Online Evaluation Method for Fault Characteristics of Rotating Machinery Based on Customized NARX Modeling

Abstract

The present invention provides an online evaluation method for rotating machinery fault characteristics based on customized NARX modeling. The harmonic product spectrum is used to determine the real-time rotational frequency of the rotor radial vibration signal, and detrending and low-pass filtering are performed. The amplitude and phase of the first n-order harmonic components of interest are extracted in combination with the least squares method. The first m-order harmonic components of interest are reconstructed and output as signals. The corresponding periodic unbalanced force is used as input and synchronously downsampled with the output. The customized NARX model is then identified using the forward orthogonal least squares method. The NOFRFs of the customized NARX model are evaluated using the generalized correlation linear function method, and the feature or its derivative feature is used as a health indicator for the status evaluation of the rotor system. The present invention effectively solves the problem of overfitting that is prone to occur in the traditional NARX model identification process and the problem of low model accuracy or even non-convergence due to strong noise, and enables users to more accurately extract the weak fault features of the system.

Description

Technical Field

[0001] The present invention relates to the technical field of fault diagnosis, and in particular to an online evaluation method for rotating machinery fault characteristics based on customized NARX modeling. Background Art

[0002] During the assembly and service life of rotating machinery, the assembly quality and operating conditions of each component significantly impact the performance of the rotor system. If these minor faults are not detected promptly during the early stages of service or failure development, and allowed to develop, they will not only shorten component lifespan but also degrade the rotor system's performance, ultimately leading to a decrease in product quality and, in severe cases, even safety accidents. Therefore, timely detection of assembly quality issues and damage and fault conditions in rotating machinery systems through online monitoring is crucial for ensuring product quality and production safety. To this end, scholars have conducted extensive research to identify suitable online condition monitoring methods to guide practical engineering practices. Traditional methods for monitoring the operating status of rotating machinery systems include time domain, frequency domain, time-frequency domain, and axis trajectory. While these methods provide valuable insights for system condition monitoring, they are significantly affected by operating conditions and noise, making them ineffective for effectively monitoring the rotor system's operating status, especially in the early stages of a fault or damage development.

[0003] In recent years, condition monitoring methods based on nonlinear analysis methods have gradually attracted widespread attention from scholars. Nonlinear output frequency response functions (NOFRFs) based on Volterra series can effectively extract nonlinear fault characteristics in the system (see the literature: ZQ Lang, S.A. Billings, Energy transfer properties of non-linear systems in the frequency domain, Int. J. Electr. Power Energy Syst. 1 (2015) 60-67.), and have been specifically applied in fields such as system design and fault diagnosis (see the literature: ZK Peng, ZQ Lang, C. Wolters, S.A. Billings, K. Worden, Feasibility study of structural damage detection using NARMAX modelling and nonlinear output frequency response function based analysis, Mech. Syst. Signal Process. 25 (2011), 1045-1061.). Compared with traditional methods, nonlinear output frequency response functions are more adaptable to complex operating conditions and have higher robustness to input conditions and noise. On this basis, Zhu Yunpeng proposed a NOFRFs evaluation method based on the NARX model for online condition monitoring, and used it for operating status monitoring of mechanical systems and their key components (see literature: YPZhu, ZQLang, HLMao, H.Laalej, Nonlinear output frequency response functions: A new evaluation approach and applications to railway and manufacturing systems'condition monitoring, Mech. Syst. Signal Process. 163 (2022), 108179.). The experimental results show that the new nonlinear output frequency response function evaluation method can meet the needs of online condition monitoring.

[0004] Further research revealed that the nonlinear output frequency response function and its related metrics, evaluated using the NARX (Nonlinear Auto Regressive with eXogenous inputs) model, are severely affected by noise, significantly impacting the accuracy and robustness of the features. However, a customized NARX modeling approach proposed in this paper can further improve the evaluation of the nonlinear output frequency response function, thereby enhancing the accuracy and robustness of the system fault signature. Summary of the Invention

[0005] In view of the shortcomings of the existing technology, this paper proposes an online evaluation method for rotating machinery fault characteristics based on customized NARX modeling to enhance the accuracy and robustness of system fault characteristics. The specific description is as follows:

[0006] Step 1: Determine the real-time rotation frequency f1 of the rotor radial vibration signal using the harmonic product spectrum, as shown in formula (1), where ω = 2πf1;

[0007]

[0008] Where H(ω) represents the harmonic product spectrum, and Z represents the highest order of the harmonics considered;

[0009] Step 2: Detrend and low-pass filter the collected vibration signal to remove the DC component and high-frequency noise to obtain the filtered signal Specifically expressed as:

[0010] Step 2.1: Detrend the collected vibration signal to remove the DC component in the signal;

[0011] Step 2.2: Filter the detrended vibration signal using Butterworth low-pass filtering or FIR low-pass filtering to remove high-frequency noise and obtain the filtered signal.

[0012] Step 3: Utilize the denoised data The amplitude and phase of the first n harmonic components of interest are extracted by combining the least squares method; the specific expression is:

[0013] Step 3.1: Based on the real-time frequency conversion f1, define the first n-order harmonic signals to be identified as:

[0014]

[0015] Where, f n =nf1,n=1,2,…,t i represents the i-th sampling time point, Y n represents the amplitude of the nth-order harmonic, Indicates the phase of the nth-order harmonic.

[0016] Step 3.2: Expand each equation in equation (2) and define it as:

[0017]

[0018] Step 3.3: Define the known coefficient matrix X and the coefficient vector α to be tested, where ζ represents the total number of sampling points;

[0019]

[0020] Step 3.4: Utilize the denoised data According to the least square method, the coefficient vector to be tested is identified, that is, the amplitude and phase of the first n-order harmonics;

[0021]

[0022] Step 4: Reconstruct the first m-order harmonic components of interest (m≤n) and use them as output;

[0023]

[0024] Where k represents the kth discrete time point and Δt represents the sampling time.

[0025] Step 5: Take the corresponding periodic unbalanced force as input and perform synchronous downsampling with the reconstructed output. The downsampling period is T d Need to meet 0.05T m ≤T d ≤0.2T m , where T m =1 / f1; then the forward orthogonal least squares method (FROLS) is used to identify the NARX model. The identified model is defined as the customized NARX model and its validity is verified;

[0026]

[0027] Among them, n y and n u The maximum number of delay points for input and output respectively; f(.) represents a nonlinear function.

[0028] Step 6: Use the generalized correlated linear function (GALEs) method to evaluate the NOFRFs characteristics of the customized NARX model and use this characteristic as a health indicator for the rotor system condition assessment; specifically, it is expressed as:

[0029] Step 6.1: Evaluate the NOFRFs feature G of the customized NARX model using the generalized correlation linear function method q(jω);

[0030] G q (jω)=Y q (jω) / U q (jω),q=1,…,N

[0031] Among them, Y q (jω) and U q (jω) represents the qth order output spectrum and input spectrum, which are respectively expressed by the qth order output y q (k) and input u q (k) Obtained by the normalized discrete Fourier transform. q (k) is the qth order output obtained by the NARX model identified by the generalized correlation linear function decomposition, and u q (k)=(u(k)) q ,q=1,…,N.

[0032] Step 6.2: Feature G q (jω) or its derivative characteristic Rn2 is used as a health indicator for the condition evaluation of the rotor system;

[0033]

[0034] Where ρ is a constant and N represents the highest order of NOFRFs.

[0035] The beneficial effects of the present invention are:

[0036] The present invention proposes an online evaluation method for rotating machinery fault characteristics based on customized NARX modeling. The nonlinear output frequency response function is a frequency domain analysis method for nonlinear systems. The method itself has a certain inhibitory effect on the noise in the signal, which makes the method have certain advantages in the nonlinear analysis of the system. A customized NARX modeling method is proposed for the online evaluation method of the nonlinear output frequency response function. Unlike the traditional NARX model, the customized NARX model does not represent the complete physical characteristics of the system, but only represents part of the dynamic characteristics of the system. Therefore, it can more accurately characterize the fault state of the system. The accuracy and robustness of NOFRFs evaluated based on the customized NARX model are significantly improved, which better solves the problem that the traditional NARX model identification process is prone to overfitting and the model accuracy is not high or even does not converge due to strong noise, and can enable users to more accurately extract the weak fault characteristics of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a flow chart of the online evaluation method for rotating machinery fault characteristics based on customized NARX modeling in the present invention;

[0038] Figure 2 Schematic diagram of the online evaluation method for rotating machinery fault characteristics based on customized NARX modeling in the present invention;

[0039] Figure 3 Schematic diagram of a rotor system bearing misalignment fault simulation test bench in the present invention;

[0040] Figure 4 is the time domain response of the healthy rotor system in the present invention;

[0041] Figure 5 is the frequency domain response of the healthy rotor system in the present invention;

[0042] Figure 6 The health index values of the rotor system in the present invention under healthy, slightly misaligned, and severely misaligned conditions, (a) is the traditional NARX model, and (b) is the customized NARX model;

[0043] In the figure, 1-motor, 2-rotating shaft, 3-turntable with symmetrical bolt holes, 4-unbalanced bolt, 5-steel gasket, 6-eddy current sensor, 7-data acquisition device, 8-computer. DETAILED DESCRIPTION

[0044] The invention is further described below with reference to the accompanying drawings and specific implementation examples. The present invention proposes an online evaluation method for rotating machinery fault features based on customized NARX modeling. This method addresses the problem that traditional NARX modeling is susceptible to factors such as signal smoothness and noise, which can lead to model overfitting or even non-convergence, resulting in low accuracy and robustness of the evaluated NOFRFs features. Based on signal decomposition and reconstruction, a customized NARX modeling method is proposed.

[0045] like Figures 1-2 As shown in FIG, a method for online evaluation of rotating machinery fault characteristics based on customized NARX modeling includes:

[0046] Harmonic excitation signals are used to stimulate the system to be tested, and the corresponding vibration response signals (or other types of signals) are collected. Depending on the object of study, the input and output signals of the system are collected (input and output signals include physical information measured by various sensors, such as displacement, velocity, acceleration, force, stress, strain, temperature, voltage, and current). For online condition monitoring of certain special systems, such as rotor systems, which operate at a fixed speed most of the time, periodic unbalanced forces can be used as input and the rotor vibration response as output.

[0047] Step 1: Use the harmonic product spectrum to determine the real-time rotation frequency f1 in the rotor radial vibration signal, as shown in formula (1);

[0048]

[0049] Where, ω=2πf1, f1 represents the real-time rotation frequency of the rotor.

[0050] Step 2: Detrending and low-pass filtering the collected vibration signal to remove the DC component and high-frequency noise in the signal; Step 2 is specifically expressed as follows:

[0051] Step 2.1: Detrend the collected vibration signal to remove the DC component in the signal;

[0052] Step 2.2: Filter the detrended vibration signal using Butterworth low-pass filtering or FIR low-pass filtering to remove high-frequency noise and obtain the filtered signal.

[0053] Step 3: Utilize the denoised data The amplitude and phase of the first n harmonic components of interest are extracted by combining the least squares method; the specific expression is:

[0054] Step 3.1: Based on the real-time frequency conversion f1, define the first n-order harmonic signals to be identified as:

[0055]

[0056] Where, f n =nf1,n=1,2,…,t i represents the i-th sampling time point, Y n represents the amplitude of the nth-order harmonic, Indicates the phase of the nth-order harmonic.

[0057] Step 3.2: Expand each equation in equation (2) and define it as:

[0058]

[0059] Step 3.3: Define the known coefficient matrix X and the coefficient vector α to be tested, where ζ represents the total number of sampling points;

[0060]

[0061] Step 3.4: Utilize the denoised data According to the least square method, the coefficient vector to be tested is identified, that is, the amplitude and phase of the first n-order harmonics;

[0062]

[0063] Step 4: Reconstruct the signal of the first m harmonic components of interest (m≤n) and use it as the output

[0064]

[0065] Step 5: Take the corresponding periodic unbalanced force as input and perform synchronous downsampling with the reconstructed output. The downsampling period is T d Need to meet 0.05T m ≤T d ≤0.2T m , where T m =1 / f1; then the NARX model is identified using the FROLS method, the identified NARX model is defined as a customized NARX model, and its validity is verified;

[0066]

[0067] Among them, n y and n u The maximum number of delay points for input and output respectively; f(.) represents a nonlinear function.

[0068] Step 6: Use the GALEs method to evaluate the NOFRFs characteristics of the customized NARX model and use them as health indicators for the condition evaluation of the rotor system; specifically, the following expression is used:

[0069] Step 6.1: Evaluate the NOFRFs feature G of the customized NARX model using the generalized correlation linear function method q (jω);

[0070] G q (jω)=Y q (jω) / U q (jω),q=1,…,N

[0071] Among them, Y q (jω) and U q (jω) represents the qth order output spectrum and input spectrum, which are respectively expressed by the qth order output y q (k) and input u q (k) Obtained by the normalized discrete Fourier transform. q (k) is the qth order output obtained by the NARX model identified by the generalized correlation linear function decomposition, and u q (k)=(u(k)) q ,q=1,…,N.

[0072] Step 6.2: Feature G q (jω) or its derivative characteristic Rn2 is used as a health indicator for the condition evaluation of the rotor system;

[0073]

[0074] Where ρ is a constant, for example, ρ = 0, and N represents the highest order of NOFRFs.

[0075] The present invention is mainly intended to solve the problem that the traditional NARX model is affected by signal smoothness and strong noise, which easily leads to overfitting of the model or even non-convergence, thereby reducing the accuracy and robustness of the evaluation of NOFRFs features. When using the nonlinear output frequency response function to evaluate the system state online, this method can be used to improve the accuracy and robustness of the features. This method can be applied in situations where the nonlinear output frequency response function is used to evaluate the system state. This method has no requirements for the monitored object and is not limited to the rotor system in the original scheme. It can be any mechanical or power system under harmonic excitation, such as the rotor system and its key components.

[0076] This embodiment uses a rotor system bearing misalignment fault simulation test bench to extract features to achieve alignment status evaluation. By adjusting the deflection angle of the bearing seat, bearing angle misalignment faults of different severity are simulated. The schematic diagram of the rotor system bearing angle misalignment fault simulation test bench is shown in FIG. Figure 3 As shown, the rotor test bench features a single-disc, two-pivot structure. A motor 1 drives a rotating shaft 2, which is attached with a turntable 3 containing an imbalance 4. By adjusting the thickness of a shim 5, misalignment faults of varying severity can be simulated. An eddy current sensor 6 then measures the vibration displacement signal of the shaft at a constant speed. This signal is collected and stored by a data acquisition device 7. Finally, a computer 8 visualizes the signal and extracts fault characteristics, thereby enabling an assessment of the rotor system's condition.

[0077] The specific implementation steps are as follows:

[0078] 1) Set the unbalanced mass of the turntable to m = 8g and the eccentric distance to e = 110mm. By adjusting the thickness of the bearing seat gasket, the bearing is tilted at different angles to simulate different degrees of bearing misalignment. The motor speed is set to 2400rpm.

[0079] 2) Set the sampling frequency to 5120 Hz, and collect the vibration displacement signal of the rotating shaft near the bearing seat where the test bearing is located through the eddy current sensor 6, as shown in the following example: Figure 4 As shown, the sampling time is about 1s;

[0080] 3) Use the harmonic product spectrum to determine the real-time rotational frequency f1 in the rotor radial vibration signal. Taking a healthy rotor system as an example, the first five harmonics in the vibration signal are extracted, so Z = 5. The frequency with the maximum amplitude in the product spectrum is regarded as the rotational frequency. The rotational frequency determined by the harmonic product spectrum is 40.93 Hz.

[0081] 4) Detrend and low-pass filter the collected vibration signal to remove the DC component and high-frequency noise in the signal to obtain the filtered signal

[0082] 5) Based on the real-time frequency conversion f1, the first five harmonic signals to be identified are defined as

[0083]

[0084] 6) Expand the above formula and define

[0085]

[0086] 7) The above coefficients are defined as the known coefficient matrix X and the coefficient vector α to be detected, where ζ represents the total number of sampling points;

[0087]

[0088] 8) Using the noise-reduced data According to the least square method, the coefficient vector to be detected is identified, that is, the amplitude and phase of the first five harmonics.

[0089]

[0090] 9) Reconstruct the first three harmonic components of interest and use them as output

[0091]

[0092] 10) The periodic unbalanced force of the rotor system is obtained by pre-setting the unbalanced mass and eccentric radius as F=meω 2 sin(ωt), which is normalized and discretized to obtain the input of the system to be tested

[0093] 11) Synchronously downsample the input and output, then use the FROLS method to identify the customized NARX model and verify its effectiveness;

[0094]

[0095] Among them, n y and n u The maximum number of delay points for input and output respectively; f(.) represents a nonlinear function.

[0096] 12) The GALEs method is used to evaluate the NOFRFs and their derived characteristics of the customized NARX model and use them as health indicators to evaluate the system status.

[0097] G q (jω)=Yq (jω) / U q (jω),q=1,…,N

[0098] Among them, Y q (jω) and U q (jω) represents the qth order output spectrum and input spectrum, which are respectively expressed by the qth order output y q (k) and input u q (k) Obtained by the normalized discrete Fourier transform. q (k) is the qth order output obtained by decomposing the identified NARX model using the GALEs method, and u q (k)=(u(k)) q ,q=1,…,N.

[0099] The derived feature Rn2 of NOFRFs is constructed as a health indicator for the condition evaluation of the rotor system;

[0100]

[0101] 13) Adjust the thickness of the bearing seat gasket to increase the bearing deflection angle. At this time, it is considered that the rotor system has a slight misalignment fault. Repeat steps 1) to 12) to calculate the health index of the rotor system when a slight misalignment fault occurs.

[0102] 14) Based on step 13), the thickness of the bearing seat gasket is further increased to cause a severe misalignment fault in the test bearing, and steps 1) to 12) are repeated to obtain a health indicator of the rotor system when a severe misalignment fault occurs.

[0103] 15) Taking the health index value of the healthy rotor system as a reference, the frequency domain response of the healthy rotor system is as follows: Figure 5 As shown in the figure, the health index values under three different misalignment fault conditions are compared. The specific results are as follows: Figure 6 As shown. By comparison, it was found that the NOFRFs related features obtained based on the customized NARX modeling method showed a monotonically increasing trend with the increase of the misalignment angle, and the dispersion was small, indicating that this feature is more sensitive to faults. However, the NOFRFs obtained based on the traditional NARX modeling method showed no monotonous trend with the increase of the misalignment degree, and the dispersion was large, and could not be used for status evaluation. In addition, through the analysis of the present invention in the rotor system bearing angle misalignment fault simulation test case, the present invention requires less detection equipment and is simple to operate, which can meet the needs of online status evaluation, making the present invention easy to be implemented in engineering practice.

Claims

1. A method for online evaluation of rotating machinery fault characteristics based on customized NARX modeling, characterized in that: include: Step 1: Determine the real-time rotation frequency f1 of the rotor radial vibration signal using the harmonic product spectrum; Step 2: Detrend and low-pass filter the collected vibration signal to remove the DC component and high-frequency noise to obtain the filtered signal Step 3: Utilize the denoised data The amplitude and phase of the first n harmonic components of interest are extracted using the least squares method; Step 4: Reconstruct the first m-order harmonic components of interest and use them as output; Step 5: The corresponding periodic unbalanced force is used as input and synchronously downsampled with the reconstructed output. The NARX model is then identified using the forward orthogonal least squares method. The identified model is defined as the customized NARX model and its validity is verified. Step 6: Use the generalized correlated linear function method to evaluate the NOFRFs characteristics of the customized NARX model, and use this characteristic or its derivative characteristics as a health indicator for the condition evaluation of the rotor system.

2. The online evaluation method for rotating machinery fault characteristics based on customized NARX modeling according to claim 1 is characterized in that: The step 1 is specifically expressed as follows: Where H(ω) represents the harmonic product spectrum, and Z represents the highest order of the harmonics considered.

3. The online evaluation method for rotating machinery fault characteristics based on customized NARX modeling according to claim 1 is characterized in that: The step 3 is specifically expressed as follows: Step 3.1: Based on the real-time frequency conversion f1, define the first n-order harmonic signals to be identified as: Where, f n =nf1,n=1,2,…,t i represents the i-th sampling time point, Y n represents the amplitude of the nth-order harmonic, Indicates the phase of the nth-order harmonic; Step 3.2: Expand each equation in equation (2) and define it as: Step 3.3: Define the known coefficient matrix X and the coefficient vector α to be tested, where ζ represents the total number of sampling points; Step 3.4: Utilize the denoised data According to the least square method, the coefficient vector to be tested is identified, that is, the amplitude and phase of the first n-order harmonics; 4. The online evaluation method for rotating machinery fault characteristics based on customized NARX modeling according to claim 1 is characterized in that: The step 4 is specifically expressed as follows: Where k represents the kth discrete time point and Δt represents the sampling time.

5. The online evaluation method for rotating machinery fault characteristics based on customized NARX modeling according to claim 1 is characterized in that: The step 2 is specifically expressed as follows: Step 2.1: Detrend the collected vibration signal to remove the DC component in the signal; Step 2.2: Filter the detrended vibration signal using Butterworth low-pass filtering or FIR low-pass filtering to remove high-frequency noise and obtain the filtered signal.

6. The online evaluation method for rotating machinery fault characteristics based on customized NARX modeling according to claim 1 is characterized in that: The synchronous downsampling in step 5 is specifically expressed as follows: The corresponding periodic unbalanced force is taken as input and synchronously downsampled with the reconstructed output. The downsampling period is T d Need to meet 0.05T m ≤T d ≤0.2T m , where T m =1 / f1.

7. The online evaluation method for rotating machinery fault characteristics based on customized NARX modeling according to claim 1 is characterized in that: The step 6 is specifically expressed as follows: Step 6.1: Evaluate the NOFRFs feature G of the customized NARX model using the generalized correlation linear function method n (jω); Step 6.2: Feature G n (jω) or its derivative characteristic Rn2 is used as a health indicator for the condition evaluation of the rotor system; Where ρ is a constant and N represents the highest order of NOFRFs.

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