1.1. Vibration Signal Analysis and its importance in Monitoring MachinesHealth

Vibration signals are important for machine diagnosis, which helps to identify the faults during machine performance. These signals can be separated and transformed into different domains, such as Fourier transform and wavelet transform for deep analysis using a variety of signal processing techniques ^[1,2]. These changes make it possible to extract statistical features and properties related with physical existences, which are important for diagnostic applications ^[3-5]. Through the analysis of these data, machine learning techniques are able to model the connections between the physical events that support the extracted information and provide the knowledge about functions and health of the machine. The features are commonly obtained through statistical analysis conducted in both frequency and time domains, which helps to understand about the vibration signals. Predictive maintenance, effective problem identification, and general process improvement in machines are made possible by the combination of machine learning and signal processing. By combining these methods, it is easier to create reliable diagnostic models that can identify possible problems and improve maintenance plans also improves the dependability and effectiveness of mechanical systems.

1.2. Recent Machine Learning models and its Development under Mechanical System Diagnosis

Rolling element bearings (REB) are the important parts of mechanical systems, and the failures of this can lead to serious safety risks. Some of the existing studies which focus on these same problems by using of machine learning models, such as support vector machines (SVMs) and neural networks (NNs), to construct monitoring systems ^[6-8]. To automatically extract features from vibration signals for more efficient signal processing, deep learning techniques have recently an effective one. Frequency spectrum methods are also used in diagnosis and identification of faults, which acts as another type of investigation. Statistical features generated from these signals are used as inputs to machine learning algorithms that are designed to diagnose bearing defects ^[9,10]. Convolutional neural networks (CNN), a widely used diagnosis technique, are the main source of this research. CNN have the ability to handle the raw data extracted from the vibration signals of the machines. Vibration signals contain difficult patterns and properties that can be efficiently recorded and used to construct reliable diagnostic models by using CNN ^[11-13]. These models increase the security of mechanical systems and allow preventative care by identifying possible failures. Now a days the use of CNN is notably increased in the field of condition monitoring. Additionally, CNN provides a promising solution for real time monitoring and fault diagnosis in mechanical systems and also make sure about the performance improvement and reduce the risk of unexpectable failures ^[14,15].

1.3. Integrated Monitoring and Predictive Maintenance for Machine Tool Quality and Productivity

The impacts of machine tools caused direct impact on both quality and production. Because a damaged tool causes more vibration when it is being processed, its quality become considerably reduced. Excessive tool wear results in tool breakages. It is possible to diagnosis the condition of tools using both offline and online monitoring techniques. Machine activities must be stopped to disconnect tools for offline monitoring, which helps to measures the damaged area ^[16,17]. On the other hand, online monitoring identifies the condition of the tools using force signals, vibration and noise produced from machine tools. Recent developments in photography lead to the use of high-speed cameras for online monitoring in some devices ^[18]. Based on the condition of the tools and machinery, industries depend on product quality prediction because it gives them more control over the manufacturing process. Various researches are conducted regarding, machine features which is used to measure a quality, modeling the relationship between these factors and quality using machine learning techniques like fuzzy logic and response surface methods are clearly discussed ^[19,20]. However, the lack of tool and machine statuses is an important problem in these studies. Vibrations have an impact on quality, therefore studying vibration signals can give important information on assessing quality. Additionally, the combination of vibration with auditory signals, load cell data and several vibration sensors has been proposed as sensor fusion. These sensors act as a unique tool for fault detection. Researches have introduced fusion in both feature and frequency domains to improve the accuracy of fault detection.

1.4. Proposed HDCNN and Its Effectiveness

In this study HDCNN based vibration signal analysis is discussed. HDCNN is a unique combination, which combines 1DCNN, 2DCNN and DNN for complete vibration signal analysis and fault detection in mechanical systems ^[21,22]. By combining these effective techniques, the study aims to improve accuracy of diagnosing faults in machine tools like REB. Here the 1DCNN is used for analysing regression tasks. At the same time, 2DCNN is used to analyse classification tasks. The DNN is used to combine feature extracted from both 1DCNN and 2DCNN. This proposed HDDCNN architecture combines multiple advantages, initially it combines the strength of different neural networks and allow the model to handle various data types and identify difficult scenarios more effectively. Next by using the deep learning techniques to allow automatic feature extraction, also reducing the manual engineering. And finally, the integration of vibration signal with machine learning provides a complete solution for real time fault detection and predictive maintenance and ensuring safe surrounding under mechanical system domains. The structure of the article is a combination of two current research methodologies ^[21,22], the results of this studies show a considerable improvement in vibration analysis for fault diagnosis using machine learning techniques. This study is combination of this two, by combining these approaches the results show expectable improvement in diagnosis applications. The simulation of this study proved its efficacy by proper experiments.

3.1. Proposed HDCNN Workflow

3.1.4 Integration and training using DNN

In this section, the DNN is used to combine both the features extracted form 1DCNN and 2DCNN. By combining supervised and unsupervised learning techniques, the DNN is trained to reduce manual feature selection and improve overall mechanical fault diagnosis performance.

The DNN done unsupervised pre-training by using a collection of DAE. The input data is first encoded into a lower-dimensional space by each DAE layer, after that it get reconstruct. The encoding function transforms the input data into encoded vector. The encoding function is expressed as

(7)

$ {eh}_m=f_o\left({rx}_m\right)={as}_f(w_{{rx}_m}+b) . $

Here ${as}_f$ is the activation function, $w\ and\ b$ are the parameters of the encoding network and ${eh}_m$ is the encoded vector. Where the encoding and parameters and activation function are considered as important.

Similarly, the decoding function reconstructs the input data from the encoded vector by using the activation function and parameters of the decoding network. This can be expressed as

(8)

$ {\widehat{rx}}_m=g_{{\theta }^{'}}\left({eh}_m\right)={as}_g(w^{'}{eh}_m+d_c) . $

In Eq. (8), ${as}_g$ is the activation function of the decoding network, $w$ and $d_c$ are the parameters of the decoding network and ${\widehat{rx}}_m$ is constructed input. The goal of this process is to reduce the reconstructed error between the original input and the reconstructed output, and make sure abut the encoder vector maintains the same information of the input data. The reconstruction error of the process is defined as

(9)

$ l\left({rx}_m,{\widehat{rx}}_m\right)=\frac{1}{2M}\sum^M_{m=1}{{\left\|{rx}_m-{\widehat{rx}}_m\right\|}^2}. $

To improve the performance of feature extraction, DAE is used to introduce noise to the input samples. This can be expressed as

(10)

$ {rx}^0_m=q_d({rx}_m|{rx}^0_m). $

By using this method, the autoencoder is able to extract noise-resistant features, which improves the model's ability to deal with data changes.

Reducing the reconstruction error between the noisy input and the initial clean input is the DAE's training goal. The training objective of the DAE is defined as

(11)

$ {\mathrm{arg} min\ l({rx}_m,g_{\theta '}(f_0(\ }{rx}^0_m))) . $

A group of DAE is used in a layer-by-layer pre-training method to train the DNN. The input layer of the DNN is trained first, followed by the deeper layers in a sequential manner. The input data is encoded into a lower-dimensional representation at each layer.

(12)

$ {eh}^l_m=f^l_{\theta }(e^{\left(l-1\right)}_m) . $

The DNN is able to identify difficult patterns and features in the data because of its effective approach. After trained all layers, the final encoded representation serves as the model's input for the further stage. The final encoding is denoted as

(13)

$ {eh}^N_m=f^N_{\theta }({eh}^{\left(N-1\right)}_m) . $

The DNN goes through a small supervised learning adjustment after the completion of unsupervised pre-training. This stage involves fine-tuning the DNN parameters to increase the model's performance for particular tasks. Based on the encoded representations from the earlier layers, the DNN generates its output. This expressed as

(14)

$ ry_m=f^{(N+1)}_{\theta }({eh}^{(N)}_m . $

The optimization objective of this stage is to reduce the loss between the predicted output and true target values for improving the model's accuracy fault diagnosis.

(15)

$ {\emptyset }_{dnn}\left(\mathrm{\Theta }\right)=\frac{1}{M}\sum^M_{m=1}{l({ry}_m,t_m)} . $

Overall, the proposed HDCNN combines 1DCNN and 2DCNN features by using trained DNN, For regression tasks, 1DCNN processes raw vibration data which is performed using convolutional operations to extract relevant features. Similarly for classification tasks 2DCNN handles time frequency images obtained through STFT. The features of both 1D and 2D are combined and transform to the DNN for final classification and regression tasks, the process of feature integration and training using DNN is expressed as

(16)

$ {eh}^N_m=f^N_{\theta }({eh}^{\left(N-1\right)}_m) , $

(17)

$ ry_m=f^{\left(N+1\right)}_{\theta }({eh}^{\left(N\right)}_m) . $

Finally, the integration of 1DCNN and 2DCNN features are combined using Eqs. (16) and (17) by using trained DNN, this denotes the final output of the DNN for fault diagnosis which can be expressed as

(18)

$ ry_m=f^{\left(N+1\right)}_{\theta }(f^N_{\theta }\left({eh}^{\left(N-1\right)}_m\right)). $

In Eq. (18), ${eh}^{\left(N-1\right)}_m$ is the input of the $N-th$ layer, ${eh}^N_m$ is the output of the N$-th$ layer and $ry_m$ is the final result after applying the output layer transformation. Fig. 2 presents the whole process structure of HDCNN.

Fig. 2. Proposed HCNN combined architecture.

4.1. Simulation Setup

The proposed HDCNN is evaluated using the dataset which is inspired from ^[22]. Based on the simulation proceedings, Table 2 present the clear illustration of dataset features.

Initially, we proceed to extract features from both time domain and frequency domain signals. Based on the states of rolling bearing in both time and frequency domain signals we proceed the valuation.

Fig. 3. Time domain signals of rolling bearing status.

Fig. 3 presents the time domain signals of a rolling bearing under various faults, which includes normal state, inner ring fault, outer ring fault and rolling element fault. Fig. exactly displays that the time domain signals of the rolling bearing is not have a stable signal. So, the frequency domain signals are not obtained through FFT because FFT focused on stable signals.

Fig. 4. Frequency domain signals of rolling bearing.

Fig. 4 presents the Frequency domain signals of rolling bearing for 4 states. By comparing the figure of 3 b and 4 b of time and frequency domain figures of inner ring fault. It was not possible to extract fault feature information from the inner ring initial fault waveform. The inner ring fault spectrogram showed certain side frequencies, but the fault's features were not visible, making it difficult to identify the feature frequency that corresponded to the rolling bearing.

Fig. 5. Diagnosis Result Comparison with existing techniques.

Fig. 5 shows the efficacy of proposed HDCNN by compared with the other existing techniques in fault diagnosis. When compared the proposed HDCNN to other methods like DNN, FANN, PSONN, and GANN, it shows a considerable improvement in fault identification of mechanical systems. The HDCNN outperforms the FANN at 0.947, PSONN at 0.914, and GANN at 0.894 and reaches a maximum accuracy of 0.997, also break the DNN maximum accuracy of 0.990. This high maximum accuracy highlights that the proposed HDCNN is highly effective in diagnosing the fault in rolling bearing. Furthermore, the HDCNN minimum accuracy of 0.990 is noticeably greater than FANN 0.873, PSONN 0.809 and GANN 0.693 and higher than that of the DNN 0.976. This shows that the HDCNN maintains a high degree of accuracy even in its least effective settings. With an average accuracy rate of 0.994, the HDCNN performs well in experimental scenarios. This average accuracy is greater than the average accuracy of FANN 0.926, PSONN 0.879 and GANN 0.847, and it is superior to the DNN 0.985. Furthermore, the HDCNN shows a standard deviation of 0.50, which is significantly lower than SD of FANN 4.42, PSONN 6.96 and GANN 12.36 and lower than the DNN 0.69.

Fig. 6. (a) Final training error obtained by all the models. (b) Training error obtained over iterations.

Fig. 6 a and b presents the efficacy of proposed HDCNN in reducing training error when compared with other models like DNN, FANN, PSONN and GANN. Fig. 6a show the training error obtained by all the models which remains the same. Fig. 6b shows the efficacy regarding iterations. In final training error noticeably, all model achieves the same training error rate of 0.001. But considering iterations the proposed HDCNN achieves this efficacy in minimum number of iterations. For example, FANN obtain this error rate of 0.001 in 100 iterations, therefore PSONN in 143 iterations, GANN in 220 iterations and the exiting effective model of DNN achieves the efficacy in 48 iterations. But notably the proposed HDCNN achieved the expected efficacy of training error in 45 iteration which highlights the immediate processing ability of HDCNN.

Figs. 7-10 display the efficacy of proposed HDCNN in fault diagnosis of all four states. When compared the efficacy of proposed with other existing models it achieves the notable scores, for example, it achieves the expected score of 98.72, for normal, 98.87 for inner ring fault, 98.88 for outer ring fault and rolling element with 99.04. By analyse this scores it highlights that the proposed HDCNN achieves all most good results possible by its fusion techniques of 1DCNN, 2DCNN with DNN. This overall score highlights the HDCNN is an effective tool in analysing the vibration signals to detect the faults effectively.

Fig. 7. Overall accuracy in all states.

Fig. 8. Precision scores achieved in all states.

Fig. 9. Recall scores achieved in all states.

Fig. 10. F1-Scores achieved in all states.