A limited material-based neural network model dataset augmentation method and system
By simulating cable faults on limited materials and generating data that conforms to the laws of electromagnetic wave propagation, the problem of insufficient training data for neural network models is solved, thereby improving the accuracy and efficiency of cable fault identification.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- EAST CHINA POWER TRANSMISSION & TRANSFORMATION ENG
- Filing Date
- 2025-08-07
- Publication Date
- 2026-07-24
AI Technical Summary
In existing technologies, neural network models lack sufficient training datasets for cable fault identification, resulting in poor model training performance and an inability to effectively identify complex cable faults.
By simulating cable faults with limited materials, adding noise disturbances and waveform transformations, simulation data of various fault scenarios are generated. Then, by simulating the physical parameters of the cable through a digital twin model, data that does not conform to the laws of electromagnetic wave propagation is eliminated, and a training dataset is constructed.
It significantly improved the amount and quality of training data for neural network models, enhanced the models' anti-interference capabilities and fault identification accuracy, and reduced cable maintenance and repair time and costs.
Smart Images
Figure CN121009368B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of dataset augmentation technology, and in particular to a method for augmenting neural network model datasets based on finite materials. Background Technology
[0002] With the acceleration of urbanization and the continuous advancement of infrastructure construction, the laying of underground cables is becoming increasingly widespread. However, due to the special nature of their installation locations and methods, daily maintenance and repair are quite challenging. Locating the cable and its defects are two major problems in these processes. For cable location, there are methods such as dual-power comparison, electromagnetic radiation, infrared scanning, and high-voltage harmonic methods. Among these, the non-contact cable location method based on the principle of electromagnetic radiation has been achieved and has yielded good results. Domestic companies such as Jingmingshu and Fuyi have also developed corresponding cable locators. However, simply being able to locate the target cable is insufficient to complete the maintenance task. To solve the problem of cable fault location, some researchers have proposed a single-end detection method, which involves applying a signal to one end of the cable and using the returned signal to determine the type and location of the cable defect. In existing technologies, Jia Shih-hao, in his "Research on Fault Location and Diagnosis Methods for Power Cables [D]", Liaoning University of Engineering and Technology, 2023, proposed using a single-ended time-domain reflectometer to calculate the cable terminal distance and simple fault types (open circuit, short circuit) based on the different reflection waveforms under different cable conditions and the propagation speed and reflection time of the electrical signal in the cable. However, in actual use, there are various cable models, and the cable fault location is often somewhere between the beginning and end of the cable. Furthermore, the types of cable faults are very complex, especially incomplete core breakage and core compression deformation. Solving these problems would greatly reduce the time and cost of cable maintenance and repair.
[0003] In recent years, artificial intelligence has developed rapidly, with various improved machine learning and deep learning algorithms emerging one after another. Convolutional neural networks (CNNs), as one of the most representative models in the field of deep learning, offer a new technical path for solving complex cable fault detection problems due to their powerful feature extraction capabilities and spatial modeling advantages. Unlike traditional threshold criterion methods that rely on human experience, CNNs, through an end-to-end training mechanism, can automatically extract deep spatiotemporal correlation features from raw reflection waveforms. However, neural network models require a large amount of data for learning and training. For cable fault identification, due to limitations such as cable type and fault type, there are no readily available datasets for model training. Therefore, it is necessary to conduct as many simulation experiments as possible based on limited experimental materials to increase the quantity and type of datasets, thereby improving the training effect and robustness of the final model.
[0004] Therefore, how to expand the required training dataset using limited experimental materials has become an urgent technical problem to be solved. Summary of the Invention
[0005] The purpose of this invention is to address the problems existing in the background technology by proposing a method for expanding the dataset of a neural network model based on finite materials.
[0006] The technical solution of the present invention, in its first aspect, provides a method for augmenting a neural network model dataset based on finite materials, comprising the following specific steps: S1. Set up the experimental platform to collect data: Simulate a fault point near the end of the cable under test; capture waveform data using an oscilloscope and save the raw data to a USB flash drive; S2. Add noise disturbance to the raw waveform acquired each time in real time; S3. Perform waveform transformation based on the current cable data to obtain simulated waveform data at different fault locations; S4. Completely cut off the cable containing the faulty section to obtain a new length of cable test material without intermediate faults; S5. Generate simulation data by preserving the physical parameters of the resected segment; S6. Repeat steps S1-S5 to collect sufficient real test data until the cable length does not meet the test requirements. S7. Verify the physical consistency of all generated data and discard simulated waveform data that do not meet the constraints; S8. Mix the generated simulated waveform data with the original waveform data according to the preset ratio to construct a test dataset.
[0007] Preferably, the experimental platform built in step S1 includes: an oscilloscope, a transmitter, and a cable under test; The transmitter is used to transmit pulse signals, and the reflected waves are captured and recorded by an oscilloscope; The positive terminals of the transmitter and the oscilloscope are connected to the core of the cable under test; the negative terminals of the transmitter and the oscilloscope are connected to the shielding layer of the cable under test; the terminal of the cable under test is left floating.
[0008] Preferably, the cable type in step S1 includes 500 meters each of RVV2, BVV4 and BV6 type cables; The cables used are all multi-core wires, including three-color main core wires and their respective branch core wires.
[0009] Preferably, in step S1, the cable of different models is simulated in the actual scenario of incomplete breakage, complete breakage or short circuit. In this case, the incomplete breakage was simulated by cutting each colored core wire in half. Simulate a complete break by completely severing the entire cable; A short circuit is simulated by shorting the cable core and the shielding layer.
[0010] Preferably, in step S2, adding noise perturbation further includes the following steps: S21, Parameter perturbation: Amplitude scaling:
[0011] In the above formula, The scaling factor is for uniform distribution. The original waveform. The waveform is after amplitude scaling; Latency jitter:
[0012] In the above formula, This refers to the time delay jitter. The original waveform. The waveform after time delay jitter; Impedance mismatch simulation:
[0013] in, The waveform after impedance mismatch simulation. This is the impedance mismatch impact response function;
[0014] In the above formula, It is the attenuation constant; The resonant frequency; S22, Noise Injection: Recording background electromagnetic noise when no signal is being transmitted. ; For the original signal Add composite noise:
[0015] In the above formula The original reflected wave signal, It is a composite noise reflected wave signal. To measure the background noise, It is Gaussian white noise. The noise after the disturbance This is the background noise intensity coefficient. The Gaussian noise intensity coefficient; The noise intensity coefficient after disturbance; Adjust according to the signal-to-noise ratio (SNR), typically between 0.01 and 0.05.
[0016] Preferably, the waveform transformation in step S3 further includes the following steps: S31, Fault location interpolation:
[0017] In the above formula The waveform of the fault location after interpolation. These are the weighting coefficients. The position interpolation ratio, The waveforms represent two known fault locations; S32. Cable length transformation: Calculate the length scaling factor:
[0018] Time domain scaling:
[0019] Frequency domain compensation (preserving energy conservation):
[0020] In the above formula, This is the length scaling factor. These are the target cable length and the original cable length, respectively. The data is scaled in the time domain; F is the Fourier transform operator. It is the frequency domain energy compensation factor. This is the final output signal.
[0021] Preferably, step 5 involves generating simulation data by preserving the physical parameters of the resected segment, and establishing the physical parameter data of the resected segment based on the digital twin model to simulate concurrent failures at multiple points.
[0022] Preferably, in step S7, the physical consistency of all generated data is verified, specifically including wave velocity verification, energy conservation verification, and similarity verification. For wave velocity verification, the peak time of the reflected pulse is identified from the generated waveform, and the peak time of the reflected pulse is extracted from the original waveform and compared. Those with a deviation value greater than 2% are discarded. The energy conservation principle is verified using the following formula:
[0023] In the above formula, To generate waveforms, The original waveform is used as the basis for calculation. The total energy of the generated waveform and the original waveform is calculated and verified. Data with a deviation value greater than 5% is discarded. The similarity verification is performed using the following formula:
[0024] In the above formula, These are the mean values of the waveforms; These are the standard deviations of the waveforms; Let c be the covariance; c1 and c2 are calculation constants, where c1 is 0.01 and c2 is 0.03. Set SSIM>0.85 as a constraint condition, and discard waveform data that do not meet the condition.
[0025] Preferably, in step S8, a test dataset is constructed by mixing simulated waveform data and original waveform data in a 2:8 ratio.
[0026] A second aspect of the present invention is a neural network model dataset augmentation system based on finite materials, which uses the above-described method to augment the dataset, including a data input module, a data processing module, a verification and comparison module, and a dataset construction module; The data input module is used to input measured waveform data according to the actual experiment. The data processing module is used to process the input measured waveform data by noise disturbance and waveform transformation. The verification and comparison module is used to filter the simulated waveform data according to preset constraints and remove simulated waveform data that do not meet the constraints. The dataset construction module mixes simulated waveform data with measured waveform data according to a preset ratio to generate a dataset for training neural network models.
[0027] Compared with the prior art, the present invention has the following beneficial technical effects: 1. This invention achieves multi-length level reuse of a single cable by segmenting and cutting the faulty cable, which significantly increases the sample size; 2. This invention simulates actual environmental variations by perturbing three parameters: amplitude scaling, time delay jitter, and impedance mismatch. It enhances the model's anti-interference capability by injecting composite noise: fusing measured background electromagnetic noise with Gaussian white noise. Furthermore, it extends the model through mathematical transformations: using fault location interpolation and cable length transformations, it generates simulated waveforms at arbitrary locations and lengths.
[0028] 3. This invention establishes a triple verification system based on wave velocity deviation, energy conservation, and structural similarity (SSIM), eliminating simulated data that does not conform to the laws of electromagnetic wave propagation to ensure the physical rationality of the augmented data. Finally, a test set is constructed by proportionally mixing simulated and real data, providing a training foundation for neural network models that combines scalability and reliability. Attached Figure Description
[0029] Figure 1 This is a schematic diagram of the experimental platform in an embodiment of the present invention; Figure 2 This is a flowchart illustrating the dataset augmentation method in an embodiment of the present invention; Figure 3 This is a schematic diagram of the data set augmentation system in an embodiment of the present invention; Figure 4 This is a graph showing the experimental results of training a neural network model using the amplified dataset in an embodiment of the present invention. Detailed Implementation
[0030] Hereinafter, exemplary embodiments according to this application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this application, and not all embodiments of this application. It should be understood that this application is not limited to the exemplary embodiments described herein. Example 1
[0031] like Figure 2 As shown, the present invention proposes a method for augmenting a neural network model dataset based on finite materials, which includes the following specific steps: S1. Set up the experimental platform to collect data: Simulate a fault point near the end of the cable under test; capture waveform data using an oscilloscope and save the raw data to a USB flash drive; the experimental platform built in step S1 includes: an oscilloscope, a transmitter, and the cable under test; the experimental platform is as follows: Figure 1 The connections are as shown. Specifically, the transmitter is used to transmit pulse signals, and the oscilloscope captures the reflected waves and records the waveform data. The positive terminal of the transmitter and the positive probe of the oscilloscope are connected to the core of the cable under test. The negative terminal of the transmitter and the negative probe of the oscilloscope are connected to the shielding layer of the cable under test. The terminal of the cable under test is left floating.
[0032] A narrow pulse signal of approximately 90V with a rise time of about 350ps is sent to the core of the cable under test via a transmitter. The reflected wave is then captured by an oscilloscope and the data is stored on a USB flash drive.
[0033] In step S1, the cable types include 500 meters each of RVV2, BVV4, and BV6 cables; all cables used are multi-core cables, including three-color main cores and their respective branch cores. Step S1 simulates incomplete breakage, complete breakage, or short circuit scenarios for different cable types in a real-world context; incomplete breakage is simulated by cutting half of each color branch core; complete breakage is simulated by cutting the entire cable; and short circuit is simulated by short-circuiting the cable cores to the shielding layer.
[0034] S2. Add noise disturbance to the raw waveform acquired each time in real time; Step S2, adding noise perturbation also includes the following steps: S21, Parameter perturbation: Amplitude scaling:
[0035] In the above formula, The scaling factor is for uniform distribution. The original waveform. The waveform is after amplitude scaling; Latency jitter:
[0036] In the above formula, This refers to the time delay jitter. The original waveform. The waveform after time delay jitter; Impedance mismatch simulation:
[0037] in, The waveform after impedance mismatch simulation. This is the impedance mismatch impact response function;
[0038] In the above formula, It is the attenuation constant; The resonant frequency; S22, Noise Injection: Recording background electromagnetic noise when no signal is being transmitted. ; For the original signal Add composite noise:
[0039] In the above formula The original reflected wave signal, It is a composite noise reflected wave signal. To measure the background noise, It is Gaussian white noise. The noise after the disturbance This is the background noise intensity coefficient. The Gaussian noise intensity coefficient; The noise intensity coefficient after disturbance; Adjust according to the signal-to-noise ratio (SNR), typically set to 0.01-0.05; in this step, you can use only one of amplitude scaling, time delay jitter, and impedance mismatch simulation to process the original signal, or you can choose any two or three methods to process the original signal; then add composite noise to the processed signal; for example, when processing the original waveform... After scaling the amplitude, we get can The delay jitter is calculated using the input, that is... Enter to In the middle, the calculated
[0040] S3. Perform waveform transformation based on the current cable data to obtain simulated waveform data at different fault locations; The waveform transformation in step S3 also includes the following steps: S31, Fault location interpolation:
[0041] In the above formula The waveform of the fault location after interpolation. These are the weighting coefficients. The position interpolation ratio, The waveforms represent two known fault locations; S32. Cable length transformation: Calculate the length scaling factor:
[0042] Time domain scaling:
[0043] Frequency domain compensation (preserving energy conservation):
[0044] In the above formula, This is the length scaling factor. These are the target cable length and the original cable length, respectively. The data is scaled in the time domain; F is the Fourier transform operator. It is the frequency domain energy compensation factor. This is the final output signal.
[0045] S4. Completely cut off the cable containing the faulty section to obtain a new length of cable test material without intermediate faults; Taking the 500-meter cable used in this embodiment as an example, open circuit and short circuit faults are created at different locations of the three-color wire cores to improve material utilization. Including the case of terminal open circuit, there are four types of fault locations for each cable length. These are selected near the cable terminal. This way, when a certain length of cable is tested, the faulty section can be cut off to obtain a new length of cable test material without intermediate faults (e.g., open circuit and short circuit faults are set at 410, 440, and 470 of the 500m cable, and then the last 100m of the original 500m cable is cut off to obtain a 400m cable). The final dataset is shown in Table 1 below: Table 1 Dataset Summary
[0046] 1. In the table above, the omitted parts refer to the cases where the cable length is 400m, 300m, or 200m; 2. The above is the dataset obtained from the experiment of a single type of cable. The final dataset should be increased by 3 times, that is, 3×420×5=6300 sets; 3. The total number of samples is only 30 when the fault location is equal to the cable length, but not 60 when it is equal to the cable length. This is because the former only has complete faults, while the latter is divided into complete faults and incomplete faults. For example, when the cable is in an open circuit state and the fault location is 480m, breaking half of the cable core is considered an incomplete fault, while breaking it completely is considered a complete fault.
[0047] 4. The open circuit state of a cable is not strictly distinguished between a completely open circuit and a partially open circuit, and the same applies to the short circuit state. In addition, the short circuit state refers to the short circuit between the conductor and the layer. 5. Fault location refers to the distance of the fault location from the beginning of the cable along the cable path. When the cable terminal is open or short-circuited, the fault location is equal to the cable length. When the open or short circuit at the cable terminal coexists with an intermediate fault point, the fault location is the intermediate fault point. 6. The oscilloscope used in this experiment has a sampling rate of 1GHz, and each set of data contains 8000 data points.
[0048] S5. Retain the physical parameters of the resected segment to generate simulation data; In step 5, retain the physical parameters of the resected segment to generate simulation data. Based on the digital twin model, establish the physical parameter data of the resected segment to simulate concurrent failures at multiple points.
[0049] S6. Repeat steps S1-S5 to collect sufficient real test data until the cable length does not meet the test requirements. S7. Verify the physical consistency of all generated data and discard simulated waveform data that do not meet the constraints; Step S7 verifies the physical consistency of all generated data, specifically including wave velocity verification, energy conservation verification, and similarity verification. For wave velocity verification, the peak time of the reflected pulse is identified from the generated waveform, and the peak time of the reflected pulse is extracted from the original waveform and compared. Those with a deviation value greater than 2% are discarded. The energy conservation principle is verified using the following formula:
[0050] In the above formula, To generate waveforms, The original waveform is used as the basis for calculation. The total energy of the generated waveform and the original waveform is calculated and verified. Data with a deviation value greater than 5% is discarded. The similarity verification is performed using the following formula: , In the above formula, These are the mean values of the waveforms; These are the standard deviations of the waveforms; Let c be the covariance; c1 and c2 are calculation constants, where c1 is 0.01 and c2 is 0.03. Set SSIM>0.85 as a constraint condition, and discard waveform data that do not meet the condition.
[0051] S8. Mix the generated simulated waveform data with the original waveform data according to the preset ratio to construct a test dataset.
[0052] In step S8, a test dataset is constructed by mixing simulated waveform data and original waveform data in a 2:8 ratio.
[0053] By following the steps above, the amount of data in the dataset can be significantly increased by fusing physical and simulated data based on the original experimental materials. Simultaneously, the simulated data is fused with real experimental data to construct a new dataset. This dataset is then used for training, and the hyperparameters of the neural network model are configured as shown in Table 2. For data partitioning, a training set:validation set:test set configuration of 7:1.5:1.5 is chosen. Furthermore, this experimental model uses PyTorch as the training platform and is accelerated using a GPU.
[0054] Table 2 Model Hyperparameter Configuration Table
[0055] After multiple training iterations, the training loss remained almost constant after approximately 800 iterations. However, a sudden drop in model performance might occur between 600 and 800 iterations. This could be because the model is adapting to defect detection for a particular cable type (mainly BVV4 cable), causing deterioration in results for the other two cable types. To be on the safe side, this embodiment selects 1000 iterations. Training results show that with this number of iterations, model adaptation issues can be largely avoided while maintaining training time. One training result is shown below. Figure 4 As shown, the training loss decreases as the number of iterations increases. For fault classification, the training set and test set eventually stabilize at around 93% and 90%, respectively. For fault distance prediction, the MAE eventually stabilizes at around 0.8m, with a maximum prediction error of 1.6m. Example 2
[0056] like Figure 3 The system described above is a neural network model dataset augmentation system based on finite materials. The system uses the above method to augment the dataset and includes a data input module, a data processing module, a verification and comparison module, and a dataset construction module. The data input module is used to input measured waveform data according to the actual experiment. The data processing module is used to process the input measured waveform data by noise disturbance and waveform transformation. The verification and comparison module is used to filter the simulated waveform data according to preset constraints and remove simulated waveform data that do not meet the constraints. The dataset construction module mixes simulated waveform data with measured waveform data according to a preset ratio to generate a dataset for training neural network models.
[0057] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited thereto. Various changes can be made within the scope of knowledge possessed by those skilled in the art without departing from the spirit of the present invention.
Claims
1. A method for augmenting a neural network model dataset based on finite materials, characterized in that, The specific steps include the following: S1. Set up the experimental platform and collect data: Simulate a fault point near the end of the cable under test; capture waveform data using an oscilloscope and save the raw data to a USB flash drive; S2. Add noise disturbance to the raw waveform acquired each time in real time; S3. Perform waveform transformation based on the current cable data to obtain simulated waveform data at different fault locations; waveform transformation also includes the following steps: S31, Fault location interpolation: ; In the above formula The waveform of the fault location after interpolation. These are the weighting coefficients. The position interpolation ratio, The waveforms represent two known fault locations; S32. Cable length transformation: Calculate the length scaling factor: ; Time domain scaling: ; Frequency domain compensation: ; In the above formula, This is the length scaling factor. These are the target cable length and the original cable length, respectively. The data is scaled in the time domain; F is the Fourier transform operator. It is the frequency domain energy compensation factor. This is the final output signal; S4. Completely cut off the cable containing the faulty section to obtain a new length of cable test material without intermediate faults; S5. Generate simulation data by preserving the physical parameters of the resected segment; S6. Repeat steps S1-S5 to collect sufficient real test data until the cable length does not meet the test requirements. S7. Verify the physical consistency of all generated data and discard simulated waveform data that do not meet the constraints; S8. Mix the generated simulated waveform data with the original waveform data according to the preset ratio to construct a test dataset.
2. The method for augmenting a neural network model dataset based on finite materials according to claim 1, characterized in that, The experimental platform built in step S1 includes: an oscilloscope, a transmitter, and a cable under test; The transmitter is used to transmit pulse signals, and the reflected waves are captured and recorded by an oscilloscope; The positive terminals of the transmitter and the oscilloscope are connected to the core of the cable under test; the negative terminals of the transmitter and the oscilloscope are connected to the shielding layer of the cable under test; the terminal of the cable under test is left floating.
3. The method for augmenting a neural network model dataset based on finite materials according to claim 1 or 2, characterized in that, The cable types in step S1 include 500 meters each of RVV2, BVV4, and BV6 type cables; The cables used are all multi-core wires, including three-color main core wires and their respective branch core wires.
4. The method for augmenting a neural network model dataset based on finite materials according to claim 3, characterized in that, In step S1, different types of cables are simulated in real-world scenarios of incomplete breakage, complete breakage, or short circuit. In this case, the incomplete breakage was simulated by cutting each colored core wire in half. Simulate a complete break by completely severing the entire cable; A short circuit is simulated by shorting the cable core and the shielding layer.
5. The method for augmenting a neural network model dataset based on finite materials according to claim 1, characterized in that, Step S2, adding noise perturbation also includes the following steps: S21, Parameter perturbation: Amplitude scaling: ; In the above formula, The scaling factor is for uniform distribution. The original waveform. The waveform is after amplitude scaling; Latency jitter: ; In the above formula, This refers to the time delay jitter. The original waveform. The waveform after time delay jitter; Impedance mismatch simulation: ; in, The waveform after impedance mismatch simulation. This is the impedance mismatch impact response function; ; In the above formula, It is the attenuation constant; The resonant frequency; S22, Noise Injection: Recording background electromagnetic noise when no signal is being transmitted. ; For the original signal Add composite noise: ; In the above formula The original reflected wave signal, It is a composite noise reflected wave signal. To measure the background noise, It is Gaussian white noise. The noise after the disturbance This is the background noise intensity coefficient. The Gaussian noise intensity coefficient; The noise intensity coefficient after disturbance; , , Adjust according to the signal-to-noise ratio (SNR), typically between 0.01 and 0.
05.
6. The method for augmenting a neural network model dataset based on finite materials according to claim 1, characterized in that, Step 5 involves generating simulation data by preserving the physical parameters of the resected segment. The physical parameter data of the resected segment is established based on the digital twin model to simulate concurrent failures at multiple points.
7. The method for augmenting a neural network model dataset based on finite materials according to claim 1, characterized in that, Step S7 verifies the physical consistency of all generated data, specifically including wave velocity verification, energy conservation verification, and similarity verification. For wave velocity verification, the peak time of the reflected pulse is identified from the generated waveform, and the peak time of the reflected pulse is extracted from the original waveform and compared. Those with a deviation value greater than 2% are discarded. The energy conservation principle is verified using the following formula: ; In the above formula, To generate waveforms, The original waveform is used as the basis for calculation. The total energy of the generated waveform and the original waveform is calculated and verified. Data with a deviation value greater than 5% is discarded. The similarity verification is performed using the following formula: ; In the above formula, These are the mean values of the waveforms; These are the standard deviations of the waveforms; Let c be the covariance; c1 and c2 are calculation constants, where c1 is 0.01 and c2 is 0.
03. Set SSIM>0.85 as a constraint condition, and discard waveform data that do not meet the condition.
8. The method for augmenting a neural network model dataset based on finite materials according to claim 1, characterized in that, In step S8, a test dataset is constructed by mixing simulated waveform data and original waveform data in a 2:8 ratio.
9. A dataset augmentation system for neural network models based on finite materials, comprising augmenting the dataset using the method described in any one of claims 1-8, characterized in that, It includes a data input module, a data processing module, a verification and comparison module, and a dataset construction module; The data input module is used to input measured waveform data according to the actual experiment. The data processing module is used to process the input measured waveform data by noise disturbance and waveform transformation. The verification and comparison module is used to filter the simulated waveform data according to preset constraints and remove simulated waveform data that does not meet the constraints. The dataset construction module mixes simulated waveform data with measured waveform data according to a preset ratio to generate a dataset for training neural network models.