KR20240044851A - Rotational shaft crack detection system and method using torsional stifness estimation - Google Patents

Abstract

The present invention relates to a system and method for detecting rotational shaft cracks using torsional stiffness estimation, wherein a rotation control unit applies rotational drive to one side and the other side of the rotational shaft, and a model building unit measures the rotation information applied to each side of the rotational shaft. To minimize noise, a linear model is constructed using a loop adaptive extended Kalman filter in which the covariance error is minimized and the forgetting factor that increases inversely with the Kalman gain is updated, and the input is based on the linear model in which the crack detection unit is built. This system calculates the torsional stiffness estimate of the rotating shaft based on the rotation information and detects cracks in the rotating shaft using the calculated torsional stiffness estimate. As crack detection is possible with only two speed sensors, the cost of crack detection can be reduced. The speed of detection can be improved.

Description

Rotational shaft crack detection system and method using torsional stiffness estimation {ROTATIONAL SHAFT CRACK DETECTION SYSTEM AND METHOD USING TORSIONAL STIFNESS ESTIMATION}

The present invention relates to a system and method for detecting cracks in a rotating shaft using torsional stiffness estimation, and to a technology that allows detecting cracks in a rotating shaft through torsional stiffness estimation.

Even if the same load is applied to structures such as machines or buildings with defects, additional strain energy exists due to cracks in addition to the strain energy caused by the structure's own elasticity, and additional strain occurs as much as the added energy. In addition, when any load or external force is applied to a structure with a crack, the structure cannot receive the force beyond a certain limit and the crack rapidly propagates from the crack as a starting point and is destroyed. Therefore, detection of cracks or defects in structures or rotating bodies is an important factor in minimizing safety accidents resulting from sudden failures due to continuous crack propagation.

Conventional crack detection methods include surface visual evaluation, sampling fracture inspection and radiography, magnetic particle inspection, non-destructive monitoring techniques (NDT) such as fluorescent die penetration and ultrasonic methods, and deep learning algorithms during operation. Diagnose and monitor machine operation.

In the case of surface visual inspection, detection speed and accuracy can depend on the experience, level of technology, and image quality of the crack detection expert to detect internal defects, so effective non-destructive testing is widely used to detect cracks. The crack detection method using camera images, which is a non-destructive testing equipment, detects initial cracks using morphological calculations and detects cracks through closing calculations using line shape elements, but it consumes additional time and requires inspecting all elements, so it is not suitable for large systems. It costs a lot to apply it.

Recently, cracks are detected by analyzing changes in natural frequency, mode shape, and amplitude peak that occur at high frequencies. However, these crack detection methods cannot accurately detect cracks because the high-frequency amplitude is too small and are dependent on assembly tolerances, manufacturing condition noise, and other defects. This makes it difficult to detect defects precisely. In addition, the algorithm that collects and analyzes defect signals to derive abnormalities also has the problem of not being able to detect small changes due to the signal analysis algorithm's complexity and low sensitivity.

Republic of Korea Patent No. 10-2273705 (2021.07.06)

The present invention can provide a rotary shaft crack detection system and method using torsional stiffness estimation that can estimate crack intensity of shaft stiffness over time.

A rotary shaft crack detection system using torsional rigidity estimation according to one aspect of the present invention includes a rotation control unit that applies rotational drive to each of one side and the other side of the rotary shaft; In order to minimize noise in the measured value of rotation information applied to each side of the rotation axis, a loop adaptive extended Kalman filter is used to minimize covariance error and update the forgetting factor whose Kalman gain increases inversely. a model building unit that builds a model; and a crack detection unit that calculates a torsional rigidity estimate of the rotation shaft based on the input rotation information based on the constructed linear model and detects cracks in the rotation shaft using the calculated torsional rigidity estimate.

Preferably, the rotation information may be rotation torque, angular velocity, and angle difference between one side and the other side.

Preferably, the loop adaptive extended Kalman filter can discretize a nonlinear model based on a discrete time domain.

Preferably, an estimation unit for deriving an estimate value for at least one of a scheduled torque to be applied to one side and the other side of the rotation axis, a scheduled angular velocity, a scheduled angle of one side, and a scheduled angle of the other side at each time interval preset with the rotation information is further provided. It can be included.

Preferably, the model building unit may set the estimated forgetting factor to the maximum value if the residual between the derived forgetting factor and the estimated forgetting factor is within a preset value.

Preferably, the model building unit may calculate and linearize a Jacobian matrix based on previous estimates.

Preferably, the model building unit may apply a weight to the measured value if the residual between the measured value and the estimated value of the rotation information is within a preset value.

A method of detecting cracks in a rotating shaft using torsional stiffness estimation according to another aspect of the present invention includes a rotation control step of applying rotational drive to one side and the other side of the rotating shaft; In order to minimize noise in the measured value of the rotation information applied to each side of the rotation axis, the covariance error is minimized and the forgetting factor that increases the Kalman gain inversely is updated using a linear linear adaptive extended Kalman filter. A model building stage in which a model is built; and a crack detection step in which a torsional stiffness estimate of the rotation axis is calculated based on the input rotation information based on the constructed linear model, and a crack in the rotation shaft is detected using the calculated torsional rigidity estimate.

Preferably, an estimation step in which an estimated value for at least one of the scheduled torque to be applied to one side and the other side of the rotation axis, the scheduled angular velocity, the scheduled angle of one side, and the scheduled angle of the other side is derived at each preset time interval using the rotation information More may be included.

Preferably, in the model building step, if the residual of the derived forgetting factor and the estimated forgetting factor is within a preset value, the estimated forgetting factor may be set to the maximum value.

Preferably, the model building step can be linearized by calculating a Jacobian matrix based on previous estimates.

Preferably, in the model building step, if the residual between the measured value and the estimated value of the rotation information is within a preset value, a weight may be applied to the measured value.

According to the present invention, not only can the decrease in rigidity due to cracks be estimated, but also the fatigue crack growth can be quantitatively evaluated by directly estimating the shaft torsional rigidity. In addition, since crack detection is possible with only two speed sensors, the cost of crack detection can be reduced and the speed of crack detection can be improved.

1 is a configuration diagram of a rotary shaft crack detection system according to an embodiment.
Figure 2 is a diagram illustrating rotation axis modeling according to one embodiment.
Figure 3 is a diagram illustrating the entire estimation process using forgetting factor update and AEKF algorithm according to one embodiment.
Figure 4 is a graph showing stiffness due to crack initiation over a certain period of time according to one embodiment.
Figure 5 is a graph showing the estimation results for a sudden decrease in torsional rigidity according to one embodiment.
Figure 6 is a graph showing simulation results of shaft stiffness estimation under noise uncertainty according to one embodiment.
Figure 7 is a graph showing estimation results according to one embodiment.
Figure 8 is a diagram showing the configuration of a system for estimating torsional rigidity according to an embodiment.
Figure 9 is a convergence history graph according to one embodiment.
Figure 10 is a graph showing experimental results of a stiffness estimation system according to an embodiment.
Figure 11 is a graph showing experimental results for a crack scenario.
Figure 12 is a graph showing the torsional stiffness response estimated from the electrical sensor noise uncertainty.
Figure 13 is a flowchart showing a method of detecting cracks in a rotating shaft according to an embodiment.

Hereinafter, the rotation axis crack detection system and method using torsional stiffness estimation according to the present invention will be described in detail with reference to the attached drawings. In this process, the thickness of lines or sizes of components shown in the drawings may be exaggerated for clarity and convenience of explanation. In addition, the terms described below are terms defined in consideration of functions in the present invention, and may vary depending on the operator's intention or custom. Therefore, definitions of these terms should be made based on the content throughout this specification.

The purpose and effect of the present invention can be naturally understood or become clearer through the following description, and the purpose and effect of the present invention are not limited to the following description. Additionally, in describing the present invention, if it is determined that a detailed description of known techniques related to the present invention may unnecessarily obscure the gist of the present invention, the detailed description will be omitted.

1 is a configuration diagram of a rotary shaft crack detection system according to an embodiment.

As shown in FIG. 1, the rotation shaft crack detection system according to one embodiment includes a rotation control unit 100, a model construction unit 300, and a crack detection unit 500.

The rotation control unit 100 applies rotational drive to each of one side and the other side of the rotation shaft. The rotation control unit 100 is equipped with speed sensors on one side and the other side, and can measure the angular speed generated as it rotates in each direction.

The model building unit 300 uses a loop adaptive loop in which the covariance error is minimized to minimize noise in the measured value of the rotation information applied to each side of the rotation axis, and the forgetting factor is updated in which the Kalman gain increases inversely. Build a linear model using the extended Kalman filter.

The crack detection unit 500 calculates a torsional rigidity estimate of the rotation shaft for the input rotation information based on the constructed linear model and detects cracks in the rotation shaft using the calculated torsional rigidity estimate.

Here, it may further include an estimation unit that derives an estimated value for at least one of a scheduled torque to be applied to one side and the other side of the rotation axis, a scheduled angular velocity, a scheduled angle of one side, and a scheduled angle of the other side at each time interval preset by the rotation information. You can.

The rotation information may be rotational torque, angular velocity, and the angle difference between one side and the other side. The loop adaptive extended Kalman filter can discretize a nonlinear model based on an abnormal time domain.

The model building unit 300 may set the estimated forgetting factor to the maximum value if the residual of the derived forgetting factor and the estimated forgetting factor are within a preset value, and calculate the Jacobian matrix based on the previous estimate value. It can be linearized, and if the residual between the measured value and the estimated value of the rotation information is within a preset value, a weight can be applied to the measured value.

FIG. 2 is a diagram illustrating rotation axis modeling according to an embodiment, and FIG. 3 is a diagram illustrating the entire estimation process using forgetting factor update and the AEKF algorithm according to an embodiment.

As shown in Figures 2 and 3, the system model of the entire estimation process using the AEKF algorithm can be based on a dynamic circular shaft with torque and rotational speed applied together, similar to an actual drive line. System elements can perform simulations of the drive load motor Dynamo to experimentally verify the proposed algorithm. The stiffness of the bellows coupling connecting the shaft and the damping effect of the bearing stand can be neglected. do As shown in 2, the rotation axis model can be composed of four components. The governing equations for shaft rotation can be given as:

[Equation 1]

[Equation 2]

In equations 1 and 2, is the moment of inertia (drive motor), is the moment of inertia (load motor), is the torsional stiffness of the shaft, is the viscous friction damping coefficient of the drive motor. When torque is applied by a load motor, a difference in angular velocity on both sides may occur due to the rigidity of the shaft connecting the two motors. In order to implement the Kalman filter algorithm, the dynamic model must be expressed as a state space model, which can be expressed as the following equation.

[Equation 3]

[Equation 4]

In equations 3 and 4, x is the state vector, u is the input vector, is the time derivative of the state vector. In Equation 3, A is the state matrix and B is the input matrix. In Equation 4, y is a measurement variable, C is a measurement matrix, and D is a feed-forward matrix. The three state variables for stiffness estimation can be expressed by the following equation.

[Equation 5]

[Equation 6]

In equation 5, is the difference between the angular displacements of both sides, is the angular velocity of the load motor. fourth state variable is the angular velocity of the driving motor. Drive motor torque is the input to the system. The state space equation can be derived from Equations 1 and 2 and can be expressed as the following equation.

[Equation 7]

[Equation 8]

In Equation 7, the reconstructed system model f(x,u) is a non-linear model, and in Equation 8, the measurement model h(x) is a linear model whose output is the actual measurable angular velocity value. For torsional stiffness estimation, an Extended Kalman Filter (EKF), which linearizes a nonlinear model, is considered, and an adaptive EKF (Adaptive EKF, AEKF) with a P-adaptive loop is proposed to improve estimation performance. Since the proposed AEKF algorithm is based on the discrete time domain, the continuity equation was discretized using the Euler method expressed as the following equation.

[Equation 9]

In equation 9, is the time step, Is and It represents the instantaneous time in . By substituting equation 7 into equation 9, it can be defined as the following equation.

[Equation 10]

[Equation 11]

Here, the discrete time equation can be expressed as the following equation.

[Equation 12]

The recursive structure optimally estimates the state of a linear dynamic system based on measurements contaminated by noise. The general linear discrete-time system model needed to design a KF is:

[Equation 13]

In equation 13, is the noise variable of a multivariate Gaussian distribution system with a covariance matrix, is a multivariate Gaussian distributed measurement variable with a covariance matrix. Here, there is no input to the measurement model, and the application of EKF is based on a nonlinear model. The general discrete time equation can be expressed as the following equation.

[Equation 14]

In Equation 14, the extended Kalman filter can assume the differentiability of the state change function instead of the linearity of the model. The nonlinear system model is linearized using Jacobian, and the Jacobian matrix can be calculated based on the previous estimate and expressed in the following equation.

[Equation 15]

[Equation 16]

The matrices A and B of the linearized rotation axis system model using Equation 15 and Equation 16 are as follows.

[Equation 17]

[Equation 18]

[Equation 19]

Here, (*) represents the system model matrix linearized using Jacobian. The form of the discrete-time EKF algorithm can be composed of an initial estimation step, a prediction step, and a correction step at k = 0, and each step can be expressed by the following equation.

[Equation 20]

[Equation 21]

[Equation 22]

[Equation 23]

Equation 20 is the initial estimation step at K=0, Equation 21 is the prediction step, and Equations 22 and 23 are the correction steps. In Equation 20, E represents the expected value of the random variable, and in Equation 15, the matrix was differentiated using the Jacobian matrix. The variables predicted in the prediction step are the a priori state variables and the error covariance matrix.

Because the filter estimation depends on historical data, it is difficult to estimate time-varying parameters (shaft stiffness) using EKF, and the state estimation may diverge if the historical data is not suitable for the recursive estimation method. Therefore, to solve this technical limitation, the forgetting factor ( ) is used. The updated forgetting factor modifies the error covariance matrix and the Kalman gain matrix increases by the reciprocal of the forgetting factor. The forgetting factor is considered a constant tuning parameter. However, it decreases when uncertainty is large, such as in non-linear models. Therefore, an adaptive loop can be used to apply more weight to recent data using the residual between measured and estimated values. The AEKF equation is the same as the EKF in Equation 21 except for the forgetting factor of the error covariance equation, and when λ (k) ≥1, it can be expressed as the following equation.

[Equation 24]

Therefore, divergence can be prevented by considering the impact of the most recently measured data on the state and parameters. The performance of AEKF is completely dependent on the forgetting factor, so it is the most important factor. Here, the residual z(k) is defined as the difference between the measured value and the estimated value, and is the white noise sequence when the optimal filtering gain is used, and the residual can be expressed by the following equation.

[Equation 25]

Here, the covariance of the residuals for all gains can be expressed as follows.

[Equation 26]

The autocovariance of the residuals can be expressed by the following equation.

[Equation 27]

In equation 27, is equal to 0 when substituting Equation 22 and Equation 26 into Equation 27, which may mean that the residual sequence is uncorrelated when applying optimal gain. But the residual The actual covariance of may differ from the theoretical covariance due to errors in system model parameters and noise covariance. thus, may not be 0. Accordingly, in Equation 27 The forgetting factor can be derived so that the last term of is 0, and this can be expressed as the following equation.

[Equation 28]

In Equation 28, under optimal conditions and can be expressed by the following equation:

[Equation 29]

[Equation 30]

The optimality of the Kalman filter can be determined through Equation 29, which is a scalar function. Is It is the (i, j)th element of . The smaller is the optimal filter, so the forgetting factor By selecting must be minimized. To track parameters that change over time, a recursive estimation method using forgetting factor updates can be introduced. Additionally, the constant forgetting coefficient can be optimally updated according to the following equation (i.e., gradient descent), which can be expressed as the following equation:

[Equation 31]

The equation for the initial conditions in Equation 31 is as follows.

[Equation 32]

In equations 31 and 32, is a time series is the repetition time of the moment. is the step length (i.e. learning rate, 0 < <1). If Equation 33 is satisfied at the pth iteration (i.e., convergence), the iteration is stopped and the optimal forgetting factor is determined using Equation 34.

[Equation 33]

[Equation 34]

However, iterative numerical methods do not guarantee real-time processing. Finally, the onestep AEFK algorithm can be used to solve this computational burden. For a given system, the state equations (14, 20, and 21) can have the following assumptions: [Assumption 1: Q(k), R(k) and P(0) are positive definite] and [Assumption 2: The measurement matrix H(k) is fully ranked] Accordingly, the optimal forgetting factor is It can be calculated as follows:

[Equation 35]

In equation 35, and can be expressed by the following equation:

[Equation 36]

[Equation 37]

In equation 37, The value can be estimated using the following recursive equation:

[Equation 38]

[Equation 39]

[Equation 40]

initial conditions and In, the proof of Equations 35, 36, and 37 was derived by substituting Equation 22, which derives the Kalman gain value, into Equation 28, which can be expressed as the following equation.

[Equation 41]

[Equation 42]

Equation 42 can mean that under assumptions 1 and 2, the optimal condition disclosed in Equation 28 is the same as Equation 26. Therefore, by substituting Equation 16 into Equation 42 and reorganizing, it can be generated as follows.

[Equation 43]

Based on the proposed algorithm, MATLAB can be used to simulate a situation in which cracks occur due to shaft damage. Although there are various connection structures such as bearings and shafts in the actual rotating shaft system, the main purpose of this simulation is to verify the changing stiffness estimates with a simplified model. The parameter values of the system model can be shown in Table 1.

A sinusoidal torque input can be applied (frequency 1 Hz, Tm(t) = 10,000 sin(2ðt) Nmm) to mimic cracking due to continuous cycling. The angular velocity measurement data of the simulation model can be set to be contaminated by white Gaussian random noise v(k) = N(0,(10 ³ ) ² ).

Figure 4 is a graph showing stiffness due to crack initiation over a certain period of time according to one embodiment.

For the crack initiation scenario, as shown in Figure 4, in the 20-second time data, the stiffness decreases from 735,000 to 345,000 Nmm/rad over 10 seconds due to crack initiation.

Parameters (unit) Value Inertia moment of load motor J _l (Nmm ² ) 580 Inertia moment of driving motor J _m (Nmm ² ) 180 Damping constant cm (Nmm·s/rad) 1,000 Shaft torsional stiffness ks (Nmm/rad) 735,000

The initial state value and error covariance for estimation can be expressed by the following equation.

[Equation 44]

The system noise covariance matrix Q and the measurement noise covariance R for Equation 23 and Equation 24 were adjusted in various cases as follows and the optimal estimate can be derived.

[Equation 45]

To evaluate the basic estimation performance of AEKF, the root-mean-squared error (RMSE) at the kth time point can be calculated for more precise analysis, which can be expressed in the following equation.

[Equation 46]

In equation 46, k is At the time moment, and are the true and estimated values, respectively. The steady-state average of the RMSE (MRMSE) can then be calculated to exclude the effects of transient behavior.

Figure 5 is a graph showing the estimation results for a sudden decrease in torsional rigidity according to one embodiment.

As shown in Figure 5, AEKF can accurately estimate rapid torsional stiffness changes. In contrast, EKF does not track shaft stiffness changes over time. The forgetting factor is changed appropriately by the P-adaptation loop when the stiffness decreases rapidly at 10 s. The robustness of the proposed estimation model under noise and parameter model uncertainty is analyzed by introducing sensor noise and perturbations to the main parameters. To assess robustness under noise and parameter uncertainty, the relative error (i.e., normalized performance measure) with respect to the nominal value can be quantitatively calculated, which can be expressed as the following equation:

[Equation 47]

Since sensor information is inherently contaminated by electrical noise, the impact of electrical noise on estimation performance is considered. Sensor data can be contaminated by adding white Gaussian random noise.

Figure 6 is a graph showing simulation results of shaft stiffness estimation under noise uncertainty according to one embodiment.

As shown in FIG. 6, the probability density function according to one embodiment can be shown in (a) and (b) of FIG. 6 as an example, and the random noise (error) distribution can be fit to a normal Gaussian distribution with variance. can be considered (σ ² = 0.00197, Case 1; σ ² = 0.00298, Case 2), and can be confirmed with white Gaussian random noise. As shown in Figures 6 (c) and (d), the estimation results are similar to the original data and there is no significant difference, indicating that the proposed AEKF is robust against Gaussian random noise extracted from sensor data.

Figure 7 is a graph showing estimation results according to one embodiment.

As shown in Figure 7, the estimation performance of the AEKF model can be evaluated under parametric uncertainty such as the moment of inertia. Both moments of inertia can be important model uncertainties because they depend on the size, weight, and connection structure of the coupling. The nominal value for the moment of inertia of the load motor (580 Nmm ² ) was perturbed by -20% (464 Nmm ² ) and +20% (696 Nmm ² ), and the nominal moment of inertia of the drive motor (180 Nmm ² ) was also changed. It can be. It can be perturbed by -20% (144 Nmm ² ) and +20% (216 Nmm ² ). The damping coefficient varies under normal operating conditions (800~1200 Nmm·s/rad) depending on the bearing lubrication conditions, and the estimation results are similar to the nominal value within a reasonable range under various parametric uncertainties, as shown in Figure 7-(d). It demonstrates the robustness of the proposed model.

Figure 8 is a diagram showing the configuration of a system for estimating torsional rigidity according to an embodiment.

As shown in Figure 8, the proposed shaft condition monitoring method was experimentally verified using a torque generator as the rotation control unit 100. An aluminum hollow bar specimen (o D: 20 mm, i D: 18.2 mm, L: 550 mm) was used for the rotation axis as shown in Figure 8. The torque generator may be composed of a drive motor and a torque-controlled load motor. (Mitsubishi HG-SR152, 10Hz bandwidth). A sinusoidal torque (Tm(t) = 10,000 sin(2π t) Nmm) was applied at a rotational speed of 5.23 rad/s (50 RPM). In the case of the shaft crack scenario, the shafts were alternately replaced from a normal shaft without cracks to a cracked shaft at a 45° direction, as shown in Figure 8(b).

The crack depth was set to 5 mm to allow the shaft stiffness to suddenly drop from its original value, and to examine the applicability of a non-contact angular velocity sensor (tachometer), the measurement model considered angular velocity values on both sides of the rotation axis. The angular velocities on both sides were measured using a photoelectric detector-type rotational speed sensor (ONO SOKKI, model name: LG-930), and the rotational speed was calculated by calculating the light reflected by the gear per rotation as a pulse. Real-time monitoring performance was evaluated using the dSPACE® system (DS1104).

Here, the Recursive Least Square Estimator (RLSE) was used to identify unknown model parameters. Accordingly, the above-described rotation axis model, Equation 1 and Equation 2, can be reconstructed in matrix form as follows.

[Equation 48]

[Equation 49]

In addition to the data measured from the sensor, two matrices and Other information is needed about . The mathematical equation for the necessary information can be expressed as follows.

[Equation 50]

[Equation 51]

[Equation 52]

[Equation 53]

[Equation 54]

Equations 50 and 51 are the initial evaluation equations, Equation 52 is the Kalman gain calculation equation, Equation 53 is the parameter update equation, and Equation 54 is the covariance update equation. First, the input torque (T _m ) of Equation 52 was measured using an in-line torque sensor, as shown in FIG. 8. procession Angular displacement for ( ) and two angular accelerations ( ) was derived by direct differentiation and integration using low-pass filtering of the angular velocity signal. Then RLSE was designed as follows:

Figure 9 is a convergence history graph according to one embodiment.

As shown in Figure 9, (a) in Figure 9 is the moment of inertia of the load motor, (b) is the moment of inertia of the drive motor, (c) is the damping constant, and (d) is the shaft torsional stiffness. It was estimated successfully because it converged to the steady-state final positive value after 5000 iterations. The identified system parameters of the rotating shaft model are listed in Table 2.

Parameters (unit) Value Inertia moment of load motor J _l (Nmm ² ) 595 Inertia moment of driving motor J _m (Nmm ² ) 20 Damping constant cm (Nmm·s/rad) 280 Shaft torsional stiffness ks (Nmm/rad) 13,000

Figure 10 is a graph showing experimental results of a stiffness estimation system according to an embodiment.

As shown in Figure 10, (a) and (b) are the estimated responses of torsional stiffness, (c) and (d) are the angular velocity inputs, (a) and (c) are graphs without cracks, and (b) are the estimated responses of torsional stiffness. ) and (d) are graphs of cracks (crack depth 5 mm). For the AEKF estimation model, by setting the initial state and the two noise covariance matrices (Q and R) through trial and error, P ₀ is diag[0.1 1 650000 1], Q was adjusted to diag[1 2.1 2 2.1]×10 ⁵ , and R was adjusted to diag[9 9]×10 ⁸ . The shaft stiffness estimated using the proposed algorithm is compared in Figure 10, and the estimated stiffness reached a steady state after 15 seconds in both cases. Additionally, different crack scenarios can be set up to further investigate the effectiveness of the proposed algorithm. The crack depth was increased (11 mm) to rapidly decrease from 15,000 Nmm/rad to less than 7,500 Nmm/rad due to the decrease in cross-sectional area (the ratio of the crack segment area to the original cross-sectional area was 65%). Similar to Figure 10, the proposed algorithm can track stiffness degradation due to severe cracking, as shown in Figure 11. The proposed estimation model can not only estimate the stiffness reduction due to cracking, but also can quantitatively evaluate fatigue crack growth by directly estimating shaft torsional stiffness.

Figure 11 is a graph showing experimental results for a crack scenario. Figure 12 is a graph showing the torsional stiffness response estimated from the electrical sensor noise uncertainty.

In Figure 11, (a) indicates no crack, (b) indicates the presence of a crack (crack depth: 11 mm), and in Figure 12, (a) indicates a crack depth of 5 mm, (b) indicates a crack depth of 11 mm, (c) is the probability density distribution of sensor noise extracted from the original sensor signal, and (d) is the relative error to nominal.

The robustness of the proposed estimation model under noise uncertainty was assessed by introducing perturbations to the sensor noise. The original sensor signal was filtered with a digital moving average filter (no phase delay). Low-pass filtering produced two corrupted signals: small (case 1, less polluted) and off (case 2, more polluted, i.e. raw data). The probability density distribution of sensor noise extracted from the original sensor signal is similar to a Gaussian distribution, as shown in Figure 12(c).

The estimation model appeared to be robust against Gaussian random noise in all sensor data, as the estimation results were similar regardless of the degree of contamination, as shown in Figure 12(a) and (b). For severe cracks (crack depth 11 mm), the proposed estimation model is shown to be more robust to Gaussian random noise, as shown in Figure 12(d).

Figure 13 is a flowchart showing a method of detecting cracks in a rotating shaft according to an embodiment.

As shown in FIG. 13, the method for detecting cracks in a rotating shaft according to an embodiment includes a rotation control step (S100), a model building step (S300), and a crack detection step (S500), and may further include an estimation step. .

In the rotation control step (S100), rotational drive is applied to one side and the other side of the rotation shaft.

The model building step (S300) is a loop adaptive loop in which the covariance error is minimized and the forgetting factor is updated in which the Kalman gain increases inversely to minimize noise in the measured value of the rotation information applied to each side of the rotation axis. A linear model can be built using an extended Kalman filter.

Here, in the model building step (S300), if the residual of the derived forgetting factor and the estimated forgetting factor is within a preset value, the estimated forgetting factor can be set to the maximum value, and the Jacobian matrix is calculated based on the previous estimate. This can be calculated and linearized, and if the residual between the measured value and the estimated value of the rotation information is within a preset value, a weight can be applied to the measured value.

In the crack detection step (S500), a torsional stiffness estimate of the rotation axis is calculated based on the input rotation information based on the constructed linear model, and a crack in the rotation shaft can be detected using the calculated torsional rigidity estimate.

In the estimation step, an estimated value for at least one of a scheduled torque to be applied to one side and the other side of the rotation axis, a scheduled angular velocity, a scheduled angle of one side, and a scheduled angle of the other side at each preset time interval may be derived from the rotation information.

Although the present invention has been described in detail through representative embodiments above, those skilled in the art will understand that various modifications can be made to the above-described embodiments without departing from the scope of the present invention. will be. Therefore, the scope of rights of the present invention should not be limited to the described embodiments, but should be determined not only by the claims described later, but also by all changes or modified forms derived from the claims and the concept of equivalents.

100: rotation control unit 300: model construction unit
500: Crack detection unit

Claims (12)

a rotation control unit that applies rotational drive to each of one side and the other side of the rotation axis;
In order to minimize noise in the measured value of rotation information applied to each side of the rotation axis, a loop adaptive extended Kalman filter is used to minimize covariance error and update the forgetting factor whose Kalman gain increases inversely. a model building unit that builds a model; and
A rotation shaft crack detection system comprising a crack detection unit that calculates a torsional rigidity estimate of the rotation shaft for input rotation information based on the constructed linear model and detects cracks in the rotation shaft using the calculated torsional rigidity estimate.
According to claim 1,
A rotation shaft crack detection system using torsional stiffness estimation, characterized in that the rotation information is rotation torque, angular velocity, and the angle difference between one side and the other side.
According to claim 1,
The loop adaptive extended Kalman filter is a rotation axis crack detection system using torsional stiffness estimation, characterized in that it discretizes a nonlinear model based on a discrete time domain.
According to claim 1,
Torsional rigidity further comprising an estimation unit that derives an estimate for at least one of a scheduled torque to be applied to each of one side and the other side of the rotation axis, a scheduled angular velocity, a scheduled angle of one side, and a scheduled angle of the other side at preset time intervals using the rotation information. Rotational axis crack detection system using estimation.
According to claim 1,
The model construction unit sets the estimated forgetting factor to the maximum value if the residual of the derived forgetting factor and the estimated forgetting factor is within a preset value. A rotation axis crack detection system using torsional stiffness estimation.
According to claim 1,
A rotation axis crack detection system using torsional stiffness estimation, wherein the model building unit calculates a Jacobian matrix based on the previous estimate and linearizes it.
According to claim 1,
A rotation axis crack detection system using torsional stiffness estimation, wherein the model building unit applies a weight to the measured value if the residual between the measured value and the estimated value of the rotation information is within a preset value.
A rotation control step in which a rotational drive is applied to one side and the other side of the rotation shaft;
In order to minimize noise in the measured value of the rotation information applied to each side of the rotation axis, a linear loop adaptive extended Kalman filter is used in which the covariance error is minimized and the forgetting factor that increases the Kalman gain inversely is updated. A model building stage in which a model is built; and
A crack detection step of calculating a torsional stiffness estimate of the rotating shaft for input rotation information based on the constructed linear model and detecting a crack in the rotating shaft using the calculated torsional stiffness estimate.
According to claim 8,
Torsion further comprising an estimation step of deriving an estimated value for at least one of a scheduled torque to be applied to each of one side and the other side of the rotation axis, a scheduled angular velocity, a scheduled angle of one side, and a scheduled angle of the other side at preset time intervals using the rotation information. Rotational axis crack detection method using stiffness estimation.
According to claim 8,
In the model building step, if the residual of the derived forgetting factor and the estimated forgetting factor is within a preset value, the estimated forgetting factor is set to the maximum value. A rotation axis crack detection method using torsional stiffness estimation.
According to claim 8,
In the model building step, a rotation axis crack detection method using torsional stiffness estimation is characterized in that a Jacobian matrix is calculated and linearized based on the previous estimate.
According to claim 8,
In the model building step, if the residual between the measured value and the estimated value of the rotation information is within a preset value, a weight is applied to the measured value. A rotation axis crack detection method using torsional stiffness estimation.