Method for evaluating seismic capacity of rc member based on coupling frequency and apparent damage
By combining dynamic response signals and blast face images, the shortcomings of existing RC component evaluation methods are addressed, enabling accurate damage assessment and decision output in the absence of prior parameters.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- TIANJIN CHENGJIAN UNIV
- Filing Date
- 2026-05-11
- Publication Date
- 2026-07-21
AI Technical Summary
Existing technologies rely on prior parameters of the explosion source to quantitatively assess the remaining seismic capacity of damaged RC components, which is difficult to achieve. Conventional contact measurements have low safety, and single global modal frequencies cannot accurately capture local damage, resulting in inaccurate assessment results.
An assessment method based on coupling frequency and apparent damage is adopted. By acquiring the dynamic response signal, the first-order modal frequency change rate and the geometric features of the local spalling area in the blast face image are extracted. Combined with the preset model, the final coupling residual seismic capacity coefficient is calculated to achieve dual coupling assessment of global hidden damage and local visible damage.
In the absence of prior explosion parameters, accurately quantifying the damage level of RC components provides reliable intervention decision recommendations, improves the accuracy and safety of assessment, and reduces the difficulty of on-site operation.
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Figure CN122154053B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of seismic assessment of building structures, specifically a method for assessing the seismic capacity of RC components based on coupling frequency and apparent damage. Background Technology
[0002] Accidental explosions, such as industrial explosions, can damage the core load-bearing reinforced concrete (RC) components of a building structure, leading to a decrease in the overall structural load-bearing capacity and a degradation in seismic performance. Accurate post-disaster assessment of the remaining seismic capacity of damaged RC components is crucial for making emergency rescue decisions and implementing structural repair and reinforcement.
[0003] Existing assessment methods often rely on prior parameters of the blast source, which are frequently impossible to quantify at the post-disaster site, making the assessment process difficult to implement. Furthermore, conventional contact measurement or damage sampling methods are difficult to operate and have low safety in complex post-disaster environments. In addition, non-destructive testing assessment methods based on single modal frequencies have limitations. Although the degradation of the overall stiffness of a component can be reflected by the decrease in its natural frequency, damage such as localized concrete spalling in the plastic hinge zone of the blast-facing surface caused by the blast shock wave is difficult to capture sensitively by global modal frequencies. Using only a single global dynamic index can easily overestimate the remaining seismic energy dissipation capacity of damaged components.
[0004] Existing damage assessment systems, when translating physical damage characteristics into engineering application judgments, lack a quantitative penalty reduction mechanism based on the internal physical dimensional relationships of components and the critical failure point of core constraints. This makes it difficult to effectively compare energy dissipation values with structural seismic fortification thresholds, and thus fails to provide an intuitive and actionable quantitative evaluation basis for the subsequent treatment of damaged RC components. Therefore, how to obtain global dynamic response and local apparent damage characteristics through non-destructive and non-contact detection methods in the absence of prior explosion parameters, and then construct a dual-index coupled assessment system to accurately determine the damage level of damaged RC components and output intervention decision recommendations, is a problem that needs to be solved in this field. Summary of the Invention
[0005] To address the shortcomings of existing technologies, this invention provides a method for assessing the seismic resistance of RC components based on coupling frequency and apparent damage. This method solves the problems of existing post-explosion assessment methods that rely on prior parameters of the explosion source, have low safety of conventional contact damage detection, and cannot accurately capture local concrete spalling damage using a single global modal frequency index, thus overestimating the remaining seismic energy dissipation capacity of damaged components.
[0006] To address the above problems, the present invention provides the following technical solution: This invention provides a method for evaluating the seismic resistance of RC components based on coupling frequency and apparent damage, employing the following technical solution: The seismic resistance assessment method for RC members based on coupling frequency and apparent damage includes the following steps: Obtain the initial design parameters of the RC component to be evaluated, and determine the physical parameters of the component cross section based on the initial design parameters of the RC component to be evaluated; The dynamic response signal of the damaged RC component is obtained and the measured first-order modal frequency corresponding to the dynamic response signal of the damaged RC component is extracted. The first-order modal frequency change rate is calculated by combining the preset initial undamaged first-order modal frequency. Obtain an image of the blast-facing surface of the damaged RC component and extract the geometric features of the local spalling area of the concrete in the blast-facing surface image of the damaged RC component. Construct a local damage correction coefficient based on the geometric features of the local spalling area of the concrete and the physical parameters of the component section. The initial design parameters of the RC component to be evaluated and the rate of change of the first-order modal frequency are input into the preset seismic capacity prediction model to calculate the benchmark remaining seismic capacity coefficient. The benchmark remaining seismic capacity coefficient is then reduced by the local damage correction coefficient to obtain the final coupled remaining seismic capacity coefficient. The final coupling remaining seismic capacity coefficient is compared with the preset seismic fortification threshold, and the damage level of the damaged RC component is determined based on the comparison result.
[0007] By employing the above technical solution, the degree of degradation of the overall stiffness of the component is characterized by the first-order modal frequency change rate extracted from the dynamic response signal, while the degree of weakening of local energy dissipation capacity is quantified by the geometric features extracted from the blast face image. Furthermore, the benchmark remaining seismic capacity coefficient is reduced using the local damage correction coefficient characterizing local damage. Therefore, a damage assessment result with dual coupling of global latent damage and local apparent damage is obtained. This method overcomes the deficiency of a single global modal parameter being insensitive to local damage in the plastic hinge zone of the component, and achieves quantitative analysis of the remaining seismic capacity after an explosion in the absence of prior parameters for the blast load.
[0008] Furthermore, the initial design parameters of the RC component to be evaluated include the volumetric stirrup ratio, the longitudinal reinforcement ratio, and the slenderness ratio of the component; the physical parameters of the component section include the effective height of the component section and the theoretical plastic hinge length of the component; the specific steps for determining the physical parameters of the component section based on the initial design parameters of the RC component to be evaluated include: calculating and determining the effective height of the component section and the theoretical plastic hinge length of the component based on the volumetric stirrup ratio, the longitudinal reinforcement ratio, and the slenderness ratio of the component, wherein the effective height of the component section is the vertical distance from the resultant point of the tensile reinforcement in the component section to the compression edge, and the theoretical plastic hinge length of the component is the theoretical length of the plastic deformation zone of the component under compression and bending.
[0009] By adopting the above technical solution, and by defining the effective height of the component section and the theoretical plastic hinge length of the component, the effective working depth of the RC component to resist external bending moment and the core concentrated area for absorbing and dissipating impact energy are clarified, laying the physical structural model foundation for the subsequent dimensionless processing of local physical damage characteristics and seismic reserve assessment.
[0010] Furthermore, the specific steps for obtaining the dynamic response signal of the damaged RC component include: applying a non-destructive transient pulse excitation to the damaged RC component in the mid-span region using a hammer impact method; and using an acceleration sensor arranged in the main bending deformation zone of the back surface of the damaged RC component to collect the dynamic response signal of the damaged RC component generated after being subjected to the non-destructive transient pulse excitation. The collected dynamic response signal of the damaged RC component is a time-domain vibration signal.
[0011] By adopting the above technical solution, transient pulse excitation is used to avoid secondary physical damage to the damaged components. At the same time, the sensor is placed in the main bending deformation zone of the back blast face, avoiding the damage interference area of the front blast face, ensuring that the vibration pickup point is located at the maximum amplitude of the first-order vibration mode, thereby increasing the signal-to-noise ratio and fidelity of the measured dynamic signal.
[0012] Furthermore, the specific steps for extracting the measured first-order modal frequency corresponding to the dynamic response signal of the damaged RC component include: performing baseline drift removal and bandpass filtering preprocessing on the time-domain vibration signal; performing fast Fourier transform processing on the preprocessed time-domain vibration signal to convert the time-domain vibration signal to the frequency domain, generating a frequency domain response spectrum; extracting the natural frequency peak parameters in the frequency domain response spectrum, and establishing the extracted natural frequency peak parameters as the measured first-order modal frequency.
[0013] By adopting the above technical solution, high-frequency noise and low-frequency zero-drift interference in the field environment are pre-filtered out by baseline drift removal and bandpass filtering, and the time-domain vibration signal is mapped to the frequency domain space by combining fast Fourier transform, thereby separating and extracting the measured first-order modal frequency that can reflect the overall stiffness state of the damaged component.
[0014] Furthermore, the specific steps for extracting the geometric features of the localized spalling area of concrete in the blast-facing image of the damaged RC component include: While acquiring the blast-facing image of the damaged RC component, a depth data matrix corresponding to the blast-facing image of the damaged RC component is also acquired. The blast-facing image of the damaged RC component is input into a preset image recognition model, and the two-dimensional physical boundary of the damaged area is defined by edge detection processing and semantic segmentation processing. The two-dimensional physical boundary of the damaged area is mapped to a three-dimensional physical space by combining the acquired depth data matrix. The maximum length and maximum spalling depth of the spalling area in the mapped three-dimensional physical space are extracted as the geometric features of the local spalling area of the concrete.
[0015] By adopting the above technical solution, and using a depth data matrix in conjunction with a two-dimensional image recognition model, the damage detection in the plane pixel dimension is extended to the volumetric extraction in the three-dimensional space dimension. This allows for the acquisition of the maximum length and maximum depth of the spalling zone that can characterize the amount of concrete material loss, thereby reducing the errors and safety hazards associated with manual contact measurement.
[0016] Furthermore, the specific steps for constructing the local damage correction coefficient based on the geometric features of the local spalling zone of concrete and the physical parameters of the component section include: normalizing the maximum spalling depth and the maximum length of the spalling zone in the geometric features of the local spalling zone of concrete by introducing the effective height of the component section and the theoretical plastic hinge length of the component; and performing dimensionless calculation on the normalized maximum spalling depth and the maximum length of the spalling zone by combining the weight index to construct the local damage correction coefficient.
[0017] By adopting the above technical solution, the measured geometric features of the damage are normalized using the inherent dimensions of the physical structure, eliminating the dimensional differences between components of different sizes. This allows the local damage correction coefficient to overcome the size limitations of the components and quantify the reduction ratio of apparent volume defects on the rotational deformation capacity of the plastic hinge zone and the total energy dissipation capacity.
[0018] Furthermore, the preset seismic capacity prediction model is a multivariate linear regression prediction model; the specific steps for inputting the initial design parameters of the RC component to be evaluated and the first-order modal frequency change rate into the preset seismic capacity prediction model to calculate the benchmark remaining seismic capacity coefficient include: extracting the total absorbable energy of the RC component to be evaluated in the undamaged state, and establishing the total absorbable energy as the energy comparison benchmark value; substituting the volumetric stirrup ratio, the longitudinal reinforcement ratio, the slenderness ratio of the component, and the first-order modal frequency change rate into the multivariate linear regression prediction model to solve for the remaining absorbable energy in the damaged state; and extracting the ratio of the remaining absorbable energy in the damaged state to the energy comparison benchmark value as the benchmark remaining seismic capacity coefficient.
[0019] By adopting the above technical solution, absorbable energy based on macroscopic hysteresis characteristics is used as the basis for seismic capacity evaluation. The quantitative mapping relationship between the initial design parameters of component resistance, global modal degradation index and remaining absorbed energy is established using the multivariate linear regression prediction model. The complex nonlinear dynamic damage evolution process is transformed into an evaluation of structural energy dissipation retention rate.
[0020] Furthermore, the specific steps for calculating the final coupled residual seismic capacity coefficient by reducing the benchmark residual seismic capacity coefficient using the local damage correction coefficient include: Obtain the thickness of the concrete cover of the component; determine the local damage penalty amplification factor based on the dimensional relationship between the maximum spalling depth and the thickness of the concrete cover of the component; when the maximum spalling depth does not exceed the thickness of the concrete cover of the component, the local damage penalty amplification factor is taken as the basic set value; when the maximum spalling depth exceeds the thickness of the concrete cover of the component, the local damage penalty amplification factor is taken as the penalty amplification value; introduce the local damage penalty amplification factor and the local damage correction factor to reduce the benchmark remaining seismic capacity coefficient, and calculate the final coupled remaining seismic capacity coefficient.
[0021] By adopting the above technical solution, a physical judgment logic is introduced to compare the maximum spalling depth with the thickness of the concrete protective layer of the component, thereby capturing the critical point of failure of the internal core constraint state. When the protective layer spalls, a penalty mechanism is activated to avoid overestimating the compressive ductility and bearing capacity of the exposed core component, ensuring that the final output of the final coupled residual seismic capacity coefficient meets the structural safety requirements.
[0022] Furthermore, the specific steps for comparing the final coupled remaining seismic capacity coefficient with a preset seismic fortification threshold and determining the damage level of the damaged RC component based on the comparison result include: The preset seismic fortification threshold is set as the minimum residual absorbable energy ratio limit that the RC component to be evaluated must have to maintain the overall seismic continuity of the building; when the final coupled residual seismic capacity coefficient is greater than or equal to the preset seismic fortification threshold, the damage level of the damaged RC component is determined to be in the moderate to mild damage stage; when the final coupled residual seismic capacity coefficient is less than the preset seismic fortification threshold, the damage level of the damaged RC component is determined to be in the severe ultimate damage state.
[0023] By adopting the above technical solution, the preset seismic fortification threshold, which represents the minimum safety limit, is used to divide the continuous energy consumption values into intervals. The results of the dual-index coupled calculation are transformed into damage classification conclusions at the engineering level, and the reliability of the components after the explosion in resisting subsequent aftershocks or maintaining the ability to prevent progressive collapse is evaluated.
[0024] Furthermore, after determining the damage level of the damaged RC component, the following intervention decision execution steps are also included: when the damage level of the damaged RC component is determined to be in the moderate to mild damage stage, a decision suggestion is output to allow continued use or to carry out conventional surface repair; when the damage level of the damaged RC component is determined to be in the severe ultimate damage state, a high-risk structural warning signal is triggered, and a decision suggestion is output to implement temporary support reinforcement, local replacement of special components, or structural demolition.
[0025] By adopting the above technical solution and matching the damage level of the damaged RC components with the feasible intervention measures, a closed-loop operation was completed from on-site inspection and damage assessment to post-disaster disposal decision-making, providing guidance for emergency rescue and post-disaster structural reconstruction.
[0026] This invention provides a method for evaluating the seismic resistance of RC (reinforced concrete) components based on coupling frequency and apparent damage. It offers the following advantages: 1. This invention obtains the final coupled residual seismic capacity coefficient by coupling the first-order modal frequency change rate, which characterizes the overall stiffness degradation of the component and is extracted based on dynamic response signals, with the local damage correction coefficient, which quantifies the degree of weakening of local energy dissipation capacity and is extracted based on image recognition. This makes up for the deficiency of the single global dynamic index being insensitive to local damage of the component, eliminates the overestimation of the residual seismic capacity, and improves the accuracy of determining the damage level of the damaged RC component.
[0027] 2. This invention obtains dynamic response signals by applying non-destructive transient pulse excitation using a hammer impact method, and extracts geometric features of local spalling areas of concrete in three-dimensional physical space by combining a depth data matrix and an image recognition model. This enables non-contact and non-destructive testing of RC components under evaluation even in the absence of prior parameters for explosive loads. It eliminates the need for destructive sampling of RC components under evaluation, reduces the difficulty of parameter acquisition in complex post-disaster environments, and increases the safety of testing operations.
[0028] 3. This invention introduces a local damage penalty amplification factor that compares the physical dimensional relationship between the maximum spalling depth and the thickness of the concrete protective layer of the component. This factor reduces the baseline residual seismic capacity coefficient calculated by the preset seismic capacity prediction model. The final coupled residual seismic capacity coefficient is then compared with the preset seismic fortification threshold to output intervention decision suggestions. This establishes a quantitative evaluation system based on the failure critical point of the structural core constraint, providing a physically meaningful guiding basis for the repair or demolition of damaged RC components. Attached Figure Description
[0029] Figure 1 This is a structural block diagram of a system for evaluating the seismic resistance of RC components based on coupling frequency and apparent damage, according to an embodiment of the present invention. Figure 2 This is a flowchart illustrating a method for evaluating the seismic resistance of RC components based on coupling frequency and apparent damage, according to an embodiment of the present invention. Figure 3 This is a schematic diagram of the arrangement for acquiring transient pulse excitation and dynamic response signals in the field according to an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the principle of extracting local spalling damage features on the blast-facing surface of a damaged RC component based on machine vision, according to an embodiment of the present invention. Figure 5 This is a schematic diagram comparing the low-cycle repeated loading skeleton curves of non-destructive and damaged RC components based on energy dissipation theory, according to an embodiment of the present invention. Figure 6 This is a comparison chart of the remaining seismic capacity predictions under the condition of slight surface peeling, according to an embodiment of the present invention. Figure 7 This is a comparison chart of the remaining seismic capacity predictions using different assessment methods under severe local spalling conditions, according to an embodiment of the present invention.
[0030] The module includes: 10. Parameter input module; 20. Dynamics acquisition and analysis module; 30. Image recognition module; 40. Evaluation calculation module; and 50. Decision output module. Detailed Implementation
[0031] The technical solutions in 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.
[0032] See attached document Figure 1 The present invention provides a seismic capacity assessment system for RC components based on coupling frequency and apparent damage, comprising: a parameter input module 10, a dynamic acquisition and analysis module 20, an image recognition module 30, an assessment calculation module 40, and a decision output module 50.
[0033] The parameter input module 10 is configured to acquire and record the initial design parameters of the RC member to be evaluated. The initial design parameters include the volumetric stirrup ratio, longitudinal reinforcement ratio, slenderness ratio, effective height of the member section, and theoretical plastic hinge length. The parameter input module 10 is communicatively connected to the evaluation calculation module 40, transmitting the acquired initial design parameters to the evaluation calculation module 40.
[0034] The dynamic acquisition and analysis module 20 is used to acquire the dynamic response signal of the damaged RC component in the field through transient pulse excitation. The module receives the time-domain vibration signal collected by an accelerometer installed on the back surface of the component, performs a fast Fourier transform on the time-domain vibration signal, and extracts the measured first-order modal frequency of the damaged RC component. The module then calculates the rate of change of the first-order modal frequency by combining the component's initial undamaged first-order modal frequency.
[0035] Image recognition module 30 is used to acquire images of the blast-facing surface of the damaged RC component and extract the geometric features of the local spalling zone of concrete. Image recognition module 30 processes the image to obtain the maximum length and maximum spalling depth of the spalling zone. Image recognition module 30 calculates a local damage correction coefficient based on the extracted maximum length and maximum spalling depth of the spalling zone.
[0036] The evaluation calculation module 40 performs a dual-index coupled calculation based on energy dissipation theory. The evaluation calculation module 40 receives data transmitted from the parameter input module 10, the dynamic acquisition and analysis module 20, and the image recognition module 30, respectively. The evaluation calculation module 40 inputs the volumetric stirrup ratio, longitudinal reinforcement ratio, member slenderness ratio, and first-order modal frequency change rate into a multivariate linear regression prediction model to calculate the baseline residual seismic capacity coefficient. The evaluation calculation module 40 then couples the baseline residual seismic capacity coefficient with the local damage correction coefficient to calculate the final coupled residual seismic capacity coefficient.
[0037] The decision output module 50 receives the final coupled remaining seismic capacity coefficient output by the evaluation and calculation module 40. The decision output module 50 stores preset structural seismic fortification thresholds. The decision output module 50 compares the final coupled remaining seismic capacity coefficient with the structural seismic fortification thresholds, generates damage level classification results for the RC components, and outputs corresponding decision recommendation information. The decision recommendation information includes repair, reinforcement, or demolition. All modules interact and transmit commands via a communication network.
[0038] See attached document Figure 2 This invention provides a method for evaluating the seismic resistance of RC components based on coupling frequency and apparent damage, comprising the following steps: S1. Extract the initial design parameters of the RC component to be evaluated. The initial design parameters include the volumetric stirrup ratio, longitudinal reinforcement ratio, slenderness ratio of the component, effective height of the component section, and theoretical plastic hinge length of the component. S2. At the explosion site, the dynamic response signal of the damaged RC component is obtained by transient pulse excitation. The dynamic response signal is collected by an acceleration sensor placed on the back surface of the component. The collected signal is extracted by fast Fourier transform to obtain the measured first-order modal frequency. Combined with the initial undamaged first-order modal frequency, the first-order modal frequency change rate characterizing the overall stiffness degradation of the component is calculated. S3. Obtain images of the blast-facing surface of the damaged RC component, extract the geometric features of the local spalling zone of concrete using image recognition algorithms, and based on the extracted maximum length and maximum spalling depth of the spalling zone, construct a local damage correction coefficient to characterize the degree of weakening of the local energy dissipation capacity of the component by combining the effective height of the component section and the theoretical plastic hinge length of the component. S4. Based on the energy dissipation theory, the volumetric stirrup ratio, longitudinal reinforcement ratio, slenderness ratio of the member and the rate of change of the first-order modal frequency are input into the multivariate linear regression prediction model to calculate the benchmark residual seismic capacity coefficient. The local damage correction coefficient and the local damage penalty amplification coefficient are introduced to reduce the benchmark residual seismic capacity coefficient to obtain the final coupled residual seismic capacity coefficient. S5. Compare the final coupling remaining seismic capacity coefficient with the preset structural seismic fortification threshold, determine the damage level of the RC component based on the comparison results, and output corresponding subsequent repair, reinforcement or demolition decision suggestions.
[0039] The specific implementation details of each of the above steps will be further explained below.
[0040] Step S1 includes the specific operations of extracting the initial design parameters of the RC component to be evaluated. The initial design parameters are the basic input variables for constructing the subsequent multivariate linear regression prediction model based on energy dissipation theory and the local damage correction coefficient. Step S1 further includes the following sub-steps: S11. Obtain the geometric characteristic parameters and reinforcement parameters of the RC component to be evaluated. At the post-explosion site, the initial design parameters of the RC component to be evaluated are obtained by reviewing the structural design drawings of the damaged building. In cases where structural design drawings are missing, the corresponding parameters are obtained through on-site measurements using a rebar location measuring instrument and an ultrasonic testing instrument (non-destructive testing equipment).
[0041] Extracting and obtaining geometric feature parameters and reinforcement parameters, including volumetric stirrup ratio. Longitudinal reinforcement ratio and the slenderness ratio of the components .in, Calculate the length of the component. The height of the component section. Longitudinal reinforcement ratio. Volumetric stirrup ratio reflects the flexural capacity reserve of a component. Characterizing the confinement effect of stirrups on the core concrete and the member's resistance to shear deformation, the member's slenderness ratio. Used to determine whether the overall failure mode of a component under explosive impact is primary bending failure or primary shear failure.
[0042] When conducting on-site measurements using non-destructive testing equipment, the diameter and spacing of the internal reinforcing bars are obtained by scanning with a rebar location measuring instrument, and the actual cross-sectional dimensions of the component are obtained by an ultrasonic testing instrument. Then, the volumetric stirrup ratio is calculated by comparing the measured cross-sectional area of the reinforcing bars with the cross-sectional area of the concrete. and longitudinal reinforcement ratio Volumetric stirrup ratio Longitudinal reinforcement ratio and the slenderness ratio of the components As a basic input variable in the multiple linear regression prediction model, it is used in the calculation of the benchmark residual seismic capacity coefficient.
[0043] S12. Define the effective height of the member section and the theoretical plastic hinge length of the member. Based on the geometric characteristic parameters and reinforcement parameters obtained in step S11, determine the effective height of the member section. With respect to the theoretical plastic hinge length of the component Effective height of component cross-section This is the vertical distance from the resultant point of the tensile reinforcement in the member section to the compression edge; it represents the effective working depth of the member section resisting external bending moments. The theoretical plastic hinge length of the member. This is the theoretical length of the region where the component undergoes plastic deformation under bending or compressive bending conditions. This region is the core concentrated area where the RC component absorbs and dissipates the energy input from explosive impacts.
[0044] Effective height of component section and the theoretical plastic hinge length of the component This serves as a baseline physical parameter in the subsequent construction of local damage correction coefficients. For the effective height of the component cross-section... and the theoretical plastic hinge length of the component For specific calculation processes and standard values, those skilled in the art can consult current concrete structure design codes to derive and determine the values by combining the actual cross-sectional dimensions and material strength of the RC component to be evaluated. The calculation and value determination methods are well-known technologies in this field and will not be elaborated here.
[0045] See attached document Figure 3 Step S2 includes the specific operation of acquiring the dynamic response signal of the damaged RC component at the post-explosion site through transient pulse excitation, and calculating the rate of change of the first-order modal frequency in combination with the initial undamaged first-order modal frequency. Step S2 further includes the following sub-steps: S21. A transient pulse excitation without damage is applied to the damaged RC component in the mid-span region using a hammer impact method. The blast shock wave exhibits distinct directional impact characteristics. Accelerometers are positioned in the main bending deformation zone of the damaged RC component's back-blast face, for example, at the mid-span location, avoiding the damaged area on the front-blast face, ensuring the pickup point is located at the maximum amplitude of the first-order vibration mode. The accelerometers positioned on the back-blast face of the component are used to collect the dynamic response signal generated by the damaged RC component after being subjected to transient pulse excitation. The collected dynamic response signal is a time-domain vibration signal.
[0046] S22. Extract the measured first-order modal frequencies of the damaged RC component. Since the structural modal frequencies are inherent dynamic characteristic parameters reflecting the overall stiffness and mass distribution of the component, when the component develops internal micro-cracks, concrete spalling, or steel bar yielding due to explosive impact, its mass change is relatively small, but its overall stiffness degrades significantly, leading to a decrease in the natural frequency.
[0047] Before frequency extraction, the acquired time-domain vibration signal undergoes baseline drift removal and bandpass filtering preprocessing to eliminate high-frequency noise and low-frequency zero-drift interference from the field environment. Subsequently, a Fast Fourier Transform (FFT) is performed on the preprocessed dynamic response signal. The FFT transforms the time-domain dynamic response signal to the frequency domain, generating the frequency response spectrum.
[0048] The low-order natural frequency peak parameters are extracted from the frequency domain response spectrum, and the extracted low-order natural frequency peaks are established as the measured first-order modal frequencies of the damaged RC component. The algorithm for converting time-domain signals to frequency-domain signals using the Fast Fourier Transform (FFT) can be performed by those skilled in the art by calling standard transform functions in conjunction with the fundamental theories of digital signal processing. The frequency domain conversion method is a well-known technique in this field and will not be elaborated upon here.
[0049] S23. Calculate the rate of change of the first-order modal frequency. Obtain the initial undamaged first-order modal frequency corresponding to the damaged RC component. Initial lossless first-order mode frequency The methods for obtaining these values include calculations based on the initial design parameters of the component combined with the mass and stiffness matrices from structural dynamics theory, or field measurements using transient pulse excitation on non-destructive components of the same batch and specifications. This is based on the initial non-destructive first-order modal frequency. Compared with the measured first-order modal frequency Calculate the rate of change of first-order modal frequency Rate of change of first-order modal frequency The calculation formula is as follows: ; In the formula, The rate of change of the first-order modal frequency. The initial lossless first-order modal frequency, To measure the first-order modal frequency. Rate of change of the first-order modal frequency. It is used to quantify the overall stiffness degradation of damaged RC components caused by explosive impact, and is used as a dynamic characteristic parameter to be input into a multivariate linear regression prediction model to reflect the global structural degradation state.
[0050] See attached document Figure 4 Step S3 includes acquiring an image of the blast-facing surface of the damaged RC component, extracting local features using an image recognition algorithm, and constructing a local damage correction coefficient. The blast shock wave has directional impact characteristics, easily causing large-area concrete spalling and exposed rebar in the plastic hinge zone of the component's blast-facing surface. Step S3 aims to compensate for the low sensitivity of global dynamic indicators to local severe damage by quantifying microscopic, apparent damage. Step S3 further includes the following sub-steps: S31. Acquire images of the blast-facing surface of damaged RC components. At the post-explosion site, use image acquisition equipment with depth sensing capabilities, such as RGB-D depth cameras or binocular stereo vision cameras, to take high-resolution images of the blast-facing surface of damaged RC components. Acquire digital image data covering the plastic hinge zone and the apparent damage area of the concrete, as well as synchronous depth data, which will serve as the input source for subsequent machine vision analysis.
[0051] S32. Extract geometric features of localized concrete spalling areas using image recognition algorithms. Input the acquired image of the blast-facing surface into the image recognition model. Define the two-dimensional physical boundary of the damaged area through edge detection and semantic segmentation. Combine this with the simultaneously acquired depth data matrix to map the two-dimensional pixel coordinates to three-dimensional physical space, thereby extracting the corresponding geometric feature parameters.
[0052] The extracted geometric feature parameters include the maximum length of the exfoliated area. and maximum spalling depth Maximum length of the spalled area The maximum dimension of the concrete spalling area in the longitudinal direction of the component; the maximum spalling depth. This represents the maximum size of concrete spalling along the depth direction of the component's cross-section. For edge detection and pixel dimension conversion in image recognition algorithms, those skilled in the art can configure them based on existing computer vision models. The image feature segmentation and size extraction methods are well-known technologies in this field and will not be elaborated upon here.
[0053] S33. Constructing the local damage correction coefficient Localized concrete spalling on the explosion-facing surface of a component reduces the effective compression zone of the section and causes the core concrete and longitudinal reinforcement to lose their protective layer, thus significantly weakening the rotational deformation capacity and hysteretic energy dissipation ability of the plastic hinge zone.
[0054] Based on the extracted maximum length of the exfoliated area and maximum spalling depth Combined with the extracted effective height of the component cross-section and the theoretical plastic hinge length of the component Local damage correction coefficients are constructed through dimensionless calculation. Local damage correction factor The formula used to characterize the degree of weakening of a component's local energy dissipation capacity is as follows: ; In the formula, This is the local damage correction factor. For the maximum peeling depth, The effective height of the component section. The maximum length of the spalled area. The theoretical plastic hinge length of the component. As a weighted index, This is the weighting index. and weight index The parameters, calibrated through component impact tests and low-cycle cyclic loading tests, are used to adjust the sensitivity ratio of depth damage and length damage in the overall weakening effect, with a weighting index. The range of values satisfies Weighting index The range of values satisfies .
[0055] Introducing the effective height of the component section With respect to the theoretical plastic hinge length of the component The measured damage depth and length were normalized and weighted accordingly. and weight index Accurately quantify the proportion of the reduction in the overall energy dissipation capacity of the damaged RC component due to local concrete spalling.
[0056] See attached document Figure 5 Step S4 includes the specific operation of coupling the global dynamic latent damage index and the local apparent overt damage index based on energy dissipation theory. Step S4 further includes the following sub-steps: S41. Establish a quantitative index for seismic energy dissipation capacity based on energy dissipation theory. The damage to a structure caused by seismic action is essentially a process of energy input and dissipation. The elastoplastic deformation of components under cyclic loading is the main pathway for absorbing seismic energy. The area enclosed by the skeleton curve of an RC component under low-cycle cyclic loading is defined as the total absorbable energy.
[0057] Damaged components, due to the overall stiffness degradation and localized concrete spalling caused by the blast impact, will have their corresponding skeleton curve enclosed area reduced compared to the undamaged state. (Baseline residual seismic capacity coefficient) This is the ratio of the remaining absorbable energy of a damaged component to the total absorbable energy in its undamaged state, used to quantify the retention of the foundation's seismic performance after an explosion. For the extraction and area integration calculation of the skeleton curve under low-cycle repeated loading, those skilled in the art can derive it using conventional structural seismic test data processing standards. The energy area integration method is a well-known technique in this field and will not be elaborated upon here.
[0058] S42. Calculate the baseline residual seismic capacity coefficient The extracted volumetric stirrup ratio Longitudinal reinforcement ratio Component slenderness ratio With the rate of change of first-order modal frequency The input feature parameters are substituted into the multivariate linear regression prediction model for solution. (Baseline residual seismic capacity coefficient) The mathematical expression is as follows: ; In the formula, The baseline residual seismic capacity coefficient, For volumetric stirrup ratio, This refers to the longitudinal reinforcement ratio. The slenderness ratio of the component, The first-order modal frequency change rate is denoted as . The above prediction model, through a linear combination of multiple parameters, achieves an integrated characterization of the initial physical characteristic parameters of the component and the macroscopic stiffness degradation index, where the first-order modal frequency change rate is denoted as . The overall stiffness degradation is determined by the reinforcement parameters, such as the stirrup ratio, which reflect the initial resistance reserve potential of the component itself.
[0059] S43. Introduce a local damage penalty mechanism to calculate the final coupled residual seismic capacity coefficient. A single benchmark residual seismic capacity coefficient This would overestimate the actual load-bearing energy dissipation state of components experiencing severe localized spalling. A local damage correction factor is introduced. For the benchmark residual seismic capacity coefficient The reduction is applied, and the reduction force is determined by the local damage penalty amplification factor. Decision. Obtain the thickness of the concrete cover of the component. Thickness of concrete protective layer of component The location of the steel reinforcement is obtained by consulting the initial design drawings or by conducting on-site measurements using a steel reinforcement location measuring instrument.
[0060] Based on maximum peeling depth With respect to the thickness of the concrete cover of the component The physical dimensional relationship determines the local damage penalty amplification factor. The value determination logic is as follows: when the maximum peeling depth Not exceeding the thickness of the concrete cover of the component At that time, the damage was only on the surface, and the internal core components were not seriously threatened, resulting in a local damage penalty amplification factor. Take a base value, which is 1.0; when the maximum peeling depth Exceeding the thickness of the concrete cover of the component This indicates that the internal stirrups and longitudinal bars have lost the enclosure and restraint of the surrounding concrete. The longitudinal bars are prone to buckling instability at the compression end, the ductility characteristics of the member section are significantly lost, and the local damage penalty amplification factor increases. An amplified value, ranging from 1.2 to 1.5, is used to characterize the abrupt loss of ductility caused by concrete spalling in the plastic hinge zone of the component.
[0061] Final coupling residual seismic capacity coefficient The calculation formula is as follows: ; In the formula, To finally couple the remaining seismic capacity coefficient, The baseline residual seismic capacity coefficient, This is the amplification factor for local damage penalty. This is the local damage correction coefficient. Through the above coupled calculation formula, the global stiffness degradation data and the local apparent spalling characteristic data are combined and reduced in dimension to obtain a high-precision residual seismic capacity assessment value that does not depend on the prior parameters of the explosive load.
[0062] Step S5 includes the specific operations of comparing the final coupled remaining seismic capacity coefficient with the structural seismic fortification threshold, determining the damage level, and outputting subsequent engineering decision-making recommendations. Step S5 further includes the following sub-steps: S51. Set seismic fortification thresholds for structures. After an explosion, building structures typically need to retain a certain amount of seismic energy reserve to withstand aftershock loads and prevent progressive collapse. Seismic fortification thresholds for structures. This represents the minimum residual absorbable energy ratio that a structural RC component must possess to maintain the overall seismic continuity of a building after an explosive impact. It is also the seismic fortification threshold for structures. The specific numerical values can be derived and determined by those skilled in the art in combination with the current building seismic assessment standards, structural importance coefficients and component service environment. The value range is usually set between 0.6 and 0.75 to ensure that the damaged component still has 60% to 75% of the hysteretic energy dissipation reserve in the initial state. The threshold calibration method is a well-known technology in the field and will not be described in detail here.
[0063] S52. Perform numerical comparison and damage level determination. Use the final coupled residual seismic capacity coefficient calculated in step S4. Seismic fortification threshold of structure The input judgment logic unit performs numerical comparison and analysis.
[0064] When the final coupling residual seismic capacity coefficient Greater than or equal to the structural seismic fortification threshold At this time, it indicates that the core concrete confinement inside the component is still effective, the steel reinforcement has not undergone large-area buckling fracture, the overall stiffness and energy dissipation attenuation are within a controllable range, and the RC component to be evaluated is determined to be in the stage of slight or moderate damage.
[0065] When the final coupling residual seismic capacity coefficient Less than the structural seismic fortification threshold When the condition is met, it indicates that the cross section of the component has lost most of its plastic deformation capacity and the bearing capacity exhibits brittle degradation characteristics, and the RC component to be evaluated is determined to be in a state of severe damage or ultimate damage that endangers the continuity of the structure.
[0066] S53. Generate and output decision recommendation information. Based on the damage level determination result generated in step S52, the system matches the corresponding engineering treatment strategy.
[0067] When the RC component to be evaluated is determined to be in a minor or moderate damage stage, a decision recommendation is generated and output to allow continued use or routine surface repair, in order to guide on-site crack grouting or protective layer re-plastering.
[0068] When the RC component under evaluation is determined to be in a state of severe or extreme damage, a high-risk structural warning is triggered, and decision recommendations are generated to immediately implement temporary support reinforcement, partial replacement of specialized components, or direct structural demolition. Through the above-mentioned hierarchical damage assessment and decision-making logic, the dual-indicator quantitative calculation results of dynamic characteristics and image geometric features are transformed into intuitive engineering application basis, providing contactless and rapid risk assessment guidance for high-risk components at the post-explosion site.
[0069] Specific application examples: To better understand the technical solution of this invention, the following detailed description is provided in conjunction with specific application scenarios and accompanying drawings. This specific application embodiment is built upon a system for assessing the residual seismic capacity of damaged reinforced concrete components. This system is responsible for collecting macroscopic dynamic characteristics and performing a dual-index coupled assessment by combining them with apparent damage images.
[0070] During the assessment phase for minor surface spalling, the assessment system needs to perform steps to acquire structural physical parameters and extract macroscopic dynamic characteristics in order to determine the baseline residual seismic capacity coefficient. The parameters are set as follows: Based on the design drawings, obtain the volumetric stirrup ratio of a representative damaged reinforced concrete member. The longitudinal reinforcement ratio is 0.006. The slenderness ratio of the component is 0.011. The value is 12; the first-order modal frequency change rate is extracted based on the on-site transient pulse excitation measurement. The value is 0.09. The evaluation system substitutes this value into the formula to calculate the baseline residual seismic capacity coefficient. : ; The numerical calculation process is as follows: ; Calculation results show that relying solely on the first-order modal frequency change rate The baseline residual seismic capacity coefficient of the damaged reinforced concrete member It is 0.89.
[0071] Subsequently, the evaluation system performs a step of quantifying local apparent damage and calculating a dual-index coupling mechanism. The parameters are set as follows: surface detachment data is extracted via image recognition, and the calculated local damage correction coefficient is... The value is 0.034, and because the peeling did not penetrate the protective layer, the local damage penalty amplification factor is... Set to 1.0. The evaluation system substitutes the values into the formula to calculate the final coupled residual seismic capacity coefficient. : ; The numerical calculation process is as follows: ; Calculation results show that, after reduction and correction, the final coupled residual seismic capacity coefficient The value is 0.86, which is greater than the seismic fortification threshold of 0.65 for the structure. The system then outputs a decision recommendation that the structure can continue to be used and that routine surface repairs can be carried out.
[0072] See attached document Figure 6 , Figure 6 The horizontal axis represents the number of the damaged reinforced concrete component, and the direction of the horizontal axis represents the increasing degree of minor spalling. The vertical axis represents the remaining seismic capacity coefficient. The dashed line with hollow squares in the figure represents the traditional single-frequency prediction method, which, lacking a micro-damage quantification mechanism, overestimates its predicted value as it is above the actual experimental value represented by the solid line with solid dots. The dotted line with hollow triangles in the figure represents the dual-index coupled prediction method of this invention, which, due to the implementation of apparent damage reduction, predicts a lower value than the traditional single-frequency prediction method, making the prediction curve fit the actual experimental value curve. This result verifies that the present invention has error correction capabilities in the minor damage stage.
[0073] During the assessment phase for severe localized spalling, the assessment system performs a coupled assessment of another group of damaged reinforced concrete members that have experienced severe localized spalling. The parameters are set as follows: for representative damaged reinforced concrete members, the volumetric stirrup ratio... The longitudinal reinforcement ratio is 0.006. The slenderness ratio of the component is 0.011. The value is 12, and the rate of change of the first-order modal frequency is extracted. The value is 0.32. The assessment system uses the aforementioned formula to calculate the baseline residual seismic capacity coefficient. The value is 0.75. If only this step is relied upon, the system determines the baseline residual seismic capacity coefficient. It is 0.75.
[0074] Next, the evaluation system performs local apparent damage quantification and coupling reduction steps. The parameters are set as follows: image recognition measures the ratio of the maximum length of the spalled area to the theoretical plastic hinge length. The ratio is 0.8, representing the maximum spalling depth to the effective height of the component cross-section. The value is 0.28, so the weighted index is taken. The weight index is 1. The value is 1. The evaluation system substitutes the values into the formula to calculate the local damage correction factor. : ; The numerical calculation process is as follows: ; The assessment system is based on the spalling depth exceeding the thickness of the concrete cover of the component. The condition is to take the local damage penalty amplification factor. The value is 1.2. Substitute this value into the formula to calculate the final coupled residual seismic capacity coefficient. : ; The numerical calculation process is as follows: ; Calculation results show that after local spalling occurs, the final coupling residual seismic capacity coefficient of the component is... The value was reduced to 0.5484, which is below the structural seismic fortification threshold of 0.65. The system then outputs an early warning and decision-making suggestions for implementing support reinforcement or replacement.
[0075] See attached document Figure 7 , Figure 7The horizontal axis represents the number of the damaged reinforced concrete component, and the direction of the horizontal axis represents the increasing depth of severe local spalling. The vertical axis represents the remaining seismic capacity coefficient. The dashed line with hollow squares in the figure represents the traditional single-frequency prediction method, whose prediction curve shows a flat trend due to the low sensitivity of the first-order modal frequency to local mass loss. The dotted line with hollow triangles in the figure represents the dual-index coupled prediction method of this invention, which, due to the calculation of the local damage penalty mechanism, shows a similar decreasing trend to the actual experimental value represented by the solid line with solid dots. This result verifies that this invention corrects the error caused by the low sensitivity of the traditional dynamic method to local spalling and calculates the degree of reduction in seismic capacity.
Claims
1. A method for assessing the seismic resistance of RC components based on coupling frequency and apparent damage, characterized in that, Includes the following steps: Obtain the initial design parameters of the RC component to be evaluated, and determine the physical parameters of the component cross section based on the initial design parameters of the RC component to be evaluated; The dynamic response signal of the damaged RC component is obtained and the measured first-order modal frequency corresponding to the dynamic response signal of the damaged RC component is extracted. The first-order modal frequency change rate is calculated by combining the preset initial undamaged first-order modal frequency. Obtain an image of the blast-facing surface of the damaged RC component and extract the geometric features of the local spalling area of the concrete in the blast-facing surface image of the damaged RC component. Construct a local damage correction coefficient based on the geometric features of the local spalling area of the concrete and the physical parameters of the component section. The initial design parameters of the RC component to be evaluated and the rate of change of the first-order modal frequency are input into the preset seismic capacity prediction model to calculate the benchmark remaining seismic capacity coefficient. The benchmark remaining seismic capacity coefficient is then reduced by the local damage correction coefficient to obtain the final coupled remaining seismic capacity coefficient. The final coupling remaining seismic capacity coefficient is compared with the preset seismic fortification threshold, and the damage level of the damaged RC component is determined based on the comparison result. The initial design parameters of the RC component to be evaluated include the volumetric stirrup ratio, longitudinal reinforcement ratio, and slenderness ratio of the component. The physical parameters of the component cross-section include the effective height of the component cross-section and the theoretical plastic hinge length of the component; The geometric features of the localized spalling zone in the concrete include the maximum length and maximum spalling depth of the spalling zone; The steps for constructing a local damage correction coefficient based on the geometric characteristics of the local spalling zone of the concrete and the physical parameters of the component cross-section specifically include: The maximum spalling depth and the maximum length of the spalling zone are normalized by introducing the effective height of the component cross section and the theoretical plastic hinge length of the component. By combining the weighted index with the normalized maximum peeling depth and the maximum length of the peeling area, a dimensionless calculation is performed to construct the local damage correction coefficient. The preset seismic resistance prediction model is a multivariate linear regression prediction model; The steps of inputting the initial design parameters of the RC component to be evaluated and the first-order modal frequency change rate into a preset seismic capacity prediction model to calculate the baseline remaining seismic capacity coefficient specifically include: Extract the total absorbable energy of the RC component to be evaluated in a non-destructive state, and establish the total absorbable energy as the energy comparison benchmark value; Substitute the volumetric reinforcement ratio, the longitudinal reinforcement ratio, the slenderness ratio of the component, and the rate of change of the first-order modal frequency into the multivariate linear regression prediction model to solve for the remaining absorbable energy in the damaged state; The ratio of the remaining absorbable energy in the damaged state to the energy comparison benchmark value is extracted as the benchmark remaining seismic capacity coefficient. The steps for obtaining the final coupled residual seismic capacity coefficient by reducing the benchmark residual seismic capacity coefficient using the local damage correction coefficient specifically include: Obtain the thickness of the concrete cover of the component; The local damage penalty amplification factor is determined based on the relationship between the maximum spalling depth and the thickness of the concrete protective layer of the component. When the maximum spalling depth does not exceed the thickness of the concrete protective layer of the component, the local damage penalty amplification factor is taken as the basic set value; When the maximum spalling depth exceeds the thickness of the concrete protective layer of the component, the local damage penalty amplification factor is taken as the penalty amplification value; The local damage penalty amplification factor and the local damage correction factor are introduced to reduce the benchmark residual seismic capacity coefficient, and the final coupled residual seismic capacity coefficient is calculated.
2. The method for evaluating the seismic resistance of RC components based on coupling frequency and apparent damage according to claim 1, characterized in that, Based on the volumetric stirrup ratio, the longitudinal reinforcement ratio, and the slenderness ratio of the member, the effective height of the member section and the theoretical plastic hinge length of the member are calculated and determined. The effective height of the member section is the vertical distance from the resultant point of the tensile reinforcement in the member section to the compression edge, and the theoretical plastic hinge length of the member is the theoretical length of the plastic deformation zone of the member under compression and bending.
3. The method for evaluating the seismic resistance of RC components based on coupling frequency and apparent damage according to claim 1, characterized in that, The steps for obtaining the dynamic response signal of the damaged RC component specifically include: A non-destructive transient pulse excitation was applied to the damaged RC component in the mid-span region using a hammer impact method. An accelerometer placed in the main bending deformation zone of the back surface of the damaged RC component is used to collect the dynamic response signal of the damaged RC component after it is excited by the non-destructive transient pulse. The collected dynamic response signal of the damaged RC component is a time-domain vibration signal.
4. The method for evaluating the seismic resistance of RC components based on coupling frequency and apparent damage according to claim 3, characterized in that, The steps for extracting the measured first-order modal frequencies corresponding to the dynamic response signals of the damaged RC component specifically include: The time-domain vibration signal is subjected to baseline drift removal and bandpass filtering preprocessing. The preprocessed time-domain vibration signal is converted to the frequency domain by performing a fast Fourier transform, generating a frequency domain response spectrum. Extract the inherent frequency peak parameters from the frequency domain response spectrum, and establish the extracted inherent frequency peak parameters as the measured first-order mode frequency.
5. The method for evaluating the seismic resistance of RC components based on coupling frequency and apparent damage according to claim 2, characterized in that, The steps for extracting the geometric features of the local concrete spalling area in the blast-facing image of the damaged RC component specifically include: While acquiring the blast-facing image of the damaged RC component, a depth data matrix corresponding to the blast-facing image of the damaged RC component is also acquired. The image of the damaged RC component's blast-facing surface is input into a preset image recognition model, and the two-dimensional physical boundary of the damaged area is defined through edge detection processing and semantic segmentation processing; The acquired depth data matrix is used to map the two-dimensional physical boundary of the damaged area to a three-dimensional physical space; The maximum length and maximum depth of the spalling zone in the mapped three-dimensional physical space are extracted as the geometric features of the local spalling zone of the concrete.
6. The method for evaluating the seismic resistance of RC components based on coupling frequency and apparent damage according to claim 1, characterized in that, The step of comparing the final coupled remaining seismic capacity coefficient with the preset seismic fortification threshold and determining the damage level of the damaged RC component based on the comparison result specifically includes: The preset seismic fortification threshold is set as the minimum residual absorbable energy ratio limit that the RC component to be evaluated must have to maintain the overall seismic continuity of the building. When the final coupling remaining seismic capacity coefficient is greater than or equal to the preset seismic fortification threshold, the damage level of the damaged RC component is determined to be in the medium-to-light damage stage. When the final coupling remaining seismic capacity coefficient is less than the preset seismic fortification threshold, the damage level of the damaged RC component is determined to be a severe ultimate damage state.
7. The method for evaluating the seismic resistance of RC components based on coupling frequency and apparent damage according to claim 6, characterized in that, After determining the damage level of the damaged RC component, the following intervention decision execution steps are also included: When the damage level of the damaged RC component is determined to be in the moderate to mild damage stage, a decision recommendation is output to allow continued use or to perform routine surface repair. When the damage level of the damaged RC component is determined to be the severe limit damage state, a high-risk structural warning signal is triggered, and decision suggestions for implementing temporary support reinforcement, partial replacement of special components, or structural demolition are output.