineering applications. Therefore, their modeling and understanding is of vital importance. In contrast to direct acquisition of three-dimensional (3D) images of this type of medium, obtaining its subregion (s) such as 2D images or several small areas can be feasible. Therefore, reconstructing whole images from limited information is a primary technique in these types of cases. Given data in practice cannot generally be determined by users and may be incomplete or only partially informed, thus making existing reconstruction methods inaccurate or even ineffective. To overcome this shortcoming, in this study we propose a deep-learning-based framework for reconstructing full images from their much smaller subareas. In particular, conditional generative adversarial network is utilized to learn the mapping between the input (a partial image) and output (a full image). To ensure the reconstruction accuracy, two simple but effective objective functions are proposed and then coupled with the other two functions to jointly constrain the training procedure. Because of the inherent essence of this ill-posed problem, a Gaussian noise is introduced for producing reconstruction diversity, thus enabling the network to provide multiple candidate outputs. Our method is extensively tested on a variety of porous materials and validated by both visual inspection and quantitative comparison. It is shown to be accurate, stable, and even fast ($\sim 0.08$ s for a $128\times 128$ image reconstruction). The proposed approach can be readily extended by, for example, incorporating user-defined conditional data and an arbitrary number of object functions into reconstruction, while being coupled with other reconstruction methods.

The three-dimensional (3D) structure of a digital core can be reconstructed from a single two-dimensional (2D) image via mathematical modeling. In classical mathematical modeling algorithms, such as multipoint geostatistics algorithms, the optimization of pattern sets (dictionaries) and the mapping problems are important issues. However, they have rarely been discussed thus far. Pattern set (dictionary)-related problems include the pattern set (dictionary) size problem and the one-to-many mapping problem in a pattern set (dictionary). The former directly affects the completeness of the dictionary, while the latter is manifested such that a single to-be-matched 2D patch has multiple matching patterns in the library and it is hence necessary to select these modes to establish an optimal mapping relationship. Whether the two above-mentioned problems can be properly resolved is directly related to the accuracy of the reconstruction results. Super-dimension reconstruction is a new 3D reconstruction method proposed by introducing the concepts of training dictionary, prior model, and mapping into the reconstruction of the digital core from the field of super-resolution reconstruction. In addition, mapping relationship extraction and dictionary building are also key issues in super-dimension reconstruction. Therefore, this paper discusses these common dictionary-related problems from the perspective of super-dimension dictionaries. We propose dictionary optimization using augmentation dictionaries and clustering based on the boundary features of the dictionary elements to improve the completeness and expand the expression ability of the dictionary. Furthermore, we propose constraint neighbor embedding-based dictionary mapping to establish a more reasonable dictionary mapping relationship for super-dimension reconstruction, and we solve the one-to-many mapping problem in the dictionary. Our experimental results show that the performance of the super-dimension dictionary can be improved by the above-mentioned algorithm. Thus, through the optimized dictionary structure and mapping relationship determined by the above-mentioned methods, the 2D patch to be reconstructed can match a more accurate 3D block in the dictionary. Consequently, the reconstruction precision is improved.

It is very challenging to accurately understand and characterize the internal structure of three-dimensional (3D) rock masses using geological monitoring and conventional laboratory measures. One important method for obtaining 3D core images involves reconstructing their 3D structure from two-dimensional (2D) core images. However, traditional 2D–3D reconstruction methods are mostly designed for binary core images, rather than grayscale images. Furthermore, the reconstruction structure cannot reflect the gray level distribution of the core. Here, by combining the dimension promotion theory in super-dimension (SD) reconstruction and framework of deep learning, we propose a novel convolutional neural network framework, the cascaded progressive generative adversarial network (CPGAN), to reconstruct 3D grayscale core images. Within this network, we propose a loss function based on the gray level distribution and pattern distribution to maintain the texture information of the reconstructed structure. Simultaneously, by adopting SD dimension promotion theory, we set the input and output of every single node of the CPGAN network to be deep gray-padding structures of equivalent size. Through the cascade of every single node network, we thus ensured continuity and variability between the reconstruction layers. In addition, we used 3D convolution to determine the spatial characteristics of the core. The reconstructed 3D results showed that the gray level information in the 2D image were accurately reflected in the 3D space. This proposed method can help us to understand and analyze various parameter characteristics in cores.

Research on damage diagnosis or safety monitoring based on structural vibration response is one of the hot issues in the engineering field. The characteristic information of the structure is obtained by analyzing the structure response data. In the process of data analysis, the choice of data length is very important, which is related to the validity of the structure monitoring results. At present, the selection of data length is usually subjective, which reduces the rigor of the structure monitoring process. Therefore, a method based on improved multiscale permutation entropy (IMPE) is proposed to determine the optimal data analytical length (ODAL) of vibration data. This method creatively applies multiscale permutation entropy (MPE) to the field of data length analysis when processing nonlinear and nonstationary signals and optimizes MPE with the help of the improved coarse‐grained method to obtain IMPE. IMPE is sensitive to different data lengths, and the entropy changes with the increase of the data length and tends to be stable. Here, the stable value is defined as a standard entropy. The entropy satisfying 97% of the standard entropy is used as the effective entropy, and the corresponding data length value of the effective entropy is selected as the ODAL of the vibration data. This method is suitable for many fields, provides a reliable data analytical length for data analysis, and has good engineering practicability.

Aiming at the detection problem of blockage in urban water supply pipelines and drainage pipelines, also the problem to distinguish commonly used pipe components such as lateral connection from the actual blocking conditions. A method based on dual-tree complex wavelet transform and Safe Semi-Supervised Support Vector Machine for blockage recognition is proposed in this paper. The first step of this method is to decompose the acoustic signals obtained from the pipeline by the dual-tree complex wavelet transform, and then convert the acquired components into Sound pressure level. Secondly, the pulse factor and the average acoustic energy density are extracted respectively from the effective components as acoustical features. Finally, the S4VM classifier is applied to cluster and label the untrained data, furthermore the different degree of the blocking is able to identify as well as the pipe components.