A program control-based stamping process parameter intelligent optimization method

Abstract

The present application relates to the field of intelligent manufacturing and data processing, in particular to a stamping process parameter intelligent optimization method based on program control, which firstly collects multi-source sensor data of a stamping machine tool, and constructs a standard benchmark characteristic vector. Secondly, the mean of Mahalanobis distance of the standard benchmark characteristic vector in a short time window is calculated to obtain the state fluctuation intensity. Further, linear regression is performed on the intensity sequence in a long time window to obtain the process degradation momentum. Then, the degradation momentum and the historically accumulated fluctuation energy are nonlinearly combined to obtain a time series risk index. Finally, the dimensionless time series risk index and the standard benchmark characteristic vector are fused and input into a pre-trained classification model to accurately evaluate the stability state of the current stamping process, and the stamping control strategy is optimized accordingly, realizing comprehensive management and control of the stamping process from instantaneous disturbance to long-term die wear trend.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing and data processing, specifically to a method for intelligent optimization of stamping process parameters based on program control. Background Technology

[0002] Automated stamping production lines controlled by programs are a core production link in modern automobile manufacturing, hardware processing, and other industries. The stability of their process parameters directly affects the dimensional accuracy, surface quality, and production efficiency of the formed parts. To avoid batch scrap and equipment damage caused by die wear, lubrication failure, or material fluctuations, effective condition monitoring of the stamping process, and the subsequent parameter optimization or maintenance early warning, is of paramount importance.

[0003] Existing stamping process monitoring methods typically rely on analyzing sensor data collected during equipment operation. However, the performance degradation of stamping dies is a gradual process from normal to failure. Early characteristic signals such as edge wear or clearance changes are weak and often drowned out by the high-frequency impact noise and complex operating conditions during stamping. This makes it difficult for traditional alarm methods based on fixed thresholds to effectively capture early abnormal states, easily leading to missed or false alarms.

[0004] To address these issues, a common technical approach is to introduce time-series analysis to determine short-term fluctuations in process conditions by calculating the statistical distance of eigenvectors, and further capture signs of die performance degradation through long-term trends. However, this method, which focuses solely on the rate of change of process conditions, has limitations. While it can identify trends of deteriorating process conditions, it fails to account for historical load-bearing damage to the die or equipment. For example, the actual risk level represented by the same degradation rate of a process parameter occurring on a brand-new die after die replacement is drastically different from that occurring on an old die that has undergone tens of thousands of stamping cycles and accumulated significant fatigue. Therefore, relying solely on degradation trend analysis makes it difficult to comprehensively and accurately assess the true risk level of the current stamping process. Summary of the Invention

[0005] To address the problem that relying solely on degradation trend analysis makes it difficult to comprehensively and accurately assess the true risk level of the current stamping process, this invention proposes a program-controlled intelligent optimization method for stamping process parameters. The method includes: collecting process operation data from the stamping equipment and extracting a baseline feature vector; performing dimensionless standardization on the baseline feature vector to obtain a standard baseline feature vector; calculating the Mahalanobis distance of the standard baseline feature vector relative to the data distribution within a short-term sliding window of a preset length, and using the average value of the Mahalanobis distance as the state fluctuation intensity; performing linear regression analysis on the time series of the state fluctuation intensity within a long-term analysis window of a preset length, and using the slope of the fitted line as the process degradation momentum; calculating a time-series risk index, which is positively correlated with the historical cumulative value of the process degradation momentum and the state fluctuation intensity; concatenating the time-series risk index with the standard baseline feature vector to form a fused feature vector; and inputting the fused feature vector into a pre-trained classification model to determine the current operating state of the stamping equipment, and generating process parameter optimization instructions based on the current operating state.

[0006] To address the shortcomings of existing stamping monitoring technologies, such as missed early-stage faults due to single data dimensions or focus only on instantaneous thresholds, and model training failures caused by differences in the dimensions of multi-source features, this invention eliminates the masking effect of large numerical features like stamping force on small numerical features like waveform factors through dimensionless standardization, ensuring fair model weight allocation. Simultaneously, by fusing the intensity of state fluctuations representing short-term instability, degradation momentum representing long-term deterioration rates, and a time-series risk index representing historical accumulated damage, a full-time-domain process state profile is constructed. This allows for accurate risk identification and optimization command generation in the early stages of die wear or parameter drift, significantly improving the adaptive control capability and finished product yield of the stamping process.

[0007] Further, calculating the Mahalanobis distance of the standard reference feature vector relative to the data distribution within the window also includes: calculating the mean vector and covariance matrix of all standard reference feature vectors within the short-time sliding window, multiplying the difference between the standard reference feature vector at the current time and the mean vector by the inverse of the covariance matrix, and then multiplying by the transpose of the difference to obtain the Mahalanobis distance.

[0008] Compared to measurement methods such as Euclidean distance that do not consider the correlation between variables, this invention uses Mahalanobis distance to calculate the intensity of state fluctuations. This can effectively decouple strongly coupled characteristic variables in the stamping process and accurately eliminate spurious fluctuations caused by normal coupling changes in operating conditions. Thus, in the complex stamping production environment, it can more objectively measure the statistical deviation of the current process state from the baseline distribution.

[0009] Furthermore, the preset length of the short-term sliding window is 50 to 200 sampling time points, and the length of the long-term analysis window is 10 to 50 times the length of the short-term sliding window.

[0010] Furthermore, the specific method for calculating the time-series risk index is as follows:

[0011] ; in Indicates time The time-series risk index; This represents the process degradation momentum; This represents the historical cumulative value of the intensity of state fluctuations; This represents the natural logarithm function.

[0012] To address the problem that relying solely on degradation rate cannot distinguish the risk differences between new and old molds, this invention constructs a time-series risk index that couples degradation momentum with historical cumulative damage through a nonlinear function, thereby achieving dynamic amplification of risk signals. When an old mold that has already endured a large amount of cumulative load shows a degradation trend, this index will show a more dramatic increase than that of a new mold, thus improving the sensitivity of early warning of failures in old equipment in accordance with the laws of physical fatigue and avoiding chipping accidents.

[0013] Furthermore, the method for obtaining the historical cumulative value of the state fluctuation intensity includes: summing up all state fluctuation intensity values ​​from the start of the current service cycle of the stamping die to the current moment.

[0014] Furthermore, the process operation data of the stamping equipment includes vibration signals, temperature signals, and stamping force signals.

[0015] Furthermore, the reference feature vector includes at least one feature selected from the following: root mean square value, peak-to-peak value, kurtosis factor, margin factor, waveform factor, and average value of temperature and impulse signals.

[0016] Furthermore, the pre-trained classification model is a random forest model.

[0017] Compared to linear classifiers, this invention uses a random forest model to process fused features, which has strong anti-overfitting ability and nonlinear mapping ability. It can effectively handle high-dimensional data noise and complex feature interaction relationships in the stamping process. While ensuring high classification accuracy, the decision tree ensemble mechanism improves the system's tolerance to false alarms.

[0018] Furthermore, in response to the current operating state of the stamping equipment being a preset abnormal state, a predictive maintenance warning is triggered or a compensation correction of the stamping process parameters is performed.

[0019] Furthermore, the dimensionless standardization process of the benchmark feature vector to obtain the standard benchmark feature vector also includes: using the Z-score standardization method to obtain the mean and standard deviation of each feature data in the benchmark feature vector, and subtracting the mean from the original feature value extracted at the current time and dividing by the standard deviation, thereby transforming the benchmark feature vectors of different dimensions into dimensionless standard benchmark feature vectors with a mean of 0 and a standard deviation of 1.

[0020] This invention uses the Z-score standardization method to force all features with different physical dimensions to be uniformly mapped to the same numerical scale, fundamentally eliminating the interference of numerical magnitude differences on machine learning algorithms. This ensures that dimensionless micro-features such as kurtosis and waveform factors play their due role in decision tree splitting, greatly improving the interpretability of the model and its ability to capture early and weak fault features.

[0021] The technical effects of this invention are as follows: This invention proposes a stamping process optimization method that integrates dimensionless processing and temporal evolution analysis. To address the model weight imbalance problem caused by differences in the dimensions of multi-source features, Z-score standardization is introduced to ensure the fairness of feature contributions. Simultaneously, a temporal risk index is constructed, which, through nonlinear coupling of degradation momentum and historical accumulated damage, overcomes the deficiency of traditional monitoring methods that neglect equipment fatigue history. This amplifies the signal of subtle degradation trends in aging dies, thereby achieving precise process parameter optimization throughout the entire lifecycle. Attached Figure Description

[0022] Figure 1 This is a schematic flowchart illustrating an embodiment of the present invention of an intelligent optimization method for stamping process parameters based on program control. Figure 2 This is a schematic diagram illustrating the variation of the intensity of stamping process state fluctuations with a time window in an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the curve of the stamping process timing risk index changing with time window in an embodiment of the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0025] An example of a program-controlled intelligent optimization method for stamping process parameters: like Figure 1 As shown, the present invention provides a method for intelligent optimization of stamping process parameters based on program control, comprising: S1. Collect multi-source heterogeneous data from stamping equipment, extract the baseline feature vector, and perform dimensionless standardization processing.

[0026] In one embodiment of the present invention, to comprehensively capture operational information during the stamping process, various types of sensors can be deployed on key components of the stamping machine. For example, acceleration sensors, temperature sensors, and stamping force sensors can be installed at locations such as the press slide, die mounting base, and guide pillars. These sensors are used to collect multi-source heterogeneous signals such as vibration signals, die temperature, and stamping force curves during the stamping process in real time.

[0027] In this embodiment, a preset sampling frequency can be set. The aforementioned multi-source signals are continuously acquired. As a preferred approach, for vibration and impact signals with strong instantaneous impact, the sampling frequency is... The sampling frequency can be set from 10kHz to 50kHz to ensure that the high-frequency impact characteristics generated when early faults such as die chipping and scrap re-tracing occur can be captured. For temperature signals with relatively gentle changes, the sampling frequency can be appropriately reduced. The acquired continuous signal stream can be divided according to the stamping stroke or a fixed time length to form a series of continuous time window sequences.

[0028] For any time From the data within the latest time window, a set of baseline statistical features characterizing the instantaneous state of the current stamping process is extracted. Specifically, these include, but are not limited to: the root mean square value, peak-to-peak value, kurtosis factor, and margin factor of the vibration and stamping force signals, as well as the average value of the die temperature. It is important to note that Z-score normalization can be applied to each extracted feature to transform all features into dimensionless standard features with a consistent numerical distribution.

[0029] In this embodiment, the root mean square value of the vibration signal after standardization is preferred. kurtosis factor Average mold temperature and the average value of the punching force To obtain the standard baseline feature vector, we have: ,symbol This indicates the transpose of a vector. In this example, the baseline eigenvector is a 4-dimensional dimensionless numerical vector.

[0030] S2. Divide the short-time sliding window and obtain the state fluctuation intensity based on the standard baseline feature vector and Mahalanobis distance.

[0031] To effectively capture short-term stability changes in the stamping process state, this step aims to determine the degree of deviation of the current state from its nearest historical state. A stable stamping process should exhibit characteristics of fluctuations within a small range, while die wear or abnormal lubrication can disrupt this stability.

[0032] Mahalanobis distance effectively measures the distance from a point to the center of the data distribution and takes into account the correlation between features. Since the input data has been dimensionless, the calculated Mahalanobis distance more purely reflects the statistical deviation at the data distribution level.

[0033] In this embodiment, the current time is used Short-term sliding window with endpoint (length is) Within this window, calculate all standard baseline feature vectors. mean vector Covariance Matrix Then, for the window Every moment within Standard baseline feature vector Calculate the Mahalanobis distance relative to the statistical distribution of the window. Finally, take the arithmetic mean of the Mahalanobis distances at all times within the window to obtain the result for the current time step. State fluctuation intensity Specifically: ; in Indicates time The intensity of state fluctuations is used to characterize the short-term instability of equipment states; Indicates a short-term sliding window The length of represents the timescale for short-term stability assessment. As a preferred approach, The value range can be set to At a specific point in time. If The value is too small, and the calculated value is too small. It is susceptible to noise and therefore exhibits significant fluctuations; if If the value is too large, it will smooth out rapid changes in state and reduce sensitivity to transient anomalies; Indicates a past moment within the window. Extracted baseline feature vector; and These represent short-term sliding windows. All reference eigenvectors The mean vector and covariance matrix.

[0034] According to the above formula, when the stamping production line is operating stably, the reference eigenvector at each moment is... Will closely revolve around the distribution center The fluctuations result in generally small Mahalanobis distances at all points, thus affecting the final calculated intensity of the state fluctuations. The value is also lower. Conversely, when the stamping production line experiences abnormal operation, causing its operating characteristics to deviate from recent stable normal conditions, at least one... The farther away from the distribution center, the greater its Mahalanobis distance will be, thus raising the value. The average value effectively indicates the intensified short-term fluctuations in the operating status of the stamping production line.

[0035] like Figure 2 As shown, this graph illustrates the trend of the intensity of fluctuations in the stamping process state over time. The horizontal axis represents the time window sequence (unit: seconds), and the vertical axis represents the calculated state fluctuation intensity value. The curve trend shows that in the first half of the monitoring period, the fluctuation intensity value maintains a relatively stable oscillation within a certain range, indicating that the stamping process is in a stable and controlled state. However, in the final part of the monitoring period, the curve exhibits a clear upward shift in the center of gravity and a violent fluctuation trend, indicating that the state of the stamping process is gradually deviating from its stable state, and the instability is significantly increasing, foreshadowing potential process anomalies.

[0036] S3. Divide the long-term analysis window and calculate the process degradation momentum based on the intensity of state fluctuations and linear regression analysis.

[0037] Intensity of process state fluctuation at a single moment Higher fluctuations may be caused by transient operating disturbances, such as slight changes in sheet thickness or environmental noise, while continuous or increasing fluctuations are more likely signs of irreversible physical degradation of the stamping die or machine tool, such as cutting edge wear or increased guide post clearance. To accurately capture the trend of this state evolution, this step calculates the process degradation momentum to determine the rate of change of the state fluctuation intensity.

[0038] Linear regression analysis can be used to reveal the linear trend between variables. By linearly fitting the intensity sequence of state fluctuations over a period of time, the slope of the fitted line can intuitively reflect the average trend of the index, i.e., the degenerative momentum.

[0039] In a shorter sliding window Longer long-term analysis window (length is) Within ) first obtain a by A sequence consisting of consecutive state fluctuation intensity values Then, a univariate linear regression analysis is performed on the time series to calculate the slope of the fitted line, which is defined as the slope at the current time. Process degradation momentum Specifically: ; in Indicates time The process degradation momentum is used to describe the deterioration trend of the stamping process state; Represents a long-term analysis window The length. As a preferred option, The value should be significantly greater than For example, it can be set to of This is to ensure that a stable and reliable trend model can be established over a sufficiently long timescale; Indicates in window The time step index within, from arrive ; It represents the intensity of state fluctuation at a certain point in the past within a long time window.

[0040] As can be seen from the above formula, if the stamping process state is within the window... If the internal conditions continue to deteriorate, for example, if increased die wear leads to a sustained increase in stamping pressure fluctuations, then... The sequence will show an overall upward trend, and the slope calculated by linear regression will be... This will be a significantly positive value, and a larger value indicates a faster rate of deterioration. If the process conditions remain stable or improve after parameter optimization, The sequence will exhibit a stable or declining trend, making It approaches zero or becomes negative. Therefore, The description of process status has been upgraded from a static, instantaneous fluctuation to a dynamic evolutionary trend.

[0041] like Figure 3 As shown, this graph illustrates the trend of the time-series risk index over time. The horizontal axis represents the time window series, and the vertical axis represents the dimensionless time-series risk index. Figure 2 Compared to the fluctuation intensity curve in the middle, Figure 3 The risk index curve in the middle shows a more rapid and significant increase at the end of the cycle. This signal amplification phenomenon is due to the fact that the present invention nonlinearly couples the positive process degradation momentum with the large amount of accumulated damage that has been suffered in the past, thereby generating a fault warning signal that is stronger and has a higher signal-to-noise ratio than a single fluctuation intensity or momentum index, which can more clearly indicate the failure risk that the stamping die will face.

[0042] S4. Obtain the cumulative fluctuation energy based on the intensity of state fluctuations; obtain the time series risk index based on the process degradation momentum and the cumulative fluctuation energy; and combine the time series risk index with the standard benchmark feature vector to obtain the final feature vector.

[0043] Process degradation momentum While reflecting the rate of deterioration in process conditions to some extent, the risk level is not isolated. A slight degradation momentum appearing on a mold that has already suffered significant historical damage poses a far greater risk than the same momentum on a brand-new mold. Therefore, this step comprehensively assesses the current degradation momentum and historical cumulative damage by calculating a time-series risk index.

[0044] S4.1 Obtain cumulative fluctuation energy based on state fluctuation intensity.

[0045] First, define the time from the start of the current mold installation and commissioning cycle or the last maintenance to the current moment. The cumulative fluctuation energy, i.e. the historical cumulative value of the state fluctuation intensity, is obtained here by performing a discrete integral over time on all historical state fluctuation intensities.

[0046] Each irregular impact and vibration of the stamping die and machine tool components consumes its lifespan. Accumulated fluctuation energy aims to physically determine the total energy of all irregular stamping impacts the system has endured so far, specifically: ;in Indicates time The accumulated fluctuation energy, and The value remains monotonically constant over time, intuitively reflecting the degree of accumulated damage to the equipment; Indicates the start time of this running cycle; Representing historical moments The intensity of state fluctuations.

[0047] S4.2. Obtain the time series risk index based on process degradation momentum and cumulative fluctuation energy; combine the time series risk index with the benchmark feature vector to obtain the final feature vector.

[0048] Subsequently based on process degradation momentum With accumulated fluctuation energy Calculate the time series risk index Specifically: ; in Indicates time The temporal risk index is used to incorporate the temporal evolution characteristics of the random forest model; Indicates the momentum of process degradation; Indicates accumulated fluctuation energy; It is the natural logarithm function, used to smoothly scale the accumulated energy, avoiding order-of-magnitude imbalance in the product due to excessively large values, while preserving its monotonicity.

[0049] The time series risk index in the above formula The level of degenerate momentum and accumulated fluctuation energy This is a joint decision. When the stamping process is in a degradation process (i.e....) When ), the cumulative damage it has already suffered The larger the value, the more accurate the calculation. The higher the value, the higher the risk level of the current degradation trend.

[0050] Finally, the calculated time-series risk index Compared with the baseline feature vector extracted and dimensionlessly standardized in step S1 The features are then concatenated to form an enhanced final feature vector that incorporates temporal evolution information. .

[0051] It should be noted here that: because the original data such as vibration, temperature, and impact force have been standardized in step S1, eliminating dimensional differences, and because the data in this step... It is also a dimensionless exponent derived from the dimensionless fluctuation intensity, therefore the spliced... All values ​​are dimensionless. This effectively avoids the problem of uneven model weight distribution caused by different physical dimensions of the features.

[0052] The specific formula is as follows: ,in This represents a vector concatenation operation. Specifically, in this embodiment, the final feature vector is: ; in These represent the root mean square value and kurtosis factor of the vibration signal after standardization, respectively. This represents the average value of the temperature signal after standardization. This represents the average value of the standardized punch force signal; and the sign... This represents the transpose of a vector.

[0053] S5. Use the trained model based on the fusion features to evaluate the operating status of the equipment.

[0054] The dimensionless fusion feature vector obtained in step S4 As input, it is fed into a pre-trained random forest classification model to perform real-time evaluation of the stamping process operation status.

[0055] In this embodiment, the random forest model is a well-known technique, and its training process specifically involves supervised training using a historical stamping dataset containing rich operating conditions and fault types. Each sample in this dataset is represented by its corresponding fused feature vector. It consists of real-world state labels (such as "process stability", "parameter drift", "mold microcrack risk"). During training, the hyperparameters of the random forest model can be tuned. For example, the number of decision trees (n_estimators) can be preferably 100~500, and the maximum depth of the decision trees (max_depth) can be preferably 10~30.

[0056] During the real-time monitoring phase, the random forest model analyzes the input... The analysis is performed, and the probability of the current stamping process belonging to each predefined state category is output. By comparing these probability values, the process at time [time value missing] is finally determined. The system can detect the most likely operating state. When monitoring results indicate an abnormal state multiple times consecutively or in a specific pattern, the system can trigger an early warning, generate process parameter optimization instructions such as adjusting the punching pressure compensation value, or issue forward-looking predictive maintenance instructions to maintenance personnel.

[0057] In summary, this invention effectively overcomes the limitations of traditional static feature analysis, such as unclear physical meaning and uneven weight distribution, by capturing short-term changes in the stamping process state from stable to fluctuating, medium-term trends from fluctuating to deteriorating, and the long-term cumulative effect of die damage, and by incorporating these into a machine learning model using dimensionless processing technology. This enables sensitive capture of weak faults in the early stages of the stamping process and robust differentiation of fluctuations in normal operating conditions, thereby significantly improving the accuracy, reliability, and interpretability of parameter optimization and condition monitoring.

Claims

1. A method for intelligent optimization of stamping process parameters based on program control, characterized in that, The method includes: collecting process operation data of the stamping equipment and extracting a reference feature vector; performing dimensionless standardization on the reference feature vector to obtain a standard reference feature vector; calculating the Mahalanobis distance of the standard reference feature vector relative to the data distribution within a preset short-time sliding window; and using the average value of the Mahalanobis distance as the intensity of state fluctuation. Within a long-term analysis window of a preset length, linear regression analysis is performed on the time series of the state fluctuation intensity, and the slope of the fitted line is used as the process degradation momentum; the time series risk index is calculated, which is positively correlated with the process degradation momentum and the historical cumulative value of the state fluctuation intensity. The time-series risk index is concatenated with the standard benchmark feature vector to form a fused feature vector; the fused feature vector is input into a pre-trained classification model to determine the current operating state of the stamping equipment, and process parameter optimization instructions are generated based on the current operating state.

2. The intelligent optimization method for stamping process parameters based on program control according to claim 1, characterized in that, Calculating the Mahalanobis distance of the standard baseline feature vector relative to the data distribution within the window includes: Calculate the mean vector and covariance matrix of all standard reference eigenvectors within the short-time sliding window, and multiply the difference between the current standard reference eigenvector and the mean vector by the inverse of the covariance matrix, and then multiply by the transpose of the difference to obtain the Mahalanobis distance.

3. The intelligent optimization method for stamping process parameters based on program control according to claim 1, characterized in that, The preset length of the short-time sliding window is 50 to 200 sampling time points, and the length of the long-time analysis window is 10 to 50 times the length of the short-time sliding window.

4. The intelligent optimization method for stamping process parameters based on program control according to claim 1, characterized in that, The specific method for calculating the time series risk index is as follows: ； in Indicates time The time-series risk index; This represents the process degradation momentum; This represents the historical cumulative value of the intensity of state fluctuations; This represents the natural logarithm function.

5. The intelligent optimization method for stamping process parameters based on program control according to claim 4, characterized in that, The method for obtaining the historical cumulative value of the state fluctuation intensity includes: The summation is performed on all state fluctuation intensity values ​​from the start of the current service cycle of the stamping die to the current moment.

6. The intelligent optimization method for stamping process parameters based on program control according to claim 1, characterized in that, The process operation data of the stamping equipment includes vibration signals, temperature signals, and stamping force signals.

7. The intelligent optimization method for stamping process parameters based on program control according to claim 1, characterized in that, The baseline feature vector includes at least one feature selected from the following: The root mean square value, peak-to-peak value, kurtosis factor, margin factor, waveform factor, and average values ​​of temperature and impulse signals.

8. The intelligent optimization method for stamping process parameters based on program control according to claim 1, characterized in that, The pre-trained classification model is a random forest model.

9. The intelligent optimization method for stamping process parameters based on program control according to claim 1, characterized in that, When the current operating state of the stamping equipment is a preset abnormal state, a predictive maintenance warning is triggered or the stamping process parameters are compensated and corrected.

10. The intelligent optimization method for stamping process parameters based on program control according to claim 1, characterized in that, The reference feature vector is subjected to dimensionless standardization to obtain a standard reference feature vector, including: The Z-score standardization method is used to obtain the mean and standard deviation of each feature data in the baseline feature vector. The original feature value extracted at the current time is subtracted from the mean and then divided by the standard deviation, thereby transforming the baseline feature vectors of different dimensions into dimensionless standard baseline feature vectors with a mean of 0 and a standard deviation of 1.

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