Research on Diagnosis Method of Rotor Misalignment-bumping Coupling Fault Based on Nonlinear Output Frequency Response Function

The analysis of multidegree-of-freedom (MDOF) nonlinear systems is studied using the concept of nonlinear output frequency response functions (NOFRFs), which are a series of one-dimensional functions of frequency recently proposed by the authors to facilitate the analysis of nonlinear systems in the frequency domain. By inspecting the relationships between the NOFRFs of two consecutive masses in the locally nonlinear MDOF systems, a series of properties about the NOFRFs of the nonlinear systems are obtained. These properties clearly reveal how the system linear characteristic parameters govern the distribution of nonlinear effects induced by the system nonlinear component within the whole systems. The results obtained in the present work are of significance to the frequency response analysis for nonlinear systems. One important potential application of these results is the detection and location of damages in engineering structures, which make the structures behave nonlinearly.

The current paper is concerned with the investigation of the relationship between the harmonic balance method (HBM) and the non-linear output frequency response function (NOFRF) approach in the analysis of non-linear systems. Both are applied to the Duffing's oscillator to demonstrate their relationships. The results reveal that, if the Volterra series representation of a non-linear system is convergent, the harmonic components calculated by the NOFRFs are a solution of the HBM. Moreover, the simulation studies show that, in the convergent cases, the NOFRF method can give more accurate results for the higher-harmonic components than the HBM. The relationship investigated in the current study between the two methods should help researchers and engineers to understand the HBM and the NOFRF methods.

Non-linear output frequency response functions of MDOF systems with multiple non-linear components

The concept of Nonlinear Output Frequency Response Functions (NOFRFs) was introduced in [1] for the analysis of nonlinear systems in the frequency domain where a least-squares (LS) method was proposed for the evaluation of the NOFRFs using system input-output data. However, this leastsquares (LS) based approach may experience numerical errors due to matrix inversion and consequently cannot produce accurate NOFRFs sometimes. In order to mitigate this problem, in the present study, a modified LS method (M-LS) is proposed to make sure that the information matrix to be inverted for the LS solution is appropriately constructed so as to improve the condition number of the information matrix and reduce the numerical errors. Simulation results have demonstrated the effectiveness of the newly proposed method and indicated that the new method will enable a more accurate evaluation of the NOFRFs and facilitate the frequency analysis of nonlinear systems directly using system input-output data.

The evaluation of Nonlinear Output Frequency Response Functions based on tailored data-driven modelling for rotor condition monitoring

It is well-known that if one or a few components in a structure are of nonlinear properties, the whole structure will behave nonlinearly, and the nonlinear component is often the component where a fault or an abnormal condition occurs. Therefore it is of great significance to detect the position of nonlinear components in structures. Nonlinear output frequency response functions (NOFRFs) are a new concept proposed by the authors for the analysis of nonlinear systems in the frequency domain. The present study is concerned with investigating the NOFRFs of nonlinear one-dimensional chain type systems, which have been widely used to model many real life structures. A series of important properties of the NOFRFs of locally nonlinear one-dimensional chain type structures are revealed. These properties clearly describe the relationships between the NOFRFs of different masses in a one-dimensional chain type system, and allow effective methods to be developed for detecting the position of a nonlinear component in the system. The results are an extension of the authors’ previous research studies to a more general and practical case, and have considerable significance in fault diagnosis and location in engineering systems and structures.

Transmissibility of non-linear output frequency response functions with application in detection and location of damage in MDOF structural systems

The nonlinear output frequency response function and its application to fault detection

Fault diagnosis of multivariable dynamic systems is studied by combining nonlinear spectrum feature with support vector machine. In order to resolve the problem of large calculated amount of solving nonlinear spectrum, a frequency domain variable step size normalized LMS adaptive algorithm is proposed based on the one-dimensional nonlinear output frequency response function (NOFRF). The step size is updated in real time according to the spectrum estimation error and the previous step size. After obtaining nonlinear spectrum data, kernel principal component analysis is used to compress data and extract spectrum feature. In order to improve fault recognition precision, a multi-feature fusion SVM fault classifier is established based on different frequency domain scales. Every sub-classifier is constructed by the spectrum feature of each order, and the diagnosis result can be obtained by weighed fusion of all sub-classifiers. Consider the difference of classification reliability for input features, sub-classifier weight is obtained using the distance between input and SVM separating hyperplane. Simulation experiments indicate that the proposed fault diagnosis method has good real-time performance and high recognition rate, so it can meet the requirements of online diagnosis of multivariable dynamic system.

In this work, an effective approach based on a nonlinear output frequency response function (NOFRF) and improved convolution neural network is proposed for analog circuit fault diagnosis. First, the NOFRF spectra, rather than the output of the system, are adopted as the fault information of the analog circuit. Furthermore, to further improve the accuracy and efficiency of analog circuit fault diagnosis, the batch normalization layer and the convolutional block attention module (CBAM) are introduced into the convolution neural network (CNN) to propose a CBAM-CNN, which can automatically extract the fault features from NOFRF spectra, to realize the accurate diagnosis of the analog circuit. The fault diagnosis experiments are carried out on the simulated circuit of Sallen-Key. The results demonstrate that the proposed method can not only improve the accuracy of analog circuit fault diagnosis, but also has strong anti-noise ability.

Conventional Volterra series model is hardly applied to engineering practice due to its parametric complexity and estimation difficulty. To solve this problem, nonlinear system identification using reduced complexity Volterra models is proposed. Since the nonlinear components often play a secondary role compared to the dominant, linear component of the system, they spend the most of identification cost. So it is worth establishing a balance between identification cost and model accuracy by reducing the complexity of nonlinear components. Refer to the idea of nonlinear output frequency response function, conventional Volterra model is simplified. And then a minimum mean square error criterion based method to identify the simplified model is proposed. The distinguishing feature of this method is high accuracy, good robustness, and significant reduction in the computational requirements compare to the identification of conventional Volterra models. The simulation show that the proposed method is effective, and the reduced complexity Volterra model is of good generalization ability in general. So this nonlinear system identification approach is quite applicable to engineering practice.

Experimental Study on Structural Damage Detection of Cracked Beams Based on Nonlinear Output Frequency Response Functions

The pillar porcelain insulator is an important protection device that is related to the safety of the entire power grid. Small damage of it may even cause a disaster. Nonlinear output frequency response functions (NOFRFs) can well reflect the nonlinear characteristics of early damage in the system. This paper uses the NOFRF entropy-based harmonic excitation detection method to detect the damage of the structure. Its effect has been verified by using metal specimens. Then, the pulse hammer detection and harmonic detection are carried out to detect the early-stage damage of the pillar porcelain insulator, and they achieve a good result, which verifies that the harmonic detection method can detect the early-stage damage in the pillar porcelain insulator as well. In addition, the orthogonal test of the simulated breathing crack model is used to search the greatest influence of the parameters of crack on the detection index. Through the orthogonal analysis, the results show that among the lengths, positions, and angles of the crack, the length of crack is the main factor that affects the detection index.

Nonlinear frequency response functions of a chromatographic column—A critical evaluation of their potential for estimation of single solute adsorption isotherms

Response functions used in crop simulation models are usually different for different physiological processes and cultivars, resulting in many unknown coefficients in the response functions. This is the case of African violet (Saintpaulia ionantha Wendl.), where a generalized temperature response for leaf growth and development has not been developed yet. The objective of this study was to develop a generalized nonlinear temperature response function for leaf appearance rate and leaf elongation rate in African violet. The nonlinear function has three coefficients, which are the cardinal temperatures (minimum, optimum, and maximum temperatures). These coefficients were defined as 10, 24, and 33ºC, based on the cardinal temperatures of other tropical species. Data of temperature response of leaf appearance rate and leaf elongation rate in African violet, cultivar Utah, at different light levels, which are from published research, were used as independent data for evaluating the performance of the nonlinear temperature response function. The results showed that a generalized nonlinear response function can be used to describe the temperature response of leaf growth and development in African violet. These results imply that a reduction in the number of input data required in African violet simulation models is possible.