CN113158548A - Structural damage assessment method based on distributed vibration data and convolution self-coding deep learning - Google Patents
Structural damage assessment method based on distributed vibration data and convolution self-coding deep learning Download PDFInfo
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Abstract
The invention discloses a structural damage assessment method based on distributed vibration data and convolutional self-coding deep learning, which comprises the following steps of: s1, selecting acceleration response monitoring points, and arranging acceleration sensors at the monitoring points; s2, acquiring monitoring data of n acceleration sensors of the structure in a normal use state, and performing data preprocessing to form a data set for deep learning network training; s3 building a convolution self-coding deep learning network suitable for the data set of the step S2; s4, preprocessing massive structure monitoring data in a normal use state according to the step S2, and inputting the preprocessed structure monitoring data into a convolution self-encoder to train to obtain a deep learning network file; s5 evaluates the structural damage status through a data reconstruction correlation function. The invention does not need to pre-classify the data, realizes real-time quantification of the structural damage state by using real-time vibration monitoring data, and gives a score.
Description
Technical Field
The invention belongs to the field of structural health monitoring vibration data damage assessment, and particularly relates to a structural damage assessment method based on distributed vibration data and convolutional self-coding deep learning.
Background
The problem of evaluating the structural safety and damage of buildings and bridges is always a problem which is concerned in the field of structural safety, disaster prevention and reduction engineering at home and abroad. In the service process of a bridge or a building/structure, due to the extreme dynamic effects caused by loads of vehicles, pedestrians and cargos, typhoons and earthquakes, various macroscopic or microscopic damages are inevitably generated in the interior and the surface of the structure, so that the materials in the structure, stress distribution and the like are degraded or changed. These invisible damage (e.g., cracks, fatigue fractures, etc.) and the resulting internal structural changes (e.g., material properties, structural geometry, etc.) if not discovered and effectively repaired in a timely manner at an early stage, will locally create stress concentrations and exacerbate the development of structural damage. Therefore, it is important to establish a convenient, efficient and practical structural damage assessment method to effectively assess the damage state of the structure and accurately judge the normal safe use performance.
Traditional structural assessment or identification is often based on field non-destructive testing by professionals. Based on the means such as ultrasonic detection, rebound method detection and the like, after key component judgment and component material local measurement are carried out by means of professional detection equipment, engineering experience and structural model analysis are combined to evaluate the damage state of an identified object. Such methods have important reference values for the assessment of structural damage, but still have certain limitations. On one hand, due to the restriction of the field environment, the nondestructive detection method is mostly used for detecting the damage of the surface or the near surface of the structure, and the single detection range is very small, so that all parts are difficult to cover, and the damage inside the structure is often omitted or ignored; on the other hand, the traditional assessment method is poor in real-time performance and often cannot meet the requirement of rapid emergency response for ensuring the safety of personnel and property.
In recent years, breakthroughs in computer science and sensing technologies have promoted further development of structural health monitoring technologies and provide reliable guarantee for rapid evaluation based on monitoring data. Aiming at massive distributed vibration data of a monitoring system, the invention provides a structural damage assessment method based on distributed vibration data and convolutional self-coding deep learning, and the structural state can be rapidly and accurately analyzed and assessed through vibration sensor data.
A structural health monitoring system that integrates multiple vibration sensors may generate a vast amount of structural dynamic response data. When the data are analyzed, the traditional vibration data identification method based on the frequency domain and the mode often cannot accurately judge the damage state of the structure. The main reason is that the method is easily interfered by external environment, and the modal shape parameters are not sensitive to the abnormal state of the structure. Therefore, in recent years, with the improvement of computing power of computers, the search for vibration analysis of structures tends to directly analyze time domain data. Compared with frequency domain analysis, time domain analysis is based on vibration data acquired in real time, material, power and geometric nonlinear changes possibly generated by a structure under extreme conditions are reserved in data changes, and data characteristics are more complete than frequency domain and modal data. Furthermore, inspired by deep learning in the fields of vision and voice recognition, in recent years, researchers at home and abroad have tried to apply a new generation convolutional neural network method to time series data processing in the engineering field. However, because the structural form, materials and environment in engineering are too complex, analyzing the real-time vibration data of the structure by adopting a deep learning method is always a difficult point in the scientific field of engineering structure data; the application of the related method in the aspects of structure, especially the structure with more degrees of freedom and constraint like a bridge, a building and the like, and overall state evaluation is rarely reported.
The existing deep learning method mainly converts the damage recognition problem into a classification problem, namely, the obtained vibration data are classified into several categories in advance in a manual distinguishing mode according to different damage degrees, and then training is carried out through a convolutional neural network, so that the occurrence probability of the vibration form in the classification categories is respectively calculated after new vibration data are input into the network. Although the supervised learning method can realize the structural damage category and degree through classification, the method is based on known or predicted damage state of the vibration data, and for monitoring vibration data with unknown damage state, the method is often poor in damage identification and evaluation capability.
Disclosure of Invention
Based on the bottleneck problem in the structural damage identification and safety evaluation field and the requirement of actual engineering, the invention provides a structural distributed vibration data damage assessment method based on a deep learning theory. The method can acquire scattered acceleration vibration data from a monitoring system in an actual operating environment, extract main influence characteristics and perform structural abnormality diagnosis and scoring, thereby providing reference for rapidly determining a structural disaster prevention risk avoiding strategy and subsequent identification reinforcement measures.
In order to achieve the above technical object, the present invention is based on the following solving ideas:
a structural damage assessment method based on distributed vibration data and convolutional self-coding deep learning comprises the following steps:
s1, modeling and analyzing the monitoring structure, selecting acceleration response monitoring points by combining experience, and arranging acceleration sensors at each monitoring point according to the dynamic characteristics and the excitation types of the structure so as to monitor the vibration acceleration data of the structure in a characteristic position and a specific direction;
s2, acquiring monitoring data sources of n distributed acceleration sensors of the monitoring structure in use, recording the monitoring data sources as a data source 1, a data source 2 and a data source …, and preprocessing data to form a data set for deep learning network training;
s3, building a convolution self-coding deep learning network suitable for the data set in the step S2, and building a convolution self-coder, wherein the method specifically comprises the following steps:
scanning and feature extraction are carried out on the distributed vibration data through a convolutional encoder by adopting a convolutional self-coding network, and reconstruction of the compressed data is realized through a deconvolution decoder after the distributed vibration data are compressed;
selecting a loss function, carrying out multiple training and error transfer on the data in the data set in the step S2, adjusting each weight coefficient in the convolutional self-coding deep learning network, and finally obtaining the deep learning network which has generalization capability and grasps the internal rule of the input data set;
s4, preprocessing massive structure monitoring data in a normal use state according to the step S2, and inputting the preprocessed structure monitoring data into a convolutional self-encoder to be trained to obtain a convolutional self-encoder deep learning network file;
with the increase of daily operation period year by year, the quantity and scale of normal data are continuously expanded, and the network file is called for multiple times to carry out secondary training and optimization, so that the convolution self-coding network with wide adaptability is finally obtained;
s5, for data monitored by a sensor during daily service of the structure, preprocessing the data by using the method of step S2, and estimating the damage state of the structure by using a data reconstruction correlation function by using a trained convolutional self-encoder deep learning network.
The data preprocessing in step S2 includes data segmentation, data normalization and data random arrangement, and specifically includes:
the data monitored by the n acceleration sensors in a nondestructive state can be expressed as formula (1).
Und=[u1 u2 ... un] (1)
Each acceleration sensor records Na acceleration data, and the Na acceleration data is divided into Ng vibration data signal segments containing Ns acceleration data according to the sampling frequency, namely Ns is not less than the sampling frequency as shown in a formula (2);
each acceleration data ui,jCarrying out normalization processing, and carrying out random sequencing on Ng acceleration signals corresponding to each sensor to generate new uiAnd Und, finishing the preprocessing of the training data set.
The characteristics of the data structure of the deep learning network in step S3 include:
1) a one-dimensional convolution neural network is adopted as a basic data processing structure;
2) the tensor size of the data of the input layer and the output layer is 1 multiplied by Ns, the tensor size is a real value and is expressed as x by tensor, the tensor size is a predicted value and is expressed as r by tensor;
3) the convolution coding layer compresses data and extracts features through 3 times of convolution kernel scanning and down-sampling work, and the size of the compressed expansion is LXNc, wherein L is more than or equal to 2, and Nc is less than Ns;
4) the deconvolution decoding layer reconstructs compressed data through 3 times of transposition convolution kernel scanning and up-sampling work, and finally outputs tensor data with the dimension and the size consistent with those of the input layer.
In step S4, the pre-processed data training specifically includes the following:
defining the loss function of the predicted value tensor r and the true value tensor x, as shown in equation (3),
in the formula: r denotes the predicted value tensor, x denotes the true value tensor, N denotes the data length of the tensor r, xiThe ith element in the representation tensor x,the arithmetic mean, r, of the tensor xiThe ith element in the representation tensor r,an arithmetic mean representing the tensor r;
the formula (3) is formed by adding 2 terms, wherein the former is a mean square error function and aims to reduce the error between a predicted value and a true value; the latter is a correlation function of a predicted value and a true value, and after the correlation function is differentiated from 1, the term is from 1 to 0 along with the process that a predicted value tensor r is gradually close to a true value tensor x;
and (4) inputting the acceleration data in the data set in the step S2 into the convolutional self-coding network by using a correlation function, adjusting and optimizing weight parameters in the network by using an Adam optimization algorithm, finishing training of the network when the loss function loss is less than 0.1, and obtaining a deep learning network file of the convolutional self-coder after training.
Step S5 specifically includes the following steps:
firstly, generating a data set according to the step S2, compressing and reconstructing data through the deep learning network, comparing a predicted value tensor r serving as reconstruction with a true value tensor x serving as reconstruction to obtain a correlation function Cor, using the correlation function Cor as a score value of a safety state of input data, wherein an average value of monitoring reconstruction rates of n sensors is a comprehensive safety probability of the structure, the more the structural state is changed, the more serious the damage is, the lower the comprehensive safety score is, the correlation function Cor is shown as a formula (4),
in the formula, xiThe ith element in the representation tensor x,the arithmetic mean, r, of the tensor xiRepresenting the ith element in the predictor tensor r,representing the arithmetic mean of the predictor tensor r.
Has the advantages that:
the structural damage assessment method based on the distributed vibration data and the convolution self-coding deep learning has the following beneficial effects:
firstly, the damage assessment method provided by the invention directly scans and extracts the characteristics of the input acceleration time-course data through the one-dimensional convolutional neural network, so that the characteristics contained in the time-domain vibration data can be more completely retained, and the structural nonlinear behavior which is not easy to show in frequency-domain analysis can be found.
The invention adopts a convolution self-encoder, can extract common characteristics of different time domain vibration data under different noise levels, and has strong robustness. Because the data are respectively subjected to the processes of compression and reconstruction in the coding layer and the decoding layer, after massive data training, the network can extract the common characteristics of the vibration data with the same characteristics (the same monitoring position, the same sensor and external environment excitation) and has stronger robustness. Compared with the traditional wavelet transform, HHT transform or Fourier transform based on frequency domain based on a time-frequency domain method, the method does not need to carry out integral transform on input data in advance, can save calculation power and simultaneously keep the characteristic of a structure, and can still extract the characteristics in time series data under the interference of stable and random white noise due to the characteristic of the convolution self-encoder, which is an important reason for adopting the convolution self-encoder.
And thirdly, different from the traditional damage assessment method based on supervised learning, the vibration correlation function is introduced as a scale coefficient for measuring the damage degree of the structure, and the vibration response data under different working conditions and structural states can be quantitatively assessed. The data training by the convolutional autocoder does not need to provide corresponding labels for input data, and the rapid damage assessment can be performed only by the collected original data, which is the most obvious difference between the method and the regression or classification model commonly used in the traditional machine learning.
The invention adopts a mode of distributed damage identification, namely, the overall damage of the structure can be evaluated in a distributed single vibration data scoring and integrating mode. The method has the characteristics of high evaluation speed, high efficiency, self-adaptability and self-learning, and only needs to select proper monitoring points according to the basic concept and experience of the structure, thereby saving the complex workload of structural modeling and the like.
Drawings
FIG. 1 is a schematic diagram of a three-dimensional model of a typical steel structural frame;
FIG. 2 is a plan view of the location of the sensor points of the base layer monitoring structure;
FIG. 3 is a plan view of the sensor measuring point position of the first layer monitoring structure;
FIG. 4 is a plan view of the sensor measuring point positions of the two-layer monitoring structure;
FIG. 5 is a plan view of the positions of the measuring points of the sensor with a three-layer monitoring structure;
FIG. 6 is a plan view of the positions of the measuring points of the sensor with a four-layer monitoring structure;
FIG. 7 is a diagram of a convolutional autoencoder network structure;
FIG. 8 is a graph of training loss parameters of a convolutional self-coding network as a function of training times;
FIG. 9 is a correlation function for reconstructing distributed vibration data under different safety conditions;
FIG. 10 shows the reconstruction rate of 15 measured point monitoring data sets processed by a convolutional self-encoder under different conditions;
FIG. 11 shows the integrated safety probabilities of the structures under 5 different conditions;
FIG. 12 is a flowchart illustrating an implementation of a distributed structure damage assessment method based on distributed vibration data and convolutional self-coding deep learning according to the present invention.
Detailed Description
The following describes the embodiment of the damage score according to the present invention with reference to the drawings.
Firstly, acquiring measured data through a sensor and a health monitoring system.
Figure 1 shows a typical steel structural frame with a total of 4 levels, 2 x 2 spans, and a height of 3.6 m. Wherein, the additional mass of each floor slab is 4000kg, 4140kg, 4000kg and 3000kg respectively. The acceleration distributed vibration data of the structure under the environmental excitation are monitored by arranging 15 acceleration sensors as shown in the accompanying figures 2-6. The sampling frequency of the sensor is 200 Hz. Structural states of different damage degrees are simulated from strong to weak by using 5 working conditions in a mode of removing supporting and loosening the node bolts, as shown in the attached drawing 3, and acceleration distributed vibration data of corresponding sensors are recorded respectively.
And secondly, processing the nondestructive structure data acquired by the 15 sensors under the working condition 1 state to form a deep learning network training data set.
The vibration data monitored by 15 scattered acceleration sensors in a nondestructive state are represented as:
Und=[u1 u2 ... u15] (1)
wherein each acceleration sensor recorded 60000 acceleration data. 60000 pieces of acceleration data are divided into 300 distributed vibration data signal segments containing 200 pieces of acceleration data according to sampling frequency, that is
Each acceleration data ui,jCarrying out normalization processing, randomly disordering and sequencing 300 acceleration signals corresponding to each sensor to generate new uiAnd Und, finishing the preprocessing of the training data set.
And thirdly, building a deep learning network suitable for the data set in the step S2.
Fig. 7 is a diagram showing the structure of the convolutional self-encoder network constructed in this example. Firstly, inputting a data set with the length of 200 into a left network, and then performing convolution kernel scanning and down-sampling for 3 times, wherein the sizes of convolution kernels of the 3 times of convolution compression are respectively as follows: 24, 11,4. In the convolution work of 2 nd and 3 rd times, LeakyReLu is selected as an activation function, the processing capacity of a network structure on a complex nonlinear data structure is effectively improved, and the number of activated neurons in a convolution neural network is enhanced. In addition, original single-channel one-dimensional data is gradually expanded into 16-channel data and 32-channel data, so that the structural feature storage space is further expanded, and finally the data is compressed into 4-channel and 25-element compressed data, namely, the convolutional encoding work is completed. The data passing through the convolutional encoder may represent the main features of the input data by a shorter feature array. Then, through a deconvolution decoder opposite to the above process, the compressed data can be expanded and reconstructed, and finally output data with consistent input data size and dimensionality is obtained. The structure is repeatedly trained through the 300 acceleration data sets processed in the second step, so that the convolution encoder and the deconvolution decoder have wide applicability for processing the data.
Fourthly, defining a loss function of the predicted value r and the true value x, as follows:
in the formula: r denotes the predicted value tensor, x denotes the true value tensor, N denotes the data length of the tensor r, xiThe ith element in the representation tensor x,the arithmetic mean, r, of the tensor xiThe ith element in the representation tensor r,an arithmetic mean representing the tensor r;
the formula (3) is formed by adding 2 terms, wherein the former is a mean square error function and aims to reduce the error between a predicted value and a true value; the latter is a correlation function of the predicted value and the true value, and after being differentiated from 1, the term tends from 1 to 0 as the predicted value tensor r gradually approaches the true value tensor x. Therefore, through repeated training, the network has stronger reconstruction capability on specific data, and higher correlation of the reconstructed data in the statistical sense can be ensured.
Inputting each acceleration data in the data set in the second step into the convolutional self-coding network by a related function, adjusting and optimizing weight parameters in the network by an Adam optimization algorithm, finishing the training of the network when the loss function loss is less than 0.1, obtaining a network file after training, continuously expanding the quantity and the scale of normal data along with the increase of daily operation period year by year, and calling the network file for multiple times to carry out secondary training and optimization to finally obtain the convolutional self-coding network with wide adaptability;
fig. 8 shows the variation curve of the sub-data training loss parameter of the sensor 10 in the data set generated in step two. With the increase of training times, the correlation function of the reconstructed data (predicted value) and the original data (true value) gradually tends to 1, and the reconstruction loss value gradually tends to 0. The deep learning network has better reconstruction performance for the sensor 10 data set. And storing the trained deep learning network file in a format of pk l.
And fifthly, respectively acquiring data aiming at 5 different working conditions: 1) a damage-free structure; 2) removing the first layer of southeast corner one-span support; 3) removing the first layer and the four layers of southeast horns one-span supports; 4) removing all supports on the east; 5) and removing all supporting and loosening bolts at two ends of the beams spanned on the north east side of each layer.
And then, generating a data set according to the second step method, compressing and reconstructing data through the deep learning network, and comparing the reconstructed data with the original data to obtain a correlation function Cor serving as a score value of the safety state of the input data. Cor expression is as formula (4):
in the formula, xiThe ith element in the representation tensor x,the arithmetic mean, r, of the tensor xiThe ith element in the representation tensor r,representing the arithmetic mean of the tensor r.
Fig. 9 shows the correlation function for reconstructing distributed vibration data under different safety conditions. The closer the correlation function is to 1, the closer the reconstructed acceleration signal is to the original signal. The reconstruction rate of the 15 measuring point monitoring data sets corresponding to the 5 working conditions after convolutional self-coding is shown in fig. 10. The average value of the monitoring reconstruction rates of the 15 sensors is the comprehensive safety probability of the structure.
As shown in FIG. 11, the self-coding evaluation of distributed vibration data under different working conditions can effectively distinguish the structural state change degree. The more the structural state changes, the more severe the damage, and the lower the safety score.
The invention relates to a structural damage assessment method based on distributed vibration data and convolutional self-coding deep learning, wherein a loss function formed by combining a mean square error function and a correlation function is defined in the fourth step, an object for comparison is an original input real value x and a predicted value r reconstructed by a convolutional self-coder, and a data label value is not required to be provided in advance.
In the stages of building a convolution self-coding deep learning network, training parameters and generating network files, only vibration monitoring data in normal operation is used, and in addition, the integral transformation in advance is not needed, so that the characteristics of the vibration data in a time domain are reserved.
And thirdly, the data of the input layer and the output layer of the constructed convolutional self-encoder deep learning network have the same physical significance, the data tensor of the input layer is a real value, the data tensor of the output layer is a predicted value, and the network has the functions of feature extraction, convolution dimensionality reduction and deconvolution prediction.
In the actual structure evaluation, the damage score of the monitored structure reflected by the monitoring data of the structure in the corresponding time period can be obtained only by inputting the real-time monitoring data of the corresponding sensor into the convolutional self-coding deep learning network after the real-time monitoring data of the corresponding sensor is preprocessed in the second step.
Claims (5)
1. A structural damage assessment method based on distributed vibration data and convolutional self-coding deep learning is characterized by comprising the following steps:
s1, modeling and analyzing the monitoring structure, selecting acceleration response monitoring points by combining experience, and arranging acceleration sensors at each monitoring point according to the dynamic characteristics and the excitation types of the structure so as to monitor the vibration acceleration data of the structure in a characteristic position and a specific direction;
s2, acquiring monitoring data sources of n distributed acceleration sensors of the monitoring structure in use, recording the monitoring data sources as a data source 1, a data source 2 and a data source …, and preprocessing data to form a data set for deep learning network training;
s3, building a convolution self-coding deep learning network suitable for the data set in the step S2, and building a convolution self-coder, wherein the method specifically comprises the following steps:
scanning and feature extraction are carried out on the distributed vibration data through a convolutional encoder by adopting a convolutional self-coding network, and reconstruction of the compressed data is realized through a deconvolution decoder after the distributed vibration data are compressed;
selecting a loss function, carrying out multiple training and error transfer on the data in the data set in the step S2, adjusting each weight coefficient in the convolutional self-coding deep learning network, and finally obtaining the deep learning network which has generalization capability and grasps the internal rule of the input data set;
s4, preprocessing massive structure monitoring data in a normal use state according to the step S2, and inputting the preprocessed structure monitoring data into a convolutional self-encoder to be trained to obtain a convolutional self-encoder deep learning network file;
with the increase of daily operation period year by year, the quantity and scale of normal data are continuously expanded, and the network file is called for multiple times to carry out secondary training and optimization, so that the convolution self-coding network with wide adaptability is finally obtained;
s5, for data monitored by a sensor during daily service of the structure, preprocessing the data by using the method of step S2, and estimating the damage state of the structure by using a data reconstruction correlation function by using a trained convolutional self-encoder deep learning network.
2. The structural damage assessment method based on distributed vibration data and convolutional self-coding deep learning as claimed in claim 1, wherein the data preprocessing in step S2 includes data segmentation, data normalization and data random arrangement, specifically:
the data monitored by the n acceleration sensors in a nondestructive state can be expressed as formula (1).
Und=[u1 u2 ... un] (1)
Each acceleration sensor records Na acceleration data, and the Na acceleration data is divided into Ng vibration data signal segments containing Ns acceleration data according to the sampling frequency, namely Ns is not less than the sampling frequency as shown in a formula (2);
each acceleration data ui,jCarrying out normalization processing, and carrying out random sequencing on Ng acceleration signals corresponding to each sensor to generate new uiAnd Und, finishing the preprocessing of the training data set.
3. The structural damage assessment method based on distributed vibration data and convolutional self-coding deep learning of claim 1, wherein the characteristics of the data structure of the deep learning network of step S3 include:
1) a one-dimensional convolution neural network is adopted as a basic data processing structure;
2) the tensor size of the data of the input layer and the output layer is 1 multiplied by Ns, the tensor size is a real value and is expressed as x by tensor, the tensor size is a predicted value and is expressed as r by tensor;
3) the convolution coding layer compresses data and extracts features through 3 times of convolution kernel scanning and down-sampling work, and the size of the compressed expansion is LXNc, wherein L is more than or equal to 2, and Nc is less than Ns;
4) the deconvolution decoding layer reconstructs compressed data through 3 times of transposition convolution kernel scanning and up-sampling work, and finally outputs tensor data with the dimension and the size consistent with those of the input layer.
4. The structural damage assessment method based on distributed vibration data and convolutional self-coding deep learning as claimed in claim 1, wherein in step S4, the pre-processed data training specifically comprises the following steps:
defining the loss function of the predicted value tensor r and the true value tensor x, as shown in equation (3),
in the formula: r denotes predictionThe value tensor, x denotes the real value tensor, N denotes the data length of the tensor r, xiDenotes the i-th element in the tensor x, x denotes the arithmetic mean of the tensor x, riRepresenting the ith element in the tensor r, r representing the arithmetic mean of the tensor r;
the formula (3) is formed by adding 2 terms, wherein the former is a mean square error function and aims to reduce the error between a predicted value and a true value; the latter is a correlation function of a predicted value and a true value, and after the correlation function is differentiated from 1, the term is from 1 to 0 along with the process that a predicted value tensor r is gradually close to a true value tensor x;
and (4) inputting the acceleration data in the data set in the step S2 into the convolutional self-coding network by using a correlation function, adjusting and optimizing weight parameters in the network by using an Adam optimization algorithm, finishing training of the network when the loss function loss is less than 0.1, and obtaining a deep learning network file of the convolutional self-coder after training.
5. The structural damage assessment method based on distributed vibration data and convolutional self-coding deep learning according to claim 1, wherein step S5 specifically comprises the following steps:
firstly, generating a data set according to the step S2, compressing and reconstructing data through the deep learning network, comparing a predicted value tensor r serving as reconstruction with a true value tensor x serving as reconstruction to obtain a correlation function Cor, using the correlation function Cor as a score value of a safety state of input data, wherein an average value of monitoring reconstruction rates of n sensors is a comprehensive safety probability of the structure, the more the structural state is changed, the more serious the damage is, the lower the comprehensive safety score is, the correlation function Cor is shown as a formula (4),
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CN113742983A (en) * | 2021-10-09 | 2021-12-03 | 福州大学 | Long-span structural damage identification method based on depth self-encoder neural network |
CN114565003A (en) * | 2021-11-11 | 2022-05-31 | 哈尔滨工业大学(深圳) | Underdetermined working mode analysis method based on compression sampling and dictionary sparse decomposition |
CN114755122A (en) * | 2022-04-19 | 2022-07-15 | 西南交通大学 | Testing device and testing method for subway tunnel structure full life cycle health monitoring |
CN114755122B (en) * | 2022-04-19 | 2023-09-01 | 西南交通大学 | Test device and test method for full life cycle health monitoring of subway tunnel structure |
CN115331391A (en) * | 2022-08-03 | 2022-11-11 | 东南大学 | Distributed structure vibration monitoring data intelligent alarming and recovering method |
CN115331391B (en) * | 2022-08-03 | 2023-09-12 | 东南大学 | Distributed structure vibration monitoring data intelligent alarm and recovery method |
CN116728291A (en) * | 2023-08-16 | 2023-09-12 | 湖南大学 | Robot polishing system state monitoring method and device based on edge calculation |
CN116728291B (en) * | 2023-08-16 | 2023-10-31 | 湖南大学 | Robot polishing system state monitoring method and device based on edge calculation |
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