A box girder quality evaluation method based on MH wavelet average evolution power spectrum

Abstract

This invention belongs to the field of bridge quality inspection technology, specifically a method for evaluating the quality of box girders based on the MH wavelet average evolved power spectrum. The method includes: selecting a qualified standard beam, deploying vibration sensors to collect vertical acceleration time-history signals; preprocessing the signals by performing wavelet transform, calculating the squared modulus of the wavelet coefficients and normalizing them to obtain a three-dimensional evolved power spectrum, and then averaging the time dimension to obtain the average evolved power spectrum; extracting three characteristic parameters—frequency at maximum power, half-power bandwidth, and skewness—using the standard beam spectrum as a benchmark; repeating the above steps on the beam to be evaluated, comparing the deviations of the characteristic parameters, and combining a grading threshold and a differentiated review process to determine the quality, and statistically analyzing the batch data dispersion to provide feedback on the stability of the beam manufacturing process. This invention achieves non-destructive, batch, and accurate evaluation of box girder quality, and can effectively identify hidden defects such as insufficient elastic modulus of concrete and prestress loss.

Description

Technical Field

[0001] This invention relates to the field of bridge quality inspection technology, and in particular to a method for evaluating the quality of box girders based on the MH wavelet average evolution power spectrum. Background Technology

[0002] Prestressed concrete box girders have become one of the most commonly used superstructure forms in modern bridge engineering due to their advantages such as large span capacity, high torsional stiffness, and good driving comfort. However, during the standardized production process in precast girder yards, the combined effects of various factors, including batch differences in raw materials, fluctuations in concrete mix proportions, variations in curing conditions, deviations in tensioning age control, and the precision of tensioning processes, can lead to varying degrees of dispersion or even defects in key quality indicators of the finished box girders, such as concrete strength, modulus of elasticity, effective prestress, and mid-span camber. These inherent quality hazards (such as early micro-cracks and excessive prestress loss) will gradually deteriorate during the operational phase, significantly affecting the bridge's durability and traffic safety.

[0003] Currently, quality acceptance during the beam fabrication stage mainly relies on:

[0004] (1) Visual quality inspection, this method is powerless against micro-cracks inside concrete and loss of initial prestress;

[0005] (2) The 28-day concrete block strength test results are difficult to accurately characterize the true mechanical state of the beam concrete at the moment of prestressing tension;

[0006] (3) The reverse tension method is used to sample and inspect the effective prestress. This method is a destructive test, which is inefficient and cannot achieve full screening.

[0007] In recent years, modal analysis methods based on environmental vibration testing have been increasingly applied to structural damage identification. However, conventional power spectrum (PSD) analysis relies on the assumption of signal stationarity, while actual collected response signals from vehicles, wind, and environmental micro-vibrations are typical non-stationary random signals with low signal-to-noise ratios. Traditional Fourier transforms are insufficient to effectively characterize the time-frequency local features of signals, resulting in poor stability of extracted modal parameters such as frequency and damping. A single fundamental frequency change cannot distinguish whether the stiffness reduction is caused by insufficient concrete elastic modulus or prestress loss, and the evaluation accuracy and depth cannot meet the needs of batch testing in engineering projects.

[0008] Therefore, there is an urgent need for a non-destructive, efficient, and batch-based quality evaluation method that can suppress noise interference, accurately characterize the features of non-stationary signals, and comprehensively reflect the mechanical properties and prestressing state of the beam concrete. Summary of the Invention

[0009] This invention proposes a box girder quality evaluation method based on MH wavelet average evolution power spectrum, aiming to solve the technical problems of existing box girder quality evaluation relying on visual inspection, destructive sampling inspection, and low accuracy and limited information of traditional spectrum analysis.

[0010] This invention provides a method for evaluating the quality of box girders based on the MH wavelet average evolved power spectrum, comprising:

[0011] S1. Select a qualified beam as a standard beam, and arrange vibration sensors at key vibration measurement points on the surface of the standard beam to collect vertical acceleration time history signals.

[0012] S2. The Mexican Hat wavelet is used to perform continuous wavelet transform, the modulus square of the wavelet coefficients is calculated and normalized to obtain the wavelet evolution power spectrum EPSD, and then the average is taken over the time dimension to obtain the wavelet average evolution power spectrum AEPSD.

[0013] S3, extract the frequency, half-power bandwidth and skewness at the maximum power from the wavelet average evolved power spectrum (AEPSD), and use the wavelet average evolved power spectrum (AEPSD) and its characteristic parameters as the reference evolved power spectrum and reference parameters.

[0014] S4. Repeat steps S1-S3 for the same batch of beams to be evaluated, obtain the wavelet average evolution power spectrum (AEPSD) and corresponding characteristic parameters of each beam to be evaluated, and compare the characteristic parameters of the beams to be evaluated with the benchmark parameters; combine the graded evaluation standard and the differentiated processing procedure to complete the quality judgment of the box girder.

[0015] The technical advantages of the box girder quality evaluation method based on the MH wavelet average evolution power spectrum disclosed in this invention are as follows: First, by establishing a standard beam reference spectrum and comparing the characteristic parameters of the MH wavelet average evolution power spectrum of beams in the same batch, this invention achieves non-destructive, efficient, and batch testing of the elastic modulus of concrete, overall stiffness, and prestressing state of box girders, completely avoiding the limitations of traditional destructive sampling inspection. Second, this method utilizes the time-frequency focusing characteristics of the MH wavelet transform to suppress non-stationary signals and noise interference, and introduces three complementary characteristic parameters: frequency at maximum power, half-power bandwidth, and skewness. This enables accurate identification of hidden quality defects such as insufficient concrete strength, microcracks, and prestress loss. Furthermore, by combining graded thresholds and differentiated review processes, the false judgment rate is significantly reduced, and the stability of the beam manufacturing process is fed back through batch data discrete statistical analysis.

[0016] Furthermore, in S1, the key vibration measurement points include the junction of the top web plate at 1 / 2 span and 1 / 4 span of the beam; the sampling frequency is selected as 100-200Hz to satisfy the Nyquist sampling theorem; the vibration sensor is rigidly fixed to the beam surface by high-viscosity mortar; the data acquisition time is not less than 5 minutes, and the data is collected during a period when the external environmental interference is less than a preset threshold.

[0017] Furthermore, before step S2, the vibration signal acquired in step S1 is preprocessed, specifically as follows:

[0018] The time-history signal M is subjected to mean removal processing to obtain signal Q1 = M - mean(M); the signal Q1 is then filtered by a bandpass filter to remove low-frequency trend terms and high-frequency noise, resulting in preprocessed signal Q2.

[0019] Furthermore, S2 specifically includes:

[0020] Based on the estimated fundamental frequency of the beam, the scale range of the wavelet transform is determined. The Mexican Hat wavelet is used to perform continuous wavelet transform on the preprocessed signal to obtain the wavelet coefficients coef(a,b), where a is the scale variable and b is the time variable.

[0021] The square of the wavelet coefficient modulus is calculated and normalized according to the sampling interval and wavelet allowable constant. At the same time, the scale variable a is converted into the corresponding frequency variable or f to generate the three-dimensional wavelet evolution power spectrum EPSD(f,b).

[0022] The one-dimensional wavelet average evolutionary power spectrum EPSD(f) is obtained by taking the average value of EPSD(f,b) over the entire time history b.

[0023] Furthermore, the time-domain expression of the Mexican Hat wavelet is:

[0024] ;

[0025] Where t is the interval used.

[0026] Further, in S3, the half-power bandwidth is defined as the absolute value of the difference between two frequency points corresponding to the point where the maximum power value drops to half its value on the AEPSD spectrum curve; the skewness is defined as a statistical characteristic characterizing the asymmetry of the AEPSD spectrum distribution, obtained by calculating the third standard moment of the spectrum amplitude distribution. ;

[0027] in, Let E represent the skewness of the spectral distribution, and E represent the expectation. The mean frequency is... This represents the standard deviation of the frequency.

[0028] Furthermore, the grading evaluation criteria in S4 include three characteristic parameters within a preset deviation threshold:

[0029] The frequency deviation at maximum power shall not exceed ±5%, the half-power bandwidth deviation shall not exceed ±10%, and the skewness deviation shall not exceed ±10%.

[0030] Furthermore, the differentiation process in S4 includes:

[0031] If all three characteristic parameters are within the limits, the beam is determined to be a qualified beam.

[0032] If two or more of the three characteristic parameters exceed the limit, the beam is directly judged as a beam with questionable quality.

[0033] If only the frequency at maximum power exceeds the limit, and the exceedance value is in the range of 5% to 10%, the elastic modulus of the beam concrete should be checked using a rebound hammer. If the measured elastic modulus E satisfies:

[0034] ;

[0035] If the beam is deemed to be of acceptable quality, it is considered to be of questionable quality. The ratio of the frequency of the beam to be evaluated to that of the standard beam. The elastic modulus of a standard beam;

[0036] If only half-power bandwidth or skewness exceeds the limit, first check the prestressing tension data in the construction log. If the tension data meets the design requirements, conduct three independent repeat tests. If at least two of the three evaluations are deemed qualified, the beam is finally determined to be of qualified quality; otherwise, it is still determined to be a beam of questionable quality.

[0037] Furthermore, in step S4, for box girders determined to be of questionable quality, a comprehensive verification procedure is then performed:

[0038] Verify whether the concrete compressive strength, elastic modulus, effective prestress, and mid-span arch test indicators of the beam meet the design requirements, and review the records of concrete pouring, prestressing tensioning, grouting and anchoring, steam curing, and test blocks to comprehensively determine the final quality status of the beam.

[0039] Furthermore, the method also includes: generating a control chart for feedback on the process stability of the beam manufacturing production line by statistically analyzing the dispersion of the characteristic parameters of the wavelet average evolution power spectrum of all beams to be evaluated in the same batch and the standard beam. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating a box girder quality evaluation method based on the MH wavelet average evolution power spectrum proposed in an embodiment of the present invention.

[0041] Figure 2 This is a schematic diagram of the average evolution power spectrum of a standard beam provided in an embodiment of the present invention;

[0042] Figure 3 A schematic diagram of the average evolution power spectrum of beam A (a qualified beam) provided in an embodiment of the present invention;

[0043] Figure 4 This is a schematic diagram of the average evolution power spectrum of beam B (a beam of questionable quality) provided in an embodiment of the present invention. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] The following are explanations of the proper nouns used in this invention:

[0046] Power Spectral Density (PSD)

[0047] Evolutionary Power Spectral Density (EPSD) in three dimensions.

[0048] Average Evolutionary Power Spectral Density (AEPSD);

[0049] Mexican Hat wavelet (MH wavelet for short);

[0050] To address the issues mentioned in the background section, where traditional Fourier transform struggles to effectively characterize the local time-frequency features of signals, leading to poor stability of extracted modal parameters such as frequency and damping, and the inability to distinguish between insufficient concrete elastic modulus and prestress loss-induced stiffness reduction based solely on a single fundamental frequency change, the present invention provides a box girder quality evaluation method based on the MH wavelet average evolution power spectrum. This method uses a standard beam that meets quality standards as a benchmark, and by comparing the refined time-frequency characteristics of the vibration response signals of beams from the same batch, it achieves a comprehensive non-destructive evaluation of the box girder's concrete elastic modulus, overall stiffness, and prestress state, while also providing feedback on the stability of the beam manufacturing process.

[0051] refer to Figures 1 to 4As shown, this embodiment uses a 30-meter span C50 prestressed concrete simply supported box girder from the same batch produced by a bridge precast beam yard as the evaluation object, and elaborates on the specific implementation process of the present invention in detail:

[0052] S1: Vibration signal acquisition and standard beam establishment. Select a beam that has been fully tested and confirmed to be of qualified quality as the standard beam. Arrange vibration sensors at key vibration measurement points on the surface of the standard beam to collect vertical acceleration time history signals.

[0053] Standard beam selection: A box girder that has completed 28 days of standard curing, and whose visual inspection, concrete rebound strength, elastic modulus, and mid-span camber test all meet the design requirements, and whose construction records (concrete pouring, prestressing tensioning, grouting) are complete, was selected as the "standard beam." The quality condition of this beam was defined as the "gold standard" for this batch. This ensures the scientific validity and reliability of the evaluation benchmark, providing a credible reference for subsequent comparisons.

[0054] Measurement point arrangement: Vertical acceleration sensors are placed at the junction of the top slab and web at the 1 / 2 span (mid-span) and 1 / 4 span sections of the beam. These locations are the inverse nodes of the first-order vertical bending vibration mode of the box girder, exhibiting the largest response amplitude and highest signal-to-noise ratio. This maximizes the acquisition of sensitive information about structural vibration and improves the accuracy of feature extraction.

[0055] Acquisition parameter settings: The sampling frequency was set to 100Hz to satisfy the Nyquist sampling theorem (target analysis frequency band 0-50Hz), fully covering the first few vertical bending modes of the box girder. High-viscosity special adhesive was used to bond the sensor to the concrete surface. Testing was conducted after the adhesive had fully hardened to ensure a rigid connection between the sensor and the beam, avoiding contact resonance. This eliminated the contamination of the spectrum by sensor installation resonance, ensuring signal authenticity.

[0056] Data collection period and duration: The data collection period was selected at night (20:00-05:00) when there was no interference from large-scale mechanical construction. Each data collection session lasted 5 minutes, and 30,000 data points were recorded continuously. This suppressed random environmental noise, and the long-term signal provided statistical stability for subsequent averaging processing.

[0057] S2: Calculation of Average Evolved Power Spectrum (AEPSD) based on wavelet transform: After preprocessing the vibration signal acquired in step S1, continuous wavelet transform is performed using Mexican Hat wavelets to calculate the modulus square of the wavelet coefficients. Normalization is then performed using the sampling interval and wavelet allowable constant to obtain the true time-frequency energy density and the wavelet evolved power spectrum (EPSD). Finally, the average is taken over the time dimension to obtain the wavelet average evolved power spectrum (AEPSD).

[0058] Signal preprocessing: The original acceleration signal is denoted as M. The first step is mean removal: Q1 = M - mean(M), eliminating the DC component. The second step is bandpass filtering: A 0.1Hz–20Hz bandpass filter is designed to filter Q1 to obtain Q2, removing low-frequency trend terms caused by temperature drift and high-frequency electromagnetic noise. This improves the signal-to-noise ratio and highlights the true vibration components of the structure.

[0059] Continuous wavelet transform: The Mexican Hat wavelet is selected as the mother wavelet, and the expression is:

[0060] ;

[0061] Where t represents the interval. Based on the estimated fundamental frequency of the box girder (approximately 4-5Hz), the scale range is set so that the center frequency fa corresponding to the scale variable a covers 1-15Hz (fc is the center frequency of the MH wavelet, approximately 0.251). A continuous wavelet transform is performed on Q2 to obtain the wavelet coefficient matrix coef(a,b), where a is the scale variable and b is the translation factor (i.e., the time variable). The excellent time-frequency localization characteristics of the MH wavelet accurately capture the instantaneous frequency components of non-stationary signals.

[0062] Evolutionary power spectrum calculation: The squared modulus of the wavelet coefficients is calculated, representing the instantaneous energy distribution of the signal at scale a (frequency) and time b. To ensure the wavelet power spectrum has physical units consistent with the Fourier spectrum, normalization is necessary. This invention employs the following normalization formula:

[0063] ;

[0064] in =0.01s is the sampling interval. The MH wavelet admissibility constant is calculated to be approximately 3.541. Simultaneously, the scale a is converted to the actual frequency fc = a / This yields the three-dimensional time spectrum: MH wavelet evolution power spectrum EPSD}(f,b). After normalization, EPSD has absolute amplitude significance, allowing for amplitude comparison between different beams.

[0065] Average Evolutionary Power Spectrum Generation: To obtain a stable spectrum representing the average dynamic characteristics of the beam, the average value of EPSD}(f,b) is taken over the entire time history b (30,000 points) to eliminate the random influence of time-varying noise, resulting in the final one-dimensional spectrum: MH wavelet average evolutionary power spectrum EPSD}(f,b). The reference AEPSD for a standard beam is as follows: Figure 2 As shown, the spectral peaks are prominent, sidelobes are well suppressed, and the signal-to-noise ratio is extremely high. Time averaging greatly suppresses noise, resulting in excellent repeatability of the extracted feature parameters.

[0066] S3: Spectral Feature Parameter Extraction: Three physically meaningful and sensitive features to stiffness, damping, and boundary conditions are extracted from the wavelet average evolved power spectrum (AEPSD): the frequency at maximum power, the half-power bandwidth, and the spectral distribution skewness. The AEPSD and its characteristic parameters of the standard beam are used as the baseline evolution power spectrum and baseline parameters.

[0067] from Figure 2 Three core feature parameters were extracted from the AEPSD spectrum of the standard beam shown:

[0068] The frequency fp at maximum power: the frequency corresponding to the spectral peak, which is 4.33333Hz for a standard beam. This parameter is directly related to the overall bending stiffness EI of the beam. Frequency is a direct characterization of stiffness, and deviation reflects changes in stiffness.

[0069] Half-power bandwidth f: First find the maximum power value Pmax, then calculate the two intersection frequencies f1 and f2 (f2>f1) of the horizontal line Pmax / 2 with the AEPSD spectral line. f = f2 - f1. Standard beam f = 5.5 - 3.16666 = 2.33334 Hz. This parameter is sensitive to the energy dissipation due to friction from microcracks and the energy dissipation due to slippage of prestressing tendons. The half-power bandwidth is a damping index used to identify latent defects such as microcracks and prestress loss.

[0070] Spectral distribution skewness Treating the AEPSD spectrum as a probability density function, it is obtained by calculating the third standard moment of the spectral amplitude distribution: ;

[0071] Where E represents expectation, The mean frequency is... The standard deviation is the frequency. The standard beam skewness value is 0.011339, close to 0, indicating that the spectrum is basically symmetrical, the beam boundary conditions are good, and the mass distribution is uniform. Skewness reflects the symmetry of the spectrum and indirectly assesses the support anchorage status and the uniformity of mass distribution. The above parameters are used as the "benchmark parameters" for the quality evaluation of this batch of box girders, thereby constructing a multi-dimensional evaluation index system and breaking through the limitations of single-frequency evaluation.

[0072] S4: Quality Evaluation: Repeat steps S1-S3 for the same batch of beams to be evaluated to obtain the wavelet average evolved power spectrum (AEPSD) and corresponding characteristic parameters of each beam. Compare the characteristic parameters of the beams to be evaluated with the benchmark parameters item by item. Based on preset multi-level deviation thresholds and differentiated verification processes, intelligently determine the quality grade of the box girder. Statistical analysis of the batch data dispersion provides feedback on the process stability of the beam fabrication production line.

[0073] Repeat steps S1-S3 for each beam to be evaluated (beam A, beam B) to obtain their respective AEPSD spectra. Figure 3 , Figure 4 Enter the information and characteristic parameters into Table 1.

[0074] Table 1. Beam Quality Inspection and Evaluation Table

[0075]

[0076] Deviation calculation and initial judgment:

[0077] Beam A: fp = 4.34211 Hz (deviation +0.2%) f = 2.30264Hz (deviation -1.32%), Sk = 0.011376 (deviation +0.33%). All three indicators meet the threshold requirements (±5%, ±10%, ±10%). Beam A is directly determined to be a "qualified beam". Rapid screening and efficient processing.

[0078] Beam B: fp = 4.10471Hz (deviation -5.28%) f = 2.35294Hz (deviation +0.84%), Sk = 0.011311 (deviation -0.24%). Frequency deviation exceeds the limit (5%-10%), initiating differential processing.

[0079] Differential processing – frequency exceeding limit by 5%-10%:

[0080] To address the negative frequency deviation of beam B, a rebound hammer was used to verify the elastic modulus of the concrete. (Standard beam elastic modulus) Estimated springback value of beam B And the frequency ratio k = f / f_0 = 0.947.

[0081] Calculation criteria:

[0082]

[0083] Measured elastic modulus of beam B Since the conditions are not met, beam B is determined to be a "beam of questionable quality". Quantifying the frequency deviation as a criterion for the qualification of the elastic modulus scientifically defines the boundary between "questionable" and "qualified", avoiding over-testing or under-judgment.

[0084] Differential processing – Half-power bandwidth or skewness exceeding limits:

[0085] If the beam only exceeds the half-power bandwidth or skewness limit, the procedure is as follows: First, check the prestressing tension data in the construction log. If it meets the design requirements, conduct three independent retests. If at least two of the three evaluations are qualified, it is finally deemed qualified; otherwise, it remains questionable. In this embodiment, beam B did not trigger this situation, but the procedure is clear. A secondary confirmation mechanism is provided for damping and boundary-type anomalies to reduce misjudgments caused by accidental environmental factors.

[0086] In-depth verification of beams with questionable quality:

[0087] A comprehensive review process was initiated for beam B: Construction logs were reviewed, revealing that the elastic modulus of the concrete test blocks under the same conditions during prestressing was only 89% of the design value; the measured value of the mid-span camber was 12% lower than that of the standard beam. Based on these findings, it was determined that beam B had quality issues with both the concrete elastic modulus and effective prestress, and a special assessment was recommended. This investigation aims to trace the root cause, provide a basis for repair and reinforcement, and simultaneously inform process improvements.

[0088] Beneficial effects:

[0089] (1) Non-destructive, efficient, and batch testing: Environmental vibration testing is adopted, which does not require loading equipment and is completely non-destructive; a single beam test only takes a few minutes, which is inexpensive and can achieve 100% full testing of box beams in the same batch, completely avoiding the limitations of traditional reverse tension method sampling inspection.

[0090] (2) Robust time-frequency feature extraction: The excellent time-frequency localization capability of MH wavelet transform is utilized to effectively overcome the shortcomings of traditional Fourier spectral analysis in handling non-stationary signals. Through the "time averaging" operation, the influence of random noise and transient interference is greatly suppressed, and the extracted AEPSD spectrum is smooth and stable with extremely high repeatability of feature parameters.

[0091] (3) Multi-dimensional comprehensive evaluation index system: Unlike the one-dimensional evaluation that only relies on fundamental frequency changes, this invention creatively introduces two complementary features: "half-power bandwidth" and "skewness". Among them, half-power bandwidth is extremely sensitive to the structural damping characteristics (related to microcrack propagation and frictional energy dissipation caused by prestress loss); skewness reflects the symmetry of the spectrum distribution and indirectly characterizes the uniformity of boundary constraints (support anchorage) and mass distribution. The combination of the three realizes the leap from "single stiffness" evaluation to "stiffness-damping-boundary" comprehensive evaluation.

[0092] (4) Scientific hierarchical evaluation and closed-loop processing: A mechanism for initial screening based on deviation thresholds and secondary confirmation based on on-site verification (rebound method, prestressed data verification, and retesting) was established, which not only ensured evaluation efficiency but also significantly reduced the misjudgment rate. In particular, an engineering-based approximate judgment formula was proposed for the quantitative relationship between frequency deviation and elastic modulus. It takes into account both safety and economic efficiency in testing.

[0093] (5) Quantitative feedback on the stability of beam fabrication process: Through statistical analysis of the deviation of characteristic parameters of batch beams, the results are directly mapped to the beam fabrication process, providing data support for the optimization of concrete mix ratio, adjustment of steam curing regime, and control of prestressing tension age in the precast beam yard, realizing the transformation from "result acceptance" to "process control".

[0094] Example embodiments have been disclosed herein, and while specific terminology has been used, it is for illustrative purposes only and should be construed as such, and is not intended to be limiting. In some instances, it will be apparent to those skilled in the art that features, characteristics, and / or elements described in conjunction with particular embodiments may be used alone, or in combination with features, characteristics, and / or elements described in conjunction with other embodiments, unless otherwise expressly indicated. Therefore, those skilled in the art will understand that various changes in form and detail may be made without departing from the scope of the invention as set forth in the appended claims.

Claims

1. A method for evaluating the quality of box girders based on the MH wavelet average evolution power spectrum, characterized in that, include: S1. Select a qualified beam as a standard beam, and arrange vibration sensors at key vibration measurement points on the surface of the standard beam to collect vertical acceleration time history signals. S2. The Mexican Hat wavelet is used to perform continuous wavelet transform, the modulus square of the wavelet coefficients is calculated and normalized to obtain the wavelet evolution power spectrum EPSD, and then the average is taken over the time dimension to obtain the wavelet average evolution power spectrum AEPSD. S3, extract the frequency, half-power bandwidth and skewness at the maximum power from the wavelet average evolved power spectrum (AEPSD), and use the wavelet average evolved power spectrum (AEPSD) and its characteristic parameters as the reference evolved power spectrum and reference parameters. S4. Repeat steps S1-S3 for the same batch of beams to be evaluated, obtain the wavelet average evolution power spectrum (AEPSD) and corresponding characteristic parameters of each beam to be evaluated, and compare the characteristic parameters of the beams to be evaluated with the benchmark parameters; combine the graded evaluation standard and the differentiated processing procedure to complete the quality judgment of the box girder.

2. The method according to claim 1, characterized in that, In S1, the key vibration measurement points include the junction of the top web plate at 1 / 2 span and 1 / 4 span of the beam; the sampling frequency is selected as 100-200Hz to satisfy the Nyquist sampling theorem; the vibration sensor is rigidly fixed to the beam surface by high-viscosity mortar; the data acquisition time is not less than 5 minutes, and the data is collected during a period when the external environmental interference is less than a preset threshold.

3. The method according to claim 1, characterized in that, Before step S2, the vibration signal acquired in step S1 is preprocessed, specifically as follows: The time-history signal M is subjected to mean removal processing to obtain signal Q1 = M - mean(M); the signal Q1 is then filtered by a bandpass filter to remove low-frequency trend terms and high-frequency noise, resulting in preprocessed signal Q2.

4. The method according to claim 1, characterized in that, S2 specifically includes: Based on the estimated fundamental frequency of the beam, the scale range of the wavelet transform is determined. The Mexican Hat wavelet is used to perform continuous wavelet transform on the preprocessed signal to obtain the wavelet coefficients coef(a,b), where a is the scale variable and b is the time variable. The square of the wavelet coefficient modulus is calculated and normalized according to the sampling interval and wavelet allowable constant. At the same time, the scale variable a is converted into the corresponding frequency variable or f to generate the three-dimensional wavelet evolution power spectrum EPSD(f,b). The one-dimensional wavelet average evolutionary power spectrum EPSD(f) is obtained by taking the average value of EPSD(f,b) over the entire time history b.

5. The method according to claim 4, characterized in that, The time-domain expression of the Mexican Hat wavelet is as follows: ； Where t is the interval used.

6. The method according to claim 1, characterized in that, In S3, the half-power bandwidth is defined as the absolute value of the difference between two frequency points on the AEPSD spectrum curve when the maximum power value drops to half of its value; the skewness is defined as a statistical characteristic characterizing the asymmetry of the AEPSD spectrum distribution, obtained by calculating the third standard moment of the spectrum amplitude distribution. ; in, Let E represent the skewness of the spectral distribution, and E represent the expectation. The mean frequency is... This represents the standard deviation of the frequency.

7. The method according to claim 1, characterized in that, The grading evaluation criteria in S4 include three characteristic parameters that are within a preset deviation threshold: The frequency deviation at maximum power shall not exceed ±5%, the half-power bandwidth deviation shall not exceed ±10%, and the skewness deviation shall not exceed ±10%.

8. The method according to claim 7, characterized in that, The differentiation processing flow in S4 includes: If all three characteristic parameters are within the limits, the beam is determined to be a qualified beam. If two or more of the three characteristic parameters exceed the limit, the beam is directly judged as a beam with questionable quality. If only the frequency at maximum power exceeds the limit, and the exceedance value is in the range of 5% to 10%, the elastic modulus of the beam concrete should be checked using a rebound hammer. If the measured elastic modulus E satisfies: ； If the beam is deemed to be of acceptable quality, it is considered to be of questionable quality. The ratio of the frequency of the beam to be evaluated to that of the standard beam. The elastic modulus of a standard beam; If only half-power bandwidth or skewness exceeds the limit, first check the prestressing tension data in the construction log. If the tension data meets the design requirements, conduct three independent repeat tests. If at least two of the three evaluations are deemed qualified, the beam is finally determined to be of qualified quality; otherwise, it is still determined to be a beam of questionable quality.

9. The method according to claim 8, characterized in that, In step S4, for box girders determined to be of questionable quality, a further comprehensive verification procedure is performed: Verify whether the concrete compressive strength, elastic modulus, effective prestress, and mid-span arch test indicators of the beam meet the design requirements, and review the records of concrete pouring, prestressing tensioning, grouting and anchoring, steam curing, and test blocks to comprehensively determine the final quality status of the beam.

10. The method according to claim 1, characterized in that, The method further includes: generating a control chart for feedback on the process stability of the beam manufacturing production line by statistically analyzing the dispersion of the characteristic parameters of the wavelet average evolution power spectrum of all beams to be evaluated in the same batch and the standard beam.

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