| Author: | Wei, Yuanhao |
| Title: | Innovative blind source separation techniques combining gaussian process algorithms and variational autoencoders with applications in structural health monitoring |
| Advisors: | Ni, Yi-qing (CEE) |
| Degree: | Ph.D. |
| Year: | 2024 |
| Subject: | Optical fiber detectors Fiber optics Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Civil and Environmental Engineering |
| Pages: | xxxi, 300 pages : color illustrations |
| Language: | English |
| Abstract: | This study aims to utilize the Variational Autoencoder (VAE) framework to establish a series of algorithms for addressing Blind Source Separation (BSS) problems and to explore their applicability in processing Structural Health Monitoring (SHM) data. The VAE is a machine learning algorithm that integrates the variational inference algorithm with the architecture of an Autoencoder (AE). Through variational inference, estimations about unknown data can be drawn based on known information. When applied to BSS tasks, the variational inference process can be analogized as deriving source signals from mixed observational ones. Since variational inference operates within the Bayesian framework, the source signals estimated are represented in probabilistic distributions rather than as deterministic values. Such probabilistic representations offer the capacity to quantify uncertainties caused by interferences or noise. Moreover, in contrast to the traditional Independent Component Analysis (ICA) and Second Order Statistics (SOS) methods, the VAE-based techniques, benefiting from the nonlinear mapping capabilities of neural networks, hold the potential to tackle BSS issues under nonlinear mixing conditions. The encoder of the VAE maps the input data to the posterior parameters of the latent variables, while the decoder utilizes samples from the posterior distributions to reconstruct the input data. Within the framework of this study, the posteriors of the latent variables are equated to the distributions of the desired source signals. In this way, the encoding process of the VAE is equivalent to the process of inferring the posterior distributions of source signals, and the decoding process is equivalent to the process of remixing the source signals to observation signals. To adapt to sources with underlying temporal structures, the prior of the latent variables in the VAE is altered from a standard normal distribution to Gaussian Processes (GP). Under the GP framework, the correlation between data points of a signal is determined by a kernel function (also referred to as a covariance function). Different priors of source signals (also referred to as the priors of the latent variables) are pre-set with their own independent adaptive kernel function parameters. Although each source signal’s posterior is defined by a diagonal multivariate Gaussian, the source signals are influenced by their own GP priors. As the adaptive parameters converge to different values, the sources with distinct temporal structures can be obtained. To address the BSS task using the above model, it is crucial to introduce an additional hyperparameter to balance the weights of various terms in the model’s objective function. This hyperparameter plays a pivotal role in the performance of the proposed method in solving BSS problems. The study designs a mechanism to determine an appropriate value of the hyperparameter solely based on the reconstruction quality of the observation signals. Since the observation signals are known in BSS problems, this mechanism does not alter the essence of the proposed method as a BSS approach. The proposed method for solving BSS problems is named Kernel Adaptive GP VAE (KA-GPVAE). The main framework of KA-GPVAE is built upon the VAE, and its nonlinear mapping capability can be adjusted by configuring the hidden layers of the encoder and decoder. The study delves into how the complexity settings of the encoder/decoder hidden layers in KA-GPVAE affect its ability to address BSS problems. It provides valuable insights for reasonable configuration of the encoder/decoder in KA-GPVAE, tailored to the characteristics of the problem being addressed. Upon investigation, it is found that the performance of KA-GPVAE in addressing the problem is notably affected by noise. Therefore, to enhance its denoising capability, further refinements are proposed. The Gaussian Process Regression (GPR) is integrated into KA-GPVAE, leading to the development of a new method called Kernel Adaptive Gaussian Process Regression Embedded VAE (KA-GPRE-VAE). In KA-GPRE-VAE, the distribution of a source signal is no longer determined by a diagonal multivariate Gaussian generated through the encoder. Instead, the mean vector of this Gaussian is taken as the target, while its covariance matrix serves as the noise matrix for the GPR. Consequently, the posterior resulting from the GPR represents the distribution of this source signal. To achieve this objective, the original KA-GPVAE objective function is modified to embed the full GPR process into each iteration of the KA-GPRE-VAE model. It is important to emphasize that, in KA-GPVAE, the posterior distributions of the source signals are directly inferred through the encoder. However, the inference process of the source signals’ posteriors in KA-GPRE-VAE encompasses both the encoding process and the GPR process, which together constitute the inference steps of KA-GPRE-VAE. Simulation results show that KA-GPRE-VAE significantly outperforms the KA-GPVAE in solving BSS problems under various noise scenarios. Both KA-GPVAE and KA-GPRE-VAE techniques predominantly leverage the temporal characteristics inherent in signals to address the BSS problem. However, their efficacy diminishes when confronted with independent and identically distributed (i.i.d.) signals. To surmount this limitation, we integrate adversarial training into the KA-GPRE-VAE framework, culminating in a paradigm of the Adversarial Training assisted KA-GPRE-VAE (ATa-KA-GPRE-VAE). Numerical simulations illustrate that in comparison to its counterparts (KA-GPVAE and KA-GPRE-VAE), ATa-KA-GPRE-VAE demonstrates a balanced proficiency in handling both temporal and i.i.d. signals. The aforementioned methods are employed to process monitoring data from experimental and real-world structures to validate their performance in addressing SHM challenges. The experimental studies include a cantilever beam and a continuous beam structure, while the exploration of real-world structures is exemplified by the case study on the Canton Tower. By conducting modal decomposition on the real-world and experimental structures under random or free vibration, the capabilities of KA-GPVAE, KA-GPRE-VAE, and ATa-KA-GPRE-VAE methods in handling SHM data are verified. In particular, both KA-GPRE-VAE and ATa-KA-GPRE-VAE show effectiveness in separating distinct modal responses and also offer denoising capabilities that were not observed in other methods. Furthermore, ATa-KA-GPRE-VAE is used to assist in defect detection of train wheels. The defect-induced responses are successfully separated by the ATa-KA-GPRE-VAE method. The performance of these methods suggests broad applicability within the SHM domain and potential extensions to other fields. |
| Rights: | All rights reserved |
| Access: | open access |
Copyright Undertaking
As a bona fide Library user, I declare that:
- I will abide by the rules and legal ordinances governing copyright regarding the use of the Database.
- I will use the Database for the purpose of my research or private study only and not for circulation or further reproduction or any other purpose.
- I agree to indemnify and hold the University harmless from and against any loss, damage, cost, liability or expenses arising from copyright infringement or unauthorized usage.
By downloading any item(s) listed above, you acknowledge that you have read and understood the copyright undertaking as stated above, and agree to be bound by all of its terms.
Please use this identifier to cite or link to this item:
https://theses.lib.polyu.edu.hk/handle/200/13076