Ultrasonic guided wave nondestructive testing of anchorage quality of rebar resin bolt based on EMD-PCA

Abstract

Currently, the ultrasonic guided wave inspection of the anchoring quality of rebar resin bolts in coal mine tunnels faces issues such as rapid signal energy attenuation, waveform superposition of reflected waves, and waveform complexity, making it difficult to effectively identify anchoring quality. Therefore, a method combining Empirical Mode Decomposition (EMD) with Principal Component Analysis (PCA) is proposed for processing and analyzing ultrasonic guided wave detection signals. This study employs numerical simulation combined with laboratory testing, selecting low-frequency guided waves at 50 kHz with lower attenuation as excitation signals to simulate the propagation process of ultrasonic guided waves through rebar resin bolt and surrounding anchorage media. Concurrently, an indoor nondestructive testing experimental platform was established to investigate signal propagation patterns across specimens with varying anchorage qualities. Finally, the EMD-PCA method was applied to process and analyze defect signals. Results demonstrate that this signal processing method can accurately identify the actual positions and lengths of anchorage defects, with discrepancies between numerical simulations and laboratory measurements remaining within 9.5%. For extended anchorage defects, the positioning error of defect locations is less than 2%. When defect interfaces approach the distal end of the anchorage, the IMF2 mode derived from EMD decomposition remains effective in extracting wave impedance difference interface reflections, thereby verifying the feasibility of applying the EMD-PCA signal processing method to ultrasonic guided wave nondestructive detection of defects in rebar resin bolts in coal mine tunnels.

Introduction

At present, the annual new excavation of roadways in China’s coal mines exceeds 12,000 km, equivalent to the diameter of the Earth, which is on a huge scale. Due to its significant technical superiority, the bolt reinforcement technique has become the main support form for coal mine roadways. However, due to human factors and geological conditions, problems such as insufficient length of the anchored segment of bolt and anchorage defects in the anchor segment often occur. The anchorage failure of bolt is one of the main causes of roadway roof collapse accidents¹. Therefore, to ensure the safety of bolt-supported roadway, it is necessary to conduct regular inspections of the bolt anchorage quality². Traditional detection methods have been gradually phased out due to their destructive and accidental nature, while the emerging methods of non-destructive testing (NDT) of bolts, with their non-destructive, efficient and rapid characteristics, have gradually become the preferred method for detecting the anchorage quality of anchor bolts. In recent years, ultrasonic guided wave NDT technology^3,4,5 has become a research hotspot due to its clear reflection signals at the fixed end and bottom end of the detection waveforms, and has increasingly attracted the attention of scholars.

Beard^6,7 first applied ultrasonic guided waves for nondestructive testing of mine resin anchors, which verified the possibility of using ultrasonic guided waves for nondestructive testing of mine resin anchors. Zou⁸ determined the length of the anchor solid of anchor rods by measuring the attenuation value of the ultrasonic guided waves. Wang et al.⁹ proposed to evaluate the bond quality of the anchor rods using attenuation coefficient of propagation within the anchor rods by analysing the attenuation law of ultrasonic guided wave signal propagation in different anchor strengths, it is proposed to use the attenuation coefficient of ultrasonic guided wave propagation within the anchor to evaluate the bond quality of the anchor. Cui Jiangyu, He Cunfu et al.^10,11 simplified the resin anchor bar into a columnar three-layer bar structure to study the propagation characteristics of ultrasonic guided waves in it. The experimental results show that the L(0, 1) modal attenuation in the range of 20–100 kHz is relatively small and can be used for practical engineering testing. Byun et al.¹² used ultrasonic guided waves to evaluate the grouting rate of rock anchors and analysed the group velocity of ultrasonic guided waves in using wavelet transform. The experimental results show that the ultrasonic guided wave group velocity parameter can be used as an index to evaluate the grouting rate of anchor rods. Zhang Jingke, Li Kai et al.¹³ used the Hilbert-Huang transform (HHT) signal analysis method to analyse and process the extinction signal, and was able to identify the defects and the reflective signals at the bottom of the rod more clearly. YU¹⁴ found that the ultrasonic guided wave group velocity in the anchor rod decreased with the increase of the degree of weathering of the rock by numerical simulation and indoor test. Guo Yanyu, Zhang Changsuo et al.¹⁵ constructed a model of anchored anchor rods containing different defect characteristics, and investigated the location and depth of the defects, and the results showed that the area of the defects can be roughly determined based on the ratio of the defective echo amplitude to the bottom echo amplitude. Leilei Liu and Jun Zhu et al.¹⁶ used the empirical modal decomposition (ICEEMDAN) method to process the ultrasonic guided wave reflection signals, and inferred the location and length of the defects based on the peak value of the decomposed intrinsic modal function. Wang Manman¹⁷ used ultrasonic guided waves for nondestructive testing of BFRP anchor bolts, revealing the relationship between anchor pull-out defects and wave velocity and attenuation.

Although ultrasonic guided wave technology has made some progress in the research of NDT of bolts, it is mostly concentrated in the field of geotechnical mortar anchors, and less applied to Coal Mine Rebar Resin Anchor. And in the ultrasonic guided wave detection of threaded steel rebar resin anchor, there are often faster energy attenuation and superposition of reflection waveforms, which cannot effectively identify the quality of anchorage, especially in the precise quantitative detection of the location and length of defects in the resin anchors is nearly blank^18,19,20. Therefore, it is of great significance to process the ultrasonic guided wave detection signals by using modern signal analysis techniques. The feasibility of ultrasonic guided wave nondestructive testing of coal mine rebar resin anchor quality is verified by combining numerical simulation and indoor test, and the signal processing of the collected waveforms is combined with the method of EMD combined with PCA, which is capable of effectively extracting the reflective echoes at the interface of anchorage defects, and then further performing the actual location and length of anchorage defects inversely according to the derived formulae. The actual position and length of the anchorage defects are further reflected according to the derived formula.

Detection theory and analysis

Ultrasonic guided wave detection theory

Currently, mining threaded steel resin anchor bolts are a commonly used support tool in coal mine tunnels and other underground engineering projects. It can maintain the stability of the surrounding rock to the greatest extent and can effectively limit the axial and radial deformation of the surrounding rock^{21,22,23,24,25}. A partial enlargement of the single threaded steel resin anchor support is shown in Fig. 1.

Fig. 1

Local enlarged diagram of single bolt anchorage support.

When the ultrasonic guided wave propagates in the anchored segment of bolt, the incident wave is input from the end of the free section of the anchor bar and propagates along the axial direction of the anchor bar. Since the solid end face of the anchor bar is a physically variable interface, a part of the wave transmits through the interface and continues to propagate along the axial direction of the bar after propagating to the solid end face, and the other part of the wave will be reflected. The reflection and transmission coefficients can be written in the following form:

$$R = \frac{{\sigma_{R} }}{{\sigma_{I} }} = \frac{{W_{2} - W_{1} }}{{W_{1} + W_{2} }}$$

(1)

$$T = \frac{{2W_{2} }}{{W_{1} + W_{2} }}$$

(2)

In the equation, R is the reflection coefficient; T is the transmission coefficient; and W is the wave impedance.

The transmitted wave continues to propagate in the rod axial direction towards the bottom of the anchor, and when it propagates to the bottom, it is also reflected and propagates in a continuous loop inside the anchor until the ultrasonic guided wave inside the anchor completely attenuates to zero²⁶, and the propagation process is shown in Fig. 2.

Fig. 2

Propagation of ultrasonic wave in anchorage body.

When there is a defect inside the resin anchoring agent, the local magnified view is shown in Fig. 3.

Fig. 3

Local enlargement diagram of resin anchoring agent defect bolt.

When ultrasonic guided waves propagate to the bolt’s defect zone, partial energy reflects to the transducer, while the remainder transmits through the defect and continues propagation. Assuming that the ultrasonic guided wave propagates along the x-positive direction, the interface from the end surface of the anchor solid to the upper interface of the resin anchorage defect is the first medium, and the interface from the upper interface of the resin anchorage defect to the lower interface is the second medium.

When the ultrasonic guided wave propagates in the anchored segment of bolt, let the incident wave be:

$$ux = Ie^{{i(k_{1} x - wt)}}$$

(3)

The reflected field displacement in the first medium is

$$ux^{(R)} = A{\text{Re}}^{{ - i(k_{1} x + wt)}}$$

(4)

The displacement of the transmitted field in the second medium is

$$ux^{(T)} = ATe^{{i(k_{2} x - wt)}}$$

(5)

where I represents the amplitude of the incident wave ; A_R and A_T are the coefficients to be determined; k is the wave number; The interface of the two media needs to satisfy the corresponding boundary conditions.

Detection signal analysis and processing

In this paper, ultrasonic guided wave NDT method is adopted to study the propagation characteristics of ultrasonic guided waves in defective mining rebar resin anchor rods. The wave propagation behaviour in defective anchor solid is achieved by applying the ultrasonic guided wave excitation signal along the axial direction of the rod at the coupling surface of the middle node at the top of the mining rebar resin anchor rod, and a collection point r0 is set at the end of the anchor rod to receive the reflected signal. Figure 4 shows a schematic diagram of a defective anchor rod anchored by mining rebar resin.

Fig. 4

Schematic diagram of resin anchoring defect bolt.

It should be noted that the coal mine rebar resin anchor member consists of two parts, L₁ and L₂.Part L₁ refers to the anchor not anchored in the resin anchorage, and this part should be treated as a free anchor; part L₂ refers to the anchor anchored in the resin anchorage, and this part should be calculated as a resin anchor. Therefore, the ultrasonic guided wave can be determined according to the following formula in the calculation of the length of the free and anchored sections of the anchor²⁷:

$$2L1 = V1t{\text{a 2}}L2 = V2(t{\text{b - }}t{\text{a}})$$

(6)

where V₁ is the value of the velocity of the experimental wave propagating in the free anchor; V₂ is the value of the velocity of the experimental wave propagating in the resin anchor; t_a is the return time of the experimental waveform anchorage end face; t_b is the return time of the bottom reflected signal.

For the anchor bolt containing defective resin shown in Fig. 4, the defect length L₃ calculation can be determined according to the following equation:

$$L3 = L2 - V2\frac{{[{\text{t}}b - {\text{t}}a - ({\text{tu2 - tu1}})]}}{2}$$

(7)

where L₃ is the length of the resin anchorage defect; t_u1, t_u2 are the reflection echo points at the upper and lower interfaces of the resin anchorage defect, respectively.

The length and location of the defects in resin anchoring agent L3 can be simulated and calculated based on the reflection time points of ultrasonic guided waves at different interfaces. However, the ultrasonic guided wave propagates in the defective anchor, due to the existence of multiple wave impedance hetero-interfaces in the medium, the phenomenon of superposition of incident, reflected and defective echoes will occur, and there is energy attenuation, which makes the waveform of the received signals very complex, and it is not possible to distinguish the end face echoes effectively. Therefore, a powerful signal analysis means is needed to analyse and process the detected signals. In this paper, the EMD decomposition method combined with PCA principal component analysis is used to process the detection signal, which can effectively extract the reflection echo points of the anchorage end face, defect interface and bottom position of the detection signal, so as to perform the actual position and length of the defects in resin anchoring agent.

EMD decomposition principle

EMD is a data processing method used to decompose a complex signal into a number of intrinsic mode functions with more pronounced local features²⁸. The schematic diagram of EMD decomposition is shown in Fig. 5.

Fig. 5

EMD decomposition diagram.

The basic idea is to decompose the signal into a set of oscillating functions with more distinctive local features, which are called IMFs. Each IMF satisfies the following two conditions:

• a. Throughout the signal segment, the number of extreme points (including extreme values and extreme minima) and the number of over-zero points of the IMF are equal, or there is a difference of at most one between the two.

• b. The mean of the upper and lower envelopes is zero at any given data point. This implies that the mean value of the IMF is zero and fluctuates up and down in a localised region²⁹.

The EMD decomposition method can help to analyse the local properties of the original signal signals. However, after modal decomposition using EMD, multiple IMF components and a residual are usually obtained. In some cases, it is necessary to filter out the most important or significant components from all the IMFs to reduce the dimensionality of the data or to extract key features. This is where PCA can be used to filter and reduce the dimensionality of the IMFs.

PCA principal component analysis

PCA is a dimensionality reduction method that projects the original n-dimensional data (i.e., num variables) into a k-dimensional principal component space. This process retains over 90% of the cumulative variance in the dataset (typically with a threshold set at ≥ 85%), effectively eliminating multicollinearity and noise interference.

The steps of the analysis are as follows:

• (1) Prepare the data: the IMFs obtained after EMD processing are used as samples, and the value of each IMF is used as the feature of the sample. Suppose there is a dataset X containing m samples and n features, where X = [x1,x2, …, xm], and each sample xi is an n-dimensional vector.

• (2) Standardised data: the data are standardised to ensure that each feature has a mean of 0 and a variance of 1. The vector of means for the sample $\overline{x}$:

  $$\overline{x} = \frac{1}{m}\sum\limits_{i = 1}^{m} x i$$

  (8)

• (3) Application of PCA: The PCA algorithm is applied to the normalized data to obtain the principal component (main feature) and the corresponding covariance matrix $\sum {}$:

  $$\sum { = \frac{1}{{\text{m}}}} X_{{{\text{centered}}}}^{T} X_{{{\text{centered}}}}$$

  (9)

• (4) Selection of principal components: select the most important principal components according to the magnitude of the covariance, i.e., retain the principal components that have the greatest impact on the data, and select the eigenvectors corresponding to the first k eigenvalues as the principal components, constituting a projection matrix W (each column is an eigenvector).

• (5) Reconstructing the data: using the selected principal components, the dataset is projected into a subspace consisting of the first k eigenvectors, resulting in a filtered IMF:

  $$X{\text{reduced = }}X{\text{centeredW}}$$

  (10)

  In the formula, Xreduced is the data set after dimension reduction.

• (6) Recovering data: The screened IMF is added to the residuals to recover the original data.

  Through this process, the IMF components of the original detection signals can be filtered and downscaled to transform the data from the original feature space to a new space (i.e., principal component space), thus reducing the complexity and dimensionality of the data while retaining the key features of the data. Doing so helps to improve the processing efficiency and analysis accuracy of the data, so that the location and length information of anchorage defects can be effectively detected.

Establishment of numerical model

Model parameter

In this section, CAE finite element numerical simulation software is used to establish the anchor solid model of mining rebar resin anchor rods, and “Explicit”–explicit module is used to simulate the propagation process of ultrasonic guided wave in coal mine rebar resin anchor rods. Figure 6 shows the schematic diagram of the anchor solid model of mining rebar resin defective anchor rods.

Fig. 6

Numerical model of mining screw steel resin defect bolt. (The CAE software used here is LS-DYNA, software version SMP971_S, with the official website link http://m.hgengineering.cn/display/355280.html).

In the CAE numerical model construction, it is set that the material connection between the anchor and the resin anchorage is rigid, and the two are constrained by TIE constraint. Through this constraint, the model ensures that the nodes between the anchor and the resin align with each other during the analysis, and ensures that their displacements and rotations are exactly the same; the interaction type between bolt, resin anchor and surrounding rock is set as general contact (Explicit), and there is friction and viscous behavior between each other.

In order to ensure the accuracy of the numerical simulation results, the threaded steel rebar resin anchor, resin anchoring agent and perimeter rock parameters selected for the simulation are the same as those of the field tests. The material parameters selected for the numerical model is shown in Table 1.

Table 1 Parameters of materials.

Determination of excitation wave frequency

In the low-frequency region, ultrasonic guided waves exhibit higher energies and longer wavelengths, and their dispersion effects are relatively weak. Only very few modes propagate within the anchor. Especially in the low-frequency band, the L(0, 1) mode is the fastest propagating mode. Therefore, in this paper, a simulation and analytical study of ultrasonic guided waves in the L (0, 1) mode is carried out, which helps to identify and analyse the reflected waveforms more accurately.

Hann window is a commonly used window function for signal processing and spectral analysis, sinusoidal signals in the modulation of Hann window, the energy is more concentrated, the excitation of the guided wave dispersion effect is smaller, so often as a dynamic load function. The excitation signal used in this paper is shown in Fig. 7. In the numerical simulation process, the anchorage surface boundary condition is set as a completely fixed constraint, and the load is applied to the coupling surface of the middle node at the top of the anchorage along the axial direction of the rod to achieve the excitation of ultrasonic guided waves, and the excitation signal H(t) and the Hann window function h(t) are defined as follows¹⁶:

$$H\left( {\text{t}} \right) = A{\text{sin}}\left( {2\pi fc{\text{t}}} \right) \cdot h\left( {\text{t}} \right){,}\quad {\text{t}} \in \left[ {0,\tau } \right]$$

(11)

$$h\left( {\text{t}} \right) = \frac{1}{2}\left\{ {1 - {\text{cos}}\left( {\frac{{2\pi fc{\text{t}}}}{{\text{n}}}} \right)} \right\}{,}\quad {\text{t}} \in \left[ {0,\tau } \right]$$

(12)

where the sinusoidal signal has a centre frequency of ƒc of 50kHz, amplitude A of 10, propagation of 10 cycles, number of sampling points of 200 and total signal duration of 2e–4s.

Fig. 7

Time domain diagram of excitation signal.

Analysis of simulation results

Numerical simulation of ultrasonic guided wave in bolt anchorage body

Establishment of numerical model

In order to study the propagation characteristics of ultrasonic guided waves in coal mine rebar resin anchor, three sets of CAE numerical models for free anchor bolt, fully grouted dense anchorage bolt and extended anchorage anchor bolt were established in this section, respectively. The numerical models are shown in Fig. 8, respectively.

Fig. 8

The schematic diagram of CAE numerical model.

In addition, the free anchor bolt diameter φ1 in the numerical model of this paper are all 22 mm, the anchorage thickness φ2 are all 6 mm, and the anchorage thickness φ3 are all 150 mm.

During indoor testing of mining threaded steel resin anchor bolt anchorage, as shown in Fig. 9. In laboratory testing of resin-grouted rock bolt anchorage for mining applications, as shown in Fig. 9, according to technical specifications for coal mine roadway roof anchorage³⁰, two Z2335 resin cartridges (a type of resin anchoring agent) were used for anchorage. The two Z2335 resin cartridges were placed into the pre-drilled borehole. Based on the three-diameter matching principle³¹ (bolt diameter d, borehole inner diameter D, cartridge diameter 2r), the effective anchorage length (L₂ = 1234 mm) of the two Z2335 resin cartridges in the borehole was derived using known parameters, with the calculation formula:

$$L_{2} = \frac{{\pi {\text{r}}^{2} l}}{{\pi \left[ {\left( \frac{D}{2} \right)^{2} - \left( \frac{d}{2} \right)^{2} } \right]^{2} }}$$

(13)

wherein, r is the radius of the Z2335 resin anchoring agent, with a value of 11.5 mm; l is the length of 2 rolls of the Z2335 resin anchor, with a value of 700 mm; D is the diameter of the outer ring of the resin ring of the anchorage section, with a value of 28 mm; d is the diameter of the inner ring of the resin ring of the anchorage section, with a value of 22 mm; and L₂ is the length of the anchorage section.

Fig. 9

Schematic diagram for validation of effective anchorage length L2.

Simulation results and analysis

The excitation is achieved by applying ultrasonic guided wave signals to the vertical end face of the intermediate node at the end of the anchor, simulating the propagation behaviour of the ultrasonic guided wave in the above three anchored anchor models, and receiving the reflected signals from the end face of the anchor and the bottom end according to the collection point r0, and the reflected waveforms obtained are shown in Fig. 10.

Fig. 10

Numerical simulation of reflected waveform time domain diagram.

From Fig. 10a, it can be seen that during the propagation of the ultrasonic guided wave in the free anchor, the reflection signal from the bottom end of the anchor is received at the top collection point r0 of the anchor at 0.65 ms, and the wave peaks of the two consecutive bottom reflection signals received are 0.797 ms and 1.679 ms, respectively, and from this, it can be calculated that the propagation velocity of the ultrasonic guided wave in the free anchor, V_(1), is 4988.66 m/And, from the figure, it can be seen that the propagation waveform of the ultrasonic guided wave in the free anchor is relatively stable, and there is no serious signal dispersion phenomenon.

From Fig. 10b, it can be seen that during the propagation of the ultrasonic guided wave in the full-length anchoring bolt, the top of the anchor rod receives a section of weak wave signals at 0–0.5 ms, which is due to the fact that the ultrasonic guided wave leaks through rod side interfaces to the rock layer during propagation and refracts and interferes with the collection point. At 0.68 ms, the collecting point at the top of the anchor rod receives a reflection signal from the bottom end of the anchor, and the two consecutive wave peaks of the reflection signal from the bottom end of the anchor are 0.81 ms and 1.71 ms, respectively, from which the propagation velocity of the ultrasonic guided wave in the full-length anchorage bolt can be calculated as 2742.22 m/s.

The propagation displacement cloud of the ultrasonic guided wave in the extended anchorage anchor bolt is shown in Fig. 11.

Fig. 11

Displacement cloud diagram of ultrasonic guided wave propagation process.

As can be seen from Figs. 10c and 11b, when the ultrasonic guided wave propagates in the extended anchorage anchor bolt, the ultrasonic guided wave arrives at the interface of the free section and the anchorage section at about t = 0.2 ms, and the reflection occurs by the action with the anchorage end face, and the rest of the transmission occurs, and the transmitted wave propagates to the bottom end of the anchor along the anchorage section, and the reflection occurs by the same action when it propagates to the bottom end position.

Compared with the free anchor bolt, the ultrasonic guided wave reflection waveforms of the elongated anchors are more complicated. After receiving the first bottom reflection waveform, it can be seen from the figure that the incident and reflected waves are superimposed at t = 0.9–1.5 ms, and it is not possible to accurately identify the echo point between the anchored end face and the bottom position.

In order to solve this problem, the EMD decomposition combined with PCA principal component analysis was used to signal process the acquired waveforms to obtain a series of intrinsic modal functions (IMF), as shown in Fig. 12. From top to bottom, they are IMF1, IMF2, …, residuals. Where the proportion of each element is shown in Fig. 13.

Fig. 12

Detection signal intrinsic mode decomposition.

Fig. 13

The proportion of intrinsic mode latent.

In addition, from the principle of ultrasonic guided wave propagation, it is known that the signal is most sensitive to medium changes. Therefore, the most important or significant components in the IMF need to be screened to reduce the dimensionality of the data and extract key features. The elements in the num variable with a cumulative percentage of 0.978 are selected, and finally the filtered IMF is reconstructed with residual recovery using PCA to reconstruct the data signal. The results and differences of the reconstructed data signal compared with the original signal are shown in Figs. 14 and 15.

Fig. 14

Reconstructed signal waveform of lengthened anchor bolt.

Fig. 15

Difference between reconstructed signal and original signal.

From the time domain of the reconstructed data signals, it can be seen that the incident signals at the anchored end face and the reflected signals at the bottom position are more obvious, which appear at positions A and B, respectively. Where the anchored and bottom reflected waves appear at 0.20 ms (t_a) and 0.67 ms (t_b), respectively.

Therefore, the experimental L₁ value of 0.998 m and the experimental L₂ value of 1.288 m can be calculated according to Eq. (6).The calculation can get the bolt anchoring length L is 2.286 m, and the error between it and the model setting length of 2.2 m is only 3.91%. The effectiveness and accuracy of EMD decomposition combined with PCA principal component analysis signal processing method is verified.

Study on the propagation characteristics of ultrasonic guided waves in Z2335 resin anchoring agent with different defect lengths

Establishment of numerical model

In order to investigate the effect of Z2335 defects in resin anchoring agent length on the propagation characteristics of ultrasonic guided waves, four sets of CAE numerical models were established in this section, Z2335-a, Z2335-b, Z2335-c, and Z2335-d, with defect lengths L₃ of 0.05 m, 0.2 m, 0.4 m, and 0.6 m, respectively. The numerical model of defective bolt with Z2335 resin anchoring agent is shown in Fig. 16.

Fig. 16

Z2335 resin anchoring agent defect bolt model.

Simulation results and analysis

To simulate the propagation behaviour of ultrasonic guided waves in the above Z2335 resin anchor defective anchor model, the reflected signals from the anchor end face and the bottom end were received according to the collection point r0, and the reflected waveforms obtained are shown in Fig. 17.

Fig. 17

Time domain diagram of defect signal waveform with different lengths.

As can be seen from Fig. 17, with the increase of the defect L3 length of Z2335 resin anchoring agent, the received signal wave packet energy amplitude also gradually increases, from Δ = 0.0112 to Δ = 0.0122. Moreover, with the increase of defect length L3, the signal waveform fluctuates more and more gently when t = 0.9–0.15 ms, and the amplitude becomes smaller and smaller. This is because the wave impedance of the defects of anchoring agents of different lengths is different from that of the anchor solid, and there is a wave impedance mutation interface, which will lead to the sudden change of the signal after receiving the first reflected signal from the bottom of anchoring. There are irregular features such as superposition and frequency dispersion among reflected wave, incident wave and defect echo. Therefore, the defect length L3 of Z2335 resin anchoring agent is the main reason that affects the complexity of ultrasonic guided wave detection signal.

Since the time-domain waveform of the detected defect signal cannot directly invert the location and length of the defect. Therefore, the above anchor anchorage defective signals were further analysed using EMD decomposition combined with PCA principal component partitioning to infer the location and length of the defective points and defective segments of the Z2335 resin anchors. The reconstructed data signals are shown in Figs. 18 and 19.

Fig. 18

Time domain diagram of reconstructed signal waveform of 0.05 m defect point bolt.

Fig. 19

Time domain diagram of reconstructed signal waveform of 0.2 m defect bolt.

Ultrasonic guided wave in the Z2335 resin anchoring agent end face reflection time point A is 0.2 ms (t_a); in the defects in resin anchoring agent on the interface reflection time point B is 0.445 ms (t_u1); in the bottom end of the anchor reflecting time point D is 0.670 ms (t_b); due to the defects of the Z2335 resin anchorage is too small, the ultrasonic guided wave propagation characteristics are not obvious, can only be approximate from the figure. Inferred Z2335 resin anchoring agent under the interface defect point location in the reflection time of 0.45–0.52 ms (B-C) interval, by the ultrasonic guided wave propagation principle in the medium can be seen, the defect point location and the reflection time of the relationship is

$$L_{4} = \frac{{({\text{t}}_{{{\text{u1}}}} {\text{ - ta)}}}}{2}V2$$

(14)

where L₄ is the length of the defective point of the Z2335 resin anchoring agent from the anchorage end face.

Substituting into formula (14) calculates the size of the defective point from the anchorage end face position L₄ to be 0.6718 m, with an error of 9.32% from the actual distance of 0.6145 m.

As can be seen in Fig. 19, the ultrasonic guided wave is reflected at the anchor solid end surface at time point A for 0.2 ms (t_a); at the upper interface of the Z2335 resin anchoring agent defect at time point B for 0.44 ms (t_u1); at the lower interface of the Z2335 resin anchor defect at time point C for 0.54 ms (t_u2); and at the bottom end of the anchor bar at time point D for 0.670 ms (t_b); E and F are the time points at which the reflected wave first generated at the bottom end of the anchor solid returns to the top end of the anchor and then propagates again to the upper and lower interfaces of the Z2335 resin anchoring agent defect.

Based on Eq. (7) and the time points of the ultrasonic guided waves at different interfaces the length of the Z2335 resin anchoring agent defect can be calculated as 0.219 m, with an error of 9.5% between the defects and the model setup.

The same signal processing is done for the model Z2335-c and Z2335-d numerical model detection waveforms and the reconstructed data signals are shown in Figs. 20 and 21.

Fig. 20

Time domain diagram of reconstructed signal waveform of 0.4 m defect bolt.

Fig. 21

Time domain diagram of reconstructed signal waveform of 0.6 m defect bolt.

In the numerical model Z2335-c, the ultrasonic guided wave is reflected at the end face of the resin anchorage at time point A of 0.2 ms (t_a); at the bottom end of the anchor at time point 0.668 ms (t_b), and at the upper and lower interfaces of the defective Z2335 resin anchorage at time points 0.416 ms (t_u1) and 0.570 ms (t_u2), respectively.

In the numerical model Z2335-d, the ultrasonic guided wave is reflected at the end face of the resin anchoring agent at a time point of 0.2 ms (t_a), at the bottom end of the anchor at a time point of 0.667 ms (t_b), and at the upper and lower interfaces of the defective Z2335 resin anchorage at a time point of 0.36 ms (t_u1) and 0.60 ms (t_u2), respectively.

The inversion defect lengths and errors are derived from the above deduced Eqs. (6) and (7), as shown in Table 2.

Table 2 Z2335 defect length inversion.

From the table, it can be obtained that the signal processing and analysis of the detected waveform by EMD decomposition combined with PCA principal component analysis can effectively deduce the distance between the defective point of the Z2335 resin anchorage and the anchoring end face, with an error of only 9.32%; and when the anchoring defect is sufficiently long, it can accurately deduce the length and location of the defective section of the Z2335 resin anchorage, and the inversion error can be reduced to 2% or less.

Study on ultrasonic guided wave propagation characteristics of Z2335 resin anchoring agent at different defect positions

Numerical modeling

In order to investigate the influence of the defect location of Z2335 resin anchorage on the propagation characteristics of ultrasonic guided wave, three sets of CAE numerical models with different defect locations were established in this section, and the defect locations were set at 100 mm, 300 mm, 517 mm, 717 mm and 934 mm, 1134 mm from the end, respectively, and the local enlargement of the defect location numerical model is shown in Fig. 22.

Fig. 22

Local amplification diagram of different defect positions of anchoring agent.

Simulation results and analysis

The excitation is achieved by applying ultrasonic guided wave signals in the middle node (coupling surface) of the end of the threaded steel rebar resin anchor along the rod axis, simulating the propagation behaviour of ultrasonic guided waves in the three anchor models mentioned above, receiving the reflected signals from the anchor end face and bottom end according to the collection point r0, and putting the echo signals from different defect locations together for comparison as shown in Fig. 23.

Fig. 23

Z2335 Time domain diagram of signal waveform at different defect positions.

As can be seen from Fig. 23, when ultrasonic guided wave propagates in the anchoring of defective anchor bolts, the defect echo signal appears first, and then the bottom signal. Moreover, it can be seen from the figure that the time of receiving the reflected signal by the defect waveforms at different positions is not greatly affected. The collection point r0 at the top of the anchor bolt of the three groups of models receives the reflected signal from the bottom end at 0.67ms, and the wave packet energy amplitude of the received signal from the bottom end is Δ = 0.0114. This is because the defect length of the model is set uniformly, and the energy of the waveform propagating to the bottom end is not different.

Based on the above simulation results and analysis, further EMD decomposition of the received waveforms at different defect locations combined with PCA principal component analysis reconstructs the signals to study the effect of different defect locations on the accuracy of the experimental results.Z2335-middle reconstructed data signals have been analysed in the Z2335-b model, and the reconstructed data signals of the Z2335-front-end and the Z2335-back-end are shown in Fig. 24.

Fig. 24

Time domain diagram of defect reconstruction signal waveform.

From Fig. 24, it can be seen that the ultrasonic guided wave is reflected at model Z2335-front end anchorage end face at time point A for 0.2 ms (t_a), defect upper interface at time point B for 0.380 ms (t_u1), lower interface at time point C for 0.482 ms (t_u2), and bottom end of the anchor bar at time point D for 0.67 ms (t_b); and Z2335—the reflection time point A of the rear end anchorage end face is 0.2 ms (t_a), and the reflection time point B of the defective upper interface is 0.5898 ms (t_u1); due to the fact that the distance between the defective lower interface and the bottom end of the anchor bar is too close, the reflection echo of the lower interface and the bottom echo are superimposed, and it is not easy to identify the reflection time point of the lower interface, and it is necessary to observe the IMF2 component obtained by the decomposition and processing of the original signal, and the reflection time point of the lower interface is not easy to be identified, and it is possible to observe the reflection time point of Z2335-after-end anchor bar can be derived from the IMF2 component, from which the Z2335-back end defective lower interface reflection point is 0.6920 ms (t_u2), as shown in Fig. 25.

Fig. 25

IMF2 component and residual time domain diagram.

According to the ultrasonic guided wave at different interfaces of the time point substituting into the formulae (6) and (7) and calculate the length of the Z2335-front end and Z2335-back end defects are 0.227 m, 0.225 m, respectively, and the error with the model set up between the defects are 13.5%, 12.5%, respectively, according to the above deduction formulae to derive the inversion of the defects lengths and the error, shown in Table 3.

Table 3 Z2335 defect location inversion.

From Table 3, it can be seen that when the location of Z2335 anchoring agent defect is too close to the anchorage end face and anchorage bottom, it will cause the defect interface reflection echoes to be superimposed with the anchorage segment face and anchorage bottom echo, and the waveform characteristics are more complicated, resulting in the difficulty of inversion defects. However, after reconstructing the signal by EMD decomposition and PCA principal component analysis, the reflection time points of different wave impedance interfaces can still be identified effectively.

Indoor test of anchoring quality detection

In order to further validate the accuracy of EMD decomposition combined with PCA principal component analysis signal processing method applied to ultrasonic guided wave nondestructive detection of anchorage defects in mining rebar resin anchors. In this section, an indoor test method is adopted to further conduct an experimental study on the anchorage quality of anchor rods by building an ultrasonic guided wave NDT platform.

Construction of indoor test platform

The test equipment used for the indoor test consists of a signal generator, a power amplifier, a mining rebar resin anchor bar specimen, an ultrasonic probe, a digital oscilloscope and a computer, and the instruments are connected by a double BNC signal source cable, and the connection schematic is shown in Fig. 26. The process of the indoor ultrasonic guided wave nondestructive testing test is as follows:

• a. Signal Generator Parameter Setting and Output: Start the ultrasonic guided wave signal generator and precisely configure the excitation signal parameters (frequency, amplitude, waveform type, etc.) to generate a low-distortion, high-stability initial signal.

• b. Double BNC Cable Connection and Signal Transmission: Use a double BNC signal source cable to connect the signal generator to the power amplifier, ensuring high-speed, low-loss transmission. Optimize the wiring with multiple connectors to avoid signal interference³².

• c. Power Amplifier Gain Adjustment and Signal Amplification: Start the power amplifier and adjust the gain parameters to amplify the excitation signal to the preset power level, enhancing the signal’s penetration ability to resist attenuation during long-distance propagation.

• d. Ultrasonic Probe Installation and Bolt Sample Detection: Input the amplified signal through a matching impedance ultrasonic probe into the mine-threaded resin bolt sample, ensuring good coupling between the probe and the sample, and completing the guided wave transmission and reception.

• e. Digital Oscilloscope Data Acquisition and Storage: Enable the digital oscilloscope, set the sampling rate and trigger conditions, capture and store the detection waveform in the built-in memory in real-time, ensuring data integrity and traceability.

Fig. 26

Nondestructive testing schematic diagram of indoor test.

It can be connected to signal generators and digital oscilloscopes through the USB port of a computer, and the signal analysis software can be used for further processing of the signals.

Indoor test detection and results of bolt anchorage

The laboratory test sample uses concrete as the surrounding rock, and the test concrete is composed of water, cement and sand. According to the uniaxial compressive strength test of concrete, the thickness and strength of surrounding rock under this ratio is 20Mpa, which meets the needs of the experiment. The four ultrasonic guided wave nondestructive testing samples selected in the test are shown in Fig. 27, in which sample A-1 is the free bolt. Sample A-2 is full-length anchor dense bolt; Samples C-1 and C-2 are anchors with anchoring density of 49.2% and 75.9%. The material parameters of the samples are the same as those in Table 1, and the model parameters are shown in Table 4.

Fig. 27

Indoor test bolt sample.

Table 4 Indoor test sample parameter table.

The anchor specimen was tested by the test and inspection device shown in Fig. 26, in order to avoid the air gap between the anchor and the ultrasonic probe, the ultrasonic probe was coupled with the anchor using an ultrasonic flaw detection coupler, and the testing process of the indoor test specimen is shown in Fig. 28.

Fig. 28

Indoor test bolt sample.

Since the coupling is different for each test, multiple tests are performed for each specimen to reduce the error, and the test waveforms of specimens A-1, A-2, C-1 and C-2 after reconstructing the signals by EMD decomposition in conjunction with PCA principal component analysis are shown in Fig. 29.

Fig. 29

Detection waveform of indoor test sample.

From the waveform Fig. 29a, it can be clearly seen that the time difference between the transmitted signal and the received signal Δ = 0.211 ms, substituting into the formula (6) calculated ultrasonic guided wave propagation velocity in the free anchor for 4857.14 m/s, and the numerical simulation of ultrasonic guided wave propagation velocity in the free anchor 4988.66 m/s error is only 2.63%, and from the specimen A-1 detection waveforms It can be seen that the propagation waveform of ultrasonic guided wave in the free anchor is relatively stable without serious dispersion phenomenon, which is consistent with the results of numerical simulation; Similarly, it can be obtained from the waveform Fig. 29b that the time difference between the transmitted signal and the received signal Δ = 0.170 ms, which can be substituted into Eq. (6) to calculate the propagation velocity of ultrasonic guided wave in the full-length anchored compact anchor of specimen A-2 as 2823.53 m/s, the error is only 2.97% with the propagation velocity of ultrasonic guided wave in free anchor 2742.22 m/s simulated numerically in this paper.

Based on the sampling point information of the detected signals, the following three reflection characteristics can be observed in Fig. 29c,d: when the ultrasonic guided wave propagates to the bottom of the anchor rod, the bottom waveform feature manifests as an amplitude peak at the 2500th sampling point. Subsequently, when the ultrasonic guided wave encounters an internal defect, it generates a defect echo characterized by an abnormal peak at the 4000th sampling point with lower amplitude than the bottom waveform. Following this, as the ultrasonic guided wave propagates to the fixed end and undergoes boundary condition changes, the fixed-end echo exhibits minor oscillations at the 4500th sampling point, reflecting energy dissipation at the interface.

In Fig. 29c, the black dashed line represents the ultrasonic guided wave excitation signal, and the four green curves A, B, C, and D represent the reflection time points of the bottom end of the anchor rod, the upper and lower interfaces of the defect, and the solid end after the EMD combined with PCA processing and analysis, respectively; combined with the time-domain data of the detected waveforms received by the digital oscilloscope, it can be obtained that the reflection time points of each interface were 0.744e − 4s (t_b), 1.68e − 4s (t_u2), 3.58e − 4s (t_u1), 4.48e − 4s (t_a). Considering that the reflection time point of the defect interface of the indoor test is opposite to the numerical simulation, Eq. (7) is transformed

$$L3 = \frac{{({\text{tu1 - tu2}})}}{2}V_{2}$$

(15)

Combining the actual measured ultrasonic guided wave propagation velocity of specimen A-1, A-2 free section and anchorage section specimens, substituting the defect interface detection time point into Eq. (15), the defect inversion length L₃ of specimen C-1 is calculated to be 0.268 m, which is 7.2% of the actual defect error of specimen C-1.

Similarly, observing the detection waveform time-domain data in Fig. 29d can be obtained that the detection time of each interface is 2.74e − 5s (t_b), 1.6e − 4s (t_u2), and 3.15e − 4s (t_u1), and according to the same calculation method, the inversion length of defects in specimen C-2 is obtained as L₃ is 0.2188 m, which is the same as that of the defects in the fabrication of specimen C-2 The error is 9.4%.

By comparing and analysing the waveforms of the detection signals of specimens C-1 and C-2, the following conclusions can be drawn: the inversion of the defect segment length of specimen C-1 is more accurate than that of specimen C-2. At the same time, the waveform of the detection signal of specimen C-2 is more seriously distorted, and there is an obvious dispersion phenomenon between the bottom signal and the echo waveform of the defect interface. Further analysis shows that the wave packet energy amplitude Δ of the signal at the bottom end of the anchor in sample C-1 is 0.184, which is significantly higher than the Δ value of 0.0893 in sample C-2.

The reasons are analysed as follows: the propagation of ultrasonic guided wave in coal mine rebar resin anchor has energy attenuation phenomenon. When there are defects in the anchorage, the signal will be reflected and transmitted due to the difference in wave impedance at the interface, and the interference of noise signals in the test process makes the detection waveform more complicated. By comparing specimen C-2 with C-1, it is found that the attenuation phenomenon of the detection signal is more significant in the case of higher anchorage compactness, i.e., better anchorage quality. In addition, after EMD decomposition and PCA principal component analysis of specimens C-1 and C-2, the inverted defect length results are more accurate.

Furthermore, after performing EMD and PCA on specimens C-1 and C-2, the defect length inversion results were found to be accurate.

In summary, the ultrasonic guided wave nondestructive testing platform constructed in this paper is able to identify coal mine rebar resin anchor defects more accurately.

Conclusion

The following main conclusions can be drawn from this paper:

• (1) Theoretically analysed the propagation process of ultrasonic guided wave in the solid end, bottom end and defective position of threaded steel rebar resin anchor, and pointed out that the ultrasonic guided wave propagated to the position of anchorage defects will generate scattered field, and the scattered wave will easily leak to the surrounding rock through the defective interface, which will make the reflected waveforms superposed, and the waveforms of received signals are complex, which will bring difficulties to the inversion of the signals.

• (2) Determine the optimal excitation signal frequency, numerical simulation simulated the propagation characteristics of ultrasonic guided wave in the rebar resin anchorage, pointed out that ultrasonic guided wave propagation in the free anchor is more stable, with the increase of the defect length of the Z2335 resin anchorage, the amplitude of the energy of the received signal wave packet increases gradually, and the fluctuation of the signal waveform is more and more gentle at t = 0.9–0.15 ms, indicating that the defect length is the main reason affecting the change of signal complexity.

• (3) The application of EMD decomposition combined with PCA (Principal Component Analysis) for processing the detection signals can accurately extract the defect echoes of the Z2335 resin anchor grout, and invert the defect position and length, with an error within 9.5%. For longer anchoring defects, the actual distance error of the defect position is less than 2%. When the defect interface is close to the bottom of the anchor, the IMF2 modal component of the EMD decomposition can still effectively identify the reflection echo from the wave impedance interface, verifying the feasibility of the EMD-PCA signal processing method.

• (4) The laboratory has developed an ultrasonic guided wave anchor non-destructive testing system, according to the test results: the test detection signal waveform in the EMD decomposition combined with PCA principal component analysis, can be more accurately identify the length and location of defects in the Z2335 resin anchorage information. And when the anchorage compactness is higher, i.e. the anchorage quality is better, the detection signal waveform attenuation is more serious.