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Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.Chẩn đoán kết cấu cầu dựa trên chuỗi dữ liệu đo dao động theo thời gian kết hợp sử dụng mạng học sâu tích chập.

MINISTRY OF EDUCATION AND TRAINING UNIVERSITY OF TRANSPORT AND COMMUNICATIONS Hoang Thanh Nam DIAGNOSIS OF BRIDGE STRUCTURES BASED ON TIME-SERIES VIBRATION DATA USING CONVOLUTIONAL DEEP LEARNING NETWORK Major: Transport Construction Engineering Code: 9580205 SUMMARY OF DOCTORAL THESIS HÀ NỘI – 2023 The project was communications completed at: University of transport and Supervisor 1: Associate Professor, Dr Hoang Ha Supervisor 2: Dr Nguyen Thi Cam Nhung Reviewer 1: Professor, Dr Nguyen Đong Anh Reviewer 2: Associate Professor, Dr Nguyen Binh Ha Reviewer 3: Dr Nguyen Viet Khoa The thesis will be defended in front of the University Dissertation Council in accordance with Decision No 2089/QD-DHGTVT dated 21thSep, 2023 The defense will take place at University of Transport and Communications Scheduled date and time: day, , 2023 The thesis can be found at the library: - Library of University of Transport and Communications; - National Library INTRODUCTION Introduction Diagnosing bridge structures is the process of analyzing changes in vibration characteristics such as frequency and mode of vibration to detect damage and defects of the structure based on the close correlation of the characteristics physics and mechanics with kinematic and dynamic responses of structures In the field of structural health monitoring, given the characteristics of large-scale, long-term data collected from various structures, deep learning models can overcome the limitations of traditional methods to assess, diagnose, and monitor the condition of transportation infrastructure These deep learning models are trained and capable of accurately detecting, classifying, and predicting the location and extent of damage occurring in structures Therefore, researching and applying deep learning models to detect damage in transportation infrastructure is essential in the current context These methods will facilitate the convenient, efficient, and cost-effective detection of damage, among other benefits Hence, in the scope of my research, I focus on a deep investigation into the topic of "Diagnosis of bridge structures based on time-series vibration data using convolutional deep learning network" for my doctoral thesis Objectives - Investigate the problem of diagnosing structural damage in bridge infrastructure based on dynamic data collected from sensors - Propose a convolutional neuralalgorithm to detect damage within the structure - Conduct and reference experiments involving real-world bridge vibration measurements, followed by the application of the proposed method for structural damage detection Methods - Theoretical analysis synthesis method - Numerical method - Numerical analysis combined with experimental method Scopes - Dynamic characteristics of bridge structures - Data processing methods - Combined convolutional neural networks methods - Location and damage detection of the structure Scientific and practical significance - Applying deep learning methods for structural damage detection effectively with time-series data (as a basis for developing real-time monitoring tools for infrastructure) - Proposing a method to enhance data quality, along with the proposed algorithm to improve the accuracy of deep learning methods - Establishing a database of structures as a form of storage for monitoring infrastructure health - The results of the thesis can serve as valuable reference materials for the field of infrastructure health monitoring Content and thesis structure In addition to the introduction, conclusion, and recommendations, the thesis consists of chapters with the following structure and appendices: Introduction: Chapter - overview of research on stucture health monitoring of bridge structures based on vibration recognition methods Chapter - Theoretical foundations of structural health monitoring using time-series data based on dynamic characteristics Chapter - Traditional deep learning networks and convolutional neural networks applied in damage detection Chapter - Application of combined convolutional neural networks with SAXMDWD method for detecting various types of damage in bridge models Conclusion and Recommendations References: A compilation of 130 relevant documents related to the issues and research content discussed in the thesis CHAPTER 1: OVERVIEW OF RESEARCH ON STUCTURE HEALTH MONITORING OF BRIDGE STRUCTURES BASED ON VIBRATION RECOGNITION METHODS 1.1 Overview of research on Structural Health Monitoring of bridge structures based on vibration recognition methods 1.1.1 Introduction to Structural Health Monitoring of bridge structures based on vibration recognition methods Health monitoring can assess the performance of structures actively by using measured data and data interpretation algorithms to accurately evaluate the current condition and predict the remaining lifespan of a structure The main advantage of this method is that it provides an overall view of the structural health condition to assess the structural status, and measurements at one location are sufficient to evaluate the condition of the entire structure The measurement location may differ from the location of damage Methods based on the vibration characteristics of the structure can be applied intermittently (deploying sensors temporarily) and continuously (embedding sensors in the structure) 1.1.2 Objectives of Structural Health Monitoring based on vibration recognition methods - It provides real-time monitoring, analysis, and continuous detection of decreased load-bearing capacity and damage without causing harm to the structure during the entire operational lifespan of the facility - In particular, this system also monitors and records the behavior of the structure in special cases (such as hurricanes, floods, or severe accidents) that cannot be monitored by other traditional methods 1.1.3 The development of structural health monitoring methods based on vibration pattern Recently, significant advancements have been made in various technology fields, including sensor devices, data acquisition and transmission, data processing, and numerical modeling These technological advancements enable the collection and analysis of historical and current information necessary for infrastructure monitoring SHM strategies leverage these technological advances to accurately assess the condition of structures by using real-time monitored data Structural monitoring activities have surged in recent years, thanks to continuous developments in computer science and "smart" monitoring systems The term "smart" is used to emphasize the importance of intelligent monitoring systems due to their durability, reliability, and cost-effectiveness With the continuous development of science and technology, structural health monitoring is presented with a significant opportunity to evolve toward "smart monitoring" systems In the method of evaluating structural health based on the results of vibration pattern recognition and numerical analysis, there are several main research directions: - Research direction on the devices (sensors) for measuring structural vibrations and processing (noise filtering) – transmitting measurement results to a computer - Research direction on algorithms to update the numerical model of the structure (by changing boundary conditions and physical characteristics of the structure) based on measured vibration characteristics, thereby constructing a "digital twin" of the structure on a computer that matches the real-world structure - Research direction based on updated structural models to identify or predict the locations of damage (if any) and predict the behavior of the structure These research directions are closely related and mutually important The first research direction addresses the accuracy of collecting characteristic vibration data, the second direction highlights the need to collect and store sufficient information about vibration data, and the third direction reflects the accuracy requirements for searching, detecting, and assessing the impact of damaged locations on the structure This is also the main purpose of monitoring the health of a bridge structure through the collection, analysis, and evaluation of changes in characteristic vibration parameters 1.2 International research on Structural Health Monitoring based on vibration pattern recognition methods Messina and colleagues have used statistical correlations between analyzed natural frequency changes and measurements to estimate the location and size of damage Morassi applied an inversion technique to localize cracks in steel frames through the variations in natural frequency Morassi proposed a method to detect cracks in beam-like structures based on changes in natural frequency caused by damage However, the mentioned algorithms require significant parameter tuning through iterations, which can be time-consuming when applied to optimization problems in structures with many degrees of freedom This reduces the effectiveness when using optimization algorithms for large-scale structural optimization problems Besides optimization algorithms, Artificial Neural Networks (ANN) have gained attention and successful applications in various fields Yeung and Smith used unsupervised neural networks to pattern recognition with data streams obtained from sensors installed on Tsing Ma Bridge to continuously monitor the structure's activities Later, Reda Taha and Lucero introduced a novel method by supplementing identification indices to address uncertainties related to the damage state based on ANN The acceleration obtained from sensors installed on the bridge was analyzed using a wavelet neural network module The results showed that the proposed method can accurately identify damage in structures However, some errors still occur when applying these methods In recent decades, ANN has been widely applied in various fields However, due to the application of backpropagation algorithms based on Gradient Descent (GD), the network can get stuck in local minima, reducing the accuracy and efficiency of ANN Another limitation of the ANN algorithm is that it is not suitable for processing image data and has low accuracy in handling large data The analysis above indicates the emergence of a new research direction There is a need to use and develop powerful tools with higher flexibility and diversity to process large datasets with various types of data This meets the requirements for monitoring and controlling the health status of large-scale and technically complex structures that require a large number of measurement devices 1.3 Research in Vietnam on Structural Monitoring based on vibration pattern recognition methods In Vietnam, research on structural health monitoring has gained attention and focus from scientists in recent decades Studies on damage detection in structures have been conducted on various types of structures, such as bridges, foundation systems, and drilling rigs Bui Duc Chinh introduced a method using the Hilbert-Huang transform combined with vibration measurements to diagnose damage in some bridge piers The results showed that the Hilbert-Huang transform is more sensitive than traditional transforms like Fast Fourier Transform (FFT) and Wavelet Transform (WT) in differentiating vibration behaviors of bridge piers and detecting changes in their stiffness Nguyen Huu Thuan and colleagues conducted on-site experiments combined with Finite Element Method (FEM) modeling to monitor the health of My Thuan cable-stayed bridge Eigenfrequencies and mode shapes were chosen as target functions to minimize differences between computed and measured results Nguyen Trong Nghia and colleagues proposed using graph theory to calculate tension forces in cable strands of Phu My cable-stayed bridge However, research in Vietnam mainly focuses on analyzing or determining dynamic characteristics of structures, such as natural frequencies, mode shapes, etc., and has not fully determined the values of uncertain parameters that may change over time, such as material properties (elastic modulus, etc.), cross-sectional shapes, and boundary conditions Additionally, although optimization algorithms and machine learning methods have been widely applied and proven effective for structural health monitoring worldwide, in Vietnam, these techniques are relatively new, and there are not many studies using optimization algorithms, machine learning, or deep learning models to analyze data in structural health monitoring Most recently, Ho Khac Hanh applied ANN combined with PSO for damage diagnosis in structural engineering CHAPTER THEORETICAL FOUNDATIONS OF STRUCTURAL HEALTH MONITORING USING TIME-SERIES DATA BASED ON DYNAMIC CHARACTERISTICS 2.1 Concept of Time Series Data In mathematics, time series data is defined as a sequence of data points measured at successive uniformly spaced time intervals Time series prediction is the use of models to forecast future events based on past known events, predicting data points before they occur Time series data possesses distinct characteristics, including trend, seasonality, randomness, stationarity, noise, and non-stationarity 2.2 Time Series Data for Structural Health Monitoring Continuous and online structural health monitoring (SHM) based on dynamic features to assess the operational conditions of structures has received significant attention from scientists and regulatory bodies [91] Structural health monitoring based on oscillations can be classified into the time domain, frequency domain, and time-frequency domain Among these, methods based on the time domain, using time-series data analysis obtained from sensor systems, have shown promising potential in evaluating the structural health condition [92] 2.3 Types of Time Series Data The type and nature of time series data play a prominent role in time series analysis Consequently, the most suitable time series model must be identified, one that is compatible with the data and extracts reliable DamageSensitive Features (DSFs) Based on these considerations, time series data can be categorized into four groups [113]: Stable time series vs unstable time series Linear time series vs nonlinear time series Univariate time series vs multivariate time series Gaussian time series vs non-Gaussian time series 2.4 Uncertainty in Time Series Data for Structural Health Monitoring 2.4.1 Equation of Structural Oscillation The continuous oscillation of structures is discretized with the number of degrees of freedom (DOF), denoted as "n," and expressed by a second-order differential equation (the general equation of motion) that is represented as Equation 2.1 (2.1) 𝑀𝑥̈ (𝑡) + C𝑥̇ (𝑡) + Cx(𝑡) = p(𝑡) 2.4.2 Analysis of vibration morphology The square matrix consisting of N vibrational modes will be represented by Φ as follows: 𝜙11 𝜙12 ⋯ 𝜙1𝑁 𝜙21 𝜙22 ⋯ 𝜙2𝑁 𝜙 𝜙32 ⋯ 𝜙3𝑁 𝚽 = [𝜙1 𝜙2 𝜙3 ⋯ 𝜙𝑁 ] = 31 (2.2) 𝜙41 𝜙42 ⋯ 𝜙4𝑁 (2.2) ⋯ ⋯ ⋯ ⋯ [𝜙𝑁1 𝜙𝑁2 ⋯ 𝜙𝑁𝑁 ] 2.4.3 Oscillation damping First to analyze the proportional damped vibration, the general differential equation of motion (2-1) will be developed by multiplying both sides of the equation by ϕ𝑇 𝜙𝑛𝑇 𝑚𝛷𝑌̈(𝑡) + 𝜙𝑛𝑇 𝑐𝛷𝑌̇(𝑡) + 𝜙𝑛𝑇 𝑘𝛷𝑌(𝑡) = 𝜙𝑛𝑇 𝑝(𝑡) (2.3) If equation (2.3) is divided by the overall mass, Eq This modal motion can be represented in substitution form 𝑃𝑛 (𝑡) 𝑌𝑛̈ (𝑡) + 2𝜉𝑛 𝜔𝑛 𝑌𝑛̇ (𝑡) + 𝜔𝑛2 𝑌𝑛 (𝑡) = 𝑀 (2.4) 𝑛 2.4.4 Uncertainty and Random Features of Time Series Data in Structural Health Monitoring Time series data in structural health monitoring exhibit several fundamental characteristics: Temporal Correlation, Dynamics, Cyclical properties, Noise properties, Susceptibility to Environmental Changes In structural measurement tasks, two types of measurement errors contribute to data uncertainty: systematic errors (measurement biases) and random errors Systematic errors result from discrepancies in the measurement process, leading to shifts in the measured values Random errors, on the other hand, introduce variability, causing measured values to differ when repeated measurements are taken To enhance raw data, reduce noise, and address data uncertainty, the research applies the Symbolic Aggregate Approximation (SAX) method in conjunction with Multi-Level Discrete Wavelet Decomposition (MDWD) in the data preprocessing stage Additionally, machine learning methods are employed for structural diagnosis to analyze large datasets These aspects will be further elucidated in the subsequent sections of the thesis 2.5 Symbolic Aggregate approXimation – SAX The Symbolic Aggregate approXimation (SAX) method is an important approach in the field of time series data processing, particularly in reducing the dimensionality of data and minimizing computational complexity For a time series data sequence with a length of n, it is transformed into w symbols This process involves dividing the time series data into w segments of equal size using the Piecewise Aggregate Approximation (PAA) algorithm The average value of each time segment, denoted as 𝑋‾ = ̅̅̅ 𝑋1 , ̅̅̅ 𝑋2 , … , ̅̅̅̅ 𝑋𝑤 , is calculated by taking the average of the 𝑖 segment using the following equation (2.5): 𝑛 ( )𝑖 𝑤 𝑋̅𝑖 = 𝑛 ∑𝑗𝑤   𝑋𝑗 𝑛 (2.5) j= (𝑤)(𝑖 + 1) + To divide a space into α regions with equal probabilities, we use partition points, where 𝑋𝑗 represent a point in time within the time series data 𝑋 The process of determining these dividing points involves arranging them into a list, denoted as 𝐶 = 𝑐1 , 𝑐2 , … , 𝑐𝛼−1 Furthermore, these dividing points follow a Gaussian distribution, and the distance between two consecutive dividing points, 𝑐𝑖 and 𝑐𝑖+1 , equal 1/𝛼 The SAX method has several outstanding advantages, including: Data Size Reduction, Preservation of Important Features, Consistency and Interpretability, Independence of Time Series Length, Wide Applicability 2.6 Multilevel Discrete Wavelet Decomposition – MDWD MDWD [118] is one of the recent advancements in the discrete wavelet transform (DWT) method It allows for the extraction of time-frequency features at various scales from a given time series by iteratively decomposing the sequence into low-frequency and high-frequency sub-sequences at each 11 Figure 3.1 A sample 1DCNN configuration with CNN layers and ANN layers 3.2 Proposed Convolutional Neural Networks In practice, monitoring infrastructure such as bridges requires long-term installation of sensors on the structure, continuously transmitting data to data processing centers The amount of data to be processed is very large and sequential over time However, these networks are not efficient at handling large datasets or sequential time-series data because they lack memory and the ability to link data at different time steps To address these limitations, I propose an approach based on the combined use of a 1D Convolutional Neural Network (1DCNN) and a recurrent network, specifically the Long Short-Term Memory (LSTM) method, to process time-series data obtained from sensors This approach aims to monitor structural health, diagnose structural issues, and avoid the problem of forgetting critical information ht Ct-1 Ct ht-1 Ot it ft   Ct  ht X1dcnn Figure 3.2 LSTM Model In 𝑡 condition of LSTM model:  Output: 𝑐𝑡 ; ℎ𝑡 , we call 𝑐 is cell state, ℎ is hidden state  Input: 𝑐𝑡−1 ; ℎ𝑡−1; 𝑋1dcnn Where 𝑋1dcnn is input of 𝑡 condition of model 𝑐𝑡−1 ; ℎ𝑡−1 is output of previous layer 𝑓𝑡 ; 𝑖𝑡 ; 𝑜𝑡 corresponding with forget gate, input gate and output gate Forget gate: 𝑓𝑡 = 𝑠(𝑈f ∗ 𝑋1dcnn + 𝑊f ∗ ℎt−1 + 𝑏f ) Input gate: 𝑖𝑡 = 𝑠(𝑈i ∗ 𝑋1dcnn + 𝑊i ∗ ℎt−1 + 𝑏i ) Output gate: 𝑜𝑡 = 𝑠(𝑈o ∗ 𝑋1dcnn + 𝑊o ∗ ℎt−1 + 𝑏o ) 12 Comment: < 𝑓𝑡 ; 𝑖𝑡 ; 𝑜𝑡 < 1; 𝑏f ; 𝑏i , 𝑏o are bias coefficient; coefficient 𝑊, 𝑈 is training parameters 𝑐̃𝑡 =𝑡𝑎𝑛ℎ(𝑈c ∗ 𝑋1dcnn + 𝑊c ∗ ℎt−1 + 𝑏c ), 𝑐𝑡 = 𝑓𝑡 ∗ 𝑐𝑡−1 + 𝑖𝑡 ∗ 𝑐̃𝑡 , The forget gate decides how much to take from the previous state, and the input gate decides how much to take from the inputs of previous layers ℎ𝑡 =𝑜𝑡 ∗ tanh(𝑐𝑡 ), The output port decides how much to take from the cell state to become the output of the hidden state Besides ℎ𝑡 is also used to calculate the output 𝑦𝑡 for state 𝑡 𝑐𝑡 Just like a conveyor belt, important information that needs to be preserved and used later will be carried forward and used when necessary, which can carry information from a distant point, thus constituting long-term memory Therefore, the LSTM model has both short-term memory and long-term memory When data is fed into the network, it is divided into segments of fixed length The 1-DCNN layer then extracts local relationships between data points and their neighbors before passing them to the LSTM layer Here, longterm dependencies are identified and maintained over time The output of the final LSTM cell is flattened and fed into a fully connected layer before being passed to the output layer with a softmax activation function to provide the diagnosis of structural damage This hybrid deep learning algorithm is implemented with the assistance of open-source TensorFlow code CHAPTER APPLICATION OF COMBINED CONVOLUTIONAL NEURAL NETWORKS WITH SAX-MDWD METHOD FOR DETECTING VARIOUS TYPES OF DAMAGE IN BRIDGE MODELS 4.1 Applying Convolutional neural network Combined with SAX-MDWD Method to Diagnose Defects for a Real Bridge Model 4.1.1 Introduction of the Bridge To evaluate the effectiveness of the proposed approach, I will use algorithms to identify the defects of the Z24 bridge based on time-series data The Z24 bridge (Figure 4.1) is located in the Bern canton near Solothurn 13 Figure 4.1 Vertical and horizontal projection of the Z24 bridge [129] Table 4.1 Cases of detect creation and corresponding labels [130] Label Date (1998) 04 August 10 11 12 13 14 15 August 10 August 12 August 17 August 18 August 19 August 20 August 25 August 26 August 27 August 31 August 02 September 03 September 07 September 08 September Case of damage Establish initial condition (undamaged condition) Install equipment on the pier Cut, create defects on the pier (20 mm) Cut, create defects on the pier (40 mm) Cut, create defects on the pier (80 mm) Cut, create defects on the pier (95 mm) Raise the pier, create a tilting of the foundation Establish the new undamaged state Concrete breaking (12 m2) Concrete breaking (24 m2) 1-meter landslide at the abutment Create joint damage Create damage to anchor heads Create damage to anchor heads Cut out of 16 cables Cut out of 16 cables For each damaged state, setups were conducted to collect data, with setups using 33 sensors and setup using 27 sensors, resulting in a total of 291 measurement sensors to capture vibrations on the piers (primarily in the vertical and horizontal directions) and vibrations on the bridge deck 14 (a) (b) (c ) (d) (e) (f) (g) (h) Figure 4.2 (a) – (h) Time-series acceleration data at the corresponding sensors for the damage cases from to 4.1.2 Data processing To improve the data before using it to train the network, the SAX and MDWD methods will be applied Specifically, the process of transforming continuous time-series data into discrete data using the MDWD method is performed through the following steps: - Step 1: Choose a basic wavelet function to analyze the signal - Step 2: Perform wavelet transformation on the signal using the chosen wavelet function The result of the transformation is the analyzed signal and the analysis coefficients - Step 3: Repeat steps and on the analyzed signal to generate new wavelet components These wavelet components will be used to build the model and analyze the signal - Step 4: Repeat steps 1-3 until no more wavelet components are 15 generated or the desired resolution level is achieved These steps create a resolution tree for the signal, where each node corresponds to a wavelet component Nodes at higher levels correspond to components with lower frequencies and larger delays, while nodes at lower levels correspond to components with higher frequencies and smaller delays SAX performs signal analysis using the following steps:  Step 1: Divide the data sequence into segments of equal length  Step 2: Calculate the mean value of each segment  Step 3: Calculate the standard deviation of each segment  Step 4: Transform the value of each segment into a corresponding symbol using a transformation function  Step 5: Create a discrete character string by arranging the symbols generated from the segments in order Figure 4.3 The time-domain acceleration data at a sensor after being processed using the MDWD and SAX methods Figure 4.4 The time-domain acceleration data for the 16 classes after being processed The data, after applying the SAX-MDWD method, undergoes a transformation from a continuous wave-like form to a time-varying format 16 This means that the time data will no longer exhibit continuous waveforms but will be smoothed and focused on areas with significant oscillations As a result, the new matrix will have a size of (4000, 5) instead of the original size of (8000, 5) 4.1.3 Network architecture Firstly, there is a 1D Convolutional Neural Network (1DCNN) layer used to extract important features from the model This CNN layer has the following characteristics: it uses 128 kernels, and each kernel has a size of 3x3 After extracting features from the input data, a Long Short-Term Memory (LSTM) network is employed for learning and classification The LSTM network consists of layers, and between these layers, there are Dropout layers to prevent overfitting, as well as Maxpooling layers to extract essential features These design choices help reduce the matrix size, computational load, and computation time Finally, the network is flattened with 16 output layers, each of which is labeled 4.1.4 Network training and analyze the results The Adam algorithm was used to train the network with a total of 100 training steps The network has 8,287,280 parameters that need to be trained Figure 4.5 illustrates the convergence of the training and testing processes for all three methods: 1DCNN, 1DCNN-LSTM, and MDWD-SAX-1DCNNLSTM In this thesis, the effectiveness of the proposed methods is also evaluated using ground truth maps and error matrices These tools are used to assess the performance of image processing and computer vision algorithms, helping to evaluate the model's ability to classify correctly or incorrectly for each class (b) (a) Figure 4.5 The convergence of the models: (a) Convergence of the training process of the three methods, (b) Convergence of the network evaluation process of the three methods 17 In addition, to evaluate the model's performance, I used a combination of methods through "macro avg" and "Loss validate" values Table 4.2 Training results of the network using the method 1DCNN-LSTM MDWD-SAXLayers 1DCNN 1DCNN-LSTM prec rec f1-sc prec rec f1-sc prec rec f1-sc 0.6 0.38 0.46 0.53 0.81 0.64 0.83 0.78 0.64 0.51 0.73 0.6 0.69 0.69 0.69 0.85 0.88 0.65 0.67 0.76 0.71 0.92 0.79 0.85 0.9 0.93 0.81 0.68 0.66 0.67 0.45 0.62 0.53 0.84 0.84 0.69 0.71 0.56 0.63 0.85 0.81 0.83 0.87 0.94 0.79 0.69 0.67 0.68 0.88 0.85 0.87 0.8 0.89 0.83 0.6 0.75 0.67 0.39 0.91 0.55 0.88 0.81 0.62 0.71 0.67 0.51 0.71 0.6 0.8 0.86 0.65 0.67 0.6 0.63 0.93 0.65 0.76 0.81 0.72 0.75 0.75 0.8 0.77 0.66 0.83 0.74 0.69 0.97 0.69 10 0.63 0.52 0.57 0.94 0.52 0.67 0.87 0.82 0.7 11 0.56 0.58 0.57 0.76 0.61 0.68 0.72 0.74 0.76 12 0.57 0.74 0.65 0.32 0.49 0.76 0.84 0.61 13 0.81 0.65 0.72 0.47 0.64 0.83 0.71 0.77 14 0.71 0.53 0.61 0.72 0.41 0.52 0.81 0.66 0.58 15 0.53 0.66 0.59 0.74 0.8 0.77 0.94 0.86 0.72 acc 0.64 0.67 0.83 macavg 0.65 0.64 0.64 0.75 0.68 0.68 0.83 0.83 0.83 Note: pre: precision; rec: recall; f1-sc: f1-score Error matrix: 1DCNN Error matrix: 1DCNNLSTM Error matrix: MDWDSAX-1DCNN-LSTM 18 Compare methods Accuracy Validate 0.64 0.68 1DCNN 1DCNN-LSTM 0.64 0.68 Loss Validate 3.3 Accuracy Validate 2.1 Loss Validate 0.83 MWD-SAX-… 0.83 0.69 Figure 4.6 Results of the error matrix and accuracy of the networks in the evaluation step Comments: The MDWD-SAX-1DCNN-LSTM model outperforms the 1DCNN and 1DCNN-LSTM models in terms of Ground truth maps and error matrix indices, including Recall, Precision, F1-score, and Macro avg Figure 4.6 represents the error matrix, where the vertical column represents the true label, and the horizontal column represents the predicted label Higher values on the main diagonal of the error matrix indicate higher accuracy as the predicted values match the true values Figure 4.6 also visually demonstrates the superiority of the MDWDSAX-1DCNN-LSTM method over the 1DCNN and 1DCNN-LSTM methods in diagnosing structural states from time-series data, with an accuracy rate of up to 83%, and a Loss Validate value