Method for calculating flexural capacity of fiber reinforced concrete beam
By performing frequency sweep excitation and vibration signal analysis on the mid-span section of fiber-reinforced reinforced concrete beams, and combining discrete wavelet transform and multinomial regression models, the problem of the inability to calculate the flexural bearing capacity of fiber-reinforced reinforced concrete beams in real time and accurately in traditional methods is solved, and non-destructive, dynamic, and high-precision bearing capacity prediction is achieved.
Patent Information
- Application Number
- CN202511493111.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-20
- Publication Date
- 2026-01-13
AI Technical Summary
In existing technologies, traditional methods are difficult to perform non-destructive, real-time, and high-precision calculations of the flexural bearing capacity of fiber-reinforced reinforced concrete beams, cannot dynamically monitor changes in structural health status, and rely on empirical parameters and destructive tests, which can cause secondary damage.
By performing frequency sweep excitation at the mid-span section, acquiring vibration response signals and performing discrete wavelet transform, the main resonance frequency and selected frequency band energy are extracted. Combined with a polynomial regression model, a multi-feature fusion analysis method is constructed to predict the flexural bearing capacity.
It enables real-time acquisition of dynamic response data without damaging the structure, is applicable to existing structures, avoids secondary damage, and provides more accurate calculation results, adapting to the load-bearing requirements of different fiber types, bonding layers, and beam sizes.
Smart Images
Figure CN121328121A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of structural health monitoring, in particular to a fiber reinforced concrete beam flexural capacity calculation method. BACKGROUND
[0002] With the development of civil engineering structures towards large span, high-rise and complex, traditional bearing capacity evaluation methods rely on empirical formula or destructive test, which has the defects of poor real-time performance, high cost and inability to dynamically monitor.
[0003] In the prior art, the traditional reinforced steel beam flexural capacity calculation method regards the original steel beam and the reinforcing layer as linear elastic composite material, and calculates the ultimate bending moment of the section based on the plane section assumption, which cannot reflect the nonlinear damage such as plastic deformation of steel after yielding, fiber and concrete interface slip, and the specification correction coefficient depends on test data and engineering experience, which has poor adaptability to different working conditions, and the traditional method only provides static bearing capacity evaluation, which cannot dynamically track the change of structural health state, and destructive tests such as three-point bending test are used to verify the bearing capacity, which will cause secondary damage to the structure.
[0004] Therefore, a non-destructive, real-time and high-precision fiber reinforced steel beam flexural capacity prediction is needed, which can automatically capture the nonlinear mapping relationship between input features and bearing capacity by constructing an intelligent monitoring technology driven by multi-modal data fusion, reduce the dependence on empirical parameters, and realize accurate detection and the transition from static evaluation to dynamic monitoring.
[0005] The above information disclosed in the background section is only used to strengthen the understanding of the background of the present disclosure, and therefore it can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY
[0006] The purpose of the present application is to provide a fiber reinforced concrete beam flexural capacity calculation method to solve the problems raised in the background.
[0007] To achieve the above purpose, the present application provides the following technical scheme: A fiber reinforced concrete beam flexural capacity calculation method, the specific steps include: Step 1: For a plurality of fiber reinforced concrete beam samples, sweep excitation operation is performed at the cross section according to the preset duration and frequency range, an acceleration sensor is installed at the cross section, and the vibration response signals of each fiber reinforced concrete beam sample are collected synchronously; Step 2: Discrete wavelet transform analysis is performed on the collected vibration response signal using MATLAB software, the vibration response signal is decomposed into multiple high-frequency subbands, the top 3 high-frequency subbands with the largest energy are selected as the selected frequency bands, the energy maximum frequency point of the high-frequency subband with the largest energy is taken as the main resonance frequency, and the sum of the energy of the selected frequency bands is taken as the sum of the energy of the selected frequency bands; a three-point bending test method is used for the fiber-reinforced reinforced concrete beam sample to obtain the corresponding actual flexural bearing capacity data; Step 3: The main resonance frequency, the selected frequency band energy and the sum of the selected frequency band energy of each sample are taken as input features, and the actual flexural bearing capacity is taken as output label, the training set and the test set are divided, the polynomial regression model is constructed, the mean square error, the root mean square error and the determination coefficient are calculated to evaluate the optimization, and the optimal order polynomial regression model is determined; Step 4: For the fiber-reinforced reinforced concrete beam to be detected for flexural bearing capacity, a sweep excitation is applied to the mid-span section at the same frequency range and duration, the vibration response signal is collected and discrete wavelet transform is performed, the main resonance frequency, the selected frequency band energy and the sum of the selected frequency band energy are extracted, and the optimal order polynomial regression model is input to output the predicted flexural bearing capacity.
[0008] Further, for a plurality of fiber-reinforced reinforced concrete beam samples, the method for performing sweep excitation operation at the mid-span section according to the preset duration and frequency range is: The plurality of fiber-reinforced reinforced concrete beam samples have consistent fiber types, number of pasted layers, beam sizes and concrete strengths, the loudspeaker is preset to a frequency range from a starting frequency to an ending frequency , and a duration.
[0009] Further, the method for synchronously collecting vibration response signals of each fiber-reinforced reinforced concrete beam sample is: The acceleration sensor is installed at the mid-span section of each fiber-reinforced reinforced concrete beam sample, when the loudspeaker starts the sweep excitation operation, the acceleration waveform output by the acceleration sensor is recorded, the NI USB-6363 data acquisition card is used, the sampling frequency is set to , the resolution is set to 16 bits, the input range is set to , and the cutoff frequency is set to , and the output vibration response signal is: ; In the formula, represents the vibration response signal, represents the signal length, , wherein, Further, the method for decomposing the vibration response signal into a plurality of high frequency sub-bands by using MATLAB software to analyze the discrete wavelet transform of the collected vibration response signal is: Using MATLAB software, selecting Daubechies4 wavelet base function, setting the decomposition level Discrete wavelet transform is performed on the vibration response signal, wherein the formula for performing discrete wavelet transform on the vibration response signal is: ; In the formula, is the vibration response signal, is the Daubechies4 wavelet base function, is the wavelet coefficient, is the scale factor, is the time offset, wherein The value of is automatically generated by MATLAB software, and , wherein , is the signal length, , wherein ; The frequency range of each high frequency sub-band output is: ; In the formula, is the high frequency component, i.e. the high frequency sub-band frequency range of the layer, when , , the high frequency sub-band frequency higher than is removed, and at this time ; The discrete vibration response signal is represented as: ; is the discrete vibration response signal, wherein is the time index of the discrete vibration response signal; The discrete wavelet transform coefficient output is: ; In the formula, is the th wavelet coefficient of the th layer.
[0010] Further, the method for calculating the selected frequency band, the main resonance frequency and the sum of the energy of the selected frequency band in step 3 is: The high frequency sub-band energy is calculated as: ; In the formula, Represented as high-frequency subband energy; Then, the main resonance frequency was determined: First, find the high-frequency subband with the highest energy: ; In the formula, This represents the high-frequency sub-band with the highest energy. Within this sub-band, the frequency point with the highest energy is calculated. ; In the formula, This is represented as the bandwidth of the subband, and , This represents the index of the coefficient with the highest energy in that subband. This is represented as the frequency point with the highest calculated energy in this sub-band, i.e., the main resonance frequency; High-frequency subband energy Sort the frequencies in descending order, extract the top 3 high-frequency sub-bands with the highest energy as selected frequency bands, and then extract the energy of the selected frequency bands: The sum of the selected frequency band energies is calculated based on the selected frequency band energy: ; In the formula, It is represented as the sum of energy in the selected frequency band.
[0011] Furthermore, the method for obtaining the corresponding actual flexural bearing capacity data by using a three-point bending test on fiber-reinforced reinforced concrete beam samples is as follows: The span, section width, and section height of fiber-reinforced reinforced concrete beam samples were measured using a three-point bending test method. The testing machine automatically collected load and mid-span deflection data, outputting the peak load and calibrating it as the ultimate bearing capacity. The actual flexural bearing capacity was calculated based on the span, section width, section height, and ultimate bearing capacity. ; In the formula, Indicated as span, Represented as cross-sectional width, Expressed as cross-sectional height, This is expressed as the ultimate bearing capacity. This represents the actual bending capacity.
[0012] Furthermore, the method for dividing the training set and the test set and constructing the multinomial regression model is as follows: Extract the principal resonance frequencies corresponding to each fiber-reinforced reinforced concrete beam sample. Selected frequency band energy The sum of energy in the selected frequency band With bending bearing capacity ,in The index of the number of fiber-reinforced reinforced concrete beam samples is represented by the principal resonant frequency. Selected frequency band energy The sum of energy in the selected frequency band As an input feature, flexural bearing capacity As output labels, , This represents the number of fiber-reinforced reinforced concrete beam samples. Organize the input features into dimensions... Input feature matrix: ; In the formula, Represented as The input feature matrix; Organize the output labels into an output vector: ; In the formula, Represented as an output vector; Set the training set to include The test set includes fiber-reinforced reinforced concrete beam samples. A sample of fiber-reinforced reinforced concrete beam, and The input feature matrix of the training set is denoted as The output label vector is denoted as The input feature matrix of the test set is denoted as... The output label vector is denoted as .
[0013] Furthermore, the method for evaluating and optimizing the polynomial regression model by calculating the mean squared error, root mean square error, and coefficient of determination is as follows: Extracting the input feature matrix Each sample: ; In the formula, Represented as the input feature matrix The 10 samples, of which ; Determine the order of a polynomial ,in, The characteristic of a polynomial of order 1 includes all that satisfy monomials ,in, , represented as Exponent in a monomial , ; Calculate the number of characteristics of a polynomial: ; In the formula, Represented as the number of polynomial characteristics; Find all that satisfy nonnegative integer vectors , For each condition that is met , , represented as the index of a non-negative integer vector, is used to calculate The corresponding monomial: ; non-negative integer vectors The corresponding monomials, arranged lexicographically, yield a dimension of The The polynomial eigenvectors of each sample: ; In the formula, Represented as the first The polynomial feature vector of each sample Represented as the first 1 polynomial eigenvalues ; Stacking by rows yields a dimension of The polynomial characteristic matrix: ; In the formula, Represented as a polynomial characteristic matrix; Definition of multinomial regression model: ; In the formula, Represented as the intercept term, Represented as model coefficients, Represented as an error term; The optimal coefficients are obtained by minimizing the sum of squared errors: ; In the formula, Expressed as the sum of squared errors, Represented as the first in the training set Actual flexural bearing capacity of each sample; right Taking the derivative and setting it to zero, we get: ; In the formula, Represented as a model coefficient vector, including the intercept term. Other coefficients , This is represented as the output label vector of the training set; No. For the test set of fiber-reinforced reinforced concrete beam samples, the predicted values are: ; In the formula, This represents the predicted value for a sample in the test set. Represented as the first The input feature matrix of a test set of fiber-reinforced reinforced concrete beam samples; Calculate the mean square error: ; In the formula, This is expressed as mean square error. Represented as the first in the test set Actual flexural bearing capacity of a fiber-reinforced reinforced concrete beam sample; Calculate the root mean square error: ; In the formula, This is expressed as root mean square error; Calculate the coefficient of determination: ; In the formula, This is expressed as the coefficient of determination. ; turn up The value is the smallest. Largest polynomial order As the optimal order, the optimal order polynomial regression model is: ; In the formula, This represents the predicted flexural capacity of the fiber-reinforced reinforced concrete beam to be tested. This represents the input feature vector of the fiber-reinforced reinforced concrete beam whose flexural bearing capacity is to be tested. ,in, The frequency represents the principal resonant frequency of the fiber-reinforced reinforced concrete beam whose flexural bearing capacity is to be tested. This represents the energy of the first three high-frequency sub-bands, indicating the bending capacity to be tested. This represents the total energy of the fiber-reinforced reinforced concrete beam whose flexural bearing capacity is to be tested.
[0014] Compared with the prior art, the beneficial effects of the present invention are: This invention, based on frequency sweep excitation and vibration signal acquisition at mid-span cross-section, can obtain dynamic response data in real time without damaging the structure. It is also applicable to fiber-reinforced reinforced concrete beams already in service, enabling long-term health monitoring and avoiding secondary damage caused by traditional destructive tests. Furthermore, this invention extracts the principal resonance frequency and selected energy using discrete wavelet transform, and combines it with a polynomial regression model to achieve multi-feature fusion analysis, overcoming the limitations of single parameters and adapting to the load-bearing capacity calculation needs of different fiber types, bonding layers, and beam sizes, resulting in more accurate results. Attached Figure Description
[0015] Figure 1 This is a schematic diagram of the overall method flow of the present invention; Figure 2 This is a fitting diagram of the dominant frequency and bending bearing capacity of the present invention; Figure 3 This is a fitting diagram of the total energy versus the flexural bearing capacity of the present invention; Figure 4 The frequency band energy and bending bearing capacity fitting diagram were selected for this invention; Figure 5 This is a prediction error diagram for the present invention. Detailed Implementation
[0016] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.
[0017] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.
[0018] Example: Please see Figures 1 to 5 The present invention provides a technical solution: A method for calculating the flexural bearing capacity of fiber-reinforced reinforced concrete beams, comprising the following steps: Step 1: For multiple fiber-reinforced reinforced concrete beam samples, perform frequency sweep excitation at the mid-span section according to the preset duration and frequency range, install an accelerometer at the mid-span section, and synchronously collect the vibration response signals of each fiber-reinforced reinforced concrete beam sample. Different fiber types, such as carbon fiber and glass fiber, exhibit significant differences in elastic modulus and strength, directly affecting the stiffness and vibration characteristics of beams. Different numbers of bonding layers lead to varying fiber usage, thus altering the beam's load-bearing capacity and vibration modes. Beam dimensions, such as span, cross-sectional dimensions, and concrete strength, are fundamental parameters of structural stiffness; differences in these parameters result in significant variations in natural frequencies and energy distribution. Therefore, the selected fiber-reinforced reinforced concrete beam samples must be consistent in fiber type, number of bonding layers, beam dimensions, and concrete strength. If parameters are inconsistent, they must be grouped according to key parameters such as fiber type and number of bonding layers, with consistent parameters within each group. Even if fiber type, number of bonding layers, beam dimensions, and concrete strength differ, samples with roughly the same parameters are categorized, and then the flexural capacity of fiber-reinforced reinforced concrete beams is calculated within the same category.
[0019] The loudspeaker was vertically mounted at the mid-span of the fiber-reinforced beam, at a distance of 1.5m, to ensure uniform excitation transmission. The loudspeaker was preset to its starting frequency. to the termination frequency Within the frequency range, sound wave energy attenuates with distance beyond 1.5m, making it difficult to accurately extract high-frequency sub-band energy. Mid-span alignment avoids asymmetrical vibration. Data from multiple experiments show that with a lateral offset of 50mm, the peak acceleration difference between the left and right sides of the mid-span cross-section can reach 15%. The duration of this duration, which covers the low-frequency to high-frequency vibration modes of the beam structure, ensures that the beam structure reaches steady-state vibration and avoids transient response interference in the initial stage.
[0020] In simply supported beams or under common boundary conditions, the mid-span section is usually where the maximum bending moment and deflection are located. During vibration, the acceleration response is most significant at this location, and the sensor can capture the strongest vibration signal. Therefore, the accelerometer is installed at the mid-span section of each fiber-reinforced reinforced concrete beam sample to facilitate uniform experimental conditions and reduce asymmetric vibration interference caused by positional deviations. When the loudspeaker begins frequency sweep excitation, the waveform of the acceleration output from the accelerometer over time is recorded. An NI USB-6363 data acquisition card is used. According to Nyquist's theorem, the sampling frequency must be at least twice the highest frequency of the signal, i.e., 20 kHz, to avoid aliasing distortion. Set as To ensure complete capture of high-frequency vibration components, a resolution of 16 bits is set to adapt to the dynamic range of the vibration signal, reducing quantization noise and improving small-signal detection capability. The input range is set to... This is a standard setting to ensure the signal is not saturated; the cutoff frequency is set to... Filter out high-frequency noise above 20 kHz and output vibration response signal: ; In the formula, Represented as a vibration response signal, Represented as signal length, At this point, the signal length can improve the accuracy of frequency domain analysis, thereby reducing the impact of random noise. Represented as a time index, .
[0021] Step 2: Use MATLAB software to perform discrete wavelet transform analysis on the collected vibration response signal, decompose the vibration response signal into multiple high-frequency sub-bands, select the top 3 high-frequency sub-bands with the highest energy as the selected frequency bands, take the frequency point with the highest energy of the high-frequency sub-bands as the main resonance frequency, and take the sum of the energy of the selected frequency bands as the sum of the energy of the selected frequency bands. Use the three-point bending test method on the fiber-reinforced reinforced concrete beam sample to obtain the corresponding actual bending bearing capacity data. Using MATLAB software and selecting the Daubechies4 wavelet basis function, the Daubechies wavelet is a compactly supported orthogonal wavelet with strict time-domain localization properties. The Daubechies4 wavelet basis function has fourth-order vanishing moments, making it sensitive to high-frequency details in signals, such as high-frequency vibrations caused by cracks. It can effectively capture the transient characteristics of signals by suppressing low-frequency components and highlighting local abrupt changes related to structural damage. It can effectively analyze the phase changes of vibration signals and set the number of decomposition levels. The signal can be decomposed into 5 scales, suitable for real-time processing of long signals with 400,000 points. Discrete wavelet transform is performed on the vibration response signal, and the formula used for this transform is: ; In the formula, Represented as a vibration response signal, Represented as Daubechies4 wavelet basis functions, Represented as wavelet coefficients, This is represented as a scale factor. This is expressed as a time offset, where, The value is automatically generated by MATLAB software, and ,in, , Represented as signal length, ,in, ; The frequency range of each high-frequency sub-band output is: ; In the formula, Represented as high-frequency components, i.e., the th The high-frequency sub-band frequency range of the layer, when hour, Remove those higher than The high-frequency sub-band frequency, at this time
[0022] At this point, the frequency range covered by each layer is: d1: 10–20 kHz d2: 5–10 kHz d3: 2.5–5 kHz d4: 1.25–2.5 kHz d5: 0.625–1.25 kHz The discretized vibration response signal is represented as follows: ; Represented as the discrete vibration response signal, where, This is represented as the time index of the discretized vibration response signal. Continuous vibration signals are continuous functions of time, but the ADC module of a data acquisition card cannot directly process continuous signals. The ADC converts the continuous signal into a discrete sequence through periodic sampling at fixed intervals. right At the point of time The instantaneous value at a given point, through this mapping, the discrete sequence The original signal's temporal sequence and amplitude information are fully preserved, facilitating subsequent frequency domain and multi-resolution analysis.
[0023] The output discrete wavelet transform coefficients are: ; In the formula, Represented as the first The first layer Wavelet coefficients; In structural health monitoring, changes in high-frequency energy generally reflect localized damage such as fiber debonding and crack propagation. The high-frequency subband energy is calculated as follows: ; In the formula, Represented as high-frequency subband energy; Next, the principal resonance frequency is determined. The principal resonance frequency is the frequency component in which the energy of the structure is most concentrated under free vibration or forced vibration. It usually corresponds to the natural frequency of the structure. The natural frequency is a characteristic frequency determined by mass, stiffness, and damping. Therefore, the principal resonance frequency reflects the stiffness characteristics of the structure as a whole or in a local area. First, find the high-frequency subband with the highest energy: ; In the formula, Represented as the high-frequency subband with the highest energy, the high-frequency subband corresponds to the fine scale of wavelet decomposition. Its energy concentration reflects high-frequency components such as local impact, interface slip, or microcrack propagation. The more severe the damage, the more significant the energy of the high-frequency subband. For example, debonding at the fiber-concrete interface will excite high-frequency vibrations, leading to a sudden increase in the energy of the corresponding subband.
[0024] Calculate the frequency point with the highest energy in this sub-band: ; In the formula, This is represented as the bandwidth of the subband, and , This represents the index of the coefficient with the highest energy in that subband. This is represented as the frequency point with the highest calculated energy in this sub-band, i.e., the main resonance frequency; High-frequency subband energy The frequencies were sorted in descending order. Extensive research has shown a significant positive correlation between the damage level of fiber-reinforced beams and the sum of the energies of the top three high-frequency sub-bands. The top three high-frequency sub-bands with the highest energy were extracted as selected frequency bands, and their energy was then extracted. The sum of the selected frequency band energies is calculated based on the selected frequency band energy: ; In the formula, It represents the sum of energy in the selected frequency bands. A single sub-band may miss a specific type of damage, while the sum of the energy of the first three sub-bands can cover a wider range of damage characteristic frequency bands.
[0025] Traditional formulas, such as those based on elastic theory, assume that materials are linearly elastic. However, fiber-reinforced beams exhibit nonlinear interface slip and fiber debonding under load, leading to stiffness degradation and energy dissipation. These behaviors cannot be described by linear elastic formulas, thus underestimating the actual load-bearing capacity. In other words, there is a conflict between the ideal assumptions and the actual material behavior. By measuring the span, cross-sectional width, and cross-sectional height of fiber-reinforced reinforced concrete beam samples, and employing a three-point bending test method, the dispersion of material parameters such as concrete strength and fiber modulus is naturally reflected in the measured data. The testing machine automatically collects load and mid-span deflection data, outputs the peak load, and calibrates it as the ultimate bearing capacity. Based on the span, cross-sectional width, cross-sectional height, and ultimate bearing capacity, the actual flexural bearing capacity is calculated. ; In the formula, Indicated as span, Represented as cross-sectional width, Expressed as cross-sectional height, This is expressed as the ultimate bearing capacity. This represents the actual bending capacity.
[0026] Step 3: Use the principal resonant frequency, selected frequency band energy, and the sum of selected frequency band energy of each sample as input features, and the actual flexural bearing capacity as output label. Divide the training set and the test set, construct a multinomial regression model, and evaluate and optimize it by calculating the mean square error, root mean square error, and coefficient of determination to determine the optimal order multinomial regression model. Supervised learning algorithms require a clearly defined two-dimensional matrix structure of input features and output labels to extract the principal resonance frequencies corresponding to each fiber-reinforced reinforced concrete beam sample. Selected frequency band energy The sum of energy in the selected frequency band With bending bearing capacity ,in The index of the number of fiber-reinforced reinforced concrete beam samples is represented by the principal resonant frequency. Selected frequency band energy The sum of energy in the selected frequency band The reason for using a single feature, such as the principal resonant frequency alone, as an input feature is that it is difficult to fully reflect the material properties. Therefore, a multi-dimensional feature space is chosen, including flexural bearing capacity. As output labels, , This represents the number of fiber-reinforced reinforced concrete beam samples. Organize the input features into dimensions... Input feature matrix: ; In the formula, Represented as The input feature matrix; Organize the output labels into an output vector: ; In the formula, Represented as an output vector; Set the training set to include The test set includes fiber-reinforced reinforced concrete beam samples. A sample of fiber-reinforced reinforced concrete beam, and The input feature matrix of the training set is denoted as The output label vector is denoted as The input feature matrix of the test set is denoted as... The output label vector is denoted as The training set is used to fit the model parameters, while the test set is used to verify the model's predictive ability on unseen data. By comparing the training set error, such as the mean squared error (MSE), with the test set error, it can be determined whether the model is overfitting.
[0027] Extracting the input feature matrix Each sample: ; In the formula, Represented as the input feature matrix The 10 samples, of which ; Determine the order of the optimal polynomial :in, The characteristic of a polynomial of order 1 includes all that satisfy monomials ,in, , represented as Exponent in a monomial , The order d of a multinomial regression model directly affects the model complexity. A smaller d is prone to underfitting and cannot capture the nonlinear features in the data, while a larger d may cause overfitting, resulting in a decrease in generalization ability. Calculate the number of characteristics of a polynomial: ; In the formula, Represented as the number of polynomial characteristics; Find all that satisfy nonnegative integer vectors , For each condition that is met , , represented as the index of a non-negative integer vector, is used to calculate The corresponding monomial: ; non-negative integer vectors The corresponding monomials, arranged lexicographically, yield a dimension of The The polynomial eigenvectors of each sample: ; In the formula, Represented as the first The polynomial feature vector of each sample Represented as the first 1 polynomial eigenvalues ; Stacking by rows yields a dimension of The polynomial characteristic matrix: ; In the formula, Represented as a polynomial characteristic matrix; Definition of multinomial regression model: ; In the formula, Represented as the intercept term, Represented as model coefficients, Represented as an error term; The optimal coefficients are obtained by minimizing the sum of squared errors: ; In the formula, Expressed as the sum of squared errors, Represented as the first in the training set Actual flexural bearing capacity of each sample; right Taking the derivative and setting it to zero, we get: ; In the formula, Represented as a model coefficient vector, including the intercept term. Other coefficients , This is represented as the output label vector of the training set; No. For the test set of fiber-reinforced reinforced concrete beam samples, the predicted values are: ; In the formula, This represents the predicted value for a sample in the test set. Represented as the first The input feature matrix of a test set of fiber-reinforced reinforced concrete beam samples; Calculate the mean square error: ; In the formula, This is expressed as mean square error. Represented as the first in the test set Actual flexural bearing capacity of a fiber-reinforced reinforced concrete beam sample; Calculate the root mean square error:
[0028] In the formula, This is expressed as root mean square error; Calculate the coefficient of determination: ; In the formula, This is expressed as the coefficient of determination. In the field of structural engineering, the coefficient of determination directly affects safety assessment; turn up The value is the smallest. Largest polynomial order Determine the optimal order polynomial regression model: ; In the formula, This represents the predicted flexural capacity of the fiber-reinforced reinforced concrete beam to be tested. This represents the input feature vector of the fiber-reinforced reinforced concrete beam whose flexural bearing capacity is to be tested. ,in, The frequency represents the principal resonant frequency of the fiber-reinforced reinforced concrete beam whose flexural bearing capacity is to be tested. This represents the energy of the first three high-frequency sub-bands of the flexural bearing capacity to be tested, i.e., the selected frequency band energy. This represents the total energy of the fiber-reinforced reinforced concrete beam whose flexural bearing capacity is to be tested. The value can quantify the level of absolute error, reflecting the degree of deviation between the predicted value and the actual value. Representing the reliability of the theoretical basis, the maximum value ensures the effectiveness of the model. Table 1 shows the data of the dominant frequency, total energy and selected frequency band energy E1 with the strongest correlation under different flexural bearing capacities for a certain fiber-reinforced reinforced concrete beam. The data are summarized into a data table.
[0029]
[0030] like Figures 2-4 As shown, as the bending load gradually increases, the positive correlation between each parameter and the bending load is clearly presented. Among them, the higher the dominant frequency, the greater the structural stiffness. The bending load changes approximately linearly with the dominant frequency. When the bending load is high, the energy accumulation in the fixed frequency band is more significant and exhibits a quadratic change. This quantitative relationship allows the model to be fitted using the dominant frequency, total energy, and selected frequency band energy to predict the bending load and avoid damage to the structure.
[0031] Step 4: For the fiber-reinforced reinforced concrete beam whose flexural bearing capacity is to be tested, apply a frequency sweep excitation of the same frequency range and duration at the mid-span section, collect the vibration response signal and perform discrete wavelet transform, extract the main resonance frequency, the selected frequency band energy and the sum of the selected frequency band energy, input the optimal order polynomial regression model, and output the predicted flexural bearing capacity. Accelerometers were installed at the mid-span section of each fiber-reinforced reinforced concrete beam sample. When the loudspeaker began its frequency sweep excitation operation, the waveform of the acceleration output from the accelerometer over time was recorded. An NI USB-6363 data acquisition card was used to record the sampling frequency. Set as The resolution is set to 16 bits, and the input range is set to... The cutoff frequency is set to Output vibration response signal: ; In the formula, Represented as a vibration response signal, Represented as signal length, ,in, Represented as a time index, .
[0032] Using MATLAB software, the Daubechies4 wavelet basis function was selected, and the number of decomposition levels was set. Discrete wavelet transform is performed on the vibration response signal. The formula for performing discrete wavelet transform on the vibration response signal is as follows: ; In the formula, Represented as a vibration response signal, Represented as Daubechies4 wavelet basis functions, Represented as wavelet coefficients, This is represented as a scale factor. This is expressed as a time offset, where, The value is automatically generated by MATLAB software, and ,in, , Represented as signal length, ,in, ; The frequency range of each high-frequency sub-band output is: ; In the formula, Represented as high-frequency components, i.e., the th The high-frequency sub-band frequency range of the layer, when hour, Remove those higher than The high-frequency sub-band frequency, at this time ; The discretized vibration response signal is represented as follows: ; Represented as the discrete vibration response signal, where, This is represented as the time index of the discretized vibration response signal; The output discrete wavelet transform coefficients are: ; In the formula, Represented as the first The first layer Wavelet coefficients; Calculate the energy of the high-frequency subband: ; In the formula, Represented as high-frequency subband energy; Then, the main resonance frequency was determined: First, find the high-frequency subband with the highest energy: ; In the formula, This represents the high-frequency sub-band with the highest energy. Within this sub-band, the frequency point with the highest energy is calculated. ; In the formula, This is represented as the bandwidth of the subband, and , This represents the index of the coefficient with the highest energy in that subband. This is represented as the frequency point with the highest calculated energy in this sub-band; High-frequency subband energy Sort the frequencies in descending order, extract the top 3 high-frequency sub-bands with the highest energy as selected frequency bands, and then extract the energy of the selected frequency bands: The sum of the selected frequency band energies is calculated based on the selected frequency band energy: ; In the formula, It is expressed as the sum of energy in the selected frequency band; Next, the input feature vector of the fiber-reinforced reinforced concrete beam whose flexural bearing capacity is to be tested is... Input the pre-trained optimal order multinomial regression model: ; The result obtained is the predicted flexural bearing capacity. There is no need to conduct destructive tests on the structure. The bearing capacity can be evaluated directly through vibration signal analysis, avoiding secondary damage to the structure. It also does not rely on complex material constitutive relationships or assumptions. The bearing capacity decline can be warned in real time through vibration signals. It is suitable for health monitoring of existing bridges, buildings and other engineering structures to prevent sudden accidents.
[0033]
[0034] like Figure 5 As shown, the actual and predicted values of each sample are connected by a vertical line, reflecting the difference between the two. As the serial number increases, the actual and predicted flexural bearing capacity generally show an upward trend. The error between the actual and predicted flexural bearing capacity is small, indicating that the model has high accuracy and reliability. By intuitively comparing the actual and predicted values, the effectiveness of the prediction model can be verified. When the error in the data is found to be too large, problems such as measurement error and unsuitable model can be investigated.
[0035] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.
[0036] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.
[0037] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.
[0038] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.
Claims
1. A method for calculating the flexural bearing capacity of fiber-reinforced reinforced concrete beams, characterized in that, The specific steps include: Step 1: For multiple fiber-reinforced reinforced concrete beam samples, perform frequency sweep excitation at the mid-span section according to the preset duration and frequency range, install an accelerometer at the mid-span section, and synchronously collect the vibration response signals of each fiber-reinforced reinforced concrete beam sample. Step 2: Use MATLAB software to perform discrete wavelet transform analysis on the collected vibration response signal, decompose the vibration response signal into multiple high-frequency sub-bands, select the top 3 high-frequency sub-bands with the highest energy as the selected frequency bands, take the frequency point with the highest energy of the high-frequency sub-bands as the main resonance frequency, and take the sum of the energy of the selected frequency bands as the sum of the energy of the selected frequency bands. Use the three-point bending test method on the fiber-reinforced reinforced concrete beam sample to obtain the corresponding actual bending bearing capacity data. Step 3: Use the principal resonant frequency, selected frequency band energy, and the sum of selected frequency band energy of each sample as input features, and the actual flexural bearing capacity as output label. Divide the training set and the test set, construct a multinomial regression model, and evaluate and optimize it by calculating the mean square error, root mean square error, and coefficient of determination to determine the optimal order multinomial regression model. Step 4: For the fiber-reinforced reinforced concrete beam whose flexural bearing capacity is to be tested, apply a frequency sweep excitation of the same frequency range and duration at the mid-span section, collect the vibration response signal and perform discrete wavelet transform, extract the main resonance frequency, the selected frequency band energy and the sum of the selected frequency band energy, input the optimal order polynomial regression model, and output the predicted flexural bearing capacity.
2. The method for calculating the flexural bearing capacity of fiber-reinforced reinforced concrete beams according to claim 1, characterized in that: For multiple fiber-reinforced reinforced concrete beam samples, the method for performing frequency sweep excitation at the mid-span section according to a preset duration and frequency range is as follows: Multiple fiber-reinforced reinforced concrete beam samples must have identical fiber type, number of bonding layers, beam dimensions, and concrete strength. The speaker should be preset to the starting frequency. to the termination frequency The frequency range The duration.
3. The method for calculating the flexural bearing capacity of fiber-reinforced reinforced concrete beams according to claim 1, characterized in that: The method for synchronously collecting vibration response signals from each fiber-reinforced reinforced concrete beam sample is as follows: Accelerometers were installed at the mid-span section of each fiber-reinforced reinforced concrete beam sample. When the loudspeaker began its frequency sweep excitation operation, the waveform of the acceleration output from the accelerometer over time was recorded. An NI USB-6363 data acquisition card was used to record the sampling frequency. Set as The resolution is set to 16 bits, and the input range is set to... The cutoff frequency is set to Output vibration response signal: ； In the formula, Represented as a vibration response signal, Represented as signal length, ,in, Represented as a time index, .
4. The method for calculating the flexural bearing capacity of fiber-reinforced reinforced concrete beams according to claim 3, characterized in that: The method of using MATLAB software to perform discrete wavelet transform analysis on the acquired vibration response signal and decompose the vibration response signal into multiple high-frequency subbands is as follows: Using MATLAB software, the Daubechies4 wavelet basis function was selected, and the number of decomposition levels was set. Discrete wavelet transform is performed on the vibration response signal. The formula for performing discrete wavelet transform on the vibration response signal is as follows: ； In the formula, Represented as a vibration response signal, Represented as Daubechies4 wavelet basis functions, Represented as wavelet coefficients, This is represented as a scale factor. This is expressed as a time offset, where, The value is automatically generated by MATLAB software, and ,in, , Represented as signal length, ,in, ; The frequency range of each high-frequency sub-band output is: ； In the formula, Represented as high-frequency components, i.e., the th The high-frequency sub-band frequency range of the layer, when hour, Remove those higher than The high-frequency sub-band frequency, at this time ; The discretized vibration response signal is represented as follows: ； Represented as the discrete vibration response signal, where, This is represented as the time index of the discretized vibration response signal; The output discrete wavelet transform coefficients are: ； In the formula, Represented as the first The first layer Wavelet coefficients.
5. The method for calculating the flexural bearing capacity of fiber-reinforced reinforced concrete beams according to claim 4, characterized in that: The method for calculating the sum of the selected frequency band, the main resonant frequency, and the energy of the selected frequency band in step 3 is as follows: Calculate the energy of the high-frequency subband: ； In the formula, Represented as high-frequency subband energy; Then, the main resonance frequency was determined: First, find the high-frequency subband with the highest energy: ； In the formula, This represents the high-frequency sub-band with the highest energy. Within this sub-band, the frequency point with the highest energy is calculated. ； In the formula, This is represented as the bandwidth of the subband, and , This represents the index of the coefficient with the highest energy in that subband. This is represented as the frequency point with the highest calculated energy in this sub-band, i.e., the main resonance frequency; High-frequency subband energy Sort the frequencies in descending order, extract the top 3 high-frequency sub-bands with the highest energy as selected frequency bands, and then extract the energy of the selected frequency bands: The sum of the selected frequency band energies is calculated based on the selected frequency band energy: ； In the formula, It is represented as the sum of energy in the selected frequency band.
6. The method for calculating the flexural bearing capacity of fiber-reinforced reinforced concrete beams according to claim 1, characterized in that: The method for obtaining the corresponding actual flexural bearing capacity data for fiber-reinforced reinforced concrete beam samples using the three-point bending test is as follows: The span, section width, and section height of fiber-reinforced reinforced concrete beam samples were measured using a three-point bending test method. The testing machine automatically collected load and mid-span deflection data, outputting the peak load and calibrating it as the ultimate bearing capacity. The actual flexural bearing capacity was calculated based on the span, section width, section height, and ultimate bearing capacity. ； In the formula, Indicated as span, Represented as cross-sectional width, Expressed as cross-sectional height, This is expressed as the ultimate bearing capacity. This represents the actual bending capacity.
7. The method for calculating the flexural bearing capacity of fiber-reinforced reinforced concrete beams according to claim 1, characterized in that: The method for dividing the training set and the test set and constructing the multinomial regression model is as follows: Extract the principal resonance frequencies corresponding to each fiber-reinforced reinforced concrete beam sample. Selected frequency band energy The sum of energy in the selected frequency band With bending bearing capacity ,in The index of the number of fiber-reinforced reinforced concrete beam samples is represented by the principal resonant frequency. Selected frequency band energy The sum of energy in the selected frequency band As an input feature, flexural bearing capacity As output labels, , This represents the number of fiber-reinforced reinforced concrete beam samples. Organize the input features into dimensions... Input feature matrix: ； In the formula, Represented as The input feature matrix; Organize the output labels into an output vector: ； In the formula, Represented as an output vector; Set the training set to include The test set includes fiber-reinforced reinforced concrete beam samples. A sample of fiber-reinforced reinforced concrete beam, and The input feature matrix of the training set is denoted as The output label vector is denoted as The input feature matrix of the test set is denoted as... The output label vector is denoted as .
8. The method for calculating the flexural bearing capacity of fiber-reinforced reinforced concrete beams according to claim 7, characterized in that: The method for evaluating and optimizing a polynomial regression model of optimal order by calculating the mean squared error, root mean square error, and coefficient of determination is as follows: Extracting the input feature matrix Each sample: ； In the formula, Represented as the input feature matrix The 10 samples, of which ； Determine the order of a polynomial ,in, The characteristic of a polynomial of order 1 includes all that satisfy monomials ,in, , represented as Exponent in a monomial , ; Calculate the number of characteristics of a polynomial: ； In the formula, Represented as the number of polynomial characteristics; Find all that satisfy nonnegative integer vectors , For each condition that is met , , represented as the index of a non-negative integer vector, is used to calculate The corresponding monomial: ； non-negative integer vectors The corresponding monomials, arranged lexicographically, yield a dimension of The The polynomial eigenvectors of each sample: ； In the formula, Represented as the first The polynomial feature vector of each sample Represented as the first eigenvalues of a polynomial ; Stacking by rows yields a dimension of The polynomial characteristic matrix: ； In the formula, Represented as a polynomial characteristic matrix; Definition of multinomial regression model: ； In the formula, Represented as the intercept term, Represented as model coefficients, Represented as an error term; The optimal coefficients are obtained by minimizing the sum of squared errors: ； In the formula, Expressed as the sum of squared errors, Represented as the first in the training set Actual flexural bearing capacity of each sample; right Taking the derivative and setting it to zero, we get: ； In the formula, Represented as a model coefficient vector, including the intercept term. Other coefficients , This is represented as the output label vector of the training set; No. For the test set of fiber-reinforced reinforced concrete beam samples, the predicted values are: ； In the formula, This represents the predicted value for a sample in the test set. Represented as the first The input feature matrix of a test set of fiber-reinforced reinforced concrete beam samples; Calculate the mean square error: ； In the formula, This is expressed as mean square error. Represented as the first in the test set Actual flexural bearing capacity of a fiber-reinforced reinforced concrete beam sample; Calculate the root mean square error: ； In the formula, This is expressed as root mean square error; Calculate the coefficient of determination: ； In the formula, This is expressed as the coefficient of determination. ; turn up The value is the smallest. Largest polynomial order As the optimal order, the optimal order polynomial regression model is: ； In the formula, This represents the predicted flexural capacity of the fiber-reinforced reinforced concrete beam to be tested. This represents the input feature vector of the fiber-reinforced reinforced concrete beam whose flexural bearing capacity is to be tested. ,in, The frequency represents the principal resonant frequency of the fiber-reinforced reinforced concrete beam whose flexural bearing capacity is to be tested. This represents the energy of the first three high-frequency sub-bands, indicating the bending capacity to be tested. This represents the total energy of the fiber-reinforced reinforced concrete beam whose flexural bearing capacity is to be tested.