Method for predicting concrete critical instability state based on wavelet packet energy entropy

Abstract

The invention relates to a method for predicting a concrete critical instability state based on wavelet packet energy entropy, and belongs to the technical field of structural health monitoring. The method comprises the following steps: (1) arranging an acoustic emission sensor on to-be-monitored concrete, collecting an acoustic emission signal at a sampling rate of 1MHz, the maximum frequency of the acoustic emission signal of 500kHz, and the number of sampling points of the acoustic emission signal of 1024; (2) selecting a db3 wavelet basis according to the waveform characteristics of the acoustic emission signal, performing two-stage wavelet packet transformation on the acoustic emission signal, and decomposing and reconstructing the acoustic emission signal into four frequency band signals; (3) calculating a frequency band signal, a frequency band signal, and energy spectrum coefficients H1, H2, H3 and H4 of the frequency band signal and the frequency band signal; (4) calculating the wavelet packet energy entropy P of the acoustic emission signal; (5) sequentially selecting m acoustic emission signals as a window according to an acquisition sequence, calculating an average value P0 of P in each window, and drawing a distribution diagram of the P0 along with the number of the windows; and (6) judging whether the to-be-monitored concrete is in a critical instability state or not according to the change state of the P0. According to the method, the quantitative characterization information of concrete damage evolution is obtained in real time by using the acoustic emission technology, and the critical instability state of the concrete can be visually and quantitatively evaluated.

Description

Technical Field

[0001] This invention relates to a method for predicting the critical instability state of concrete based on wavelet packet energy entropy, belonging to the field of structural health monitoring technology. Background Technology

[0002] Before reaching instability, concrete structures in service accumulate numerous microcracks. The generation and propagation of these microcracks trigger the instantaneous release of elastic strain energy, generating high-frequency stress waves. Acoustic emission, as a dynamic non-destructive testing technique, can analyze the stress wave signals released by the evolution of microcracks in real time, thereby assessing the critical instability state of concrete and enabling early warning of concrete structural failure.

[0003] Acoustic emission signals accompanying different damage processes often exhibit different frequency distribution characteristics. By analyzing the frequency components of acoustic emission signals, a distinguishable correspondence can be established between signal characteristics and specific damage modes. Wavelet packet energy spectral coefficients play a crucial role in damage identification and quantitative analysis, effectively characterizing the energy distribution of acoustic emission signals across various frequency bands. Wavelet packet energy entropy can describe the dispersion or complexity of the energy distribution of acoustic emission signals across multiple frequency bands. As damage to concrete structures intensifies, the frequency distribution characteristics of acoustic emission signals change, and the wavelet packet energy entropy also undergoes regular changes accordingly. Therefore, by analyzing the evolution characteristics of wavelet packet energy entropy, a quantitative assessment of the critical instability state of concrete can be achieved. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting the critical instability state of concrete based on wavelet packet energy entropy. This method can obtain the acoustic emission quantitative characterization information of concrete damage evolution and quantitatively assess the critical instability state of concrete.

[0005] The objective of this invention is achieved through the following technical solutions.

[0006] A method for predicting the critical instability state of concrete based on wavelet packet energy entropy, the specific operation steps are as follows:

[0007] Step 1: Place acoustic emission sensors on the concrete to be monitored to collect acoustic emission signals released by the concrete damage in real time. The sampling rate is 1MHz, the maximum frequency of the acoustic emission signal is 500kHz, and the number of sampling points for the acoustic emission signal is 1024.

[0008] Step 2: Select the db3 wavelet basis and perform a two-level wavelet packet transform on the acoustic emission signal acquired in Step 1. The acoustic emission signal is decomposed and reconstructed into four frequency bands from low to high. The frequency range of the band signal is (0, 125) kHz. The frequency range of the band signal is (125, 250) kHz. The frequency range of the band signal is (250, 375) kHz. The frequency range of the band signal is (375,500) kHz.

[0009] Step 3: Calculation Frequency band signals, Frequency band signals, Frequency band signals and The energy spectral coefficients of the frequency band signals are represented by the symbols H1, H2, H3, and H4, respectively.

[0010] Step 3.1: Expressed using formula (1) Wavelet packet reconstruction coefficients of the frequency band signal; expressed by formula (2). Wavelet packet reconstruction coefficients of the frequency band signal; expressed by formula (3). Wavelet packet reconstruction coefficients of the frequency band signal; expressed by formula (4). Wavelet packet reconstruction coefficients of frequency band signals;

[0011] T 1i ={y 1,i ,i=1,2,...,1024} (1)

[0012] Among them, T 1i express The set of wavelet packet reconstruction coefficients for frequency band signals; y 1,i express The coefficients for wavelet packet reconstruction of the frequency band signal;

[0013] T 2i ={y 2,i ,i=1,2,...,1024} (2)

[0014] Among them, T 2i express The set of wavelet packet reconstruction coefficients for frequency band signals; y 2,i express The coefficients for wavelet packet reconstruction of the frequency band signal;

[0015] T 3i ={y 3,i ,i=1,2,...,1024} (3)

[0016] Among them, T 3i express The set of wavelet packet reconstruction coefficients for frequency band signals; y 3,i express The coefficients for wavelet packet reconstruction of the frequency band signal;

[0017] T4i ={y 4,i ,i=1,2,...,1024} (4)

[0018] Among them, T 4i express The set of wavelet packet reconstruction coefficients for frequency band signals; y 4,i express The coefficients for wavelet packet reconstruction of the frequency band signal;

[0019] Step 3.2: Expressed using formula (5) The energy of the frequency band signal is represented by the symbol J1; it is expressed by formula (6). The energy of the frequency band signal is represented by the symbol J2; it is expressed by formula (7). The energy of the frequency band signal is represented by the symbol J3; it is expressed by formula (8). The energy of a frequency band signal is represented by the symbol J4;

[0020]

[0021]

[0022] Step 3.3: Obtain the result using formula (9) The energy spectrum coefficient H1 of the frequency band signal is obtained through formula (10). The energy spectral coefficient H2 of the frequency band signal is obtained through formula (11). The energy spectral coefficient H3 of the frequency band signal is obtained through formula (12). The energy spectrum coefficient H4 of the frequency band signal.

[0023] H1=J1 / (J1+J2+J3+J4) (9)

[0024] H2=J2 / (J1+J2+J3+J4) (10)

[0025] H3=J3 / (J1+J2+J3+J4) (11)

[0026] H4=J4 / (J1+J2+J3+J4) (12)

[0027] Step 4: Calculate the wavelet packet energy entropy of the acoustic emission signal using formula (13), denoted by P.

[0028] P=-H1*ln(H1)-H2*ln(H2)-H3*ln(H3)-H4*ln(H4) (13)

[0029] Step 5: Select 20 acoustic emission signals in the order of acquisition as a window, calculate the average value of P in each window and denote it as P0, and draw a distribution graph of P0 as a function of the number of windows. The horizontal axis is the window number and the vertical axis is P0 in the corresponding window.

[0030] Step 6: Determine whether the concrete to be monitored is in a critical instability state based on the distribution of P0 with the number of windows. The specific method for determining whether the concrete to be monitored is in a critical instability state is as follows: count P0 sequentially in ascending order of the number of windows. When P0 is greater than 1 for the first time, record the number of windows where P0 is located as A. When P0 is less than 0.8 in window B (B>A) and the next two consecutive windows, it is determined that the concrete to be monitored is in a critical instability state.

[0031] Beneficial effects

[0032] The method for predicting the critical instability state of concrete based on wavelet packet energy entropy proposed in this invention has the following advantages compared with existing technologies: it can quantitatively characterize the frequency evolution features of acoustic emission signals in the concrete damage evolution process, and realize real-time quantitative assessment of the critical instability state of concrete. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of two-layer wavelet packet transform in a specific embodiment of the present invention.

[0034] Figure 2 This is a distribution diagram of P0 with the number of windows in a specific embodiment of the present invention. Detailed Implementation

[0035] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0036] Example 1

[0037] In this embodiment, a three-point bending failure test is performed on the concrete to be monitored.

[0038] The method for predicting the critical instability state of concrete based on wavelet packet energy entropy proposed in this invention is used to predict the critical instability state of concrete. The specific operation steps are as follows:

[0039] Step 1: Place acoustic emission sensors on the concrete to be monitored to collect acoustic emission signals released by the concrete damage in real time. The sampling rate is 1MHz, the maximum frequency of the acoustic emission signal is 500kHz, and the number of sampling points for the acoustic emission signal is 1024.

[0040] Step 2: Select the db3 wavelet basis and perform a two-layer wavelet packet transform on the acoustic emission signal acquired in Step 1. The acoustic emission signal is decomposed and reconstructed into four frequency bands from low to high. The schematic diagram of the two-layer wavelet packet transform is shown below. Figure 1As shown. Among them, The frequency range of the band signal is (0, 125) kHz. The frequency range of the band signal is (125, 250) kHz. The frequency range of the band signal is (250, 375) kHz. The frequency range of the band signal is (375,500) kHz.

[0041] Step 3: Calculation Frequency band signals, Frequency band signals, Frequency band signals and The energy spectral coefficients of the frequency band signals are represented by the symbols H1, H2, H3, and H4, respectively.

[0042] Step 3.1: Expressed using formula (1) Wavelet packet reconstruction coefficients of the frequency band signal; expressed by formula (2). Wavelet packet reconstruction coefficients of the frequency band signal; expressed by formula (3). Wavelet packet reconstruction coefficients of the frequency band signal; expressed by formula (4). Wavelet packet reconstruction coefficients of frequency band signals;

[0043] Step 3.2: Expressed using formula (5) The energy of the frequency band signal is represented by the symbol J1; it is expressed by formula (6). The energy of the frequency band signal is represented by the symbol J2; it is expressed by formula (7). The energy of the frequency band signal is represented by the symbol J3; it is expressed by formula (8). The energy of a frequency band signal is represented by the symbol J4;

[0044] Step 3.3: Obtain the result using formula (9) The energy spectrum coefficient H1 of the frequency band signal is obtained through formula (10). The energy spectral coefficient H2 of the frequency band signal is obtained through formula (11). The energy spectrum coefficient H3 of the frequency band signal; f2 is obtained through formula (12). 4 The energy spectrum coefficient H4 of the frequency band signal.

[0045] Step 4: Calculate the wavelet packet energy entropy of the acoustic emission signal using formula (13), denoted by P.

[0046] Step 5: Select 20 acoustic emission signals sequentially as a window, calculate the average value of P in each window, denoted as P0, and plot the distribution of P0 as a function of the number of windows. The horizontal axis represents the window number, and the vertical axis represents P0 in the corresponding window. Figure 2 As shown.

[0047] Step 6: Determine whether the concrete to be monitored is in a critical instability state based on the distribution of P0 with the number of windows. The specific method for determining whether the concrete to be monitored is in a critical instability state is as follows: Count P0 sequentially in ascending order of the number of windows. If P0 in the first window is 1.09, which is greater than 1 for the first time, and P0 in the 71st window and the next two consecutive windows is less than 0.8, then the concrete to be monitored is determined to be in a critical instability state.

[0048] The present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A method for predicting the critical instability state of concrete based on wavelet packet energy entropy, characterized in that: The specific operating steps are as follows: Step 1: Place acoustic emission sensors on the concrete to be monitored to collect acoustic emission signals released by the concrete damage in real time. The sampling rate is 1MHz, the maximum frequency of the acoustic emission signal is 500kHz, and the number of sampling points for the acoustic emission signal is 1024. Step 2: Select the db3 wavelet basis and perform a two-level wavelet packet transform on the acoustic emission signal acquired in Step 1. The acoustic emission signal is decomposed and reconstructed into four frequency bands from low to high. The frequency range of the band signal is (0, 125) kHz. The frequency range of the band signal is (125, 250) kHz. The frequency range of the band signal is (250, 375) kHz. The frequency range of the band signal is (375,500) kHz; Step 3: Calculation Frequency band signals, Frequency band signals, Frequency band signals and The energy spectral coefficients of the frequency band signals are represented by the symbols H1, H2, H3, and H4, respectively. Step 3.1: Expressed using formula (1) Wavelet packet reconstruction coefficients of the frequency band signal; expressed by formula (2). Wavelet packet reconstruction coefficients of the frequency band signal; expressed by formula (3). Wavelet packet reconstruction coefficients of the frequency band signal; expressed by formula (4). Wavelet packet reconstruction coefficients of frequency band signals; T 1i ={y 1,i ,i=1,2,...,1024}(1) Among them, T 1i express The set of wavelet packet reconstruction coefficients for frequency band signals; y 1,i express The coefficients for wavelet packet reconstruction of the frequency band signal; T 2i ={y 2,i ,i=1,2,...,1024}(2) Among them, T 2i express The set of wavelet packet reconstruction coefficients for frequency band signals; y 2,i express The coefficients for wavelet packet reconstruction of the frequency band signal; T 3i ={y 3,i ,i=1,2,...,1024}(3) Among them, T 3i express The set of wavelet packet reconstruction coefficients for frequency band signals; y 3,i express The coefficients for wavelet packet reconstruction of the frequency band signal; T 4i ={y 4,i ,i=1,2,...,1024}(4) Among them, T 4i express The set of wavelet packet reconstruction coefficients for frequency band signals; y 4,i express The coefficients for wavelet packet reconstruction of the frequency band signal; Step 3.2: Expressed using formula (5) The energy of the frequency band signal is represented by the symbol J1; it is expressed by formula (6). The energy of the frequency band signal is represented by the symbol J2; it is expressed by formula (7). The energy of the frequency band signal is represented by the symbol J3; it is expressed by formula (8). The energy of a frequency band signal is represented by the symbol J4; Step 3.3: Obtain the result using formula (9) The energy spectrum coefficient H1 of the frequency band signal is obtained through formula (10). The energy spectral coefficient H2 of the frequency band signal is obtained through formula (11). The energy spectral coefficient H3 of the frequency band signal is obtained through formula (12). The energy spectral coefficient H4 of the frequency band signal; H1=J1 / (J1+J2+J3+J4) (9) H2=J2 / (J1+J2+J3+J4) (10) H3=J3 / (J1+J2+J3+J4) (11) H4=J4 / (J1+J2+J3+J4) (12) Step 4: Calculate the wavelet packet energy entropy of the acoustic emission signal using formula (13), denoted by P; P=-H1*ln(H1)-H2*ln(H2)-H3*ln(H3)-H4*ln(H4) (13) Step 5: Select m acoustic emission signals in the order of acquisition as a window, calculate the average value of P in each window, denoted as P0, and draw a distribution graph of P0 as a function of the number of windows, with the horizontal axis representing the window number and the vertical axis representing P0 in the corresponding window. Step 6: Determine whether the concrete to be monitored is in a critical instability state based on the distribution of P0 with the number of windows. The specific method for determining whether the concrete to be monitored is in a critical instability state is as follows: count P0 sequentially in ascending order of the number of windows. When P0 is greater than 1 for the first time, record the number of windows where P0 is located as A. When P0 is less than 0.8 in window B (B>A) and the following n consecutive windows, it is determined that the concrete to be monitored is in a critical instability state.

2. The method for predicting the critical instability state of concrete based on wavelet packet energy entropy as described in claim 1, characterized in that: The value of m is 20; the value of n is 2.

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