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Nonlinearity can take an important and critical role in engineering systems, and thus cannot be simply ignored in structural design, dynamic response analysis, and parameter selection. A key issue is how to analyze and design potential nonlinearities introduced to or inherent in a system under study. This is a must-do task in many practical applications involving vibration control, energy harvesting, sensor systems, robotic technology, etc. This paper presents an up-to-date review on a cutting-edge method for nonlinearity manipulation and employment developed in recent several years, named as the X-structure/mechanism approach. The method is inspired from animal leg/limb skeletons, and can provide passive low-cost high-efficiency adjustable and beneficial nonlinear stiffness (high static & ultra-low dynamic), nonlinear damping (dependent on resonant frequency and/or relative vibration displacement), and nonlinear inertia (low static & high dynamic) individually or simultaneously. The X-structure/mechanism is a generic and basic structure/mechanism, representing a class of structures/mechanisms which can achieve beneficial geometric nonlinearity during structural deflection or mechanism motion, can be flexibly realized through commonly-used mechanical components, and have many different forms (with a basic unit taking a shape like X/K/Z/S/V, quadrilateral, diamond, polygon, etc.). Importantly, all variant structures/mechanisms may share similar geometric nonlinearities and thus exhibit similar nonlinear stiffness/damping properties in vibration. Moreover, they are generally flexible in design and easy to implement. This paper systematically reviews the research background, motivation, essential bio-inspired ideas, advantages of this novel method, the beneficial nonlinear properties in stiffness, damping, and inertia, and the potential applications, and ends with some remarks and conclusions.

A novel adaptive neural network tracking control method is systematically investigated for a unique double-pendulum tower crane system model in this article. Several critical and practical application-oriented control issues, including robustness, tracking error limitation, double-pendulum effects, and input dead zone nonlinearity, are considered simultaneously, which have never been well addressed in the existing literature. Technically, neural networks are employed to approximate the functions with uncertain/unknown dynamics and nonideal inputs. Several barrier Lyapunov functions are proposed that can circumvent the violation of tracking error limitations in the proposed control method. Importantly, based on the designed adaptive neural network tracking control method, the jib and trolley can track their desired trajectories very fast, and the hook and payload sway can be completely eliminated. The Lyapunov stability theory and Babalat's lemma are utilized to theoretically prove the convergence and stability of the proposed control system. Finally, well-designed simulation studies are carried out to verify the excellent performance and strong robustness of the control method. This article should be the first work considering a double-pendulum tower crane system with guaranteed convergence and performance without any linearization for the original nonlinear dynamic model.

This work is devoted to solving the control problem of vehicle active suspension systems (ASSs) subject to time-varying dynamic constraints. An adaptive control scheme based on nonlinear state-dependent function (NSDF) is proposed to stabilize the vertical displacement of the vehicle body. It provides a reliable guarantee of driving safety, ride comfort, and operational stability. It is commonly known that in the existing work, either the state constraints are ignored which may reduce the stability and safety of the system, or the virtual controller is subjected to some feasibility conditions affecting real system implementation. In this work, it is the first attempt to directly deal with the time-varying displacement and velocity of the vehicle constraints in ASSs without involving any specific feasibility conditions. A novel coordinate transformation based on the NSDF is introduced and integrated into each step of the backstepping design. Thus, the proposed control scheme not only adapts to the time-varying motion (time-varying vertical displacement and velocity) constraints, but also eliminates the feasibility conditions of the virtual controller without the difficulty of obtaining system parameters. Finally, the control scheme for ASSs used in this work is compared with existing control schemes in order to demonstrate its superiority and rationality.

A unique adaptive neural network control scheme is proposed for active suspension systems by employing bioinspired nonlinear dynamics, so as to address several critical engineering issues including energy efficiency, input delay, and unknown/uncertain dynamics simultaneously. A novel constructive predictor is firstly designed to solve the effect of input delay. Neural networks are then adopted to approximate the uncertain/unknown dynamics, and importantly, a unique finite-time adaptive control is established which can not only online update the input and output weights of the neural networks but also intentionally introduce beneficial nonlinear dynamics to vibration control. The significant difference from most existing controllers lies in that the designed controller can effectively utilize beneficial nonlinear stiffness and damping characteristics of a novel bioinspired reference model and, thus, purposely achieve superior vibration suppression and obvious energy-saving performance simultaneously. Theoretical analysis and experimental results vindicate that the proposed controller can effectively suppress vibration with much more improved control performance and considerably reduced control energy consumption more than 44%. This should be for the first time to reveal both in theory and experiments that a superior suspension performance is achieved simultaneously with an obvious control energy saving, by employing beneficial bioinspired nonlinear dynamics, compared to most traditional control methods.

The beam-like structures commonly exist in engineering systems and there are many critical issues relevant to fault diagnosis of those structures. Noticeably, among all other existing methods, transmissibility function-based diagnostic methods, providing much more sensitive damage indexes, are frequently applied and extensively studied, and it is thus meaningful to have a thorough review on most recent advance and related technical difficulties. This paper is, therefore, to present a comprehensive review on this topic for those engineering-oriented beam-like structures, focusing on fundamental theory, critical fault properties and potential applications, respectively. According to different transmissibility function-based features, existing methods are classified into several categories, i.e. general linear transmissibility function, general nonlinear transmissibility function, generalized frequency response function and the second-order output spectrum. With a chain-type multi-degree-of-freedom model with additional connections used for analysing dynamics of beam-like engineering structures, essential topics of these methods including types of transmissibility functions, damage indexes and procedures are discussed in detail. Moreover, the effectiveness, merits and demerits are illustrated by the numerical and experimental results, respectively. It should be noted that some methods discussed here can be readily extended and applied to diagnosis of other plate-like and rotor-like, etc., engineering structures. Apart from fault detection and localization, more sensitive transmissibility function-based damage indicators providing severity and residual life of damaged structures would be further development topics in this area.

Passive vibration isolation is always preferable in many engineering practices. To this aim, an innovative, compact, and passive vibration isolation mount is studied in this paper. The novel mount is adjustable to different payloads due to a special oblique and tunable stiffness mechanism, and of high vibration isolation performance with a wider quasi-zero-stiffness range due to the deliberate employment of negative stiffness of the X-shaped structure. The X-shaped structure has been well studied recently due to its excellent nonlinear stiffness and damping properties. In this study, by using of the negative stiffness property within the X-shaped structure, the X-shaped mount (X-mount) can have an obviously larger vibration displacement range which maintains the quasi-zero-stiffness property. A special oblique spring is thus introduced such that the overall equivalent stiffness can be much easily adjusted. Systematic parametric study is conducted to reveal the critical design parameters and their relationship with vibration isolation performance. A prototype and experimental validations are implemented to validate the theoretical results. It is believed that the X-mount would provide an innovative technical upgrade to many existing vibration isolation mounts in various engineering practices and it could also be the first prototyped mount which can offer adjustable quasi-zero stiffness conveniently.

System parameters identification of nonlinear bistable structures has attracted considerable interest because the performance enhancement of energy harvesting and vibration control is significantly dependent on the model parameter of nonlinear systems. Therefore, a two-stage subspace method is proposed to identify the critical parameters in the system equation of nonlinear bistable piezoelectric structures. The dynamic equation of nonlinear bistable piezoelectric structures is separated into an underlying linear electromechanical coupling equation and a nonlinear mechanical equation. At first, for the underlying linear electromechanical coupling equation, a force–displacement subspace is constructed to identify the linear mass, damping and stiffness. Meanwhile, a velocity–voltage subspace is created for the identification of the electromechanical coupling coefficient. Next, for the nonlinear mechanical equation, the nonlinear restoring force in bistable structures can be estimated by the extended nonlinear frequency response function. Numerical simulation on a magnetic coupled bistable piezoelectric structure is performed to investigate the influence of frequency-swept responses, the noise intensity and polynomial order on identification accuracy. Experimental measurement of a magnetic coupled asymmetric bistable piezoelectric beam is conducted under different excitation conditions. Experimental results demonstrate the effectiveness of the proposed identification method.

Online learning methods are designed to establish timely predictive models for machine learning problems. The methods for online learning of nonlinear systems are usually developed in the reproducing kernel Hilbert space (RKHS) associated with Gaussian kernel in which the kernel bandwidth is manually selected and remains steady during the entire modeling process in most cases. This setting may make the learning model rigid and inappropriate for complex data streams. Since the bandwidth appears in a nonlinear term of the kernel model, it raises substantial challenges in the development of learning methods with an adaptive bandwidth. In this article, we propose a novel approach to address this important open issue. By a carefully casted linearization scheme, the nonlinear learning problem is reasonably transformed into a state feedback control problem for a series of controllable systems. Then, by employing optimal control techniques, an effective algorithm is developed, and the parameters in the learning model including kernel bandwidth can be efficiently updated in a real-time manner. By taking advantage of the particular structure of the Gaussian kernel model, a theoretical analysis on the convergence and rationality of the proposed method is also provided. Compared with the kernel algorithms with a fixed bandwidth, our novel learning framework can not only achieve adaptive learning results with a better prediction accuracy but also show performance that is more robust with a faster convergence speed. Encouraging numerical results are provided to demonstrate the advantages of our new method.

Complex grid-like structures such as steel truss bridges and steel truss roofs commonly exist in civil engineering applications. Since these structures are usually subject to dynamic operational forces, faults like chemical corrosion, fatigue crack, and bolt loosening arise, and seriously affect structural health. To consider some issues in existing frequency domain fault evaluation methods like applicability for complex structures, requirement of baseline data, neglect of nonlinear boundaries, and localization of local faults, a novel method using nonlinear vibration features and Euclidean distance measurement is presented in this paper. Firstly, complex grid-like structures are decomposed into a series of simple T-type substructures according to structural characteristics and load paths. Secondly, related T-type multi-degree-of-freedom model is built by simulating potential faults and nonlinear boundaries as related nonlinear damper-spring connections. Thirdly, exciting the model and extracting output responses only, novel and local fault features, which are functions of structural properties, nonlinear fault-induced loads and transmissibility functions, are defined. Then, utilizing defined features from the local substructure to be evaluated only, a novel fault index is defined with Euclidean distance measurement. Finally, corresponding evaluation method is developed, and its effectiveness and applicability are demonstrated by comparative studies on a lab bolted grid-like structure.

Most mobile robots have very simple passive suspension based on conventional mass-spring-damper methods, which bring a trade-off between loading capacity and vibration isolation, or no suspension at all with only hard contact between wheels and ground. This article presents a tracked mobile robot with a unique passive suspension, which is constructed by using a bio-inspired animal-limb-like structure, to guarantee both loading capacity and vibration isolation performance. With the novel bio-inspired suspension, the loading capacity, riding comfort and obstacle negotiation capability of the robot in various rough ground environments can be significantly enhanced. However, “soft suspension” may lead to “slippery track” due to rough terrain or irregular obstacles. To solve this problem, an advanced autonomous navigation is realized. A novel double layer nonlinear model predictive control (NMPC) architecture is adopted for optimizations of trajectory tracking. The global trajectory tracking is optimized strategically in the upper layer NMPC at a low frequency, while the local dynamics such as slippage during obstacle negotiation is timely captured in the lower layer NMPC at a high frequency. Experimental results clearly demonstrate that the superior passive suspension can efficiently absorb strong shock induced by obstacle crossing and hence guarantee smooth motion, and the double layer NMPC can effectively improve transient response and tracking accuracy ideally. This article would present a benchmark result to the design and control of mobile robots working on rough grounds.

This article is concerned with the study of the negative imaginariness of interval transfer functions. Necessary and sufficient conditions for (strictly) negative imaginary interval transfer functions subject to parameter uncertainty are first derived based on Kharitonov's theorem. Then, certain properties of the interconnection system with negative imaginary interval transfer functions are analyzed. Finally, an example is provided to illustrate the main results of the article.

This paper provides an analysis of uncertain discrete-time negative imaginary and positive real systems with state-space symmetry. First, a necessary and sufficient condition is provided for a mini...

This paper studies some useful properties of lossless negative imaginary transfer matrices for both continuous-time and discrete-time systems. Necessary and sufficient conditions are established for lossless negative imaginary systems both in frequency domain and state-space realization. Meanwhile, a minor decomposition method for lossless negative imaginary systems is proposed in terms of a partial-fraction expansion. This method is important for developing non-proper lossless negative imaginary theory in this paper by allowing poles at the origin and infinity. Two new relationships between lossless positive real and lossless negative imaginary systems are consequently established. According to these new established relationships, a generalized continuous-time lossless negative imaginary lemma and a different version of discrete-time lossless negative imaginary lemma are developed in terms of a minimal state-space realization. Several examples are provided to illustrate the main results.

Bolt-loosening faults frequently exist in industrial engineering structures since these bolted structures are often subjected to vibrations or the like in their service process. In this paper, a novel method based on the second-order output spectrum (SOOS) is proposed to detect potential bolt-loosening faults in a complex satellite-like structure. In this method, a general multi-degree-of-freedom (MDOF) model simulating bolt-loosening faults induced non-linearities and inherent boundary or material non-linearities by non-linear forces is built to describe the non-linear behaviour of the structure, and then a local damage indicator is derived for bolt-loosening fault detection through a local tuning approach (LTA) which tunes local structural properties. Results of experimental cases demonstrate that the state of bolted joint in the satellite-like structure with inherent non-linearities can be estimated by this novel SOOS based method effectively and reliably.

A novel sliding mode control method, as is shown in this paper, is proposed for the 4-DOF tower crane system by employing beneficial disturbance effects to enhance the transient control performance as well as to ensure the strong robustness simultaneously. More precisely, we deliberately construct a nonlinear disturbance observer, and then, the advantages and disadvantages of the disturbance influence on the 4-DOF tower crane system are described by a constructed disturbance effect indicator (DEI) based on the observation information. Subsequently, the novel sliding model control method is designed in the light of the estimated disturbance and the introduced DEI. Additionally, the stability of the closed-loop system is demonstrated by Lyapunov techniques. It should be pointed out that the designed method points out that besides bad effects, disturbance has the desirable side-effect of transient control performance improvement, and as a result, introducing desirable side-effect into the controller design is of great importance. The effectiveness and robustness of the designed sliding model control method can be demonstrated by simulation results.

Strongly nonlinear structures have attracted a great deal of attention in energy harvesting and vibration isolation recently. However, it is challenging to accurately characterize the nonlinear restoring force using analytical modeling or cyclic loading tests in many realistic conditions due to the uncertainty of installation parameters or other constraints, including space size and dynamic disturbance. Therefore, a displacement-measurement restoring force surface identification approach is presented for obtaining the nonlinear restoring force. Widely known quasi-zero stiffness, bistable, and tristable structures are designed in a cantilever-beam system with coupled rotatable magnets to illustrate the strongly nonlinear properties in the application of energy harvesting and vibration isolation. Based on the derived physical model of the designed strongly nonlinear structures, the displacement-measurement restoring force surface identification with a least-squares parameter fitting is proposed to obtain the parameters of the nonlinear restoring force. The comparison between the acceleration integration and displacement differentiation methods for describing the restoring force surface of strongly nonlinear structures is discussed. Besides, the influence of the noise level on identification accuracy is investigated. In experimental conditions, quasi-zero stiffness, bistable, and tristable nonlinear structures with various geometrical parameters are utilized to analyze the identified nonlinear restoring force curve and measured force–displacement trajectory. Finally, experimental results verify the effectiveness of the displacement–measurement restoring force surface method to obtain the nonlinear restoring force.

In many applications, installing an absorber/tuned mass damper (TMD) is an effective method of vibration control. To overcome the drawbacks of traditional TMDs and improve the overall performance, a bio-inspired structure (X-shaped structure) is used for a tunable and nonlinear TMD (X-absorber). In this study, multi-variable optimization, tunable stiffness and damping properties, nonlinear influence and vibration suppression performance of this novel X-absorber are systematically studied. Compared with traditional absorbers this X-absorber can provide beneficial nonlinear damping which can significantly improve system parametric robustness, tunable quasi-zero stiffness for a widen vibration suppression bandwidth with a widened anti-resonance, effectively suppress resonant peaks of ultra-low frequencies, and eliminate potential instabilities (e.g., bifurcation, detached resonance curves) inherently existing in Duffing oscillators. In the experimental testing, the robustness and effectiveness of the optimized X-absorber with different excitations are validated with comparison of a traditional spring-mass absorber. The X-absorber would provide a more reliable and flexible solution to many vibration suppression applications.

Nonlinear piezoelectric structures have attracted great attention in energy harvesting, vibration control, and morphing structures recently. The most important design and dynamic analysis parameters in a nonlinear piezoelectric structure is the nonlinear stiffness force. However, the nonlinear stiffness force is difficult to calculate analytically or measure statically under complicated practical engineering conditions. Therefore, this paper utilizes signal decomposition and the Hilbert transform-based method for the precise identification of stiffness force of a class of typical nonlinear piezoelectric structures. The quasi-zero stiffness, bistable stiffness, and tristable stiffness structures are designed in the magnetic coupled piezoelectric cantilever beam system. The identification process and the applicability based on free vibration and forced frequency-swept response for different nonlinear structures will be discussed. Numerical examples of quasi-zero stiffness, bistable stiffness, and tristable stiffness nonlinear piezoelectric structures show the necessity to choose the reasonable free decay and the forced frequency-swept response for accurate identification. In the experimental condition, the identified nonlinear stiffness force keeps in good agreement with the measurement by the dynamometer.

In recent years, in order to exploit beneficial nonlinearities, an X-shaped supporting structure with helpful nonlinear stiffness and damping characteristics has been developed and deliberately introduced to improve the energy harvesting performances. In this paper, the Volterra series-based frequency domain method is utilized to achieve a systematic analysis and design of the present X-structured nonlinear system. The generalized frequency response functions (GFRFs) and the output frequency response function (OFRF) of the system are theoretically derived using the recursive algorithm. Importantly, analytical relationships between the power generation function (PGF) of the harvesting system and the structural parameters of the X-structure would be derived, to show how the power generation is affected by the structural parameters of the system. The results indicate that, the present study could provide an effective and efficient way to characterize the nonlinear effects on the proposed energy harvesting system.

Energy harvesting technologies motivated researchers and manufacturers to develop a sustainable and eco-friendly power supply to drive low-power electronics. In electrified vehicles, regenerative automobile shock absorbers are currently receiving focus to harvest a part of the dissipated suspension’s kinetic energy. Despite other energy harvesting applications in automobiles, the car’s suspension works and dissipates kinetic energy as much as the vehicle moves on the road, which can be used in continuous vibration-to-electricity energy harvesting applications. This paper provides a full characterization of an arm-toothed rotary electromagnetic regenerative damper. The arm-toothed/flywheel mechanism converts the linear shock absorber’s motion to a rotational motion during both the compression and expansion strokes. The flywheel’s inertia helps to amplify the input speed to enhance the harvested power and provide smooth operation during random non-periodic excitations. A 2-DOF quarter model equipped with the arm-toothed energy-harvesting damper was built. The arm-toothed energy-harvester model is verified through test-bench results. The car regenerative suspension model has been entirely characterized concerning both the harvester and suspension parameters during simulations. To mimic a real-car traveling on roads, the regenerative suspension model was simulated under non-periodic ISO 8606 roads with different qualities and speeds. The results indicated that traveling on a Grade-C road with speeds between 20–100 km/h, the average power and voltage RMS outputs ranged between 5–24 mW and 0.75–1.65 V, respectively.