EKF-based gear fault real-time health monitoring method

Abstract

The invention aims to provide an EKF-based gear fault real-time health monitoring method. The method comprises the following steps: collecting a gear box vibration signal data set; on the basis of the gearbox vibration signal mathematical model, establishing a state space model of meshing frequency in the gearbox vibration signal; establishing an extended Kalman filter, setting an initial value of the extended Kalman filter, and estimating the meshing frequency of the training data set in real time; 3 sigma threshold value training is carried out on the obtained vibration signal meshing frequency of the health state under the multiple loads, and a health monitoring threshold value is obtained; if the threshold value range is exceeded, it is judged that the gear breaks down, and then health monitoring of the gear box is completed. The method improves the model precision, and enables the model to be more suitable for the actual operation state of the gearbox. The gear health state under the multi-load condition is judged online in real time, the training efficiency of the health monitoring threshold value is improved, and the monitoring accuracy is improved.

Description

Technical Field

[0001] The invention relates to a gear detection method, in particular to a gear fault detection method. Background Art

[0002] Gears bear heavy loads during the transmission process, which can lead to typical gear failure forms such as broken teeth, cracks, and wear. These faults seriously affect the smooth operation and efficiency of gear transmission. Due to the heavy gear load, the abnormal vibration generated in the early stage of the fault is relatively hidden, making it more difficult to extract signal features and perform fault diagnosis. Therefore, it is very important to carry out research on health monitoring methods to maintain the smooth operation of equipment in view of the problem of weak vibration signal characteristics of heavy-loaded gears.

[0003] In recent years, certain achievements have been made in the field of gearbox health monitoring. The literature (Ma Tongxu, Liu Shuai, Liu Weiliang, et al. Fault warning of wind turbine gearbox based on two-stage multidimensional data generation and real-time health index [J]. Journal of Scientific Instrumentation) proposed to use multidimensional signals such as vibration and lubricating oil temperature as input to build a health monitoring model based on adversarial network to achieve gearbox fault warning and reduce false alarm rate. The diagnostic means of this method are cumbersome, and the conditions for building a health monitoring model are harsh. The initial fault of the gearbox has a great influence on the frequency domain components of the vibration signal. However, in real-time online fault diagnosis, signal frequency domain analysis methods such as Fourier transform need to collect a section of signal for analysis, which leads to a decrease in computational efficiency and cannot achieve the effect of real-time diagnosis. At the same time, due to the large amount of noise and interference, the general spectrum analysis method will be affected by it. Judging the spectrum peak or other features of the signal will lead to large extraction errors, which will ultimately affect the diagnosis results. Summary of the invention

[0004] The purpose of the present invention is to provide a real-time health monitoring method for gear faults such as broken teeth and cracks based on EKF.

[0005] The object of the present invention is achieved in that:

[0006] The present invention provides a real-time health monitoring method for gear faults based on EKF, which is characterized by comprising the following steps:

[0007] (1) Collecting gearbox vibration signal datasets: The vibration signals of the active gear side bearing seat of the gearbox under various loads, such as healthy, cracked, broken teeth, and worn faults, are collected respectively. The multi-load datasets are divided into two parts, one of which is training data and the other is test data.

[0008] (2) Based on the mathematical model of the gearbox vibration signal, which includes the meshing frequency of the vibration signal, a state space model of the meshing frequency in the gearbox vibration signal is established;

[0009] (3) Based on the state space model established in step (2), an extended Kalman filter is established, and the initial value of the extended Kalman filter is set according to the healthy state vibration data under multiple loads collected in step (1), and the meshing frequency of the training data set is estimated in real time;

[0010] (4) Perform 3σ threshold training on the meshing frequency of the vibration signal in the healthy state under multiple loads obtained in step (3) to obtain the threshold for health monitoring;

[0011] (5) If it exceeds the threshold range, it is determined that the gear has failed, that is, the health monitoring of the gearbox is completed.

[0012] The present invention may further include:

[0013] 1. Establish a mathematical model of the gearbox vibration signal in step (2). When the gearbox works under ideal conditions, the vibration signal of the healthy state of the gearbox is presented in the form of multiple sine functions:

[0014]

[0015] Where A n is the amplitude at the mth meshing frequency f m of the gear (n = 0, 1, 2,..., N), and d(t) is the noise and weak interference components;

[0016] For a gear pair with the number of teeth of the driving gear being N, the gear vibration meshing frequency f m is expressed as:

[0017]

[0018] Where v is the rotational speed of the driving gear;

[0019] The signal component to be observed is expressed as

[0020] y(t) = A f sin(ω·t) + d(t)

[0021] Where, A f is the amplitude at the meshing frequency of the vibration signal, ω is a certain meshing frequency of the signal, and as a signal feature, its calculation method is as follows:

[0022] ω = 2πf m = f z v

[0023] f z As the gearbox meshing frequency coefficient, the rotational speed is measurable data;

[0024] According to the formula y(t) = A fsin(ω·t)+d(t), select the sine component in the vibration signal as one of the state variables, and the cosine component as the other state component. The multiple frequency f of the gear meshing frequency m is the main variable. Select three state variables to represent the vibration signal of the gearbox, including sine function, cosine function and rotational speed information:

[0025] x = [x 1 x 2 x 3 T

[0026] = [sinωt cosωt v] T

[0027] The rotational speed of the gearbox is constant. According to the three state variables, the continuous-time space model is obtained as:

[0028]

[0029] Let the sampling step be Δt. Then the derivative of the state variable x at time t k -1 is approximately:

[0030]

[0031] Replace t k , t k-1 with k, k - 1. The above formula is transformed into:

[0032] x(k) = x(k - 1)+Δt·f(x(k - 1))

[0033] At this time,

[0034]

[0035] Linearize by calculating the Jacobian matrix, and test its observability by constructing the observation matrix:

[0036] The Jacobian matrix of the calculated model is:

[0037]

[0038] The observable matrix is:

[0039]

[0040] It can be seen from the observable matrix that Ro is full rank, so all state variables of the state space model are observable;

[0041] Then the state space model of the meshing frequency can be expressed as:

[0042] ​

[0043] Among them, C =

[101] .

[0044] 2. The method for establishing the meshing frequency extended Kalman filter in step (3) is as follows: The optimal estimation method based on the Kalman filter includes two update processes: the time update and the measurement update. In the time update stage, the state prior estimate value is calculated using the nonlinear model. In the measurement update stage, the error between the instantaneous rotational speed measurement value and the prior estimate value is used for feedback correction to calculate the posterior estimate value, making the posterior estimate value gradually approach the true value.

[0045] Set the sampling time and the initial value of the state variable before estimation The initial value P(0) of the error covariance + , as well as the initial values of Q and R;

[0046] Time update stage:

[0047] ① Use the nonlinear model to calculate the prior estimate value

[0048]

[0049] ② Calculate the Jacobian matrices A(k - 1) and M(k - 1) of the state variable x.

[0050] ③ Calculate the prior estimate value covariance matrix P(k) - :

[0051] P(k) - = A(k - 1)P(k - 1) + A(k - 1) T + M(k - 1)Q(k - 1)M(k - 1) T

[0052] Measurement update stage:

[0053] ④ Calculate the Kalman filter gain K(k):

[0054] K(k) = P(k) - C(k) T [C(k)P(k) - C(k) T + R(k)] -1

[0055] ⑤ Feedback correction of the estimation system:

[0056]

[0057] ⑥ Calculate the posterior estimate error covariance matrix P(k) + :

[0058] P(k) + =(I - K(k)C(k))P(k) - (I - K(k)C(k)) T +K(k)R(k)K(k) T

[0059] ⑦ Calculate the estimated value of the meshing frequency in the signal:

[0060]

[0061] Then, through the vibration sensors deployed on the gearbox housing, the vibration signal is obtained in real time. Calculations are performed according to the above formula, and the process is repeated to update the system state and covariance matrix, and the estimated value of the meshing frequency in the signal is calculated.

[0062] 3. Step (5) is specifically as follows: Measure the vibration signal of the gearbox in real time, and calculate the meshing frequency of the vibration signal at intervals of N data lengths. According to the threshold range [μ - 3σ, μ + 3σ], determine whether the gear system fails.

[0063] The advantages of the present invention are as follows:

[0064] 1. According to the characteristics of the gearbox vibration signal, using the sine component, cosine component of the meshing frequency of the vibration signal and the rotational speed as three state variables, a new non - linear state - space model of the vibration signal is proposed.

[0065] 2. According to the mechanism of the gearbox vibration signal, extracting the meshing frequency of the gearbox vibration signal as the signal feature for judging the gear state, and establishing an extended Kalman filter to extract the meshing frequency in the vibration signal in real time online.

[0066] 3. Aiming at the measurement noise in the gearbox vibration signal and the problems such as the fluctuation of state variables caused by the rotational speed fluctuation, considering the measurement noise and process noise in the model, improving the model accuracy and making the model more adaptable to the actual operating state of the gearbox.

[0067] 4. Based on the 3σ criterion, the present invention establishes a threshold determination method to judge the gear health state under multiple load conditions in real time online, improving the training efficiency of the health monitoring threshold and the accuracy of monitoring. Description of the Drawings

[0068] Figure 1 is the flow chart of the present invention;

[0069] Figure 2 is the calculation flow chart of the extended Kalman filter;

[0070] Figure 3 is the estimated meshing frequency of the vibration signal of the multi-load gearbox;

[0071] Figure 4 is the probability distribution and threshold of the meshing frequency of the vibration signal of the multi-load gearbox in the healthy state;

[0072] Figure 5 is the probability distribution diagram of the meshing frequency;

[0073] Figure 6 is the characteristic curve of the gear changing from healthy to gear crack fault;

[0074] Figure 7 is the characteristic curve of the gear changing from healthy to gear wear fault;

[0075] Figure 8 is the characteristic curve of the gear changing from healthy to gear tooth fracture fault. Specific implementation manners

[0076] The present invention will be described in more detail with reference to the accompanying drawings as follows:

[0077] Combined with Figure 1-8 , a gear fault real-time health monitoring method based on EKF of the present invention includes: establishing a Kalman filter and determining parameters; inputting vibration signals and rotational speed information into an extended Kalman filter optimal estimation model to obtain the optimal estimation of the meshing frequency in the vibration signal.

[0078] The following will be described in detail respectively, including the following steps:

[0079] Step 1: Collect a gearbox vibration signal dataset. Vibration signals at the bearing seat of the driving gear side of the gearbox under various loads in the healthy, cracked, tooth-fractured, and worn fault states are collected respectively, and the multi-load dataset is divided into two parts, one of which is training data and the other is test data.

[0080] Step 2: Based on the mathematical model of the gearbox vibration signal, which includes the meshing frequency of the vibration signal, establish a state space model of the meshing frequency in the gearbox vibration signal.

[0081] Step 3: Based on the state space model established in Step 2, establish an extended Kalman filter, and the calculation steps are as Figure 2 shown. Set the initial values of the extended Kalman filter according to the vibration data in the healthy state under multiple loads collected in Step 1, and estimate the meshing frequency of the training dataset in real time.

[0082] Step 4: Perform 3σ threshold training on the meshing frequency of the vibration signal in the healthy state under multiple loads obtained in Step 3 to obtain the threshold for health monitoring.

[0083] Step 5: Apply the set threshold to the fault diagnosis process as shown in Figure 1 If it exceeds the threshold range, it is determined that the gear has a fault, that is, the health monitoring of the gearbox is completed.

[0084] In Step 1, a training set and a test set of signals are established. For example, for a single-stage reduction gearbox with 21 teeth on the driving gear, simulate the healthy state of the gear, as well as typical fault states such as cracks, broken teeth, and wear. Set the operating speed of the gearbox v = 760 rpm, with loads of 4.5, 8.0, 12.0, and 18.2 N·m, and the vibration signal sampling frequency f s = 65536 Hz, and collect the vibration signals at the bearing housing on the driving gear side of the gearbox in the healthy, cracked, broken tooth, and worn fault states respectively.

[0085] In Step 2, a mathematical model of the gearbox vibration signal is established. When the gearbox operates under ideal conditions, the vibration signal of the healthy state of the gearbox will be presented in the form of multiple sine functions.

[0086]

[0087] where A n is the amplitude at the mth-order meshing frequency f m of the gear (n = 0, 1, 2,..., N). d(t) is the noise and weak interference components.

[0088] For a gear pair with N teeth on the driving gear, the gear vibration meshing frequency f m can be expressed as.

[0089]

[0090] where v is the rotational speed of the driving gear.

[0091] In the vibration signal of the gearbox, the signal generally takes the meshing frequency of a certain order as the main component of the vibration signal. When a fault occurs in the gear at an early stage, it will cause the amplitude of the multiple frequency of another signal of the meshing frequency to increase and become the new main component in the signal. Therefore, the signal components to be observed can be expressed as

[0092] y(t) = A f sin(ω·t) + d(t) (3)

[0093] where, A f is the amplitude at the meshing frequency of the vibration signal. ω is a certain order of meshing frequency of the signal. As a signal feature, its calculation method is as follows.

[0094] ω = 2πf m = f z v (4)

[0095] fz As the gearbox meshing frequency coefficient, the rotational speed is measurable data. Under different faults, this frequency will also be different, which becomes a key feature for judging the early stage of fault occurrence.

[0096] According to Equation (3), select the sine component in the vibration signal as one of the state variables. At the same time, the cosine function is also a main component in the vibration signal. Take the cosine component as another state component, and the multiple frequency f of the gear meshing frequency m is the main variable. Therefore, select three state variables to represent the gearbox vibration signal, including the sine function, the cosine function, and the rotational speed information.

[0097]

[0098] The rotational speed of the gearbox is a constant, and its derivative is 0. Then, according to the three state variables, the continuous-time space model is obtained as:

[0099]

[0100]

[0101] Assume the sampling step is Δt. Discretize the continuous state space equations of Equations (6) and (7). Then, the derivative of the state variable x at time t k-1 can be approximated as:

[0102]

[0103] Replace t k and t k-1 with k and k - 1. Equation (8) is transformed into:

[0104] x(k) = x(k - 1) + Δt·f(x(k - 1)) (9)

[0105] At this time,

[0106]

[0107] Since the model of the present invention is a non-linear continuous-time state space model, it is necessary to linearize it by calculating the Jacobian matrix and check its observability by constructing the observation matrix.

[0108] Calculate the Jacobian matrix of the model as:

[0109]

[0110] The observability matrix is:

[0111]

[0112] It can be seen from the observable matrix that Ro is full rank, so all state variables of the state space model are observable.

[0113] Then the state space model of the meshing frequency can be expressed as:

[0114]

[0115] where C = [1 0 1].

[0116] The extended Kalman filtering method for the meshing frequency established in step 3 is as follows: The optimal estimation method based on Kalman filtering includes two update processes: time update and measurement update. In the time update stage, the state prior estimate value is calculated using the nonlinear model. In the measurement update stage, the error between the instantaneous rotational speed measurement value and the prior estimate value is used for feedback correction to calculate the posterior estimate value, making the posterior estimate value gradually approach the true value.

[0117] Before estimation, the sampling time and the initial value of the state variable the initial value of the error covariance P(0) + , as well as the initial values of Q and R should be set. The selection of Q and R mainly considers the influence of process noise and measurement noise on the filtering effect, and can be selected according to the actual situation. The observation method of the meshing frequency of the vibration signal is as Figure 2 shown, and the specific steps are as follows.

[0118] Time update stage:

[0119] ① Use the nonlinear model. Calculate the prior estimate value

[0120]

[0121] ② Calculate the Jacobian matrices A(k - 1) and M(k - 1) of the state variable x.

[0122] ③ Calculate the prior estimate value covariance matrix P(k) - :

[0123] P(k) - = A(k - 1)P(k - 1) + A(k - 1) T + M(k - 1)Q(k - 1)M(k - 1) T (15)

[0124] Measurement update stage:

[0125] ④ Calculate the Kalman filter gain K(k):

[0126] K(k) = P(k) - C(k) T [C(k)P(k)- C(k) T +R(k)] -1 (16)

[0127] ⑤ Feedback correction estimation system:

[0128]

[0129] ⑥ Calculate the posteriori estimation error covariance matrix P(k) + :

[0130] P(k) + =(I - K(k)C(k))P(k) - (I - K(k)C(k)) T +K(k)R(k)K(k) T (18)

[0131] ⑦ Calculate the estimated value of the meshing frequency in the signal:

[0132]

[0133] Then, the vibration signal is obtained in real time through the vibration sensors deployed on the gearbox housing. According to equations (14) to (19), the calculation is carried out in a loop, continuously updating the system state and covariance matrix, and the estimated value of the meshing frequency in the signal is calculated

[0134] For example, for the gearbox targeted by the present invention, first, the sampling time of the extended Kalman filter is set to be the same as the signal sampling frequency, which is 65536 Hz, and the initial value of the state variable x(0) + =[x 1 (0) + x 2 (0) + x 3 (0) + =[4 1 760], the initial value of the error covariance P(0) + =diag([100 100 100]), and the initial values of Q and R. The selection of Q and R mainly considers the influence of process noise and measurement noise on the filtering effect, and can be selected according to the actual situation. In this patent, Q = diag([0.5 0.01 30]), R = 5

[0135] Using the established extended Kalman filter, calculate the vibration signals of the healthy gearbox under the loads of 4.5, 8, 12, and 18.2 N·m in the training set in step (1), and the meshing frequencies of the vibration signals under different loads are as Figure 3 shown

[0136] The method for setting the health monitoring threshold in step 4 is:

[0137] After inspection, under healthy conditions, the meshing frequency extracted by the needle of the present invention obeys a normal distribution, as Figure 4 shown, and can be expressed as

[0138]

[0139] where μ is the mean of , and σ is the standard deviation of

[0140] Since the probability of coincidence of the characteristic parameters under faulty and healthy conditions is very low, therefore, the present patent uses the under healthy conditions as the characteristic parameter for evaluating the health state of the gear.

[0141] The probability of being distributed in (μ - 3σ, μ + 3σ) is 0.9974, and the probability of falling outside ±3σ is 0.27%. To accurately and effectively determine the threshold, the present patent proposes a threshold optimization method based on the 3σ criterion, that is, the threshold range of the characteristic parameter is [μ - 3σ, μ + 3σ].

[0142] For example, in the gearbox training dataset targeted in the present invention, the meshing frequency of the healthy state signal under load estimated through is calculated to have a 3σ of 197.10 and a mean μ of 1521.33, and the 3σ values under faulty and healthy conditions differ significantly, as Figure 5 shown. Therefore, the present patent uses the 3σ value under healthy conditions as the judgment basis for health monitoring. The health monitoring threshold for the gearbox at around 760 rpm is [1342.23; 1718.43]. When the main frequency ω(k) of the monitoring signal exceeds this range, it is found that the gear has a fault.

[0143] In step 5, according to the threshold setting in step 4, the online health state evaluation method is as follows: The vibration signal of the gearbox is measured in real time, and at intervals of N data lengths, the meshing frequency of the vibration signal is calculated According to the threshold range [μ - 3σ, μ + 3σ], to determine whether the gear system has a fault.

[0144] For example, the healthy signals and faulty signals in the test set in step (1) are spliced, the meshing frequency is estimated using steps 2 to 4, and the estimated and threshold results obtained using the threshold range in step 4 are as Figure 6 , 7 , 8 shown, and this method can clearly determine the occurrence of gear faults.

Claims

1. A real-time health monitoring method for gear faults based on EKF, characterized by: The steps include: (1) Collecting gearbox vibration signal datasets: The vibration signals of the active gear side bearing seat of the gearbox under various loads, such as healthy, cracked, broken teeth, and worn faults, are collected respectively. The multi-load datasets are divided into two parts, one of which is training data and the other is test data. (2) Based on the mathematical model of the gearbox vibration signal, which includes the meshing frequency of the vibration signal, a state space model of the meshing frequency in the gearbox vibration signal is established; (3) based on the state space model established in step (2), an extended Kalman filter is established, and the initial value of the extended Kalman filter is set according to the healthy state vibration data under multiple loads collected in step (1), and the meshing frequency of the training data set is estimated in real time; (4) performing 3σ threshold training on the meshing frequency of the vibration signal in the healthy state under multiple loads obtained in step (3) to obtain a threshold for health monitoring; (5) If the value exceeds the threshold, it is determined that the gear has failed, thus completing the health monitoring of the gearbox.

2. The method for real-time health monitoring of gear faults based on EKF according to claim 1 is characterized by: Step (2) establishes a mathematical model of the gearbox vibration signal. When the gearbox works under ideal conditions, the vibration signal of the healthy state of the gearbox is presented in the form of multiple sinusoidal functions: Among them A n is the mth order meshing frequency of the gear f m The amplitude at (n=0,1,2,…,N), d(t) is the noise and weak interference component; For a gear pair with a driving gear with N teeth, the gear vibration meshing frequency f m It is expressed as: Where v is the driving gear speed; The signal components to be observed are expressed as y(t)=A f sin(ω·t)+d(t) Among them, A f is the amplitude of the vibration signal at the meshing frequency, and ω is a certain order meshing frequency of the signal. As a signal feature, it is calculated as follows: ω=2πf m =f z v f z As the gearbox meshing frequency coefficient, the speed is a measurable data; According to the formula y(t) = A f sin(ω·t)+d(t), select the sine component in the vibration signal as one of the state variables, and the cosine component as the other state component. The multiple frequency f of the gear meshing frequency m is the main variable, and three state variables are selected to represent the gearbox vibration signal, including sine function, cosine function and speed information: x=[x1 x2 x3] T =[sinωt cosωt v] T The gearbox speed is a constant. According to the three state variables, the continuous time-space model is: Assume the sampling step is Δt, then the state variable x at t k The derivative at time -1 is approximately: t k ,t k-1 Substituting k and k-1, the above formula becomes: x(k)=x(k-1)+Δt·f(x(k-1)) at this time, Linearization is performed by computing the Jacobian matrix and its observability is checked by constructing the observation matrix: The Jacobian matrix of the computational model is: The observable matrix is: From the observable matrix, we can see that Ro is full rank, so all state variables of the state space model are observable; Then the state space model of meshing frequency can be expressed as: Among them, C=[1 0 1].

3. The method for real-time health monitoring of gear faults based on EKF according to claim 1 is characterized by: The extended Kalman filter method for establishing the meshing frequency in step (3) is as follows: The optimal estimation method based on the Kalman filter includes two updating processes: time update and measurement update. In the time update stage, a nonlinear model is used to calculate the state prior estimation value. In the measurement update stage, the error between the instantaneous speed measurement value and the prior estimation value is used for feedback correction to calculate the posterior estimation value, so that the posterior estimation value gradually approaches the true value. Set the sampling time and initial values ​​of state variables before estimation Initial value of error covariance P(0) + , and the initial values ​​of Q and R; Time update phase: ①Use nonlinear model to calculate the prior estimate ② Calculate the Jacobian matrices A(k-1) and M(k-1) of the state variable x. ③Calculate the prior estimate covariance matrix P(k) - : P(k) - =A(k-1)P(k-1) + A(k-1) T +M(k-1)Q(k-1)M(k-1) T Measurement update phase: ④Calculate the Kalman filter gain K(k): K(k)=P(k) - C(k) T [C(k)P(k) - C(k) T +R(k)] -1 ⑤ Feedback correction estimation system: ⑥ Calculate the posterior estimation error covariance matrix P(k) + : P(k) + =(I-K(k)C(k))P(k) - (I-K(k)C(k)) T +K(k)R(k)K(k) T ⑦ Calculate the estimated value of the meshing frequency in the signal: Then, the vibration sensor deployed on the gearbox body is used to obtain the vibration signal in real time. The above formula is used for calculation, and the system state and covariance matrix are updated repeatedly to calculate the meshing frequency estimate in the signal.

4. The method for real-time health monitoring of gear faults based on EKF according to claim 1 is characterized by: Step (5) is specifically as follows: real-time measurement of the gearbox vibration signal, interval N data lengths, and calculation of the meshing frequency of the vibration signal according to The threshold range [μ-3σ, μ+3σ] is used to determine whether the gear system fails.

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