Huixu Song
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Huixu Song has a total of 34 co-authors. Here are the top co-authors by number of shared publications:
Zhaoyao Shi
4 shared publications- Zhaoyao Shi
Beijing Engineering Research Center of Precision Measurement Technology and Instruments, Beijing University of Technology, Beijing 100124, China
3 shared publications Chunxu Bi
Key Laboratory of Advanced Manufacturing and Intelligent Technology, Ministry of Education, Harbin University of Science and Technology, Harbin, China
2 shared publications- Hongfang Chen
Beijing Engineering Research Center of Precision Measurement Technology and Instruments, Beijing University of Technology, Beijing 100124, People’s Republic of China
2 shared publications John Song
Physical Measurement Laboratory, Sensor Science Division National Institute of Standards and Technology (NIST) Gaithersburg Maryland USA
2 shared publicationsMingna Ding
Key Laboratory of Advanced Manufacturing and Intelligent Technology, Ministry of Education, Harbin University of Science and Technology, Harbin, China
2 shared publications
Latest Publications
- Open Access
- 25 August 2026
- Published by SAGE Publications in Measurement and Control
- Vol. 59 (9) , 1484-1503
A decoupling algorithm & its application for 3D scanning probes
The 3D scanning probe is the “eye” of precision measuring instruments, coupling errors among its axes remain an urgent problem; accurate decoupling is essential for improving probe data accuracy. This paper presents an improved algorithm that integrates Particle Swarm Optimization (PSO)、Latin Hypercube Sampling (LHS), and an Opposition-Based Learning (OBL) strategy. The inertia weight w is dynamically adjusted using a cycloidal schedule, ensuring both rapid initial convergence and refined exploration in later stages. Additionally, the cognitive and social coefficients c 1 and c 2 are linearly decreased to minimize the risk of the swarm becoming trapped in local optima. Compared with the standard PSO algorithm, the improved algorithm can obtain the global optimal solution, while the standard algorithm only achieves the local optimal solution and thus cannot be applied to probe decoupling. Compared with the LSM algorithm, the coupling matrices obtained by the two methods are basically consistent under the condition of outlier-free data. Nevertheless, when outliers exist in the dataset, the LO-PSO algorithm achieves superior robustness and decoupling accuracy relative to LSM. Tests were conducted on the original dataset, and the results show that decoupling improves the measurement accuracy of test data in the X, Y and Z directions. Compared with the pre-decoupling results, the four X-group datasets showed a maximum type-I error of 0.747%, corresponding to an average gain of 8.02%; the Y-group datasets showed a maximum type-I error of −0.956%, corresponding to an average gain of 10.82%; and the Z-group datasets showed a maximum type-I error of 1.658%, corresponding to an average gain of 8.86%. The results show that the improved algorithm significantly enhances the data accuracy of the 3D scanning probe. Under laboratory calibration test conditions, the LO-PSO algorithm achieves superior decoupling accuracy and outlier resistance robustness compared with the least squares method, and it has the engineering potential to be integrated into precision measurement software for on-site decoupling.
- 25 August 2026
- Published by SAGE Publications in Measurement and Control
- Vol. 59 (9) , 1484-1503
Open AccessA decoupling algorithm & its application for 3D scanning probes
The 3D scanning probe is the “eye” of precision measuring instruments, coupling errors among its axes remain an urgent problem; accurate decoupling is essential for improving probe data accuracy. This paper presents an improved algorithm that integrates Particle Swarm Optimization (PSO)、Latin Hypercube Sampling (LHS), and an Opposition-Based Learning (OBL) strategy. The inertia weight w is dynamically adjusted using a cycloidal schedule, ensuring both rapid initial convergence and refined exploration in later stages. Additionally, the cognitive and social coefficients c 1 and c 2 are linearly decreased to minimize the risk of the swarm becoming trapped in local optima. Compared with the standard PSO algorithm, the improved algorithm can obtain the global optimal solution, while the standard algorithm only achieves the local optimal solution and thus cannot be applied to probe decoupling. Compared with the LSM algorithm, the coupling matrices obtained by the two methods are basically consistent under the condition of outlier-free data. Nevertheless, when outliers exist in the dataset, the LO-PSO algorithm achieves superior robustness and decoupling accuracy relative to LSM. Tests were conducted on the original dataset, and the results show that decoupling improves the measurement accuracy of test data in the X, Y and Z directions. Compared with the pre-decoupling results, the four X-group datasets showed a maximum type-I error of 0.747%, corresponding to an average gain of 8.02%; the Y-group datasets showed a maximum type-I error of −0.956%, corresponding to an average gain of 10.82%; and the Z-group datasets showed a maximum type-I error of 1.658%, corresponding to an average gain of 8.86%. The results show that the improved algorithm significantly enhances the data accuracy of the 3D scanning probe. Under laboratory calibration test conditions, the LO-PSO algorithm achieves superior decoupling accuracy and outlier resistance robustness compared with the least squares method, and it has the engineering potential to be integrated into precision measurement software for on-site decoupling.
- 11 September 2025
- Published by IOP Publishing in Measurement Science and Technology
- Vol. 36 (9) , 095010
Study on the measurement capability of point autofocus microscopy for steep surfaces beyond objective numerical aperture limits
As products continue to develop towards precision and intelligence, components are increasingly trending towards miniaturization. In the era of artificial intelligence, the market demand for small components is steadily growing. The point autofocus microscopy (PAM), with its small measurement spot and high vertical resolution, offers distinct advantages in the geometric measurement of small components. However, the maximum measurable angle of PAM is limited by the numerical aperture of the objective lens, typically not exceeding 20°, which makes it challenging to meet the measurement requirements for surfaces with high curvature. To achieve full-surface geometric measurement of microstructures, traditional methods rely on multiple measurements and data stitching, which compromises efficiency and may lead to cumulative errors. This paper proposes a method to enhance the maximum measurable angle of the PAM by utilizing diffuse reflected light based on the principle of point autofocus measurement. Additionally, by incorporating the principle of biased incidence, it provides the theoretical maximum measurable angles for three different tilt directions. Experiments were conducted using three optical diffusers with varying surface roughness levels as test specimens. The results indicate that the PAM can achieve sub-micrometer measurement accuracy for the relatively rough 220 and 600-grit optical diffusers specimens at tilt angles between 0° and 80°. In contrast, for the 1500-grit optical diffusers specimen, PAM fails to meet sub-micrometer accuracy once the tilt angle exceeds 10°.
- 11 September 2025
- Published by IOP Publishing in Measurement Science and Technology
- Vol. 36 (9) , 095010
Study on the measurement capability of point autofocus microscopy for steep surfaces beyond objective numerical aperture limits
As products continue to develop towards precision and intelligence, components are increasingly trending towards miniaturization. In the era of artificial intelligence, the market demand for small components is steadily growing. The point autofocus microscopy (PAM), with its small measurement spot and high vertical resolution, offers distinct advantages in the geometric measurement of small components. However, the maximum measurable angle of PAM is limited by the numerical aperture of the objective lens, typically not exceeding 20°, which makes it challenging to meet the measurement requirements for surfaces with high curvature. To achieve full-surface geometric measurement of microstructures, traditional methods rely on multiple measurements and data stitching, which compromises efficiency and may lead to cumulative errors. This paper proposes a method to enhance the maximum measurable angle of the PAM by utilizing diffuse reflected light based on the principle of point autofocus measurement. Additionally, by incorporating the principle of biased incidence, it provides the theoretical maximum measurable angles for three different tilt directions. Experiments were conducted using three optical diffusers with varying surface roughness levels as test specimens. The results indicate that the PAM can achieve sub-micrometer measurement accuracy for the relatively rough 220 and 600-grit optical diffusers specimens at tilt angles between 0° and 80°. In contrast, for the 1500-grit optical diffusers specimen, PAM fails to meet sub-micrometer accuracy once the tilt angle exceeds 10°.
- 11 March 2025
- Published by Elsevier in Tribology International
- Vol. 207
Local surface roughness of cylindrical gears: Concept, method, and application
- 11 March 2025
- Published by Elsevier in Tribology International
- Vol. 207
Local surface roughness of cylindrical gears: Concept, method, and application
- Open Access
Intelligent Inspection Method and System of Plastic Gear Surface Defects Based on Adaptive Sample Weighting Deep Learning Model
After injection molding, plastic gears often exhibit surface defects, including those on end faces and tooth surfaces. These defects encompass a wide range of types and possess complex characteristics, which pose challenges for inspection. Current visual inspection systems for plastic gears suffer from limitations such as single-category defect inspection and low accuracy. There is an urgent industry need for a comprehensive and accurate method and system for inspecting defects on plastic gears, with improved inspection capability and higher accuracy. This paper presents an intelligent inspection algorithm network for plastic gear defects (PGD-net), which effectively captures subtle defect features at arbitrary locations on the surface compared to other models. An adaptive sample weighting method is proposed and integrated into an improved Focal-IoU loss function to address the issue of low inspection accuracy caused by imbalanced defect dataset distributions, thus enhancing the regression accuracy for difficult defect categories. CoordConv layers are incorporated into each inspection head to improve the model’s generalization capability. Furthermore, a dataset of plastic gear surface defects comprising 16 types of defects is constructed, and our algorithm is trained and tested on this dataset. The PGD-net achieves a comprehensive mean average precision (mAP) value of 95.6% for the 16 defect types. Additionally, an online inspection system is developed based on the PGD-net algorithm, which can be integrated with plastic gear production lines to achieve online full inspection and automatic sorting of plastic gear defects. The entire system has been successfully applied in plastic gear production lines, conducting daily inspections of over 60,000 gears.
Open AccessIntelligent Inspection Method and System of Plastic Gear Surface Defects Based on Adaptive Sample Weighting Deep Learning Model
After injection molding, plastic gears often exhibit surface defects, including those on end faces and tooth surfaces. These defects encompass a wide range of types and possess complex characteristics, which pose challenges for inspection. Current visual inspection systems for plastic gears suffer from limitations such as single-category defect inspection and low accuracy. There is an urgent industry need for a comprehensive and accurate method and system for inspecting defects on plastic gears, with improved inspection capability and higher accuracy. This paper presents an intelligent inspection algorithm network for plastic gear defects (PGD-net), which effectively captures subtle defect features at arbitrary locations on the surface compared to other models. An adaptive sample weighting method is proposed and integrated into an improved Focal-IoU loss function to address the issue of low inspection accuracy caused by imbalanced defect dataset distributions, thus enhancing the regression accuracy for difficult defect categories. CoordConv layers are incorporated into each inspection head to improve the model’s generalization capability. Furthermore, a dataset of plastic gear surface defects comprising 16 types of defects is constructed, and our algorithm is trained and tested on this dataset. The PGD-net achieves a comprehensive mean average precision (mAP) value of 95.6% for the 16 defect types. Additionally, an online inspection system is developed based on the PGD-net algorithm, which can be integrated with plastic gear production lines to achieve online full inspection and automatic sorting of plastic gear defects. The entire system has been successfully applied in plastic gear production lines, conducting daily inspections of over 60,000 gears.
- 25 June 2024
- Published by Elsevier in Measurement
- Vol. 237
Rapid and high-precision measurement method for fine pitch gears without high-precision installation
- 25 June 2024
- Published by Elsevier in Measurement
- Vol. 237
Rapid and high-precision measurement method for fine pitch gears without high-precision installation
- 29 January 2024
- Published by Springer Nature in The International Journal of Advanced Manufacturing Technology
- Vol. 130 (11-12) , 5895-5911
Research on design and cutting performance of revolving lemniscate milling cutter
- 29 January 2024
- Published by Springer Nature in The International Journal of Advanced Manufacturing Technology
- Vol. 130 (11-12) , 5895-5911
Research on design and cutting performance of revolving lemniscate milling cutter
- Open Access
Maximum Acceptable Tilt Angle for Point Autofocus Microscopy
The complete and accurate acquisition of geometric information forms the bedrock of maintaining high-end instrument performance and monitoring product quality. It is also a prerequisite for achieving the ‘precision’ and ‘intelligence’ that the manufacturing industry aspires to achieve. Industrial microscopes, known for their high accuracy and resolution, have become invaluable tools in the precision measurement of small components. However, these industrial microscopes often struggle to demonstrate their advantages when dealing with complex shapes or large tilt angles. This paper introduces a ray-tracing model for point autofocus microscopy, and it provides the quantified relationship formula between the maximum acceptable tilt angle and the beam offset accepted in point autofocus microscopy, then analyzing the maximum acceptable tilt angle of the objects being measured. This novel approach uses the geometric features of a high-precision reference sphere to simulate the tilt angle and displacement of the surface under investigation. The research findings show that the maximum acceptable tilt angles of a point autofocus microscope vary across different measured directions. Additionally, the extent to which the maximum acceptable tilt angles are affected by the distances of the beam offset also varies. Finally, the difference between the experiment results and the theoretical results is less than 0.5°.
Open AccessMaximum Acceptable Tilt Angle for Point Autofocus Microscopy
The complete and accurate acquisition of geometric information forms the bedrock of maintaining high-end instrument performance and monitoring product quality. It is also a prerequisite for achieving the ‘precision’ and ‘intelligence’ that the manufacturing industry aspires to achieve. Industrial microscopes, known for their high accuracy and resolution, have become invaluable tools in the precision measurement of small components. However, these industrial microscopes often struggle to demonstrate their advantages when dealing with complex shapes or large tilt angles. This paper introduces a ray-tracing model for point autofocus microscopy, and it provides the quantified relationship formula between the maximum acceptable tilt angle and the beam offset accepted in point autofocus microscopy, then analyzing the maximum acceptable tilt angle of the objects being measured. This novel approach uses the geometric features of a high-precision reference sphere to simulate the tilt angle and displacement of the surface under investigation. The research findings show that the maximum acceptable tilt angles of a point autofocus microscope vary across different measured directions. Additionally, the extent to which the maximum acceptable tilt angles are affected by the distances of the beam offset also varies. Finally, the difference between the experiment results and the theoretical results is less than 0.5°.
- Open Access
- 13 November 2023
- Published by Springer Nature in Research Square
Research on Design and Cutting Performance of Revolving Lemniscate Milling Cutter
An increasing number of cutting tools with different geometric shapes are needed owing to the increasing complexity of the workpiece surfaces in aerospace and automotive molding. A new kind of milling cutter is designed, which is named as revolving lemniscate milling cutter(RLMC for short). The parametric mathematical models of RLMC are proposed. Mathematical models of cutting edge curves are proposed to provide the theoretical basis for RLMC precision manufacturing. Equivalent helix angle, curvature radius of tool rotation surface, effective cutting linear velocity and scallop height are studied. Corresponding numerical simulation results are also provided as graphical representations. Three RLMC with different tool parameters are manufactured and contrast experiments are conducted to prove that using RLMC in end milling can achieve better machining quality. The parametric design and application research provides a new method and theoretical basis for other new types of milling cutters.
- 13 November 2023
- Published by Springer Nature in Research Square
Open AccessResearch on Design and Cutting Performance of Revolving Lemniscate Milling Cutter
An increasing number of cutting tools with different geometric shapes are needed owing to the increasing complexity of the workpiece surfaces in aerospace and automotive molding. A new kind of milling cutter is designed, which is named as revolving lemniscate milling cutter(RLMC for short). The parametric mathematical models of RLMC are proposed. Mathematical models of cutting edge curves are proposed to provide the theoretical basis for RLMC precision manufacturing. Equivalent helix angle, curvature radius of tool rotation surface, effective cutting linear velocity and scallop height are studied. Corresponding numerical simulation results are also provided as graphical representations. Three RLMC with different tool parameters are manufactured and contrast experiments are conducted to prove that using RLMC in end milling can achieve better machining quality. The parametric design and application research provides a new method and theoretical basis for other new types of milling cutters.
- 12 July 2023
- Published by IOP Publishing in Measurement Science and Technology
- Vol. 34 (10) , 105009
A speed loop control method of a laser tracing measurement control system
In a laser tracking control system, a motor drives the load to achieve continuous forward and reverse rotation speed control, and the magnitude of the load changes periodically during the motor rotation to realize tracking. Based on these characteristics, we propose an integral-separated improved variable universe fuzzy proportional-integral (PI) control method with torque feedforward compensation method in this study. The proposed method achieves the control performances of fast response, high steady-state accuracy, and strong anti-interference. The conventional fuzzy PI control method achieves good performance only in the unidirectional acceleration of a motor; therefore, we have improved its fuzzy rules, and designed a novel universe contraction–expansion factor. Additionally, a load torque observer is introduced to observe and compensate for the external load and to further improve the anti-interference performance of the tracking control system. The experimental results demonstrate that the integral-separated improved variable-universe fuzzy PI control method achieves better performance in the forward and reverse speed regulation processes of the motor. The overshoot is 92% less than that of the conventional PI control when the target speed is set to ±500 rpm. The Luenberger observer is introduced to observe and compensate for the load torque. After the stabilizing the speed and applying an external load of 0.2 N m to the motor, the maximum speed reduction is observed to be 59% less than that obtained using the conventional PI control. The improved PI control method satisfies the speed loop control requirements of the laser tracking control system and can improve the steady-state tracking accuracy and robustness of the system.
- 12 July 2023
- Published by IOP Publishing in Measurement Science and Technology
- Vol. 34 (10) , 105009
A speed loop control method of a laser tracing measurement control system
In a laser tracking control system, a motor drives the load to achieve continuous forward and reverse rotation speed control, and the magnitude of the load changes periodically during the motor rotation to realize tracking. Based on these characteristics, we propose an integral-separated improved variable universe fuzzy proportional-integral (PI) control method with torque feedforward compensation method in this study. The proposed method achieves the control performances of fast response, high steady-state accuracy, and strong anti-interference. The conventional fuzzy PI control method achieves good performance only in the unidirectional acceleration of a motor; therefore, we have improved its fuzzy rules, and designed a novel universe contraction–expansion factor. Additionally, a load torque observer is introduced to observe and compensate for the external load and to further improve the anti-interference performance of the tracking control system. The experimental results demonstrate that the integral-separated improved variable-universe fuzzy PI control method achieves better performance in the forward and reverse speed regulation processes of the motor. The overshoot is 92% less than that of the conventional PI control when the target speed is set to ±500 rpm. The Luenberger observer is introduced to observe and compensate for the load torque. After the stabilizing the speed and applying an external load of 0.2 N m to the motor, the maximum speed reduction is observed to be 59% less than that obtained using the conventional PI control. The improved PI control method satisfies the speed loop control requirements of the laser tracking control system and can improve the steady-state tracking accuracy and robustness of the system.
- 18 December 2022
- Published by Wiley in Journal of Forensic Sciences
- Vol. 68 (2) , 399-406
Reporting likelihood ratio for casework in firearm evidence identification
Likelihood ratio (LR) plays an important role in estimating the weight of evidence in firearm evidence identifications. LR is computed from a statistical model including the distribution of the known-matching (KM or within) and known-nonmatching (KNM or between) comparison scores. Current LR procedures rely on KM/KNM scores from existing reference firearm toolmark data sets or alternatively from generating a set of test fires using multiple firearms. Both procedures may contain theoretical or practical issues which may hinder the LR procedures from reporting an unbiased LR estimation in casework. In this paper, a reference data set was established from a set of firearms, each test-fired two cartridge cases, resulting in a basic data set and a control data set. The congruent matching cells (CMC) method was used to generate CMC scores that are used to fit in the KM/KNM statistical distributions for LR estimation. In the initial test, 130 firearms from eight manufacturers were used for generating a reference data set consisting of 260 cartridge cases representing 130 KM and 8378 KNM pairwise breech face images. Test results showed that the KM and KNM distribution intersect at CMC = 2, which is equivalent to LR = 1 (equally to support both the prosecutor and the defense propositions). When the CMC threshold is increased to 6 or more, the LR values are higher than a million, which can provide extremely strong support to the conclusion of the same firearm (or the prosecutor's proposition) in the casework of firearm evidence identification.
- 18 December 2022
- Published by Wiley in Journal of Forensic Sciences
- Vol. 68 (2) , 399-406
Reporting likelihood ratio for casework in firearm evidence identification
Likelihood ratio (LR) plays an important role in estimating the weight of evidence in firearm evidence identifications. LR is computed from a statistical model including the distribution of the known-matching (KM or within) and known-nonmatching (KNM or between) comparison scores. Current LR procedures rely on KM/KNM scores from existing reference firearm toolmark data sets or alternatively from generating a set of test fires using multiple firearms. Both procedures may contain theoretical or practical issues which may hinder the LR procedures from reporting an unbiased LR estimation in casework. In this paper, a reference data set was established from a set of firearms, each test-fired two cartridge cases, resulting in a basic data set and a control data set. The congruent matching cells (CMC) method was used to generate CMC scores that are used to fit in the KM/KNM statistical distributions for LR estimation. In the initial test, 130 firearms from eight manufacturers were used for generating a reference data set consisting of 260 cartridge cases representing 130 KM and 8378 KNM pairwise breech face images. Test results showed that the KM and KNM distribution intersect at CMC = 2, which is equivalent to LR = 1 (equally to support both the prosecutor and the defense propositions). When the CMC threshold is increased to 6 or more, the LR values are higher than a million, which can provide extremely strong support to the conclusion of the same firearm (or the prosecutor's proposition) in the casework of firearm evidence identification.