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Study on low-cycle fatigue life of nickel-based superalloy GH4586 at various temperatures

  • Yixin Ma EMAIL logo , Bingyang Liu , Wei Wang , Ping Jin , Hui Jin and Guobiao Cai
Published/Copyright: April 15, 2025
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Nonlinear Engineering
From the journal Nonlinear Engineering Volume 14 Issue 1

Abstract

The nickel-based superalloy GH4586 has been more widely used as the main material for the preparation of aerospace turbine components. However, with the development of reusable rocket engine technology, a more profound understanding of the low-cycle fatigue performance of the material under cyclic loading is required. In this study, the same specification of GH4586 used in the turbine disk of an engine is used to prepare test specimens, the fatigue performance at different strain levels of 0.5, 0.7, 0.9 and 1% is investigated, and fatigue tests are carried out at six temperatures from room temperature to 1,173 K. The fatigue σ–N curves of the material are obtained. In this study, the cyclic hardening/softening transformation mechanism of GH4586 alloy and its influence on the life of turbine components are systematically revealed through low-cycle fatigue tests with multiple temperature points (room temperature to 1,173 K) and multiple strain amplitudes (0.5–1%). The study shows that optimizing the strain amplitude below 900 K can improve the component life by more than 20%, which provides a quantitative basis for the strain–temperature coupling design of reusable rocket engine turbine.

Keywords: low-cycle fatigue; cyclic loading test; GH4586

1 Introduction

Reducing the cost of space activities has become an important goal and direction of space development [1]. Reuse is one of the most important ways to reduce the cost of space launches, and reusable launch vehicles, which can achieve reuse and significantly reduce the cost of launching a unit payload, have become an important development direction for the current space transport systems [2].

Reusable rockets not only have much lower launch costs than traditional rockets but also have the advantages of low technical difficulty and early operational readiness compared to space vehicles, making them the preferred option for reusable vehicles; there are already some successful cases of reusable rocket development abroad [3,4]. Compared to traditional expendable rockets, which are designed for performance and reliability for a single mission, reusable rockets have higher requirements for engine performance and cyclic life [5].

Turbine is one of the most complex components in a rocket engine and the most critical component limiting the life of the engine [6,7]. As a key component affecting the performance and cyclic life of the engine, the turbine blade produces a large plastic strain under cyclic thermal, centrifugal, and aerodynamic loads resulting in crack initiation up to fracture [8,9]. Erickson et al. [10] investigated the tensile and fatigue data of superalloy at 400°C and proposed a correction to the damage parameters, which are suitable for elasticity-dominated fatigue life prediction but are not applicable to the low-cycle fatigue condition. Gulczyński et al. [11] evaluated low-cycle fatigue of the turbine blade of a reusable rocket engine based on the nickel-based superalloys at 500 K Coffin–Manson formula for life prediction. All of these studies only carried out low-cycle fatigue analyses at a certain temperature.

The study of the low-cycle fatigue behavior of nickel-based superalloys can be traced back to the systematic exploration of aero-engine materials in the 1970s [12]. Early studies focused on the cyclic response mechanism of single-crystal alloys (e.g., CMSX-4) [13], while in recent years, much attention has been paid to the relationship between strain localization and crack initiation in polycrystalline alloys (e.g., Inconel 718) [14]. However, there is still a gap in the study of the multi-temperature fatigue properties of GH4586, a high γ′-phase volume fraction (>50%) alloy [15], especially its dynamic strain aging effect at high temperatures has not been clarified.

In the process of thermal load cycling, the temperature range is generally large, but few studies have been carried out to investigate the low-cycle fatigue performance of turbine materials at multiple temperature points, which can cause inaccuracies in the process of estimating the low-cycle life of turbines. GH4586, a nickel-based superalloy, plays a vital role in the aerospace industry. Especially in rocket engines, the use of GH4586 is crucial to improve the performance and reliability of the engines. By investigating the low-cycle fatigue of GH4586 alloy at different temperatures, this study aims to provide a scientific basis for the design and material selection of reusable rocket engines.

2 Experimental setup

2.1 Experiment method

The test equipment for cyclic loading material tests is a hydraulic servo fatigue tester, as shown in Table 1 and Figure 1 (left). The temperature control system GW900 is heated by a high-temperature electric heating alloy wire with a temperature fluctuation of less than ±2°C. The system includes a temperature sensor and a feedback regulator to ensure temperature stability and consistency throughout the experiment. In order to eliminate variables other than the preset ones, all specimens for this test are prepared from the same batch of bars with the dimensions shown in Figure 1 (lower right). Specimens were 106 mm in total length, with a test section length of 46 mm, and a minimum diameter of 5 mm according to GB/T 15248-2008 [16].

Table 1

MTS hydraulic servo fatigue testing machine parameters

Instrument types 370.10
Load Maximum static load: ±50, ±100 kN, maximum dynamic load: ±50 kN
Load accuracy Static force: ±0.5%, dynamic force: ±1%
Concentricity ±5%
Testing temperature Room temperature: ∼900°C
Temperature error ≤±2°C
Testing frequency 0–50 Hz
Type of load Axial force tension-compression testing
Figure 1 Test setup and loading conditions.
Figure 1

Test setup and loading conditions.

The loading conditions during the test are all chosen to be sinusoidal, with a constant single cycle length, varying only the strain amplitude. Based on the above test setup, the subsequent test arrangement can be obtained. Given the application of GH4586 at elevated temperatures, oxidation and corrosion are two critical environmental factors that can significantly affect material performance. In order to control these factors, our experiments were conducted in a controlled protective atmosphere to minimize the effects of oxidation and corrosion on the fatigue test results.

2.2 Experimental arrangements

The test is conducted at six temperature points: room temperature (RT), 600, 700, 900, 1,100, and 1,173 K. Strain levels of 0.5, 0.7, 0.9, and 1% have been chosen because these values cover the range of strains likely to be encountered by the GH4586 during operation of rocket motor turbine. These strain levels reflect the stress state of the material under actual service conditions, including cyclic loading during start-up, operation, and shutdown. Each temperature point is tested for low-cycle fatigue life at four strain amplitudes, and is repeated three times at a strain amplitude of 0.9% in the steady-state section of the turbine in order to eliminate the randomness in the data. The final test configuration is shown in Table 2.

Table 2

Working condition list

T(K) Variable Amplitude Average Strain ratio Strain rate Cycle number Specimen
RT, 600, 700, 900, 1,100, 1,173 Strain 0.005 0 −1 0.002 1,000 1
Strain 0.007 0 −1 0.002 800 1
Strain 0.009 0 −1 0.002 600 3
Strain 0.01 0 −1 0.002 500 1

3 Results and discussion

Due to the large number of tests involved in this study, the results of the multi-cycle stress amplitude at different temperatures and strain amplitudes will be compared in the subsequent analysis of the results; therefore, the effects of temperature and strain amplitude on the low-cycle fatigue performance of the material can be more clearly demonstrated.

3.1 Stress relaxation curve analysis

Since the experimental data for the different conditions all show stability in the stress range after 40 cycles, only the first 40 cycles are shown. First, from the change in strain amplitude at room temperature and 600 K, it can be seen from Figure 2 that the cyclic hardening of the material becomes more significant as the strain amplitude increases, while the cyclic soft hardening of the material varies at different temperatures. At 0.5% strain amplitude, the material exhibits cyclic softening at room temperature, while it remains cyclic hardening at 600 K. As the strain range increases, the cyclic hardening of the material becomes more significant, which is similar to the phenomenon found in the literature [17].

Figure 2 Stress amplitude evolution under strain amplitudes of 0.5–1% (cycles 1–40) at (a) 296 K and (b) 600 K.
Figure 2

Stress amplitude evolution under strain amplitudes of 0.5–1% (cycles 1–40) at (a) 296 K and (b) 600 K.

For the variation of stress amplitude at 700 and 900 K as shown in Figure 3, there is a similar characteristic at 600 K. As the strain amplitude increases, the cyclic hardening of the material gradually increases, and the strain amplitude increases from 0.5 to 0.9% at 900 K, and the cyclic hardening amplitude increases from 71 to 379 MPa.

Figure 3 Stress amplitude evolution under strain amplitudes of 0.5–1% (cycles 1–40) at (a) 700 K and (b) 900 K.
Figure 3

Stress amplitude evolution under strain amplitudes of 0.5–1% (cycles 1–40) at (a) 700 K and (b) 900 K.

In contrast to the previous trend of stress amplitude changes at lower temperatures, when the test temperature reaches 1,100 K, the material properties are substantially reduced, and the geometric softening is significantly enhanced, which is manifested as a cyclic softening in the cyclic loading test. In addition, although the material exhibits cyclic softening at all strain amplitudes, the degree of softening decreases with the increase in strain amplitude, as shown in Figure 4.

Figure 4 Stress amplitude evolution under strain amplitudes of 0.5–1% (cycles 1–40) at (a) 1,100 K and (b) 1,173 K.
Figure 4

Stress amplitude evolution under strain amplitudes of 0.5–1% (cycles 1–40) at (a) 1,100 K and (b) 1,173 K.

To investigate the impact of temperature on the cyclic properties of the material, we analyze the alteration in stress amplitude when subjected to the same strain amplitude, as shown in Figure 5. It can be found that as the temperature increases, the cyclic hardening characteristics of the material at the lower strain amplitude of 0.5% gradually weaken with the increase in temperature, approaching the level at 1,100 K and showing obvious cyclic softening at 1,173 K. Compared to the 0.5% strain amplitude, the cyclic softening of the material at 1,173 K is reduced at 0.7% strain amplitude.

Figure 5 Stress amplitude evolution of 600–1,173 K% (cycles 1–40) at strain amplitudes of (a) 0.5% and (b) 0.7%.
Figure 5

Stress amplitude evolution of 600–1,173 K% (cycles 1–40) at strain amplitudes of (a) 0.5% and (b) 0.7%.

3.2 Analysis of σ–ε curves and fatigue σ–N curves

Figure 6 shows the stable hysteresis curves obtained at different temperatures with a strain amplitude of 0.009, along with the repeated test results at 600 K with the same strain amplitude.

Figure 6 Stable hysteresis curves under different conditions. (a) Hysteresis curves at 0.009 strain amplitude at different temperatures. (b) Repeated test hysteresis curves with 0.009 strain amplitude at 600 K.
Figure 6

Stable hysteresis curves under different conditions. (a) Hysteresis curves at 0.009 strain amplitude at different temperatures. (b) Repeated test hysteresis curves with 0.009 strain amplitude at 600 K.

From Figure 6(a), it can be seen that the peak stress is 959 MPa at 296 K. When the temperature reaches 1,100 K, the peak stress decreases to 645 MPa, and the peak stress further decreases to 463 MPa at 1,173 K. Hence, it is evident that peak stress decreases with an increase in temperature. The hysteresis loop area increases with the intensification of the dissipated energy. As shown in Figure 6(b), there is a significant difference in the hysteresis loop area under the same strain amplitude and temperature conditions and is caused by the dispersion of the material itself.

The σ–ε curves and the fatigue σ–N curves at different temperatures are compared in Figure 7, respectively. The σ–ε curves show that the stress amplitude at equal strain amplitude decreases with increasing temperature, while the hysteresis loop area increases, indicating that the dissipated energy increases significantly.

Figure 7 (a) σ–ε curves and (b) fatigue σ–N curves at different temperatures.
Figure 7

(a) σ–ε curves and (b) fatigue σ–N curves at different temperatures.

According to the σ–N curve, the relationship between stress and life is almost linear. The position of the linear relationship decreases rapidly with the increase of temperature.

4 Conclusion

The low-cycle fatigue properties of materials at multiple temperature points and strain amplitudes can be summarized as follows:

  1. Unlike the existing studies that are limited to a certain temperature point, this study investigates the fatigue properties at different strain levels of 0.5, 0.7, 0.9, and 1%, and fatigue tests are conducted at six temperatures ranging from room temperature to 1,173 K. Fatigue σ–N curves of the material are obtained.

  2. When the temperature is in the range of 600–900 K, the cyclic hardening phenomenon of the material enhances with an increase of the strain amplitude. The amplitude of cyclic hardening increases from 71 to 379 MPa at 900 K, while the strain amplitude increases from 0.5 to 0.9%. This trend suggests that by optimizing the strain amplitude during the design process, it is possible to prolong the service life of a component while maintaining its performance.

  3. The fatigue properties of GH4586 show significant changes with increasing temperature. In the temperature range of 600–900 K, the cyclic hardening phenomenon of the material increases with increasing strain magnitude, while above 1,100 K, the geometrical softening of the material is significantly enhanced and manifests itself as cyclic softening. These findings are critical for the consideration of temperature factors when designing rocket motor components, especially those operating in high-temperature environments.

  4. As the temperature increases, the stress amplitude under the equivalent strain amplitude decreases while the hysteresis loop area increases, indicating a significant increase in the dissipated energy. The relationship between stress and life is close to linear, while the position of the linear relationship decreases significantly with increasing temperature.

  5. The results of this study provide direct guidance for GH4586 in the design of reusable rocket engine turbines. For example, below 900 K, the component life can be significantly extended by controlling the strain amplitude in the range of 0.5–0.9%, while above 1,100 K, a combination of surface-coating techniques is required to inhibit geometrical softening. Future research could explore the effect of adding rare earth elements (e.g., La, Ce) on high-temperature stability, or using gradient material design to optimize thermomechanical properties.

  6. In view of the softening phenomenon of GH4586 at high temperatures, future research could explore the adjustment of the alloy composition or surface treatment techniques to improve its stability and durability in high-temperature environments.

  1. Funding information: Authors state no funding involved.

  2. Author contributions: Yixin Ma: overall design of the study, development of the experimental protocol, data analysis, and paper writing. Bingyang Liu: experimental design and preparation of the test samples, assisted in the low-cycle fatigue test, and performed the preliminary analysis of the experimental data. Wei Wang: operation and maintenance of the experimental equipment to ensure the accuracy and safety of the experimental process and collection and processing of experimental data. Ping Jin: discussion and optimization of the experimental scheme, analysis of the experimental results, and professional technical advice. Hui Jin: statistical analysis of the experimental data, writing, and revision of the paper, and optimized the logical structure and editing. Guobiao Cai: research background and literature review, theoretical support for the study, and discussion and analysis of the experimental results. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: Authors state no conflict of interest.

  4. Data availability statement: The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Received: 2024-10-23
Revised: 2025-02-13
Accepted: 2025-02-14
Published Online: 2025-04-15

© 2025 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/nleng-2025-0093
Keywords for this article
low-cycle fatigue; cyclic loading test; GH4586
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  11. Rotor response to unbalanced load and system performance considering variable bearing profile
  12. DeepFowl: Disease prediction from chicken excreta images using deep learning
  13. Channel flow of Ellis fluid due to cilia motion
  14. A case study of fractional-order varicella virus model to nonlinear dynamics strategy for control and prevalence
  15. Multi-point estimation weldment recognition and estimation of pose with data-driven robotics design
  16. Analysis of Hall current and nonuniform heating effects on magneto-convection between vertically aligned plates under the influence of electric and magnetic fields
  17. A comparative study on residual power series method and differential transform method through the time-fractional telegraph equation
  18. Insights from the nonlinear Schrödinger–Hirota equation with chromatic dispersion: Dynamics in fiber–optic communication
  19. Mathematical analysis of Jeffrey ferrofluid on stretching surface with the Darcy–Forchheimer model
  20. Exploring the interaction between lump, stripe and double-stripe, and periodic wave solutions of the Konopelchenko–Dubrovsky–Kaup–Kupershmidt system
  21. Computational investigation of tuberculosis and HIV/AIDS co-infection in fuzzy environment
  22. Signature verification by geometry and image processing
  23. Theoretical and numerical approach for quantifying sensitivity to system parameters of nonlinear systems
  24. Chaotic behaviors, stability, and solitary wave propagations of M-fractional LWE equation in magneto-electro-elastic circular rod
  25. Dynamic analysis and optimization of syphilis spread: Simulations, integrating treatment and public health interventions
  26. Visco-thermoelastic rectangular plate under uniform loading: A study of deflection
  27. Threshold dynamics and optimal control of an epidemiological smoking model
  28. Numerical computational model for an unsteady hybrid nanofluid flow in a porous medium past an MHD rotating sheet
  29. Regression prediction model of fabric brightness based on light and shadow reconstruction of layered images
  30. Dynamics and prevention of gemini virus infection in red chili crops studied with generalized fractional operator: Analysis and modeling
  31. Qualitative analysis on existence and stability of nonlinear fractional dynamic equations on time scales
  32. Fractional-order super-twisting sliding mode active disturbance rejection control for electro-hydraulic position servo systems
  33. Analytical exploration and parametric insights into optical solitons in magneto-optic waveguides: Advances in nonlinear dynamics for applied sciences
  34. Bifurcation dynamics and optical soliton structures in the nonlinear Schrödinger–Bopp–Podolsky system
  35. Review Article
  36. Haar wavelet collocation method for existence and numerical solutions of fourth-order integro-differential equations with bounded coefficients
  37. Special Issue: Nonlinear Analysis and Design of Communication Networks for IoT Applications - Part II
  38. Silicon-based all-optical wavelength converter for on-chip optical interconnection
  39. Research on a path-tracking control system of unmanned rollers based on an optimization algorithm and real-time feedback
  40. Analysis of the sports action recognition model based on the LSTM recurrent neural network
  41. Industrial robot trajectory error compensation based on enhanced transfer convolutional neural networks
  42. Research on IoT network performance prediction model of power grid warehouse based on nonlinear GA-BP neural network
  43. Interactive recommendation of social network communication between cities based on GNN and user preferences
  44. Application of improved P-BEM in time varying channel prediction in 5G high-speed mobile communication system
  45. Construction of a BIM smart building collaborative design model combining the Internet of Things
  46. Optimizing malicious website prediction: An advanced XGBoost-based machine learning model
  47. Economic operation analysis of the power grid combining communication network and distributed optimization algorithm
  48. Sports video temporal action detection technology based on an improved MSST algorithm
  49. Internet of things data security and privacy protection based on improved federated learning
  50. Enterprise power emission reduction technology based on the LSTM–SVM model
  51. Construction of multi-style face models based on artistic image generation algorithms
  52. Research and application of interactive digital twin monitoring system for photovoltaic power station based on global perception
  53. Special Issue: Decision and Control in Nonlinear Systems - Part II
  54. Animation video frame prediction based on ConvGRU fine-grained synthesis flow
  55. Application of GGNN inference propagation model for martial art intensity evaluation
  56. Benefit evaluation of building energy-saving renovation projects based on BWM weighting method
  57. Deep neural network application in real-time economic dispatch and frequency control of microgrids
  58. Real-time force/position control of soft growing robots: A data-driven model predictive approach
  59. Mechanical product design and manufacturing system based on CNN and server optimization algorithm
  60. Application of finite element analysis in the formal analysis of ancient architectural plaque section
  61. Research on territorial spatial planning based on data mining and geographic information visualization
  62. Fault diagnosis of agricultural sprinkler irrigation machinery equipment based on machine vision
  63. Closure technology of large span steel truss arch bridge with temporarily fixed edge supports
  64. Intelligent accounting question-answering robot based on a large language model and knowledge graph
  65. Analysis of manufacturing and retailer blockchain decision based on resource recyclability
  66. Flexible manufacturing workshop mechanical processing and product scheduling algorithm based on MES
  67. Exploration of indoor environment perception and design model based on virtual reality technology
  68. Tennis automatic ball-picking robot based on image object detection and positioning technology
  69. A new CNN deep learning model for computer-intelligent color matching
  70. Design of AR-based general computer technology experiment demonstration platform
  71. Indoor environment monitoring method based on the fusion of audio recognition and video patrol features
  72. Health condition prediction method of the computer numerical control machine tool parts by ensembling digital twins and improved LSTM networks
  73. Establishment of a green degree evaluation model for wall materials based on lifecycle
  74. Quantitative evaluation of college music teaching pronunciation based on nonlinear feature extraction
  75. Multi-index nonlinear robust virtual synchronous generator control method for microgrid inverters
  76. Manufacturing engineering production line scheduling management technology integrating availability constraints and heuristic rules
  77. Analysis of digital intelligent financial audit system based on improved BiLSTM neural network
  78. Attention community discovery model applied to complex network information analysis
  79. A neural collaborative filtering recommendation algorithm based on attention mechanism and contrastive learning
  80. Rehabilitation training method for motor dysfunction based on video stream matching
  81. Research on façade design for cold-region buildings based on artificial neural networks and parametric modeling techniques
  82. Intelligent implementation of muscle strain identification algorithm in Mi health exercise induced waist muscle strain
  83. Optimization design of urban rainwater and flood drainage system based on SWMM
  84. Improved GA for construction progress and cost management in construction projects
  85. Evaluation and prediction of SVM parameters in engineering cost based on random forest hybrid optimization
  86. Museum intelligent warning system based on wireless data module
  87. Optimization design and research of mechatronics based on torque motor control algorithm
  88. Special Issue: Nonlinear Engineering’s significance in Materials Science
  89. Experimental research on the degradation of chemical industrial wastewater by combined hydrodynamic cavitation based on nonlinear dynamic model
  90. Study on low-cycle fatigue life of nickel-based superalloy GH4586 at various temperatures
  91. Some results of solutions to neutral stochastic functional operator-differential equations
  92. Ultrasonic cavitation did not occur in high-pressure CO2 liquid
  93. Research on the performance of a novel type of cemented filler material for coal mine opening and filling
  94. Testing of recycled fine aggregate concrete’s mechanical properties using recycled fine aggregate concrete and research on technology for highway construction
  95. A modified fuzzy TOPSIS approach for the condition assessment of existing bridges
  96. Nonlinear structural and vibration analysis of straddle monorail pantograph under random excitations
  97. Achieving high efficiency and stability in blue OLEDs: Role of wide-gap hosts and emitter interactions
  98. Construction of teaching quality evaluation model of online dance teaching course based on improved PSO-BPNN
  99. Enhanced electrical conductivity and electromagnetic shielding properties of multi-component polymer/graphite nanocomposites prepared by solid-state shear milling
  100. Optimization of thermal characteristics of buried composite phase-change energy storage walls based on nonlinear engineering methods
  101. A higher-performance big data-based movie recommendation system
  102. Nonlinear impact of minimum wage on labor employment in China
  103. Nonlinear comprehensive evaluation method based on information entropy and discrimination optimization
  104. Application of numerical calculation methods in stability analysis of pile foundation under complex foundation conditions
  105. Research on the contribution of shale gas development and utilization in Sichuan Province to carbon peak based on the PSA process
  106. Characteristics of tight oil reservoirs and their impact on seepage flow from a nonlinear engineering perspective
  107. Nonlinear deformation decomposition and mode identification of plane structures via orthogonal theory
  108. Numerical simulation of damage mechanism in rock with cracks impacted by self-excited pulsed jet based on SPH-FEM coupling method: The perspective of nonlinear engineering and materials science
  109. Cross-scale modeling and collaborative optimization of ethanol-catalyzed coupling to produce C4 olefins: Nonlinear modeling and collaborative optimization strategies
  110. Unequal width T-node stress concentration factor analysis of stiffened rectangular steel pipe concrete
  111. Special Issue: Advances in Nonlinear Dynamics and Control
  112. Development of a cognitive blood glucose–insulin control strategy design for a nonlinear diabetic patient model
  113. Big data-based optimized model of building design in the context of rural revitalization
  114. Multi-UAV assisted air-to-ground data collection for ground sensors with unknown positions
  115. Design of urban and rural elderly care public areas integrating person-environment fit theory
  116. Application of lossless signal transmission technology in piano timbre recognition
  117. Application of improved GA in optimizing rural tourism routes
  118. Architectural animation generation system based on AL-GAN algorithm
  119. Advanced sentiment analysis in online shopping: Implementing LSTM models analyzing E-commerce user sentiments
  120. Intelligent recommendation algorithm for piano tracks based on the CNN model
  121. Visualization of large-scale user association feature data based on a nonlinear dimensionality reduction method
  122. Low-carbon economic optimization of microgrid clusters based on an energy interaction operation strategy
  123. Optimization effect of video data extraction and search based on Faster-RCNN hybrid model on intelligent information systems
  124. Construction of image segmentation system combining TC and swarm intelligence algorithm
  125. Particle swarm optimization and fuzzy C-means clustering algorithm for the adhesive layer defect detection
  126. Optimization of student learning status by instructional intervention decision-making techniques incorporating reinforcement learning
  127. Fuzzy model-based stabilization control and state estimation of nonlinear systems
  128. Optimization of distribution network scheduling based on BA and photovoltaic uncertainty
  129. Tai Chi movement segmentation and recognition on the grounds of multi-sensor data fusion and the DBSCAN algorithm
  130. Special Issue: Dynamic Engineering and Control Methods for the Nonlinear Systems - Part III
  131. Generalized numerical RKM method for solving sixth-order fractional partial differential equations
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