Research on Manufacturing Equipment Operation State Evaluation Technology Based on Fractional Calculus
Abstract
:1. Introduction
- Limitations of application objects: Each fault diagnosis method mentioned above can only be applied to specific research objects, and cannot be extended to the diagnosis of various faults in other manufacturing equipment.
- Limitations of application functions: In equipment management, there are no real-time online monitoring and fault prediction functions that affect the reliability of equipment operation and the continuity of production system work.
2. Manufacturing Equipment Operating Condition Assessment Methods
2.1. Fundamental Principle
2.2. Implementation Steps of the Method
- The main motion units that affect the running state of the equipment were analyzed according to the type of manufacturing equipment.
- The operation law of the main motion units was analyzed, and the motion unit with the shortest life-cycle was selected.
- The main parameters affecting the running state of the motion unit and their value ranges under different working states were analyzed.
- High-precision detection data for important motion parameters can be obtained when the motion unit operates normally in real time.
- The running state of the motion unit was determined by comparing the high-precision parameter values obtained in real time with the above value range.
2.3. Premise of Method Implementation
- The judgment technology of the shortest life-cycle motion unit among many motion units;
- The real-time detection technology for the main parameters affecting the running state of the motion unit;
- The high-precision acquisition technology of the main detection information data in a complex environment.
3. High-Precision Information Data Acquisition Technology
- The detection accuracy of information data depends on the performance of the detection equipment. With improvements in detection accuracy, the cost of the detection system is higher. Therefore, they exhibit low-cost performance.
- Their essence is to reduce the signal distortion caused by energy loss and signal interference in the information transmission process by improving signal strength. However, when collecting information, the measurement error of the information data cannot be eliminated owing to the differences in the equipment performance and working environment.
- They do not improve the strength of the detection information and cannot solve the problems of energy loss and signal interference during information transmission. Therefore, it is difficult to apply these methods to engineering practice.
- These methods do not analyze the cause of the information data detection error, the change rule of each influencing factor, or its influence on the detection value. Therefore, it is difficult to improve the detection accuracy of information data by reducing the detection error caused by various influencing factors.
4. Fractional Order Differentiation
4.1. Definition of Fractional Order Differentiation
4.1.1. R–L Definition of the Fractional Differential of the Fractional
4.1.2. G–L Definition of the Fractional Differential of the Fractional
4.1.3. Caputo Definition of the Fractional Differential of the Fractional
4.2. Properties and Applications of Fractional Order Differentiation
- The signal shows different levels of signal enhancement for different fractional differential operators, so that the very-low-frequency components of the signal can be preserved nonlinearly.
- From a physical perspective, signal processing by the fractional differential operator can be understood as the generalized amplitude phase modulation of the signal. Thus, the fractional differential operator can significantly improve signal strength when processing the high-frequency part of the signal.
- The fractional differential operator significantly improved the high-frequency signal strength. It also improved low-frequency signals.
5. Fractional Order Differentiation Based Fusion Model of Equipment Operation Parameters
5.1. Characteristics of Manufacturing Equipment Inspection Information Data
5.2. Fractional Order Differential Based Operational State Evaluation Model
6. Application of Assessment Methods
6.1. Experimental Platform Construction
6.2. Information Data Collection
6.2.1. Data Collection Methods
6.2.2. Experimental Data Collection
6.3. Analysis and Processing of Detection Data
6.3.1. Selection of the Influence Factor of the Detection Value
6.3.2. The Functional Relationship between the Detection Value Fi and the Impact Factor xi
6.3.3. Selection of Fractional Order v and Step Size h Values
- Selection of order v:
- 2.
- Selection of step h:
6.3.4. Information Data Processing Techniques Based on Fractional Order Differential Operators
6.4. Analysis of Operating Condition Assessment Results
6.4.1. Evaluation Criteria for Bearing Wear
6.4.2. Evaluation of Operation Status
6.5. Application Analysis of Experimental Results
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
References
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Sensor No. | Number of Measurement | Mean Value Sc | Standard Deviation Si | |||||
---|---|---|---|---|---|---|---|---|
1st | 2nd | 3rd | 4th | 5th | 6th | |||
1# | 0.164 | 0.158 | 0.168 | 0.166 | 0.171 | 0.158 | 0.1642 | 0.0048 |
2# | 0.162 | 0.171 | 0.168 | 0.175 | 0.165 | 0.173 | 0.1690 | 0.0045 |
3# | 0.162 | 0.173 | 0.165 | 0.163 | 0.171 | 0.165 | 0.1665 | 0.0041 |
4# | 0.172 | 0.165 | 0.174 | 0.162 | 0.169 | 0.165 | 0.1678 | 0.0042 |
5# | 0.168 | 0.162 | 0.165 | 0.163 | 0.165 | 0.173 | 0.1660 | 0.0037 |
Location of Sampling Points | Sensor No. | Standard Deviation | |||||
---|---|---|---|---|---|---|---|
1# | 2# | 3# | 4# | 5# | |||
A | 0.112 | 0.105 | 0.108 | 0.118 | 0.114 | 0.1114 | 0.00454 |
B | 0.158 | 0.162 | 0.165 | 0.162 | 0.156 | 0.1606 | 0.00320 |
C | 0.175 | 0.172 | 0.178 | 0.171 | 0.177 | 0.1746 | 0.00273 |
D | 0.213 | 0.198 | 0.204 | 0.212 | 0.208 | 0.2070 | 0.00632 |
E | 0.152 | 0.147 | 0.145 | 0.149 | 0.146 | 0.1478 | 0.00248 |
Standard deviation of sensors | 0.0048 | 0.0045 | 0.0041 | 0.0042 | 0.0037 | Total average | 0.1603 |
Sampling Site Location | Sensor No. | Magnification Factor K | |||||
---|---|---|---|---|---|---|---|
1# | 2# | 3# | 4# | 5# | |||
A | 1.7734 | 1.7918 | 1.8163 | 1.8102 | 1.8408 | 1.8065 | 17.05 |
B | 2.7310 | 2.7258 | 2.7188 | 2.7205 | 2.7118 | 2.7216 | |
C | 2.8543 | 2.8695 | 2.8897 | 2.8846 | 2.9099 | 2.8816 | |
D | 3.6784 | 3.6939 | 3.6545 | 3.6694 | 3.6452 | 3.6683 | |
E | 2.6244 | 2.5991 | 2.5655 | 2.5739 | 2.5318 | 2.5789 | |
Standard deviation of sensors | 0.0048 | 0.0045 | 0.0041 | 0.0042 | 0.0037 | Average value after fusion | 2.733 |
Sampling Site Location | Sensor No. | Standard Deviation | |||||
---|---|---|---|---|---|---|---|
1# | 2# | 3# | 4# | 5# | |||
A | 0.1040 | 0.1051 | 0.1065 | 0.1062 | 0.1080 | 0.1060 | 0.00144 |
B | 0.1602 | 0.1599 | 0.1595 | 0.1596 | 0.1590 | 0.1596 | 0.00038 |
C | 0.1674 | 0.1683 | 0.1695 | 0.1692 | 0.1707 | 0.1690 | 0.00111 |
D | 0.2157 | 0.2178 | 0.2143 | 0.2152 | 0.2109 | 0.2148 | 0.00128 |
E | 0.1539 | 0.1524 | 0.1505 | 0.1510 | 0.1485 | 0.1513 | 0.00184 |
Standard deviation of sensors | 0.0048 | 0.0045 | 0.0041 | 0.0042 | 0.0037 |
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Zuo, Y.; Cheng, H.; Geng, G.; Xia, S.; Zhou, C. Research on Manufacturing Equipment Operation State Evaluation Technology Based on Fractional Calculus. Sensors 2023, 23, 3373. https://doi.org/10.3390/s23073373
Zuo Y, Cheng H, Geng G, Xia S, Zhou C. Research on Manufacturing Equipment Operation State Evaluation Technology Based on Fractional Calculus. Sensors. 2023; 23(7):3373. https://doi.org/10.3390/s23073373
Chicago/Turabian StyleZuo, Yanhong, Hua Cheng, Guoqing Geng, Shilong Xia, and Chao Zhou. 2023. "Research on Manufacturing Equipment Operation State Evaluation Technology Based on Fractional Calculus" Sensors 23, no. 7: 3373. https://doi.org/10.3390/s23073373
APA StyleZuo, Y., Cheng, H., Geng, G., Xia, S., & Zhou, C. (2023). Research on Manufacturing Equipment Operation State Evaluation Technology Based on Fractional Calculus. Sensors, 23(7), 3373. https://doi.org/10.3390/s23073373