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In this paper, a distributed formation tracking protocol is proposed for multi-robot systems with switching directed topologies based on the Udwadia-Kalaba approach. The basic idea is to use the consensus-based scheme to reconstruct formation tracking control requirement into a second-order constraint first, and then apply the Udwadia-Kalaba approach to obtain the constraint force required to achieve the formation tracking, and afterward derive the explicit equations of motion for the constrained multi-robot systems for the control algorithm design. The convergence analysis of the tracking error system is conducted to affirm that the proposed control algorithm can achieve the formation tracking when the switching directed topologies have a directed spanning tree across each switching time interval. Numerical simulations are performed to validate the effectiveness of the proposed algorithm. • The proposed strategy reconstructs the formation tracking requirement as a constrained motion problem. • The constraint forces for the kinematic performance constraints are formulated in an explicit form. • The proposed strategy is based on switching directed topologies and only needs to set two control parameters. [ABSTRACT FROM AUTHOR]

Recently, the emerging graph convolutional network (GCN) has been applied into fault diagnosis with the aim of providing additional fault features through topological information. However, there are some limitations with these methods. First, the interactions between multi-frequency scales are ignored in existing studies, while they mainly focus on constructing graphs through the relationship between channels/instances. Second, the constructed graph cannot well reflect the topology of noisy samples and lacks robust hierarchical representation learning capability, and the learned graphs have limited interpretability. Hence, a Multi-Scale GCN with Contrastive-learning enhanced Self-attention Pooling (MSGCN-CSP) method is proposed for intelligent fault diagnosis of gearbox. Time–frequency distributions are converted into multi-scale graphs to extract fault features through topological relationships between multi-frequencies. Contrastive-learning is used to implement graph pooling, which enables hierarchical representation learning. Experimental results on two gearbox datasets illustrate that the proposed method offers competitive diagnostic performance and provides good interpretability in establishing GCN. [Display omitted] • A graph modeling strategy is proposed for perceiving multi-scale frequency information. • The contrastive-learning enhanced pooling is proposed for robust hierarchical representation learning. • Physical mechanism of the method is analyzed to demonstrate its interpretability. • Comparative studies show the superiority of the method in terms of accuracy. [ABSTRACT FROM AUTHOR]

Based on a self-tuning adaptive control gain technique, this paper proposes a novel adaptive controller to implement the region-based flocking control for the networked robotic systems with communication delays. It is shown that under the proposed control strategy, all the robots can always reach into the objective region, realize velocity matching and ensure collision avoidance, if the network topology graph is connected under certain initial position conditions. Some simulation results are provided to illustrate the effectiveness and robustness of the proposed novel controller. [ABSTRACT FROM AUTHOR]

• Use Ratio-Dependent State Impulse-Control to control a predator–prey system with square root functional response. • The controlled system exists a unique k-periodic solution by using the Brouwer's fixed point theorem. • There exist orbitally asymptotically stable order-1 and order-2 periodic solutions. This paper studies the global dynamic behavior of a prey–predator model with square root functional response under ratio-dependent state impulsive control strategy. It is shown that the boundary equilibrium point of the controlled system is globally asymptotically stable. An order-k periodic orbit is obtained by employing the Brouwer's fixed point theorem. Furthermore, the critical values are determined for the existence of orbitally asymptotically stable order-1 and order-2 periodic orbits in finite time. These critical values play an important role in determining different kinds of order-k periodic orbits and can also be used for designing the control parameters to obtain the desirable dynamic behavior of the controlled prey–predator system. Moreover, it is found that the local equilibrium point is also globally asymptotically stable under the control strategy. Numerical examples are provided to validate the effectiveness and feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

• Stability and bifurcation of near-grazing period-one impact motion are studied. • High order discontinuity mapping is applied for near-grazing dynamics analysis. • Period-one impact motion can regain its stability via Neimark-Sacker bifurcation. • Neimark-Sacker bifurcation can be induced by two different ways. Impact oscillators frequently appear in various physical and engineering systems with non-smooth characteristics and can exhibit different dynamic behavior from the smooth nonlinear systems, including grazing bifurcation in which an impact with zero velocity occurs. This paper investigates the near-grazing dynamics of the multi-degree-of-freedom impact oscillators in the small neighborhood of degenerate grazing points, with a focus on the stability and potential bifurcations of near-grazing period-one impact motions. The high order zero time discontinuity mapping method is applied to perform the prospective analyses of stability and bifurcations. Particularly, this paper shows that the peculiar Neimark-Sacker bifurcations regaining the stability of near-grazing period-one impact motion can be induced by two different ways, either through the interaction between the singular and regular real eigenvalues or via a grazing bifurcation directly. A two degree-of-freedom impact oscillator is taken as an example to present detailed numerical results for the verification of proposed analysis. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Abstract This study is concerned with the region reaching formation control problem with collision and obstacle avoidance for multi-robot systems in the presence of model uncertainties and external disturbances. A novel neural network based robust control scheme combining with the adaptive compensator and the adaptive control gain is proposed to achieve the region reaching formation control with collision and obstacle avoidance. It is shown that under the proposed control method, all the robots can always reach into the objective region, maintain their formation, and guarantee collision and obstacle avoidance. Illustrative examples are presented to show the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the stability and bifurcations of periodic solutions in three-degree-of-freedom vibro-impact systems based on the explicit critical criteria and the discontinuous mapping method. Firstly, a six-dimensional Poincaré map is established by taking the impact surface as the Poincaré section. The explicit criteria including eigenvalue assignment and transversality condition are applied to determine the bifurcation point of co-dimension one pitchfork bifurcation. The stability and direction of the bifurcation solution are then studied by using center manifold reduction theory and normal form approach. Secondly, the bifurcation points of co-dimension-two Hopf–Hopf interaction bifurcation and pitchfork–Neimark–Sacker bifurcation are determined by applying the explicit critical criteria, and the local dynamic behaviors are examined in the neighborhood of these co-dimension-two bifurcation points. Finally, a six-dimensional Poincaré map formed by choosing the constant phase angle as the Poincaré section is used to investigate the existence and stability of grazing bifurcation based on the piecewise compound normal form map. The causes of the discontinuous jump and the coexistence of attractors near the grazing periodic motion are explained for the three-degree-of-freedom vibro-impact system with a moving constraint. Highlights • The complex smooth bifurcations of high dimensional vibro-impact systems are studied. • The existence and stability of grazing bifurcation of vibro-impact system are studied. • The discontinuous jumping phenomenon and co-existing multiple solutions are revealed. [ABSTRACT FROM AUTHOR]

Highlights • Aerodynamic and hydraulic excitations as well as dynamic interactions are applied on offshore floating wind turbines. • Three sea conditions, two normal and one extreme weather conditions, are considered. • The effect aerodynamic and hydraulic excitations on dynamic behaviour is studied. • Effect of the interaction between the drive-train system and support system is discussed. • Misalignment of the sea current and wind-wave direction is examined. Abstract This paper studies the dynamic response of a spar-type direct-drive wind turbine subjected to external and internal excitations. A free-free end model is developed for the wind turbine structure with a spar-type floating platform under deep sea condition. Firstly, the spar supported platform with tower structure is modelled as a rigid body while the nacelle is considered as a point mass attached on the top of the tower. Then the dynamic interaction between the drive-train system and the tower is considered by incorporating the modelling of a direct-drive drive-train system. The hydrodynamic and aerodynamic excitations applied include current, wave, and wind excitations as well as buoyant forces. The misalignments of the wind, wave and current are also considered to examine the induced response. With the help of the time history and FFT spectrum, the effects of both hydrodynamic and aerodynamic excitations along with the dynamic interaction between the drive-train system and tower structure on the dynamic behaviour of the spar-type floating platform are investigated under different sea conditions. [ABSTRACT FROM AUTHOR]

This paper studies the global dynamics of a discontinuous delayed model of malicious signal transmission in wireless sensor networks under the framework of differential inclusion. The local stability of two types of steady states are investigated for the discontinuous system by studying the corresponding characteristic equation. The sufficient conditions for the existence of two types of globally asymptotically stable steady states are obtained for the discontinuous system by using the comparison arguments method. Furthermore, the optimal control of the discontinuous system is investigated by using Pontryagin's maximum principle. Numerical simulations of two examples are carried out to illustrate the main theoretical results. The obtained results can help us to better control and predict the spread of malicious signal transmission in wireless sensor networks. [ABSTRACT FROM AUTHOR]

In this work, we investigate the global dynamics of a controlled discontinuous diffusive SIR epidemic system under Neumann boundary conditions. We first establish the conditions for the existence of the solution and obtain the boundedness of the solution for the controlled discontinuous diffusive system. Then, under the framework of differential inclusion, we study the existence of constant equilibria of the controlled diffusive epidemic system. Furthermore, we discuss the global dynamical behaviour of the controlled discontinuous diffusive epidemic system. [ABSTRACT FROM AUTHOR]

• Types and causes of fatigue failure in main bearings of Tunnel Boring Machines (TBMs) are reviewed. • It is described based on the authors' practical experiences during inspecting and maintenance of over 100 sets of TBM main bearings made by various manufacturers. • The properties of different structural designs of the main bearing and their effect on the fatigue life of the main bearing are presented. A large-scale tunnel boring machine (TBM) is currently the most advanced equipment for underground tunnel excavation. The main bearing, carrying all the load and moment from the cutterhead, is hailed as the heart of TBMs, which connects the cutterhead and main drive system. Due to the harsh underground working conditions, the main bearing is prone to fatigue failures, which decreases its service life and could lead to extremely high replacement cost. To enhance the service life, different types of main bearings are used in TBMs depending on the geological structures. To develop a reasonable asset management and maintenance solution, it is crucial to understand the types of fatigue failures of the main bearings. This paper reviews the types and causes of fatigue failures in TBM main bearings based on practical experiences during the inspection and maintenance of over 100 sets of TBM main bearings made by different manufacturers. Fatigue failures in the TBM main bearings, including fatigue wear of components, etching cracks, peelings, rustiness, crushing damages, and bolt fractures, are mainly caused by overload, poor lubrication, foreign objects entering the main bearing interior, and non-standard operation and maintenance. The properties of different structural designs and their effects on the fatigue life of the main bearings are also presented. Furthermore, the selection of main bearings under different working conditions is discussed in order to reduce the occurrence of bearing failures. Finally, future research directions for TBM main bearings are elaborated. [ABSTRACT FROM AUTHOR]

• Comparative analysis on a three-disk dynamo system with and without time delay are performed. • Regarding the local Hopf bifurcation, three different unfolding structures of delay-induced double Hopf bifurcations are presented. • For the global transitions and phenomena, the coexistence of periodic or quasi-periodic attractors and chaotic motion are observed. The disk dynamo plays an important role in studying the geodynamo and much research works have been devoted to the understanding of dynamo dynamics. This paper further investigates an extended disk dynamo system having three coupled conducting disks and incorporates the interaction-induced time delay in the dynamic governing equations. By carrying out a comparative analysis, the dynamic behaviors of the coupled three-disk dynamo system with and without time delay are studied to explore novel and complex nonlinear dynamic phenomena in the coupled delayed dynamo system. It is found that the double Hopf bifurcations can be induced in the time-delayed dynamo system. Three different topological structures of the unfolding are obtained under different time delays. Accordingly, it is shown that the novel dynamic behaviors, including quasi-periodic torus, three-dimensional torus and the coexistence of multiple attractors, can appear in the time-delayed dynamo system. Furthermore, by performing the continuation analysis on the periodic orbit generated from the Hopf bifurcation of equilibrium, some new coexistence patterns, e.g., the coexistence of periodic orbits and chaos, the coexistence of quasi-periodic orbits and chaos, are observed in the dynamo system with time delay. Based on the obtained results, it is believed that the inclusion of time delay in the modelling of the three-disk dynamo system is necessary and meaningful for developing an in-depth understanding of dynamo dynamics. Finally, the results of theoretical analyses are verified by the numerical simulations. [ABSTRACT FROM AUTHOR]

• An innovative QZS isolation system with three pairs of linear oblique springs. • Small coefficient of the 3rd order nonlinear term of the Taylor series of the stiffness. • A wider QZS range with an almost horizontal line around the equilibrium position. • lower resonance frequency and transmissibility than the system with one pair of oblique springs. • Theoretical analysis with experimental validation for the proposed QZS system. This paper presents an innovative design of the quasi-zero stiffness (QZS) isolator with three pairs of oblique springs. Formulations of stiffness are firstly derived and parameter study is then conducted to obtain an optimal design of the proposed isolator. The proposed isolator initially has five independent parameters. By imposing stiffness and its second order derivative to be zero at the static equilibrium position, there exist three independent parameters that can be optimised to design this type of QZS isolator. A distinctive feature of the proposed isolator is that there exists a nearly horizontal straight line near the equilibrium position in the stiffness curve as the nonlinear coefficient of the Taylor expansion up to the third order of the elastic force or the Duffing differential equation is very small; thus a wider QZS region with lower transmissibility can be achieved in the present isolator. Static and dynamic analyses are presented with focusing on dynamic response in terms of displacement transmissibility. A prototype is fabricated and tested to evaluate the proposed design. The experimental results validate the present formulations in static and dynamic analyses and show lower transmissibility as compared to the corresponding QZS isolator with one pair of oblique springs and the linear isolator. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Sandwich panels with cellular cores are increasingly used in engineering due to their superb dynamic performance. In this type of structure, core design significantly affects its mechanical property. This article is to study optimal design of a multi-cellular core to minimize dynamic response of the sandwich panel under harmonic excitation by use of topology optimization. In this study, structural dynamic responses to harmonic excitation are discussed and formulations of the dynamic response in terms of strain and kinetic energy densities are derived. Topology optimization with multi-fractional volume constraint is conducted for multi-cellular core design to minimize the dynamic response of the sandwich panel under harmonic excitation. The optimization to minimize or maximize the dynamic responses are discussed in optimal core designs of sandwich panels. A multi-objective optimisation problem is also considered to optimally suppress harmonic vibrations with a range of several frequencies. Numerical examples are presented to validate the derived formulations and to optimally design multi-cellular cores for sandwich panels to achieve better dynamic performance. [ABSTRACT FROM AUTHOR]

Inherent time delays are often neglected in the modeling and dynamic analysis of centrifugal governor systems for the sake of simplicity, yet they can have a significant effect on the dynamic behavior of the governor systems. This paper investigates the effect of time-delay on the dynamics of a hexagonal centrifugal governor system through a comparative study on the stability and bifurcation of the equilibrium for the system with and without delay considered. It is found that the presence of time-delay can decrease the stability region of the equilibrium and generate many fine structures on the stability boundaries. New dynamic phenomena can be induced by the time-delay, including the 1:4 resonant and non-resonant double Hopf bifurcations. In addition, generic Hopf and Bautin bifurcations can be observed in the system for both the non-delay and delay cases. The unfolding of bifurcations which exhibits all possible behavior at the points of such complicated bifurcations is given by studying the normal form of the response amplitude obtained using the method of multiple scales. Numerical simulations are performed to validate the proposed theoretical analyses. • The time delay effect is introduced in the modeling of the governor system. • Comparative studies on the dynamics with and without time delay are analyzed. • The unfolding of co-dimension -two and -three Hopf bifurcations are performed. [ABSTRACT FROM AUTHOR]

• A novel auto-denoising network-based method is proposed to denoise the signal. • A novel framework fusing multi-source information is developed for fault diagnosis. • Probabilistic committee machine is adopted to fuse features with different weights. • Measured data from an industrial plant are used to verify the proposed method. In order to denoise the raw signal and fuse multiple sources of information for the fault diagnosis of reciprocating compressor, this paper proposes a novel convolutional deep belief network-based method and employs a novel framework fusing multi-source information to improve the performance of fault diagnosis. Firstly, signals from different sensors of the RC are input into an auto-denoising network, namely, ensemble empirical model decomposition-convolutional deep belief network, to denoise the signal and to extract more robust features by the unsupervised learning. Secondly, the extracted features of each source are input into multiple Gaussian process classifiers which are adopted as the members of probabilistic committee machine (PCM) to calculate the probabilities that each fault occurs. Finally, these probabilities are combined with an optimized weight to make a committee decision on fault type. The proposed method combines the information from multiple sources and enhances the robustness of fault diagnosis. Data from an industrial plant were collected to verify the proposed method. The obtained results demonstrate that the proposed method can effectively diagnose the RC faults with the accuracy rate of up to 91.89%. Furthermore, a comparison of the proposed method with the other methods illustrates the superiority of the proposed method for the diagnosis of RC faults. [ABSTRACT FROM AUTHOR]

The double-row tapered roller bearing (TRB) widely used to support the main shaft in a modern gearless wind turbine is one of the main components and its faults can lead to the malfunctions and downtime of wind turbines. Over the past decades, some numerical approaches have been proposed for calculating the contact force and pressure distribution of double-row TRBs. Nevertheless, most of the existing studies did not take the angular misalignment between inner and outer rings and the frictional force between the rollers and raceways into account. This paper presents a comprehensive quasi-static model to investigate the internal load and contact pressure distribution in a double-row TRB by considering the angular misalignment, the combined external loads and frictional force. It is found that a small misalignment angle between inner and outer rings can result in a significant change in the magnitude and distribution of the contact force and pressure. The double-row TRB with crowned roller profile exhibits a substantial improvement in contact pressure distribution by eliminating the occurrence of pressure concentration. Moreover, the peak contact pressure can be significantly reduced on the roller with the crowned profile, even if in the case of misaligned bearing. Comparisons of the simulated contact loads and pressure distributions demonstrate the necessity of considering angular misalignment and frictional force in the modelling of large size and heavily loaded double-row TRB. • A comprehensive quasi-static model is proposed for calculating internal load and contact pressure distributions in tapered double-inner ring bearing. • The model considers the effects of friction force and angular misalignment on the contact pressure distribution. • The effects of angular misalignment, combined external loads and friction force are investigated. [ABSTRACT FROM AUTHOR]

Streaming usually happens in systems with asymmetric nonlinearity. It is a dynamic phenomenon that the midpoint of the motion shifts away from the equilibrium point of the system. It is also an ultra-low-frequency process so that its observation often distorts because of signal acquisition limitations. Extensive studies have shown that the precision of parameter identification will drop greatly if this distortion is not accurately corrected. Motivated by the intention of enhancing the parameter identification's precision via signal correction, the present paper proposes a novel approach called the orthonormal Legendre polynomial based denoising identification method (OLP-DIM). In this method, the distorted response is decomposed by the orthonormal Legendre polynomials. The polynomial coefficients corresponding to the distortion are treated as uncertain parameters and then jointly identified with the system parameters. Numerical and experimental examples with different responses show that the OLP-DIM returns parameters in excellent precision and, distinct from traditional parameter identification methods, accurately recovers the system's streaming. • The polynomials' orthonormality promises targeted distortion correction. • The process of distortion correction is embedded in parameter identification. • The accuracy of parameter identification is significantly enhanced. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the multi-objective region reaching control for a swarm of robots which are formulated by Lagrangian dynamics. Two distributed multi-objective region reaching control protocols are proposed for the networked robotic systems under directed acyclic topology, and a unifying methodology is presented to perform the convergence analysis for the robotic systems with static and moving target regions. The control strategy is developed by using the potential energy function approach, and the specified shapes of the various desired regions are constructed by selecting appropriate objective functions. In this control strategy, a network of a large number of robots evolves into multiple groups, and the robots in each group only require communicating with their neighbors. Thus, the proposed control strategy is effective for multi-objective region reaching control for a swarm of robots in practical applications. Finally, simulation examples are given to show the validity of the theoretical results., [ABSTRACT FROM AUTHOR]

Following the previous work on the degenerate grazing bifurcations of impact oscillators, this paper aims to explore novel two-parameter dynamics near the degenerate grazing points using GPU parallel computing technology. By using the technology, a further understanding of the near-grazing dynamics can be developed for impact oscillators. Three main indicators, i.e., the largest Lyapunov exponent, number of excitation periods and number of impacts, are calculated for each grid of the two-parameter plane chosen. Based on these indicators, the dynamic response in the vicinity of degenerate grazing points can be characterized and more dynamic behaviors than the published results can be discovered. Phenomena of coexisting attractors and chaotic transitions including crisis are also discussed. The single and two degree-of-freedom impact oscillators are selected as illustrative examples to demonstrate the results. • Two-parameter dynamics near the degenerate grazing points are investigated. • GPU parallel computing is applied for the unfolding of degenerate grazing. • Coexisting attractors and chaotic transitions including crisis are analyzed. [ABSTRACT FROM AUTHOR]

• Proposed anisotropic conductive network for cement-based sensors. • Experimentally tested sensors with five magneto-aligned nickel particles. • Revealed the influence of particle shape and concentration on sensor performances. • Achieved high piezorestivity with low filler content of nano-scale nickel powder. Cement-based sensors with magneto-aligned nickel fillers have the proven capability to significantly enhance piezoresistivity compared with the sensors with randomized fillers. In this paper, the influence of particle morphology and concentration of nickel particles on the piezoresistive and mechanical properties of cement-based sensors, treated with and without magnetic field intervention, are investigated experimentally. Five categories of nickel particles with different average diameters are type N50 (50 nm), N500 (0.5 μm), F(1 μm × 20 μm flake), T (5 μm) and U (25 μm). The obtained results indicate that the application of magnetic field enhances most of the piezoresistive performance and yields best piezoresistivity for the samples with type T nickel powder. Anisotropic piezoresistivity can be achieved under a very low filler content (0.1 vol%) in N50 nano-scale nickel powder and cement composite, followed by the N500 and T nickel particles in 5 vol% content. Small particles with lower content have similar piezoresistive performance to the samples with large particles and higher concentration. One half of the samples can achieve high giant gauge factor (GF) of over 500, two-thirds of which are aligned by magnetic field with anisotropic piezoresistive property. Samples with 5 vol% type T nickel content has the highest GF value, followed by the sample with 5 vol% type F nickel flakes and 10 vol% type U nickel powder. It is also found that mechanical strength decreases with the increase of particle concentration. [ABSTRACT FROM AUTHOR]