Asymmetric Potential Function Research Articles

Particle Swarm Optimization-Based Variable Scale Asymmetric Stochastic Resonance Bearing Diagnostic Method

Abstract A diagnostic method for bearing faults, centered around the extraction and identification of diagnostic signals, is introduced. This method utilizes a Particle Swarm Optimization (PSO) algorithm to optimize a variable-scale asymmetric stochastic resonance (SR) framework. The PSO algorithm dynamically fine-tunes the parameters of the asymmetric stochastic resonance system to align more effectively with the demands of bearing fault diagnosis. An asymmetric factor-controlled potential function for the stochastic resonance system is established, using the Signal-to-Noise Ratio Improvement (A-SNRI) of the fault signal as the objective function for the optimization algorithm. The PSO algorithm is employed for global optimization to adjust the structural parameters a 0, b 0 and the asymmetric factor of the asymmetric α bistable stochastic resonance system. Simulations and experimental validations are conducted using the optimized stochastic resonance system parameters, demonstrating the robustness and effectiveness of the algorithm through the extraction of fault characteristic frequencies. Experimental results indicate the proposed bearing fault diagnostic method can stably extract fault characteristic frequencies, effectively filter out noise, and the extracted fault frequencies align with theoretical values.

A new anisotropic-asymmetric yield criterion covering wider stress states in sheet metal forming

The stress state-dependent plastic anisotropy of sheet metals has drawn significant attention. Nevertheless, existing phenomenological plasticity models limitedly capture the distinctive yield strengths and plastic flow (r-values) under a wide range of stress states covering uniaxial tension (UT), equi-biaxial tension (EBT), uniaxial compression (UC), plane strain tension (PS), and pure shear (SH). This study aims to propose a new anisotropic-asymmetric plasticity model with enhanced flexibility based on the non-associated flow rule. The yield function is formulated based on the additive coupling of two stress potentials: coupling between a new anisotropic pressure-sensitive fourth-order polynomial function, and an isotropic stress invariant-based function. Then, all the anisotropic/asymmetric parameters of the yield function can be analytically identified from 7 yield stresses measured from UT tests along 0°, 45°, and 90° to the rolling direction (RD), UC tests along 0° and 90° to the RD, EBT test, and SH test along 45° to the RD. Within the scheme of no-associated flow rule, a new asymmetric fourth-order plastic potential function is proposed to analytically describe the plastic flow of sheet metals under UT, UC, EBT and SH. The additively coupled stress invariant-based term is introduced to adjust the yield stresses and plastic flow under biaxial tension including PS, which leads to an independent description of the yield stresses and plastic strain directions under SH and PS states. Various automotive sheet metals such as advanced high-strength steels, aluminum alloy, and magnesium alloy with strong asymmetry and anisotropy are investigated to verify the proposed yield criterion. The results demonstrate remarkable flexibility and accuracy of the proposed yield criterion against other existing models. Evolving yield surface and plastic potential of a quenching and partitioning steel are accurately captured by the proposed anisotropic-asymmetric yield criterion. Besides, the advantages of new model are further discussed in terms of the proof of yield surface convexity, identified parameters, and the regulation between anisotropy and isotropy in comparison with existing multiplicative coupling method.

Dynamics of a tri-stable hybrid energy harvester under narrow-band random excitation

This paper aims to reveal the stochastic dynamics of a tri-stable piezoelectric–electromagnetic hybrid vibration energy harvester (HVEH) driven by narrow-band random excitation for purpose of enhancing the energy harvesting performance. The steady-state solutions of the electromechanical coupling tri-stable HVEH in the symmetric case are derived by the method of multiple scales, which are verified by Monte Carlo simulations. Results show that the stochastic jump phenomenon exists and the operational bandwidth of HVEH can be extended. The effects of narrow-band random excitation, critical system parameters and asymmetric potential function on stochastic dynamics are discussed. It is found that the miniaturization design of the HVEH can be optimized and the mean output power can be improved by selecting appropriate system parameters. Moreover, compared with the symmetric structure, in the case of the same highest potential-well depth, the asymmetric structure with a smaller potential-well distance is beneficial for HVEH to achieve high-energy inter-well oscillation under low-level excitation. Meanwhile, the power conversion efficiency reaches the maximum in the high-energy inter-well oscillations triggered at the critical excitation amplitude.

Asymmetric tristable energy harvester with a compressible and rotatable magnet-spring oscillating system for energy harvesting enhancement

This paper proposes an asymmetric tristable energy harvester with a compressible and rotatable magnet-spring oscillating system to enhance the energy harvesting performance. The linear compressible and rotatable magnet-spring oscillating system is composed of two external magnets, a metal block and two parallel springs. The two external magnets are symmetrically located on the metal block and fixed to the base through the two parallel springs. Due to different compression of the two springs under variable magnetic force, the two external magnets can move along the spring's compression direction and rotate around the center of the metal block, thus to generate tunable and asymmetric potential function. The general governing equations and asymmetric potential function of the proposed harvester are established with Hamilton principle and point dipole method, respectively. The effects of system parameters on the nonlinear dynamic performances of the proposed harvester are numerically investigated. Experiments are carried out to validate the simulations. The results demonstrate that moderate spring stiffness can not only reduce the potential energy barrier and the threshold of snap-through, but also broaden the bandwidth of interwell motion, as well as enhance the energy harvesting efficiency. When the spring stiffness k = 900 N/m, the threshold value of snap-through of the TEH-A is 8 m/s2, the bandwidth of inter-well motion is 2.0∼4.5 Hz, and the maximum harvesting voltage and power reach 6.8 V and 4.6 × 10−5 W, respectively. These values are far better than the tristable energy harvester with symmetric potential wells, whose corresponding values are 3.8∼4.2 Hz, 9.8 m/s2, 0.81 V and 6.6 × 10−7 W, respectively.

A new approach to dominant motion pattern recognition at the macroscopic crowd level

Automatic analysis and the recognition and prediction of the behaviour of large-scale crowds in video-surveillance data is a research field of paramount importance for the security of modern societies. It serves to predict and help prevent disasters in public places where crowds of people gather. The paper proposes a novel method for generating meta-tracklets and recognition of dominant motion patterns as a basis for automatic crowd behaviour analysis at the macroscopic level, where a crowd is treated as an entity. The basic characteristic of macroscopic crowd scenes is that it is impossible to detect and track individuals in the scene. The idea of the method proposed in this paper is to recognize dominant crowd motion patterns, by avoiding time-consuming and error-sensitive crowd segmentation, crowd tracking and detection of regions of interest. Thus, the process of determining dominant motion patterns and recognizing crowd behaviour is accelerated. The method is inspired by a quantum mechanical approach. It combines a set of particles, which are considered as particles in quantum mechanics, tracklets of particles’ advection in a video clip, and the interaction of wave functions spread out from particle positions. A wave function is expressed in the form of an asymmetric potential function. Peaks of the wave field define the most probable particle flow, which defines a meta-tracklet. Dominant motion patterns are recognized by applying the functions of fuzzy predicates, which represent a combination of common-sense and human expert knowledge about crowd motions, to the meta-tracklets. The experimental results of the proposed method are presented for a subset of UCF dataset and AGORASET crowd simulation videos and have shown promising results in dominant motion pattern recognition.

Stochastic Resonance of Asymmetric Joint Potential System and Its Application in Weak Signal Detection

In order to improve the weak signal processing capability of stochastic resonance (SR), a new asymmetric SR system with nonlinear jointed potential function is proposed in this paper. Firstly, the new joint potential stochastic resonance (JPSR) system is built by combined gaussian potential function and asymmetric bistable potential function. Secondly, the analytical expression of signal-to-noise ratio (SNR) is derived based on two-state theory and adiabatic approximation theory. Meanwhile, the influence of system parameters on SNR is discussed theoretically. Thirdly, by particle swarm optimization algorithm, the JPSR system is applied to detect actual bearing fault signals. Finally, according to numerial simulation, the results show that the proposed system can detect weak signal characteristics more effectively.

Stochastic resonance of an asymmetric tristable system driven by cross-correlated Ornstein–Uhlenbeck noise

Stochastic resonance of an asymmetric tristable system driven by a periodic forcing and cross-correlated Ornstein–Uhlenbeck (O–U) noise is investigated. An approximate Fokker-Planck Equation for an asymmetric tristable system driven by a periodic forcing and cross-correlated O–U noise is derived in the adiabatic limit by using the unified colored-noise approximation method and the stochastic equivalent rules. Afterwards, the expression for spectral amplification (SA), the stationary probability density function (PDF) and the mean first passage time (MFPT) are derived. By considering the influence of asymmetric potential function and cross-correlated noise, the phenomenon of noise enhancing stability (NES) and stochastic resonance (SR) can be found. It can also be found that the response of the tristable system can be effectively improved by properly selecting the relevant noise intensity and the asymmetric constant. This proves the excellent performance of the system, and provides a good theoretical support for practical engineering application.

Analytical description of an asymmetric yield function (Yoon2014) by considering anisotropic hardening under non-associated flow rule

A simple analytical form for yield surface distortion under non-associated flow rule is developed from the expression of the transformed second and third deviatoric stress invariants in Yoon et al. (2014). The developed analytical yield criterion has the same ability as the original yield criterion to describe material's strength differential (SD) effect. Compared with Yoon et al. (2014) criterion, the material parameters in the analytical form presented in this study can be directly calculated from the tension and compression stresses along 0°, 45°, 90° and equi-biaxial directions, which doesn't need any optimization process and interpolation to describe the evolution of asymmetric yield surface under the proportional loadings. The proposed yield criterion can accurately predict the anisotropic hardening along 0°, 45°, 90° and equi-biaxial directions under tension and compression, which will make the significant improvements in the stress predictions including 15°, 30°, 60° and 75°. To guarantee the convexity of yield surface during loading history, the minimum order of principal minor determinant is checked. The proposed yield criterion has been successfully applied for HCP materials to validate its general applicability for describing anisotropy/asymmetry-induced distorted yield surface during deformation. In addition, an analytical asymmetric plastic potential function is developed based on Poly4 yield function. The accuracy of the proposed plastic potential function for r-value evolution under tension and compression has been verified by applying it to different materials.

A modified Landau phenomenological constitutive model for the tension–compression asymmetry in one-dimensional Shape Memory Alloys

Shape Memory Alloys (SMA) have unique properties because of their unique ability to reversibly transform when subjected to appropriate thermal and/or mechanical loads. A phenomenological constitutive model is constructed involving phase transformation in one-dimensional SMA. The model is based on the Landau theory and includes the coupling effect between thermal and mechanical fields. Taking into account the tension–compression asymmetry, an asymmetric potential energy function is constructed, according to the three-dimensional deformation of the crystalline lattice. Both single-crystalline model and poly-crystalline model are proposed, and the angle between the lattice plane and the force (deformation) direction is considered in the poly-crystalline model. Numerical experiments have been carried out, which can well capture the asymmetric phase transformation and tension–compression asymmetry.

Unconditionally energy stable second-order numerical schemes for the Functionalized Cahn–Hilliard gradient flow equation based on the SAV approach

In this paper, we devise and analyse three highly efficient second-order accurate (in time) schemes for solving the Functionalized Cahn–Hilliard (FCH) gradient flow equation where an asymmetric double-well potential function is considered. Based on the Scalar Auxiliary Variable (SAV) approach, we construct these schemes by splitting the FCH free energy in a novel and ingenious way. Utilizing the Crank–Nicolson formula, we firstly construct two semi-discrete second-order numerical schemes, which we denote by CN-SAV and CN-SAV-A, respectively. To be more specific, the CN-SAV scheme is constructed based on the fixed time step, while the CN-SAV-A scheme is a variable time step scheme. The BDF2-SAV scheme is another second-order scheme in which the fixed time step should be used. It is designed by applying the second-order backward difference (BDF2) formula. All the constructed schemes are proved to be unconditionally energy stable and uniquely solvable in theory. To the best of our knowledge, the CN-SAV-A scheme is the first unconditionally energy stable, second-order scheme with variable time steps for the FCH gradient flow equation. In addition, an effective adaptive time selection strategy introduced in Christlieb et al., (2014) is slightly modified and then adopted to select the time step for the CN-SAV-A scheme. Finally, several numerical experiments based on the Fourier pseudo-spectral method are carried out in two and three dimensions, respectively, to confirm the numerical accuracy and efficiency of the constructed schemes.

Performance Investigation of Stochastic Resonance in Three Types of Asymmetric Bistable System Driven by Trichotomous Noise

This paper proposes a new system whose potential function is with three types of asymmetric potential wells, driven by trichotomous noise. Firstly, the three types of asymmetric bistable system are described in detail, and the changes of asymmetric bistable system potential function under different asymmetric factors are analyzed. Secondly, the effect of potential function parameters, asymmetric factorα, noise intensity D, and the probability of particle transition q is discussed, using numerical simulation. The detection effects of traditional symmetric SR and three types of asymmetric SR are observed and compared under the driving of trichotomous noise and periodic signals. The mean of signal-to-noise ratio gain is the indicator of the system's effectiveness on enhancing weak signal. The results indicate that it can make the detection effect of the asymmetric system better than that of the traditional bistable system by adjusting the parameters of the asymmetric stochastic resonance system and trichotomous noise.

Logical stochastic resonance in a nonlinear fractional-order system

We investigate logical stochastic resonance (LSR) in a nonlinear fractional-order system with an asymmetric bistable potential function. We use the success probability of the logical output to measure the logical operation ability of the system. If the success probability is 1, the logical output presents reliable LSR completely. When there are only two logical signals existing in the excitation, LSR can be realized by varying the value of the fractional order or the bias of the potential function. If the fractional order is relatively large, the system performs correct logical operations more easily. With the increase in the bias, the interval of the fractional order corresponding to LSR increases first and then decreases. When both logical signals and Gaussian white noise exist in the excitation, the intervals of the fractional order and the bias corresponding to LSR decrease with the increase in the noise intensity. In addition, with the increase in the value of the fractional order, the maximal value of the success probability also increases. Further, the system usually performs more accurate logical operations when the value of the fractional order lies in the interval [1, 1.5]. The results expand the achievements of LSR. They also provide a reference in choosing an optimal system of LSR.

Asymmetric stochastic resonance under non-Gaussian colored noise and time-delayed feedback**Project supported by the National Natural Science Foundation of China (Grant No. 60551002) and the Natural Science Foundation of Hunan Province, China (Grant No. 2018JJ3680).

Based on adiabatic approximation theory, in this paper we study the asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored noise. The analytical expressions of the mean first-passage time (MFPT) and output signal-to-noise ratio (SNR) are derived by using a path integral approach, unified colored-noise approximation (UCNA), and small delay approximation. The effects of time-delayed feedback and non-Gaussian colored noise on the output SNR are analyzed. Moreover, three types of asymmetric potential function characteristics are thoroughly discussed. And they are well-depth asymmetry (DASR), well-width asymmetry (WASR), and synchronous action of well-depth and well-width asymmetry (DWASR), respectively. The conclusion of this paper is that the time-delayed feedback can suppress SR, however, the non-Gaussian noise deviation parameter has the opposite effect. Moreover, the correlation time plays a significant role in improving SNR, and the SNR of asymmetric stochastic resonance is higher than that of symmetric stochastic resonance. Our experiments demonstrate that the appropriate parameters can make the asymmetric stochastic resonance perform better to detect weak signals than the symmetric stochastic resonance, in which no matter whether these signals have low frequency or high frequency, accompanied by strong or weak noise.

Double Jump Broadband Energy Harvesting in a Helmholtz–Duffing Oscillator

To improve the ability of energy harvester, a Helmholtz–Duffing oscillator with nonlinear capacitance is considered, which has an asymmetric characteristic. In this paper, we investigates the effect of potential function asymmetries on the dynamic behaviors under harmonic excitation. The electromechanical coupling governing equations of Helmholtz–Duffing energy harvester is established. Then its dynamic response in the region of the primary resonance is sought by the harmonic balance method. The performances of the presented asymmetric nonlinear primary resonance energy harvester and the linear stiffness system are compared. Results clearly demonstrate an improved bandwidth over a case which does not involve an asymmetric potential energy function. It is found that multiple-valued steady-state solutions of frequency-response equation can exist, indicating that the jump phenomenon occurs. Besides, the amplitude–frequency response curves have double-jumping phenomena by the bend, first to the left and then to the right. The influence of the stiffness parameters on the shape of the frequency-response curves is also discussed. It is observed that different shapes of frequency-response curves can exist. The approximate analytical outcomes are in good agreement with the numerical results.

Stochastic resonance in a monostable system driven by time-delayed feedback

The characteristic of a monostable stochastic resonance system driven by time-delayed feedback is investigated. Under the small-delay approximation theory, the effective potential function of the system is obtained and the influence of system parameters on the shape of the potential function is also discussed. Furthermore, we consider the influence of the input signal on the system and derive the asymmetric bistable potential function. By using the adiabatic approximation theory and the two-state theory, the theoretical expressions of the steady-state probability distribution function, mean first-passage time and signal-to-noise ratio are obtained, which are three excellent metrics to measure the performance of system. Simulation results show that the parameters A, a and τ can motivate the SR phenomenon while β suppresses the SR phenomenon. At last, the numerical simulation results obtained from the original Langevin equation and the effective Langevin equation can verify whether the theoretical derivation is correct.

A theoretical description of inverse stochastic resonance in nature

The inverse stochastic resonance (ISR) phenomenon consists of an unexpected depression in the response of a system under external noise, e.g., as observed in the mean firing rate in some pacemaker neurons subject to moderate values of noise. A possible cause for such unexpected reaction is the occurrence of a bistable regime controlling these neurons dynamics. We here explore theoretically the emergence of ISR in a general bistable model system, and thus determine the specific conditions the potential function driving the dynamics must accomplish. We conclude that such an intriguing, and apparently widely observed, phenomenon ensues in the case of an asymmetric potential function when the high activity minimum state of the system is metastable having a larger basin of attraction than the low activity state which is the global minimum of the system. We then discuss on the relevance of such a picture to understand the ISR features and to predict its appearance in nature. In addition, we report on existence of another intriguing, non-standard stochastic resonance in our model even in the absence of any weak signal input. Depending on the shape of the potential function, this new phenomenon shows up together with ISR precisely within the theoretical framework we present in this paper.

Exploring the benefits of an asymmetric monostable potential function in broadband vibration energy harvesting

This letter explores the benefits offered by an asymmetric monostable potential function over the conventional symmetric linear and bistable potential functions in broadband vibration energy harvesting. Multi-stable harvesters such as the bistable and tristable harvesters provide an order of magnitude higher power than the linear harvesters while undergoing inter-well oscillations. However, when the excitation noise levels are insufficient to trigger inter-well oscillations, such harvesters provide very low power output. We propose a monostable configuration with an asymmetric potential energy function that is capable of providing a high energy output starting from excitation levels as low as 0.005 g2/Hz (g denotes acceleration due to gravity). The superior performance of the proposed asymmetric configuration over the conventional linear and bistable configurations is demonstrated through experiments, considering a band-limited white noise excitation. The experimental results also indicate that the asymmetric configuration delivers higher power at lower strain levels than the bistable configuration, mitigating the burden on the piezoelectric transducer. Thus, the asymmetric configuration offers a two-fold advantage in energy harvesting, leading to an increase in both the power output and the lifetime of the piezoelectric transducer.

Stochastic resonance in an asymmetric bistable system driven by multiplicative and additive Gaussian noise and its application in bearing fault detection

The phenomenon of stochastic resonance (SR) in a new asymmetric bistable model is investigated. Firstly, a new asymmetric bistable model with an asymmetric term is proposed based on traditional bistable model and the influence of system parameters on the asymmetric bistable potential function is studied. Secondly, the signal-to-noise ratio (SNR) as the index of evaluating the model are researched. Thirdly, Applying the two-state theory and the adiabatic approximation theory, the analytical expressions of SNR is derived for the asymmetric bistable system driven by a periodic signal, unrelated multiplicative and additive Gaussian noise. Finally, the asymmetric bistable stochastic resonance (ABSR) is applied to the bearing fault detection and compared with classical bistable stochastic resonance (CBSR) and classical tri-stable stochastic resonance (CTSR). The numerical computations results show that:(1) the curve of SNR as a function of the additive Gaussian noise and multiplicative Gaussian noise first increased and then decreased with the different influence of the parameters a, b, r and A; This demonstrates that the phenomenon of SR can be induced by system parameters; (2) by parameter compensation method, the ABSR performs better in bearing fault detection than the CBSR and CTSR with merits of higher output SNR, better anti-noise and frequency response capability.

Stochastic resonance energy harvesting for a rotating shaft subject to random and periodic vibrations: influence of potential function asymmetry and frequency sweep

Stochastic resonance is referred to as a physical phenomenon that is manifest in nonlinear systems whereby a weak periodic signal can be significantly amplified with the aid of inherent noise or vice versa. In this paper, stochastic resonance is considered to harvest energy from two typical vibrations in rotating shafts: random whirl vibration and periodic stick-slip vibration. Stick-slip vibrations impose a constant offset in centrifugal force and distort the potential function of the harvester, leading to potential function asymmetry. A numerical analysis based on a finite element method was conducted to investigate stochastic resonance with potential function asymmetry. Simulation results revealed that a harvester with symmetric potential function generates seven times higher power than that with asymmetric potential function. Furthermore, a frequency-sweep analysis also showed that stochastic resonance has hysteretic behavior, resulting in frequency difference between up-sweep and down-sweep excitations. An electromagnetic energy harvesting system was constructed to experimentally verify the numerical analysis. In contrast to traditional stochastic resonance harvesters, the proposed harvester uses magnetic force to compensate the offset in the centrifugal force. System identification was performed to obtain the parameters needed in the numerical analysis. With the identified parameters, the numerical simulations showed good agreement with the experiment results with around 10% error, which verified the effect of potential function asymmetry and frequency sweep excitation condition on stochastic resonance. Finally, attributed to compensating the centrifugal force offset, the proposed harvester generated nearly three times more open-circuit output voltage than its traditional counterpart.

Understanding price discovery in interconnected markets: Generalized Langevin process approach and simulation

While the literature on price discovery process and information flow between dominant and satellite market is exhaustive, most studies have applied an approach that can be traced back to Hasbrouck (1995) or Gonzalo and Granger (1995). In this paper, however, we propose a Generalized Langevin process with asymmetric double-well potential function, with co-integrated time series and interconnected diffusion processes to model the information flow and price discovery process in two, a dominant and a satellite, interconnected markets. A simulated illustration of the model is also provided.