Research on fault law of rolling bearing under different fault levels and loads with HHT method

Bearing is one of the most important components of rotating machinery. The vibration signals are generally nonlinear and nonstationary while operating. The failed rolling bearing will damage to the machine, or cause a serious loss of property. There are a lot of methods about fault diagnosis of bearing, such as shock pulse method, resonance demodulation. Especially the HHT (Hilbert-Huang Transform) method with the adaptive advantage has gradually become a very promising method to extract the characteristics of nonlinear, nonstationary signal. In this paper the variant energy method was introduced in HHT to reduce the computation of the decomposed signal, which effectively improved the computation, and then an experimental platform was designed and established. The bearing fault categories can be diagnosed correctly in dealing with the vibration signals using this method and the fault law is discovered that the trend of the vibration signal fault characteristic frequency amplitude changes with the load increasing. The bearing failure mechanism provides beneficial reference for further research of nonlinear signal analysis

Research on pipeline leakage identification method based on Lyapunov exponent spectrum

In terms of resource transportation, pipelines play a very important role, however, it’s leakage is almost inevitable, so leakage monitoring has always been a research hotspot. The leakage identification of water supply pipeline is studied in this paper. The vibration caused by turbulence and cavitation at the leak point has chaotic characteristics, and the spectral distribution of which has its own special area. Chaos can be judged by the Lyapunov exponent, this means that the occurrence of the leak is judged. By this method, the leakage can be effectively identified. The above theory is verified by experiments in this paper

Feature extraction and identification of leak acoustic signal in water supply pipelines using correlation analysis and Lyapunov exponent

The leakage of water supply pipeline is a common problem in the world. Timely discovery and treatment of leakage can avoid drinking water pollution, save water resources or avoid road collapse accidents. Therefore, it is of great practical significance to study pipeline leak detection methods. In this experiment, piezoelectric acceleration sensors were placed in different locations of a leak pipe to acquire the leakage signals. According to the generation mechanism of leak acoustic signals, the unpredictability characteristics of leak signal are investigated. The autocorrelation function is used to describe the unpredictability of the leak signal because it has the ability to analyze the coherent structure of time series, and the Lyapunov exponent can describe its complexity. The autocorrelation function sequence is used as featured extraction object. The Lyapunov exponent of this sequence is used to quantify the signal characteristics. By this method, the leakage can be effectively identified

Identification and location of ship pipeline leakage based on VMD

Pipeline plays an important role in various systems of the ship. However, due to the harsh environment, leakage often occurs in ship pipeline. This paper proposes a method to identity and locate the pipeline leakage. Using the variational mode decomposition (VMD) algorithm, the vibration signal is decomposed into band-limited intrinsic mode functions (BIMFs). The effective BIMFs are then selected by the correlation coefficient. Center frequency and energy value of the effective BIMFs are extracted as feature vector. Radial Basis Function (RBF) neural network is then used as a tool to identify and locate the leakage. The proposed method is finally verified by experiments

Study on the dynamics of two-degree-of-freedom system with variable stiffness magnetic isolator

This paper presents a novel variable stiffness isolator designed by magnetic springs in parallel with linear positive stiffness spring. Firstly, the two-degree-of-freedom vibration system model with variable stiffness magnetic isolator is established. The amplitude frequency characteristic equation of the system is derived based on the multi-harmonic method, and the corresponding curve of the relationship between the amplitude and frequency is given. The influence of the current on the curve is researched. Results showed that there are two pseudo-resonant peaks in the amplitude–frequency curve, and one is in the low frequency band, the other exists in higher frequency band. The first peak does not exhibit the frequency shift, but the second one bends to the natural frequency obviously. With the increasing of the current, the peaks decrease and the backbone curve changes greatly for the second resonant crest. The Lyapunov exponent curve around the resonant frequency is calculated. It is shown that there is chaotic parameter region for the system, and chaos can be controlled with the variable stiffness magnetic vibration isolator according to this research, which is beneficial to the design of nonlinear vibration isolation system

A study of a nonlinear magnetic vibration isolator with quasi-zero-stiffness

A novel quasi-zero stiffness nonlinear magnetic isolator is designed by using magnetic springs in parallel with linear positive stiffness spring. Through the static analysis, the mathematical expressions of force-displacement-current and stiffness-displacement-current of the system are established, and the necessary conditions for the normal function and geometric parameters of the system are obtained. The nonlinear dynamic equations of the system under external excitation force are established. The amplitude and frequency characteristics of the system are deduced by harmonic balance method. The influence of system parameters and external excitation amplitude on the dynamic characteristics of the system is analyzed. Results showed that the vibration of the system can be controlled by controlling the electromagnet current or increasing the damping coefficient while the external excitation amplitude is kept in a certain of range. The researches provided a theoretical guidance for the design and application of the new quasi-zero stiffness nonlinear magnetic isolation system

Characteristic analysis of vibration isolation system based on high-static-low-dynamic stiffness

The purpose of this study is to investigate the characteristics of vibration isolation system with a single degree-of-freedom (SDOF) and a two-degree-of-freedom (2DOF) respectively based on the high-static-low-dynamic-stiffness (HSLDS). This model consists of a simple configuration connecting a vertical spring and a pair of oblique springs. The restoring force of the isolation system is approximated to linear and cubic stiffness by applying the Maclaurin series expansion. The dynamic equations of the SDOF and 2DOF are established for the harmonic force excitation. The frequency-amplitude response equation of the SDOF is obtained by employing the harmonic balance method (HBM) and is demonstrated in the classical Runge-Kutta method. The solution stability is ensured by applying the Floquet theory. Effects on the frequency response curves (FRCs) for the damping ratio and excitation amplitude are explored and discussed. The force transmissibility (FT) is defined to evaluate the vibration suppression capability. Effects on the FT of the SDOF and 2DOF for the excitation amplitude, mass ratio, and damping ratio are investigated. An experimental investigation of the SDOF is carried out to evaluate the actual attenuation performance in comparison with the equivalent linear system (ELS). The simulation and experimental results show that the HSLDS system with harmonic force excitation demonstrates hardening stiffness with multi-valued solutions. The occurrence of jump phenomenon is observed and explained by the stiffness variation. The system response and resonance frequency are affected by the excitation amplitude and damping ratio. The HSLDS system outperforms the ELS in a low frequency range if an appropriate mass is mounted. It is excited by a proper force and owns a suitable damper, which offers a theoretical guidance for the design and application of a novel HSLDS isolator

Study of double-potential-well leaf spring system’s chaotic vibration

Chaotic vibration has become increasingly popular in the study of acoustic and vibration engineering. Many engineering designs have taken advantage of the special characteristics of chaos, and deliberately introduced it into the system to improve efficiency. As an important component, leaf springs have long been used in the suspension system of wheeled vehicles. Recent development is considering chaotic vibration in the design of leaf springs to improve the system’s reliability. However, little experimental research has been carried out to investigate the chaos characteristics of leaf springs. Meanwhile, a preliminary study showed that some of the conventional signal processing methods may not be able to successfully identify the chaos features from a leaf spring test rig due to the complexity of the practical signal. Therefore, in this paper, a leaf spring system’s chaotic vibration and relevant signal processing strategy were investigated in theory and experiment. Firstly, the relationship between the amplitude and frequency of the double potential well system is derived with averaging method. The stability is analyzed on the Vander pol plane and the global bifurcation diagram and Lyapunov exponent spectrum are applied to determine the chaotic regime accurately. Numerical simulation was conducted using a finite element method to give an idea of the leaf spring’s natural frequencies where chaotic vibration can be potentially generated. The experimental rig was then designed based on double potential well theory to generate stable and repeatable chaotic vibration, and an experimental study was carried out to investigate the system’s response characteristics under different excitation strengths and frequencies. An improved signal processing method, Wavelet-SG-EEMD (Wavelet, Savitzky-Golay (SG) and Ensemble Empirical Mode Decomposition (EEMD)), was used to reduce noise and beneficial to identify chaotic features of the vibration signal generated by the system. The nonlinear vibration response features of the system were carefully analyzed. Sub-harmonic phenomena, periodic modes and chaotic behavior were discovered during the experiment

Research on the application and promotion of the carbon neutral concept based on the attention mechanism in football under the end-to-end architecture

IntroductionIn light of escalating concerns regarding global warming and environmental pollution, the pursuit of carbon neutrality has emerged as a pivotal strategy to address climate change on a global scale. As society becomes increasingly conscious of its ecological impact, various sectors, including sports, are urged to embrace environmental responsibility. This study seeks to explore the integration of a carbon neutral framework utilizing artificial intelligence's attention mechanism within the realm of football, with the aim of contributing to football's adoption of carbon neutrality.MethodsThe study commences by introducing an end-to-end architectural framework capable of unifying and optimizing all facets of football to realize a comprehensive carbon-neutral objective. This architecture serves as a consolidated platform for enhancing carbon emission reduction within football pedagogical activities, fostering synergy among diverse constituents while concurrently assessing the equilibrium between carbon reduction and pedagogical effectiveness. Subsequently, attention mechanisms are leveraged to heighten the efficacy and comprehensibility of carbon-neutral strategies. The application of attention mechanisms enables the model to autonomously focus on attributes or regions closely associated with carbon neutrality objectives, thereby facilitating precision and efficacy in recommending carbon neutral strategies. By employing attention mechanisms in football, a more thorough understanding of carbon emissions' dynamics is attained, allowing for the identification of pivotal emission contributors and tailored suggestions for emission mitigation. Furthermore, the Long Short-Term Memory (LSTM) method is employed to analyze football time-series data. Given football's intricate sequence of actions, the LSTM technique adeptly captures long-term dependencies, offering improved analysis and optimization of carbon emissions during football activities.ResultsThe integrated end-to-end architectural framework offers a holistic approach to carbon-neutral football strategies. Attention mechanisms effectively enhance the focus and interpretation of carbon-neutral strategies, contributing to precise and impactful recommendations. Employing LSTM for time-series analysis aids in comprehending carbon emission dynamics, enabling the identification of efficacious carbon neutral strategies. The study underscores the potential of AI-driven attention mechanisms and LSTM in fostering carbon neutrality within football.DiscussionThe study's findings underscore the viability of integrating AI-driven methodologies, specifically attention mechanisms and LSTM, to promote carbon neutrality within the football domain. The end-to-end architecture serves as a foundational platform for comprehensive carbon emission reduction, offering potential for broader application in other sectors. The combination of attention mechanisms and LSTM engenders deeper insights into carbon emissions' intricate temporal dynamics, informing the development of targeted strategies for emission mitigation. The study's outcomes provide theoretical underpinnings for advancing sustainable football practices and inspire the broader adoption of carbon neutrality principles across diverse domains

Design and characteristic analysis of a novel quasi-zero-stiffness isolator using magnets as negative stiffness

Considering that the static load of marine equipment and the packing space of vibration isolation is limited, a novel quasi-zero-stiffness-isolator (QZSI) using magnets as negative stiffness is designed. The conditions that the QZSI realizes quasi-zero-stiffness at the equilibrium position is obtained by analyzing the static characteristics. The dynamical model of system under a vertical harmonic force is established. The harmonic balance method is used to analyze the dynamic characteristics of QZSI, and the amplitude- frequency relationship expression and force transmissibility are deduced. The influence of different parameters on the performances is analyzed by means of controlling variables. It is shown that the novel QZSI can reduce the response peaks and extend the frequency band of isolator, and that the QZSI provided suitable system parameters can outperform the linear system