Health condition prediction method of the computer numerical control machine tool parts by ensembling digital twins and improved LSTM networks

3.1 Adaptation-based CNN-LSTM prediction model construction

This section describes the construction method of CNN-LSTM prediction model based on digital twin characteristics, which combines the advantages of CNN and LSTM network to improve the monitoring ability of CNCM health.

Utilizing data from physical models, sensor updates, and operation histories, digital twins enable the integration of interdisciplinary and multiscale feature sets through feature mapping in virtual space. The unique convolutionalization operation of CNN is to utilize the feature mapping characteristics of digital twins for feature extraction. LSTM neural network has strong memory and better effect on serialized data processing. Therefore, based on the consideration of the advantages of the two neural network models, the two models are combined to construct the CNN-LSTM model. Its structure is shown in Figure 1.

Figure 1

Structure diagram of reconstructed CNN-LSTM model.

In Figure 1, at the beginning, the convolutional layer as well as the LSTM implicit layer receives the input data for transmission to the convolutional layer. The CNN convolutional layer gets the feature result map by convolution. The resultant map is parsed through the fully connected layers (FCLs) of the Reshape function to obtain the CNN’s predicted values of part health. The LSTM implicit layer similarly gets the temporal features (TFs) of the data through functions in the network structure [16]. Then, the attention mechanism is introduced in the model. The TFs are weighted and averaged by the attention mechanism to obtain the predicted values of the LSTN. The overall network combines the advantages of two different networks through divergent branching, respectively. The input data are processed differently from both temporal and global perspectives for prediction. Finally, the two different predictions are fused. A fully connected network is used to connect the two divergent branches for the final output. The final computational result can be expressed in Eq. (1).

where h i is the output data of the implicit layer. α i is the weight value of the input data. k is the iterations. Eq. (1) illustrates the relationship between the output data and the input data of the hidden layer. It also reflects the calculation method of the hidden features in the model prediction. Furthermore, it can effectively transform the features of the input data into the prediction of the health state. Finally, it can help identify and analyze the potential factors affecting the performance of the machine tool parts. The weight values can be expressed in Eq. (2).

where soft max denotes the normalization function. s i denotes the correlation calculation result of the scoring function. Eq. (2) ensures that the output of the model is within a reasonable range, avoids the negative impact of extreme values on the prediction results, makes the model more stable and improves the accuracy of the prediction. Figure 2 depicts the CNN-LSTM model’s general design.

Figure 2

Overall architecture of CNN-LSTM model.

In the model architecture of Figure 2, the inspection data of CNC parts after preprocessing is input to construct the CNC part database. The types of data in the database include the initial input data for monitoring the deformation of CNC parts, the data for spatial feature (SF) extraction by CNN and the sequence prediction for temporal extraction by LSTM [17,18]. The optimized model also needs to be tested through the algorithmic process before the final results can be obtained. The algorithmic process starts with initialization of the population and then individual fitness is evaluated by fitness function. Then, selection and mutation are performed. If the conditions are satisfied, then output the optimal solution to obtain the weights and bias output the sequence of time prediction and the data information of the FCL. If the condition is not satisfied, then return to re-do the evaluation of fitness. Finally, output the prediction model’s results if the conditions are satisfied. The cross variance in the fitness function can be expressed as Eq. (3).

where e is the function coefficient. m and a are the individual coefficients in the population. CR′ denotes the adaptation value of the individual with the largest adaptation in the population. _FIT′ denotes the value of adaptation that is greater among the individuals that have undergone mutation. Fit a denotes the average value of the fitness of all individuals in the population. _CR′ denotes the adaptive crossover rate. Eq. (3) measures the prediction effect of the model and helps optimize the model parameters in the iterative process. The adaptive mutation rate can be expressed as Eq. (4).

Eq. (4) can enhance the adaptability of the model to different data distributions and improve its generalization ability by adjusting the variation rate. The fitness function screening process has an optimal value for the evolved data. The calculation formula can be expressed in Eq. (5).

where d ( p i , p j ) is the Euclidean distance. p i and p j denote two sample objects. n denotes the number of data. Eq. (5) helps the model to improve its sensitivity to anomalies (such as faults) during the identification of similar samples. The squared intra-cluster error can be expressed in Eq. (6).

where p denotes the sample object. c i is the cluster center of the current cluster. The main function of Eq. (6) is to optimize the output of the model and improve the identification efficiency of different categories of health states (normal and fault). The total SSE value can be expressed in Eq. (7).

where k is the clusters in the dataset. i denotes the coefficient of error value within the cluster. Eq. (7) calculates the number of clusters and the total amount of errors within clusters, which helps to design more refined anomaly detection and improve the practicability of the overall monitoring system. Figure 3 displays the prediction model’s flowchart.

Figure 3

CNN-LSTM prediction model flow chart.

In the model flowchart of Figure 3, the data are first normalized after inputting the preprocessed data of the digitized automated machine part. Then, the four-dimensional input matrix of the data is obtained through the function. Through the LSTM’s network input layer, the matrix’s data are sent to the implicit layer. They are then transferred to another level of the LSTM network output layer after the computation of the attention mechanism. After the filling of the input matrix, it is transmitted to the CNN one-dimensional convolution after which it is transmitted to the CNN network output layer after the computation of the FCL. The LSTM and CNN output layers undergo the FCL of the model for the prediction of the part data of the digitized fully automated machine tool and then the prediction modeling process is concluded.

3.2 LSTM model construction with wavelet/KF fusion

In this section, the construction scheme of the LSTM model combining the wavelet denoising algorithm and the KF will be discussed. The purpose of this combination is to enhance the performance and reduce the noise effect in the monitoring data. The result of this combination is an improvement in the prediction accuracy of the model.

LSTM model is able to learn long- and short-term dependencies and has LSTM capability. However, the LSTM model requires high sample quality. Moreover, the acquisition of time series data in range monitoring often inevitably acquires noisy monitoring information due to instruments and complex environments. The study combines the wavelet threshold denoising algorithm to design an LSTM displacement prediction model that integrates wavelet/KF. The KF is chosen as the noise reduction method in the research mainly because of its superiority and flexibility in dynamic system state estimation. The KF is a recursive estimation algorithm that can dynamically update and optimally estimate the system state in the presence of random noise and measurement errors. This feature makes the KF very suitable for processing time-varying data related to the operation of CNCM tools, which can not only effectively remove process noise, but also track the change in system state in real time. In addition, KF can synthesize past measurements by using information from previous steps to improve current state estimates, thereby increasing the stability and accuracy of predictions. Compared to other noise reduction methods, such as wavelet denoising or mean filtering, KF is superior in processing dynamic and nonstationary signals, especially in high-frequency noisy environments, by dynamically adjusting the weight of prediction and measurement values, the signal characteristics can be better preserved. The CNC monitoring data collection process is shown in Figure 4.

Figure 4

Structure diagram of data machine parts collection process.

In Figure 4, the source of data is the basic equipment, such as CNC, robot, injection molding machine, metal baler, balancing machine, and so on. The data collected from the basic equipment are transmitted to the equipment number mining and analysis system, and then the equipment template and equipment center in the system analyze the parameter information of the basic production equipment [19]. The operation center and analysis center are responsible for data integration, statistics, and classification to obtain the final data analysis results and trend direction. Part of the derived data results is transferred to the enterprise information system and cloud for storage. Another part is sent back to the production equipment level for parameter reset and equipment update. The big data analysis platform reprocesses the data and sends it to the equipment data mining and analysis system. The wavelet threshold denoising flow chart is shown in Figure 5. The change characteristics of sequence data in data processing can be expressed as Eq. (8).

where x i is the sequence value of the i th data. n is the coefficient of the data. Eq. (8) is mainly used to analyze the dynamic deformation of CNC parts in the test process, laying the foundation for subsequent trend analysis. The deviation of each measurement can be expressed as Eq. (9).

where x ' represents the variation characteristic of the serial data. The error in the measurement can be expressed as Eq. (10).

where x i denotes the coarseness of the detected values. Eqs. (9) and (10) represent the deviation and error in the measurement, quantify the reliability of the monitoring data, and help judge the health state of the machine parts. The denoising flowchart for wavelet thresholding is shown in Figure 5.

Figure 5

Denoising flow chart of wavelet threshold.

In Figure 5, the noisy data are filtered by feature extraction and then by low-pass filtering for signal reconstruction and finally the data are output after denoising. A common method in signal and image processing is wavelet threshold denoising. The fundamental principle is to divide the signal into its frequency components using the wavelet transform, and then apply the threshold to eliminate noise. Ultimately, the denoised signal is obtained by applying a wavelet inverse transform on it. When realizing wavelet threshold denoising, the signal first needs to be decomposed into different frequency components by wavelet decomposition. Then, according to the characteristics of the noise, a suitable threshold is selected for the wavelet coefficients. For wavelet coefficients larger than the threshold, their true values are retained. For wavelet coefficients smaller than the threshold are set to zero. To produce the denoised signal, the processed wavelet coefficients are next subjected to wavelet inversion. Figure 6 depicts the KF-LSTM model’s denoising procedure.

Figure 6

Denoising flow chart of KF-LSTM model.

In the flowchart of the modeling algorithm in Figure 6, the data input are first subjected to wavelet decomposition to determine the number of layered layers. Thresholding is performed after selecting a suitable wavelet to decompose the preprocessed data. The appropriate thresholding principle is selected to threshold the high-frequency part obtained from the decomposition to obtain the useful signal [20]. Then, the threshold data are subjected to wavelet reconstruction to obtain the de-noised displacement trend term. Finally, the LSTM prediction model of the displacement trend term is established. The LSTM network structure, the number of iterations, and the appropriate optimization algorithm as well as the learning tuning strategy are determined. The displacement of the observation is calculated, and the displacement increment is calculated by substituting the observation as shown in Eq. (11).

where t denotes the detection period. n denotes the size of the sample training data. i denotes the dataset. The covariance of the prediction results can be expressed as Eq. (12).

where u denotes the residual term. The observation noise covariance can be expressed as Eq. (13).

where u ′ denotes the predicted residual variance, as expressed in Eq. (14).

where f ( Δ Z t − 1 ′ ) denotes the forecast result. m denotes the number of forecast days. Among them, Δ Z t + m ′ can be shown in Eq. (15).

The linear functional relationship of the fusion function can be expressed as Eq. (16).

where F Linear denotes the linear regression function and a denotes the correlation coefficient. Eqs. (11)–(16) above involve the displacement prediction, residual covariance, observed noise covariance, and calculation of linear regression relations of the LSTM model. These formulas enable accurate analysis of the monitoring data, enhance the model’s ability to predict the health of the machine parts, and help reduce the impact of noise on the results.

4.1 Performance effects of the model

This section evaluates the performance of different models in CNC part health monitoring, focusing on the comparison between the CNN-LSTM model and the traditional LSTM model.

In the research, the steps of data preprocessing are very important, including data cleaning, feature engineering, and normalization. Initially, data cleaning is employed to eliminate noise and outliers that may be generated during the detection process. This process is integral for ensuring the accuracy and validity of the data utilized. In the subsequent feature engineering stage, the features directly related to the health state of CNCM tools are selected, including vibration, temperature, load, and other monitoring indicators. The dimensions of the dataset are enriched by extracting features in the time domain and the frequency domain. In addition, to make the input data comparable at different scales, the study normalized the features and adopted the z-score standardization method, so that the mean value of each feature is 0 and the standard deviation is 1. These preprocessing steps lay the foundation for the subsequent KF and LSTM network input, enhance the model’s adaptability to the data, and thus improve the prediction accuracy and stability. By elucidating these steps, it is possible to ensure the transparency and repeatability of research methods, thereby providing substantial support for subsequent research.

The combined CNN-LSTM model has the advantages of both CNN networks being able to identify the SFs of the data in depth and LSTM networks being able to analyze the TFs of the data and having long-term memory. The CNN-LSTM model is used to analyze the performance of CNC part data processing. Table 1 displays the experimental software configuration.

In the software configuration given in Table 1, the version requirement bit for the symbolic number system is version 2.4.0, and the version requirement for the array object-based computational library is version 1.23.6. The required version for advanced neural networks is version 2.7.0, and the standard data provision tool in the computational library requires version 1.3.6. The required version of the software ML library is version 0.26.1, and the required version of the library for generating publication-quality graphs is version 3.4.3. The experiments are performed in a computer with system Windows section 1,164b. The datasets used in the study are derived from real-time monitoring systems for multiple CNCM tools, specifically designed to assess the health of machine parts. The dataset contains more than 10,000 data records covering a variety of monitoring indicators under different operating conditions, including key parameters such as vibration, temperature, pressure, and load. These machines include many types of CNC equipment such as milling machines, lathes, and EDM machines, ensuring a diverse and representative dataset. At the same time, the monitoring records in the dataset are divided into normal operating state and fault state for fault detection and prediction. Each record contains a time stamp, sensor measurements, and a corresponding health state label, which allow the study to analyze differences in machine performance under different operating conditions, thereby improving the accuracy and robustness of the health monitoring model. Figure 7 compares the error between the CNN-LSTM model’s actual and predicted values with those of other data detection procedures in the CNC parts inspection dataset.

Figure 7

The error comparison diagram of the true value and the predicted value in the testing process of CNN-LSTM model part data. (a) LSTM network model predicted and true error values. (b) CNN network model predicted and true error values. (c) M-LSTM network model predicted and true error values. (d) CNN-LSTM network model predicted and true error values.

In Figure 7(a), the LSTM network models have error values less than 0.3 during the first 10 days of part monitoring. During the period of 10–40 days, the error values are mostly concentrated above 0.2, with a difference of 0.7 between the maximum and the minimum. In Figure 7(b), the maximum error is at 0.25 and the minimum is at 0 during the 40 days of performing the fault diagnosis, which is a very obvious difference. In Figure 7(c), the single-feature LSTM network models have errors above 0.025 during the part failure monitoring. The CNN-LSTM network model and the LSTM model for machine tool part health monitoring data have a coarse difference, and the distribution of the anomalies is expressed in terms of displacements. A comparison of the two models is shown in Figure 8.

Figure 8

Abnormal point distribution of NN-LSTM network model and LSTM model in machine tool parts health monitoring data. (a) Monitoring displacement of LSTM model over time. (b) Monitoring displacement of CNN-LSTM model over time.

In Figure 8(a), when the LSTM model monitors the health status of the parts in the first week, the positive and negative displacements of the abnormal point distributions of the parts are almost always more than 5. The maximum displacement even reaches 10. In the second week, the positive and negative displacements of the abnormal point distributions are more than 5, and the number of points close to 10 becomes more. The situation in the third week is similar to that in the second week, and the distribution does not get better. In the fourth week, there are a small number of points where the displacement decreases, but most of the points are closer to 10. In Figure 8(b), the displacement of the distribution of part anomalies in the first week of part health monitoring by CNN-LSTM reaches up to 5. In the second week, the displacement of anomalies is almost less than 5, and there exists only 1 day with a displacement greater than 7. The displacement in the third week is similar to that in the first 2 weeks, and there is no large fluctuation. In the fourth week, there is a little fluctuation in the displacement, with a few days with anomalies of 5 or more. However, the fluctuation has little effect on the monitoring situation, and the overall stability of the model is good.

4.2 Application analysis of the simulation effect of the model

This section will discuss the simulation effect of the KF-LSTM model when processing actual CNC part monitoring data, and analyze its performance and accuracy in different monitoring time periods.

By choosing the wavelet basis function, the original signal is transformed from the time domain to the wavelet domain in the wavelet filtering principle. The wavelet coefficients are processed and then the processed wavelet coefficients are converted from the wavelet domain back to the time domain to get the denoised signal. Thus, KF-LSTM is able to process the noise values of the monitoring data in a better way. Table 2 displays the KF-LSTM model’s primary parameter settings.

The parameter value for the number of layers in the KF and CNN is ideally set to 1 in KF-LSTM model’s parameter settings listed in Table 2. The best optimization algorithm is the Adam algorithm and the activation function is the ReLU function. It is necessary for each layer of the LST to have 32 neurons, and the batch size parameter value must be 8. The parameter value of the number of training rounds is 200 and the byte size is 8. The function performs continuous scaling and translation-based wavelet transforms in such a setup, and the signals are computed as an inner product with the wavelet function in the non-stop transforms to obtain a series of wavelet coefficients on successive scales and translational positions. The continuous wavelet transform can provide richer time-frequency information. Figure 9 illustrates the accuracy of several detection methods in determining the condition of machine tool parts.

Figure 9

The accuracy of different detection models in detecting the health state of machine parts. (a) Monitor the change in accuracy during the first month. (b) Monitor the changes in accuracy in the second month.

Figure 9 shows the monitoring accuracy of the model for the health status of the parts. At the fifth day of monitoring, the traditional LSTM model has the lowest monitoring accuracy of 50.3%. Neither of the two improved models of LSTM had a better monitoring accuracy than the KF-LSTM model. The KF-LSTM model has the highest accuracy of 90.5%. On day 10 of monitoring, the KF-LSTM model has the highest accuracy of 92.5%. On the 20th day of monitoring, the accuracy of monitoring is 56.5% for the traditional LSTM model and 93.9% for the KF-LSTM model. During the later month, the accuracy of the models does not change particularly significantly, based on maintaining a high accuracy rate. As the monitoring time increased, the monitoring accuracy does not change, the fusion model accuracy remained at the highest level. The fit of each model to the original values (OVs) for different periods of time while monitoring the parts is shown in Figure 10.

Figure 10

The fitting of each model to the OV in different periods of part monitoring. (a) Displacement during deformation acceleration. (b) Displacement in gradient phase. (c) The displacement of each model in the convergence period.

Figure 10 shows the fitting of each model to the OV in different monitoring cycles, reflecting its error distribution in the prediction process. While the KF-LSTM model demonstrates superior performance in terms of displacement at most time nodes, with a maximum difference of −0.2, indicating a high degree of fit, the model’s prediction accuracy can be compromised under certain conditions, such as when the machine operates under high loads or in extreme environmental conditions. This phenomenon can be attributed to abnormal fluctuations in the data or dynamic changes in the characteristics, leading to increased bias in the results. In addition, the single feature model shows a large error in the monitoring process, especially in the deformation acceleration period, the maximum deviation reaches −10, indicating that the model is not sensitive enough to deal with variable working conditions. Therefore, the comprehensive error analysis not only reveals the limitations of the model under certain conditions but also provides an important improvement direction for improving the applicability and stability of the model in the future. To further verify the advanced nature of the proposed method, more real-world datasets are used for comparative analysis of the model, including Case Western Reserve bearing dataset, self-collected bearing dataset, and IMS bearing dataset, and are denoted as A, B, and C, respectively. In the research, several domain adaptive methods and several machine learning methods are selected for comparison with the proposed methods. These include the domain discriminative component (DCC), domain-adversarial neural network (DANN), and the deep convolutional transformation learning network (DCTLN). DCC is to find the feature transformation that can maximize the difference between two different domains, so that the transformed features are more discriminative, thus improving the accuracy of cross-domain classification. DANN reduces the difference between the source and target domains by introducing a domain classifier. DCTLN maps the source and target domain data by designing a transformation layer within the network, so that the model can extract a more general feature representation and perform effective transfer learning based on it. The model comparison results are shown in Table 3.

In Table 3, A → B indicates that training is conducted by combining labeled data from dataset A with unlabeled data from dataset B, and testing is performed on dataset B. The results show that the proposed method performs particularly well in the A → C scenario, achieving a prediction accuracy of 98.18%. It indicates that the algorithm demonstrates excellent performance when migrating from dataset A to dataset C. The performance of migrating from the same source dataset to different target datasets reflects the ability of each algorithm to adapt to changing environments. The average across all test scenarios reflects the overall performance of each algorithm. According to Table 3, the proposed method ranks first in terms of average accuracy, reaching 93.94%, demonstrating significant stability and efficiency in the cross-dataset migration process.