CN114757096B - Bridge temperature prediction method, device, equipment and medium based on NARX neural network - Google Patents

Bridge temperature prediction method, device, equipment and medium based on NARX neural network Download PDF

Info

Publication number
CN114757096B
CN114757096B CN202210340870.8A CN202210340870A CN114757096B CN 114757096 B CN114757096 B CN 114757096B CN 202210340870 A CN202210340870 A CN 202210340870A CN 114757096 B CN114757096 B CN 114757096B
Authority
CN
China
Prior art keywords
data
model
bridge temperature
training
meteorological
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202210340870.8A
Other languages
Chinese (zh)
Other versions
CN114757096A (en
Inventor
周林仁
陈钰萌
陈兰
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
South China University of Technology SCUT
Original Assignee
South China University of Technology SCUT
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by South China University of Technology SCUT filed Critical South China University of Technology SCUT
Priority to CN202210340870.8A priority Critical patent/CN114757096B/en
Publication of CN114757096A publication Critical patent/CN114757096A/en
Application granted granted Critical
Publication of CN114757096B publication Critical patent/CN114757096B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/045—Combinations of networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
    • G06Q50/08—Construction
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/08—Thermal analysis or thermal optimisation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/10—Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Business, Economics & Management (AREA)
  • General Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • Software Systems (AREA)
  • Health & Medical Sciences (AREA)
  • Strategic Management (AREA)
  • General Engineering & Computer Science (AREA)
  • Economics (AREA)
  • General Health & Medical Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Human Resources & Organizations (AREA)
  • Biophysics (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Mathematical Physics (AREA)
  • Computing Systems (AREA)
  • Molecular Biology (AREA)
  • Marketing (AREA)
  • Data Mining & Analysis (AREA)
  • Computational Linguistics (AREA)
  • Tourism & Hospitality (AREA)
  • General Business, Economics & Management (AREA)
  • Biomedical Technology (AREA)
  • Operations Research (AREA)
  • Computer Hardware Design (AREA)
  • Medical Informatics (AREA)
  • Quality & Reliability (AREA)
  • Game Theory and Decision Science (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Entrepreneurship & Innovation (AREA)
  • Geometry (AREA)
  • Development Economics (AREA)
  • Primary Health Care (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The invention discloses a bridge temperature prediction method, a device, computer equipment and a storage medium based on NARX neural network, wherein the method comprises the following steps: performing sequential interpolation or extraction on the obtained bridge temperature data and the corresponding meteorological data, adjusting the bridge temperature data and the corresponding meteorological data to time sequence data with the same sampling rate, and taking the adjusted meteorological data as an alternative parameter; selecting weather parameters with high correlation with bridge temperature from the alternative parameters through the maximum information coefficient, and preprocessing the selected weather parameters and the corresponding bridge temperature data to obtain sample data; the sample data is divided into training data and test data; training the open-loop architecture model by using training data, converting the open-loop architecture in the trained model into a closed-loop structure, and evaluating the prediction performance of the closed-loop structure model by using test data; and if the prediction performance is good, predicting the data value of the bridge temperature by using the closed-loop structure model. The method provided by the invention has high prediction precision and good engineering practicability.

Description

Bridge temperature prediction method, device, equipment and medium based on NARX neural network
Technical Field
The invention relates to the technical field of bridge structure health monitoring, in particular to a bridge temperature prediction method, a device, computer equipment and a storage medium based on a NARX neural network.
Background
Bridge structures are important infrastructure, are key nodes on large traffic arteries, and millions of bridges make great contributions to the development of society and economy in China. The temperature load is an important load form, the temperature change can cause the change of the bridge material property and the expansion and contraction of the volume, the structural deformation, the stress, the strain, the support counter-force and the like effect can be caused under the connection constraint between the boundary and the component, and the bridge temperature disease is caused. To ensure the safety of bridge construction and operation, it is necessary to acquire bridge temperature field data.
At present, the acquisition of bridge temperature field data seriously depends on field actual measurement, but the real-time monitoring of bridge temperature based on a structural health monitoring system has the characteristics of high cost, long time consumption and low analysis efficiency, and the sensor may have the conditions of faults, damage, loss and the like in the service life, so that the engineering analysis requirements of most bridges and the requirement of long-term stable acquisition of data cannot be met. In addition, the traditional method for acquiring the bridge temperature field by using the finite element thermal analysis method has the defects of complex thermal boundary condition calculation method, higher software writing difficulty, time consumption in operation and larger memory occupation, and has more limitations in use.
In recent years, neural network technology has been widely used in the engineering field due to its superior nonlinear fitting capability. A Nonlinear autoregressive model (NARX) with external inputs is a recursive dynamic neural network, which introduces the output of the neural network as external feedback into the input layer of the neural network based on the BP neural network and adds s unit delays to the input. Compared with a static neural network, the output of the neural network considers the time step information from t-s to t, can be regarded as a multi-layer sensor with input delay and short-term memory capability, and can better learn the relation between the input and the output of a time sequence data complex dynamic system. The model can be applied to consider the highly nonlinear and time-sequential characteristics of bridge temperature and external weather factors and output the predicted value of the bridge measuring point temperature corresponding to weather time-sequential data.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides a bridge temperature prediction method, a device, computer equipment and a storage medium based on an NARX neural network. The method has high prediction precision, better engineering practicability and shortened calculation time.
The first aim of the invention is to provide a bridge temperature prediction method based on an NARX neural network.
The second object of the invention is to provide a bridge temperature prediction device based on NARX neural network.
A third object of the present invention is to provide a computer device.
A fourth object of the present invention is to provide a storage medium.
The first object of the present invention can be achieved by adopting the following technical scheme:
a bridge temperature prediction method based on a NARX neural network, the method comprising:
performing sequential interpolation or extraction on the obtained bridge temperature data and the corresponding meteorological data, adjusting the bridge temperature data and the corresponding meteorological data to time sequence data with the same sampling rate, and taking the adjusted meteorological data as an alternative parameter; wherein the weather data includes a plurality of weather parameters;
selecting weather parameters with high correlation with bridge temperature from the candidate parameters through the maximum information coefficient as input features of the model; respectively preprocessing the selected meteorological parameters and the corresponding bridge temperature data to obtain sample data; wherein the sample data is divided into training data and test data;
training the model by utilizing the training data to obtain a trained model; the model is an NARX neural network model with an open loop architecture and external input;
converting an open-loop framework in the trained model into a closed-loop structure, and evaluating the prediction performance of the closed-loop structure model by using the test data and adopting an absolute error average value index;
if the predicted result is within the preset range, the closed-loop structure model obtains the predicted value of the bridge temperature according to the input meteorological data.
Further, the training the model by using the training data to obtain a trained model specifically includes:
training a model by utilizing the training data, wherein the training data comprises super-parameter learning and optimization of the model;
for the trained model, quantifying the relation strength between the predicted value and the target value by using the training data and adopting the fitting goodness, and if the relation strength is not high enough, retraining the model or optimizing the topological structure of the model so as to obtain the trained model;
the training data comprises meteorological data x i And corresponding bridge temperature data y i ，y i As a target value; the meteorological data x i The value output after the model is input is the predicted value
The relationship strength between the predicted value and the target value is quantified by using the training data and adopting the goodness of fit, and the relationship strength is specifically as follows:
the goodness of fit formula is as follows:
wherein R is 2 Represents the strength of the relationship between the predicted value and the target value,and n is the number of samples of the input model and is the average value of the target values.
Further, the training the model by using the training data specifically includes:
the training data is divided into three subsets, cross-validation is performed using the three subsets, wherein:
the first subset is a training set for computing gradients and updating network weights and biases to minimize network loss functions;
the second subset is a verification set, verification errors are monitored during training, and network weights and deviations are saved with minimum verification set errors;
the third subset is a test set, which is used for final test after training and verification, and outputs performance indexes after model training is completed;
selecting a Bayesian regularization algorithm or a quantized conjugate gradient algorithm to optimize the network weight and bias, and introducing a Dropout technique to avoid the occurrence of under fitting and over fitting;
in the training process of the model, a trainscg quantized conjugate gradient algorithm is selected, the training data is input into the model to perform parameter learning optimization of the neural network, if the verification error is not reduced, iteration is stopped, and otherwise, the iteration times are set.
Further, the test data comprises meteorological data and corresponding bridge temperatures;
the method for evaluating the prediction performance of the closed-loop structure model by using the test data and adopting an absolute error average value index specifically comprises the following steps:
any one of the test data is processed by the method of the meteorological data x j Inputting the closed-loop structure model to obtain a value output by the closed-loop structure model, and inversely normalizing the output value to obtain a predicted value of the bridge temperature
Weather data x in test data j The corresponding bridge temperature is inversely normalized and then used as the target value y of the bridge temperature j ；
And an absolute error average value index is adopted to reflect the error between the bridge temperature predicted value and the target value, and the absolute error average value is calculated as follows:
wherein n is the number of samples of the input model;
if the absolute error average value is near the preset value, the prediction performance is good, and the engineering precision requirement can be met.
Further, let the bridge temperature be x, and any one of the corresponding alternative parameters be y;
the selecting weather parameters with high correlation with bridge temperature from the candidate parameters through the maximum information coefficient as input features of the model specifically comprises the following steps:
the calculation formula using the maximum information coefficient is as follows:
wherein I (x; y) is a mutual information coefficient, p (x, y) is a joint probability between variables x and y, a and B represent the number of dividing lattices in the x and y directions of a two-dimensional space, and the size setting of B satisfies a x B < B;
the larger the value of MIC (x; y), the higher the correlation of x, y; if the correlation of x and y is high, y is selected as the input feature of the model.
Further, preprocessing the selected meteorological parameters and the corresponding bridge temperature data respectively to obtain sample data, which specifically comprises:
respectively performing Z-Score standardization processing on the selected meteorological parameters to obtain processed meteorological data serving as input data of a model;
performing Z-Score standardization processing on the bridge temperature data to obtain processed bridge temperature data which are used as values output by a model;
the processed weather data and the corresponding processed bridge temperature data form sample data.
Furthermore, the NARX neural network model adopts a network structure with output delay feedback, and comprises an input layer, a hidden layer and an output layer;
initializing the node number and the feedback delay number of the NARX neural network model, wherein the input-output relationship of the NARX neural network model is as follows:
y(t)＝f(x(t)，x(t-1),…,x(t-d),y(t-1))
where t represents the current time, d represents the feedback delay number, y (t), y (t-1) represent the outputs of the network model at the current time and the previous time, and x (t), x (t-d) represent the input data of the network model at the current time and the previous d time.
Further, the acquired meteorological data comprise meteorological parameters including zenith angle, air temperature, relative humidity, wind speed, rainfall and total cloud cover rate.
The second object of the invention can be achieved by adopting the following technical scheme:
a bridge temperature prediction device based on a NARX neural network, the device comprising:
the alternative parameter acquisition module is used for carrying out sequential interpolation or extraction on the acquired bridge temperature data and the corresponding meteorological data, adjusting the bridge temperature data and the corresponding meteorological data to time sequence data with the same sampling rate, and taking the adjusted meteorological data as alternative parameters; wherein the weather data includes a plurality of weather parameters;
the sample data acquisition module is used for selecting weather parameters with high correlation with bridge temperature from the candidate parameters through the maximum information coefficient as input features of the model; respectively preprocessing the selected meteorological parameters and the corresponding bridge temperature data to obtain sample data; wherein the sample data is divided into training data and test data;
the model training module is used for training the model by utilizing the training data to obtain a trained model; the model is an NARX neural network model with an open loop architecture and external input;
the model prediction performance evaluation module is used for converting an open-loop framework in the trained model into a closed-loop structure, and evaluating the prediction performance of the closed-loop structure model by using the test data and adopting an absolute error average value index;
and the bridge temperature prediction module is used for obtaining a predicted value of the bridge temperature according to the input meteorological data by the closed-loop structure model if the predicted result is in the preset range.
The third object of the present invention can be achieved by adopting the following technical scheme:
the computer equipment comprises a processor and a memory for storing a program executable by the processor, wherein the bridge temperature prediction method is realized when the processor executes the program stored by the memory.
The fourth object of the present invention can be achieved by adopting the following technical scheme:
a storage medium storing a program which, when executed by a processor, implements the bridge temperature prediction method described above.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention provides a bridge temperature prediction method based on a NARX neural network, which is the first application of a deep learning technology in the bridge temperature prediction direction. According to the method, meteorological features which are strongly related to bridge temperature are established as the input of a model, and the periodic characteristics of meteorological data time dimension, the nonlinear combination relation with the structure temperature and the short-term time sequence dependency relation are considered through a neural network; and the weight value and the threshold value of the network neuron are updated in real time by a recursion method, so that multi-step prediction of the bridge multi-measuring-point temperature in the required time step can be completed, and the prediction accuracy is higher.
2. Compared with the traditional method for acquiring the measuring point temperature based on the SHM monitoring system, the method for acquiring the bridge temperature by adopting the neural network can overcome the defects of certain service life limit and possible data loss of the health monitoring equipment, and realize the long-term stable acquisition of the bridge measuring point temperature.
3. Compared with the traditional method for calculating the temperature field based on finite element and programming software interaction program, the method provided by the invention has the advantages of shortening the calculation time, reducing the occupied space of the memory, improving the calculation efficiency and having good engineering practicability.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to the structures shown in these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flowchart of a bridge temperature prediction method based on a NARX neural network in embodiment 1 of the present invention.
Fig. 2 is a schematic diagram of an open loop topology of a NARX neural network model according to embodiment 1 of the present invention.
FIG. 3 shows the goodness of fit (R) of the NARX model of example 1 of the present invention 2 ) An index diagram.
Fig. 4 is a schematic diagram of a closed-loop topology of a NARX neural network model according to embodiment 1 of the present invention.
Fig. 5 is a schematic diagram of a section of a box bridge and a measuring point position according to embodiment 1 of the present invention.
Fig. 6 is a schematic diagram of absolute error average (MAE) index of the prediction result of the NARX model in embodiment 1 of the present invention.
FIG. 7 is a graph showing the comparison of predicted and target values of the temperature at the middle point of the top plate according to example 1 of the present invention.
FIG. 8 is a graph showing the comparison of predicted and target values of the temperature at the middle point of the soleplate in example 1 of the present invention.
FIG. 9 is a graph showing the comparison of predicted and target temperatures at the center point of the east web of example 1 of the present invention.
FIG. 10 is a graph showing the comparison of predicted and target values of the temperature at the center point of the web in example 1 of the present invention.
Fig. 11 is a block diagram of a bridge temperature prediction apparatus based on a NARX neural network according to embodiment 2 of the present invention.
Fig. 12 is a block diagram showing the structure of a computer device according to embodiment 3 of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments, and all other embodiments obtained by those skilled in the art without making any inventive effort based on the embodiments of the present invention are within the scope of protection of the present invention. It should be understood that the description of the specific embodiments is intended for purposes of illustration only and is not intended to limit the scope of the present application.
Example 1:
as shown in fig. 1, the embodiment provides a bridge temperature prediction method based on a NARX neural network, which includes the following steps:
s101, performing sequential interpolation or extraction on the acquired bridge temperature data and the corresponding meteorological data, adjusting the bridge temperature data and the corresponding meteorological data to time sequence data with the same sampling rate, and taking the adjusted meteorological data as an alternative parameter.
Wherein the weather data includes a plurality of weather parameters.
(1) And acquiring bridge temperature data and corresponding meteorological data.
Bridge temperature data for model training is from actual observations of a health monitoring system or finite element calculations, and meteorological data is from meteorological website shared data download or actual observations of a bridge site.
The bridge temperature data pre-adopted in the training in the embodiment are obtained by arranging temperature measuring points on the physical bridge structure and using a temperature acquisition instrument.
In this embodiment, the meteorological data includes 6 parameters including zenith angle, air temperature, relative humidity, wind speed, rainfall, and total cloud cover coverage. The data of the air temperature, the relative humidity, the wind speed, the rainfall and the total cloud cover rate come from weather station data provided by Meteobalue of a Meteorological platform in Switzerland, and are downloaded from a www.meteoblue.com website.
Because the distance between the meteorological station and the bridge site is only 500m, the meteorological station environment can be approximately utilized to replace the bridge site meteorological environment, and the zenith angle gamma is calculated according to the related data of the bridge site, such as the sun altitude angle, the sun declination angle, the sun hour angle, the local time and the latitude of the site, by the following formula:
sinδ＝0.39795cos[0.98563(N-173)/180*pi]
ω＝15×(ST-12)
γ＝90°-arcsin(sinh s )
wherein h is s Is the solar altitude; delta is solar declination and represents an included angle between solar rays and the earth's equatorial plane; n is the number of days, i.e. 1 month and 1 day from the current year; omega is the solar time angle; ST is the local time;is the latitude of the observation site.
(2) And performing sequential interpolation or extraction on the bridge temperature data and the corresponding meteorological data, adjusting the bridge temperature data and the corresponding meteorological data to time sequence data with the same sampling rate, and taking the adjusted meteorological data as an alternative parameter.
And (3) carrying out linear interpolation or extraction on the temperature data of the measuring point obtained by actual observation and the obtained corresponding meteorological data, adjusting the temperature data to be time sequence data with the same sampling rate, wherein the time interval of the samples is 1h, and taking the adjusted meteorological data as an alternative parameter of a training model.
S102, selecting weather parameters with high correlation with bridge temperature from the candidate parameters through the maximum information coefficient as input features of the model.
Alternative parameters in the embodiment comprise 6 parameters of zenith angle, air temperature, relative humidity, wind speed, rainfall and total cloud cover rate in meteorological data.
And (3) reducing the dimension of the 6 alternative parameters, and quantitatively selecting weather factors with strong correlation with the bridge temperature. And measuring the correlation between each of the alternative parameters and the bridge temperature by using a Maximum Information Coefficient (MIC).
MIC is the quantification of the relative entropy between the joint and edge distributions of two random variables, used to measure the degree of linear or nonlinear association between the two variables x, y. The basic idea is that two variables are scattered in a two-dimensional space and expressed by using a scatter diagram, then the two-dimensional space is divided into a certain number of square lattices in the x and y directions respectively, the scattered points of the scattered points in each square lattice are observed, and the joint probability is calculated so as to simplify the calculation of the mutual information coefficient, thus solving the problem that the joint probability is difficult to solve in the mutual information; and finally, normalizing to obtain the MIC value. The division into certain squares in the x and y directions can be performed in a plurality of different ways, and the maximum MIC value is calculated as a final result. The MIC calculation formula is as follows:
wherein I (x, y) is a mutual information coefficient, p (x, y) is a joint probability between variables x and y, a and B represent the number of dividing lattices in the x and y directions in a two-dimensional space, a is set to be a value of a < B, and B is set to be about 0.6 th power of the number of data samples.
And selecting weather parameters with high correlation with bridge temperature as input features of the model through a Maximum Information Coefficient (MIC), wherein the larger the MIC value is, the higher the correlation between x and y is.
In this embodiment, the meteorological parameters selected by MIC include 5 parameters including zenith angle, air temperature, relative humidity, wind speed and total cloud cover, which are used as input features of the model.
S103, respectively preprocessing the selected meteorological parameters and bridge temperature data under corresponding environmental conditions to obtain sample data, and dividing the sample data into training data and test data.
(1) And performing Z-Score standardization processing on the selected meteorological parameters to obtain processed meteorological data.
The selected meteorological parameters are used as input features of the model, and Z-Score standardization processing is carried out before data of the input features are input into the model, so that the influence of extremely bad differences of data dimension and different feature data can be eliminated, and the data performance is greatly improved in neural network training. The processed data of the meteorological parameters are called processed meteorological data and are used as input data of a model.
The processed data are converted into dimensionless data with the mean value of 0 and the variance of 1, and the dimensionless data accord with standard normal distribution. The method can convert different amount of data into the same magnitude so as to ensure the comparability between the data and improve the stability of the neural network. The Z-Score normalization formula is as follows:
wherein: x is the pre-treatment data, x' is the post-treatment data, μ is the mean of all pre-treatment data, σ is the standard deviation of all pre-treatment data.
(2) And performing Z-Score standardization treatment on the bridge temperature data to obtain the treated bridge temperature data.
And selecting bridge temperature data under corresponding environmental conditions from the bridge temperature data according to the selected meteorological parameters, and performing Z-Score standardization processing on the selected bridge temperature data to obtain processed bridge temperature data serving as a value output by the model.
(3) And obtaining sample data according to the processed meteorological data and the processed bridge temperature data.
The processed weather data and the processed bridge temperature data constitute sample data.
(4) The sample data is divided into training data and test data.
The total time sequence data samples are taken as training data of 80% and test data of 20% in sample data under the condition of no disorder.
S104, training the NARX neural network model by using training data.
(1) An open loop NARX neural network model with external input is built.
As shown in fig. 2, the open loop NARX neural network model provided in this example includes an input layer, a hidden layer, and an output layer.
Initializing the node number and the feedback delay number of an NARX neural network model, wherein the input-output relationship of the NARX neural network model is as follows:
y(t)＝f(x(t)，x(t-1),…,x(t-d),y(t-1))
where t represents the current time and d represents the feedback delay number.
f (x, y) is a nonlinear mapping function with respect to x, y (t), y (t-1) represent network outputs at the current time and previous time, and x (t), x (t-d) represent network inputs at the current time and previous d time. The hidden layer contains h neurons, and the optimal neuron number of the hidden layer can be selected according to an empirical formula:
wherein h is the number of neurons in the hidden layer, m is the number of neurons in the input layer, n is the number of neurons in the output layer, and a is any constant between 1 and 10.
In this embodiment, the hidden layer includes 10 neurons, the hidden layer activation function is tansig, the output layer activation function is linear function, and the feedback delay number d is set to 3.
(2) And performing super-parameter learning and optimization on the open loop NARX neural network model by using training data.
The training data is divided into three subsets for cross-validation, wherein:
the first subset is a training set for computing gradients and updating network weights and biases to minimize the network loss function MSE;
the second subset is a verification set, verification errors are monitored during training, and network weights and deviations are saved with minimum verification set errors;
the third subset is a test set, which is used for final testing after training and verification, and outputs performance indexes after model training is completed.
In the NARX model training process, an open loop network structure for disconnecting output delay feedback is adopted for training, a Bayesian regularization algorithm or a quantized conjugate gradient algorithm is selected according to the performance of the neural network to optimize the network weight and bias, and the Dropout technology is introduced to avoid the occurrence of under fitting and over fitting.
In the model training process of this embodiment, the training set accounts for 70% of the total batch of training data, and the verification set and the test set both account for 15% of the total batch of training data. Setting the iteration times epochs=150, the learning rate lr=0.01, training and selecting a quantized conjugate gradient algorithm (trainscg), and inputting training data into a model to perform parameter learning optimization of the neural network.
And in the training process of the neural network, if the verification error does not drop in six iterations, stopping the iteration, otherwise, iterating the iterations for the epochs.
S105, for the trained NARX neural network model, using the training data to quantify the relation strength between the predicted value and the target value output by the NARX neural network model by adopting the fitting goodness, and further obtaining the trained model.
After model training, the training data is used to determine the goodness of fit (R 2 ) The strength of the relationship between the input and output of the model is quantified. Wherein the training data comprises meteorological data x i And corresponding bridge temperature data y i ，y i As the target value, meteorological data x i The value output after the model is input is the predicted value
The goodness of fit formula is as follows:
wherein,and n is the number of samples of the input model and is the average value of the target values.
The goodness of fit of this example on the training set, validation set, test set is shown in FIG. 3, the goodness of fit (R 2 ) The model accuracy is high when the relation strength is high and the input characteristics are proved to be reasonable to select when the relation strength is high and the model is above 0.975.
After the goodness of fit reaches the satisfaction degree, the loss function L (y, f (x)) of the goodness of fit on the training set and the testing set needs to be further checked to measure the difference degree between the true value y and the predicted value f (x). The difference between the loss function of the test set and the training set is required to be prevented from being too large, so that overfitting is avoided; otherwise, retraining the NARX neural network model by random initial weight and threshold value, or adjusting the number of hidden layer neurons to optimize the topological structure. The network loss function is calculated using a Mean Square Error (MSE).
S106, converting an open-loop framework in the trained model into a closed-loop structure, and evaluating the prediction performance of the closed-loop structure model by using test data; if the predicted result is within the preset range, the closed-loop structure model obtains the predicted value of the bridge temperature according to the input meteorological data.
After step S105, the open loop architecture of the NARX neural network model is converted into a closed loop structure, and the NARX neural network model of the closed loop structure is shown in fig. 4.
To test the generalization ability of the NARX neural network model, the predictive performance of the NARX neural network model was evaluated, and the meteorological data x of 240 consecutive time steps (corresponding to 240 hours, 10 days) in the test data was used j Inputting the closed loop NARX neural network model to obtain the value output by the NARX neural network model, and inversely normalizing the output value to obtain the predicted value of the bridge temperatureWeather data x in test data j The corresponding bridge temperature is inversely normalized and then used as the target value y of the bridge temperature j The target value of the bridge temperature is the same as the original bridge temperature data in step S101; and comparing the predicted value of the bridge temperature with the target value of the bridge temperature.
For the assessment of the performance of the NARX neural network model, an absolute error average (MAE) index is used to reflect the error between the predicted value and the target value, and the absolute error average (MAE) is calculated as follows:
where n is the number of samples of the input model.
In the embodiment, the sectional form of the bridge and the positions of the measuring points are shown in fig. 5, and the structural temperature value within 10 days under the summer meteorological conditions of a certain place of the subtropical zone is calculated. For the evaluation of the prediction performance of the neural network model, the absolute error average (MAE) index is shown in fig. 6, and the predicted value and target value pair of the bridge temperature at each measuring point are shown in fig. 7 to 10. The result shows that the absolute error average value (MAE) of the predicted result of the bridge temperature is about 2.0, namely the predicted value and the target value are high in matching degree, the engineering precision requirement is met, and the method has good applicability.
And outputting one or more predicted values according to one or more groups of input meteorological data for the closed-loop structure model with good applicability, and performing inverse standardization on the predicted values to obtain predicted values of bridge temperature.
Those skilled in the art will appreciate that all or part of the steps in a method implementing the above embodiments may be implemented by a program to instruct related hardware, and the corresponding program may be stored in a computer readable storage medium.
It should be noted that although the method operations of the above embodiments are depicted in the drawings in a particular order, this does not require or imply that the operations must be performed in that particular order or that all illustrated operations be performed in order to achieve desirable results. Rather, the depicted steps may change the order of execution. Additionally or alternatively, certain steps may be omitted, multiple steps combined into one step to perform, and/or one step decomposed into multiple steps to perform.
Example 2:
as shown in fig. 11, the present embodiment provides a bridge temperature prediction apparatus based on a NARX neural network, which includes an alternative parameter acquisition module 1101, a sample data acquisition module 1102, a model training module 1103, a model prediction performance evaluation module 1104, and a bridge temperature prediction module 1105, wherein:
the alternative parameter obtaining module 1101 is configured to perform sequential interpolation or extraction on the obtained bridge temperature data and the corresponding meteorological data, adjust the bridge temperature data and the corresponding meteorological data to time-series data with the same sampling rate, and use the adjusted meteorological data as an alternative parameter; wherein the weather data includes a plurality of weather parameters;
the sample data obtaining module 1102 is configured to select, from the candidate parameters, weather parameters with high correlation with the bridge temperature as input features of a model through a maximum information coefficient; respectively preprocessing the selected meteorological parameters and the corresponding bridge temperature data to obtain sample data; wherein the sample data is divided into training data and test data;
the model training module 1103 is configured to train the model by using the training data to obtain a trained model; the model is an NARX neural network model with an open loop architecture and external input;
the model prediction performance evaluation module 1104 is configured to convert an open-loop architecture in the trained model into a closed-loop structure, and evaluate the prediction performance of the closed-loop structure model by using the test data and an absolute error average value index;
and the bridge temperature prediction module 1105 is configured to obtain a predicted value of the bridge temperature according to the input meteorological data by using the closed-loop structure model if the predicted result is within the preset range.
Specific implementation of each module in this embodiment may be referred to embodiment 1 above, and will not be described in detail herein; it should be noted that, the apparatus provided in this embodiment is only exemplified by the division of the above functional modules, and in practical application, the above functional allocation may be performed by different functional modules according to needs, that is, the internal structure is divided into different functional modules, so as to perform all or part of the functions described above.
Example 3:
the present embodiment provides a computer device, which may be a computer, as shown in fig. 12, and is connected through a system bus 1201, a processor 1202, a memory, an input device 1203, a display 1204 and a network interface 1205, where the processor is configured to provide computing and control capabilities, the memory includes a nonvolatile storage medium 1206 and an internal memory 1207, where the nonvolatile storage medium 1206 stores an operating system, a computer program and a database, and the internal memory 1207 provides an environment for the operating system and the computer program in the nonvolatile storage medium, and when the processor 1202 executes the computer program stored in the memory, the bridge temperature prediction method of the foregoing embodiment 1 is implemented as follows:
performing sequential interpolation or extraction on the obtained bridge temperature data and the corresponding meteorological data, adjusting the bridge temperature data and the corresponding meteorological data to time sequence data with the same sampling rate, and taking the adjusted meteorological data as an alternative parameter; wherein the weather data includes a plurality of weather parameters;
selecting weather parameters with high correlation with bridge temperature from the candidate parameters through the maximum information coefficient as input features of the model; respectively preprocessing the selected meteorological parameters and the corresponding bridge temperature data to obtain sample data; wherein the sample data is divided into training data and test data;
training the model by utilizing the training data to obtain a trained model; the model is an NARX neural network model with an open loop architecture and external input;
converting an open-loop framework in the trained model into a closed-loop structure, and evaluating the prediction performance of the closed-loop structure model by using the test data and adopting an absolute error average value index;
if the predicted result is within the preset range, the closed-loop structure model obtains the predicted value of the bridge temperature according to the input meteorological data.
Example 4:
the present embodiment provides a storage medium, which is a computer-readable storage medium storing a computer program that, when executed by a processor, implements the bridge temperature prediction method of the above embodiment 1, as follows:
performing sequential interpolation or extraction on the obtained bridge temperature data and the corresponding meteorological data, adjusting the bridge temperature data and the corresponding meteorological data to time sequence data with the same sampling rate, and taking the adjusted meteorological data as an alternative parameter; wherein the weather data includes a plurality of weather parameters;
selecting weather parameters with high correlation with bridge temperature from the candidate parameters through the maximum information coefficient as input features of the model; respectively preprocessing the selected meteorological parameters and the corresponding bridge temperature data to obtain sample data; wherein the sample data is divided into training data and test data;
training the model by utilizing the training data to obtain a trained model; the model is an NARX neural network model with an open loop architecture and external input;
converting an open-loop framework in the trained model into a closed-loop structure, and evaluating the prediction performance of the closed-loop structure model by using the test data and adopting an absolute error average value index;
if the predicted result is within the preset range, the closed-loop structure model obtains the predicted value of the bridge temperature according to the input meteorological data.
The computer readable storage medium of the present embodiment may be a computer readable signal medium or a computer readable storage medium, or any combination of the two. The computer readable storage medium can be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or a combination of any of the foregoing. More specific examples of the computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.
In summary, the present invention firstly carries out sequence interpolation or extraction on bridge measurement point temperature data and corresponding meteorological data, and adjusts the time sequence data with the same sampling rate; then, calculating and selecting weather parameters with high correlation with bridge temperature as input number characteristics of the model through the maximum information coefficient; constructing an open loop NARX neural network model with external input, and performing super-parameter learning and optimization of the NARX neural network model by adopting training data; and finally, converting an open-loop architecture in the trained NARX neural network model into a closed-loop structure, updating the weight and the threshold value of the network neurons in real time, and further recursively completing the prediction of the bridge temperature in the required time step. The method provided by the invention can realize the input of the data of the site meteorological parameters to the model of the closed-loop structure, can rapidly acquire the bridge temperature data, has high prediction precision and has stronger engineering practicability.
The above-mentioned embodiments are only preferred embodiments of the present invention, but the protection scope of the present invention is not limited thereto, and any person skilled in the art can make equivalent substitutions or modifications according to the technical solution and the inventive concept of the present invention within the scope of the present invention disclosed in the present invention patent, and all those skilled in the art belong to the protection scope of the present invention.

Claims (6)

1. A bridge temperature prediction method based on a NARX neural network, the method comprising:
performing sequential interpolation or extraction on the obtained bridge temperature data and the corresponding meteorological data, adjusting the bridge temperature data and the corresponding meteorological data to time sequence data with the same sampling rate, and taking the adjusted meteorological data as an alternative parameter; wherein the weather data includes a plurality of weather parameters;
selecting weather parameters with high correlation with bridge temperature from the candidate parameters through the maximum information coefficient as input features of the model; respectively preprocessing the selected meteorological parameters and the corresponding bridge temperature data to obtain sample data; wherein the sample data is divided into training data and test data;
training the model by utilizing the training data to obtain a trained model; the model is an NARX neural network model with an open loop architecture and external input;
converting an open-loop framework in the trained model into a closed-loop structure, and evaluating the prediction performance of the closed-loop structure model by using the test data and adopting an absolute error average value index;
if the predicted result is in the preset range, the closed-loop structure model obtains a predicted value of the bridge temperature according to the input meteorological data;
the selecting weather parameters with high correlation with bridge temperature from the candidate parameters through the maximum information coefficient as input features of a model specifically comprises the following steps:
setting the bridge temperature as x, and setting any one of the corresponding alternative parameters as y;
the calculation formula using the maximum information coefficient is as follows:
wherein I (x; y) is a mutual information coefficient, p (x, y) is a joint probability between variables x and y, a and B represent the number of dividing lattices in the x and y directions of a two-dimensional space, and the size setting of B satisfies a x B < B;
the larger the value of MIC (x; y), the higher the correlation of x, y; if the correlation of x and y is high, y is selected as the input feature of the model;
training the model by utilizing the training data to obtain a trained model, which specifically comprises the following steps:
dividing the training data into three subsets, and performing cross-validation by using the three subsets, wherein the first subset is a training set for calculating gradients and updating network weights and deviations to minimize a network loss function; the second subset is a verification set, verification errors are monitored during training, and network weights and deviations are saved with minimum verification set errors; the third subset is a test set, which is used for final test after training and verification, and outputs performance indexes after model training is completed; selecting a Bayesian regularization algorithm or a quantized conjugate gradient algorithm to optimize the network weight and bias, and introducing a Dropout technique to avoid the occurrence of under fitting and over fitting;
in the training process of the model, a trainscg quantized conjugate gradient algorithm is selected, the training data is input into the model to perform parameter learning optimization of a neural network, if the verification error is not reduced, iteration is stopped, otherwise, the iteration times are set;
for the trained model, quantifying the relation strength between the predicted value and the target value by using the training data and adopting the fitting goodness, and if the relation strength is not high enough, retraining the model or optimizing the topological structure of the model so as to obtain the trained model; wherein, the formula of the goodness of fit is as follows:
wherein y is i For meteorological data x in training data i Corresponding bridge temperature data is used as a target value;for meteorological data x i Inputting a predicted value output after the model; r is R 2 Representing the strength of the relation between the predicted value and the target value, < >>N is the number of samples of the input model and is the average value of the target values;
the method for evaluating the prediction performance of the closed-loop structure model by using the test data and adopting an absolute error average value index specifically comprises the following steps:
any one of the test data is processed by the method of the meteorological data x j Inputting the closed-loop structure model to obtain a value output by the closed-loop structure model, and inversely normalizing the output value to obtain a predicted value of the bridge temperature
Weather data x in test data j The corresponding bridge temperature is inversely normalized and then used as the target value y of the bridge temperature j ；
And an absolute error average value index is adopted to reflect the error between the bridge temperature predicted value and the target value, and the absolute error average value is calculated as follows:
if the absolute error average value is near the preset value, the prediction performance is good, and the engineering precision requirement can be met.
2. The bridge temperature prediction method according to claim 1, wherein the preprocessing is performed on the selected meteorological parameters and the corresponding bridge temperature data respectively to obtain sample data, and the method specifically comprises:
respectively performing Z-Score standardization processing on the selected meteorological parameters to obtain processed meteorological data serving as input data of a model;
performing Z-Score standardization processing on the bridge temperature data to obtain processed bridge temperature data which are used as values output by a model;
the processed weather data and the corresponding processed bridge temperature data form sample data.
3. The bridge temperature prediction method according to any one of claims 1 to 2, wherein the NARX neural network model adopts a network structure with output delay feedback, and comprises an input layer, a hidden layer and an output layer;
initializing the node number and the feedback delay number of the NARX neural network model, wherein the input-output relationship of the NARX neural network model is as follows:
y(t)＝f(x(t)，x(t-1),…,x(t-d),y(t-1))
where t represents the current time, d represents the feedback delay number, y (t), y (t-1) represent the outputs of the network model at the current time and the previous time, and x (t), x (t-d) represent the input data of the network model at the current time and the previous d time.
4. The bridge temperature prediction method according to any one of claims 1 to 2, wherein the acquired meteorological data includes meteorological parameters including zenith angle, air temperature, relative humidity, wind speed, rainfall, and total cloud cover.
5. A bridge temperature prediction device based on a NARX neural network, the device comprising:
the alternative parameter acquisition module is used for carrying out sequential interpolation or extraction on the acquired bridge temperature data and the corresponding meteorological data, adjusting the bridge temperature data and the corresponding meteorological data to time sequence data with the same sampling rate, and taking the adjusted meteorological data as alternative parameters; wherein the weather data includes a plurality of weather parameters;
the sample data acquisition module is used for selecting weather parameters with high correlation with bridge temperature from the candidate parameters through the maximum information coefficient as input features of the model; respectively preprocessing the selected meteorological parameters and the corresponding bridge temperature data to obtain sample data; wherein the sample data is divided into training data and test data;
the model training module is used for training the model by utilizing the training data to obtain a trained model; the model is an NARX neural network model with an open loop architecture and external input;
the model prediction performance evaluation module is used for converting an open-loop framework in the trained model into a closed-loop structure, and evaluating the prediction performance of the closed-loop structure model by using the test data and adopting an absolute error average value index;
the bridge temperature prediction module is used for obtaining a predicted value of the bridge temperature according to the input meteorological data by the closed-loop structure model if the predicted result is in a preset range;
the selecting weather parameters with high correlation with bridge temperature from the candidate parameters through the maximum information coefficient as input features of a model specifically comprises the following steps:
setting the bridge temperature as x, and setting any one of the corresponding alternative parameters as y;
the calculation formula using the maximum information coefficient is as follows:
wherein I (x; y) is a mutual information coefficient, p (x, y) is a joint probability between variables x and y, a and B represent the number of dividing lattices in the x and y directions of a two-dimensional space, and the size setting of B satisfies a x B < B;
the larger the value of MIC (x; y), the higher the correlation of x, y; if the correlation of x and y is high, y is selected as the input feature of the model;
training the model by utilizing the training data to obtain a trained model, which specifically comprises the following steps:
dividing the training data into three subsets, and performing cross-validation by using the three subsets, wherein the first subset is a training set for calculating gradients and updating network weights and deviations to minimize a network loss function; the second subset is a verification set, verification errors are monitored during training, and network weights and deviations are saved with minimum verification set errors; the third subset is a test set, which is used for final test after training and verification, and outputs performance indexes after model training is completed; selecting a Bayesian regularization algorithm or a quantized conjugate gradient algorithm to optimize the network weight and bias, and introducing a Dropout technique to avoid the occurrence of under fitting and over fitting;
in the training process of the model, a trainscg quantized conjugate gradient algorithm is selected, the training data is input into the model to perform parameter learning optimization of a neural network, if the verification error is not reduced, iteration is stopped, otherwise, the iteration times are set;
for the trained model, quantifying the relation strength between the predicted value and the target value by using the training data and adopting the fitting goodness, and if the relation strength is not high enough, retraining the model or optimizing the topological structure of the model so as to obtain the trained model; wherein, the formula of the goodness of fit is as follows:
wherein y is i For meteorological data x in training data i Corresponding bridge temperature data is used as a target value;for meteorological data x i Inputting a predicted value output after the model; r is R 2 Representing the strength of the relation between the predicted value and the target value, < >>N is the number of samples of the input model and is the average value of the target values;
the method for evaluating the prediction performance of the closed-loop structure model by using the test data and adopting an absolute error average value index specifically comprises the following steps:
any one of the test data is processed by the method of the meteorological data x j Inputting the closed-loop structure model to obtain a value output by the closed-loop structure model, and inversely normalizing the output value to obtain a predicted value of the bridge temperature
Weather data x in test data j The corresponding bridge temperature is inversely normalized and then used as the target value y of the bridge temperature j ；
And an absolute error average value index is adopted to reflect the error between the bridge temperature predicted value and the target value, and the absolute error average value is calculated as follows:
if the absolute error average value is near the preset value, the prediction performance is good, and the engineering precision requirement can be met.
6. A storage medium storing a program which, when executed by a processor, implements the bridge temperature prediction method according to any one of claims 1 to 4.
CN202210340870.8A 2022-04-02 2022-04-02 Bridge temperature prediction method, device, equipment and medium based on NARX neural network Active CN114757096B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210340870.8A CN114757096B (en) 2022-04-02 2022-04-02 Bridge temperature prediction method, device, equipment and medium based on NARX neural network

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210340870.8A CN114757096B (en) 2022-04-02 2022-04-02 Bridge temperature prediction method, device, equipment and medium based on NARX neural network

Publications (2)

Publication Number Publication Date
CN114757096A CN114757096A (en) 2022-07-15
CN114757096B true CN114757096B (en) 2024-03-15

Family

ID=82329658

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210340870.8A Active CN114757096B (en) 2022-04-02 2022-04-02 Bridge temperature prediction method, device, equipment and medium based on NARX neural network

Country Status (1)

Country Link
CN (1) CN114757096B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115221791A (en) * 2022-07-27 2022-10-21 浙江大学 Supercritical boiler wall temperature online prediction method and system

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2020014773A1 (en) * 2018-07-16 2020-01-23 Vineland Research And Innovation Centre Automated monitoring and irrigation of plants in a controlled growing environment
CN111339482A (en) * 2020-03-17 2020-06-26 南昌工程学院 Method for identifying outlier distribution transformer based on maximum mutual information
WO2021007812A1 (en) * 2019-07-17 2021-01-21 深圳大学 Deep neural network hyperparameter optimization method, electronic device and storage medium

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2020014773A1 (en) * 2018-07-16 2020-01-23 Vineland Research And Innovation Centre Automated monitoring and irrigation of plants in a controlled growing environment
WO2021007812A1 (en) * 2019-07-17 2021-01-21 深圳大学 Deep neural network hyperparameter optimization method, electronic device and storage medium
CN111339482A (en) * 2020-03-17 2020-06-26 南昌工程学院 Method for identifying outlier distribution transformer based on maximum mutual information

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
北京北站站台大跨度张弦桁架雨棚设计研究;罗尧治;余佳亮;;中国铁道科学;20130115(第01期);全文 *
基于相空间重构的CRTSⅡ型轨道板温度梯度预测分析;申建康;何越磊;李再帏;路宏遥;;华东交通大学学报;20190615(第03期);全文 *

Also Published As

Publication number Publication date
CN114757096A (en) 2022-07-15

Similar Documents

Publication Publication Date Title
Sarmadi et al. Bridge health monitoring in environmental variability by new clustering and threshold estimation methods
Jiang Computation of monthly mean daily global solar radiation in China using artificial neural networks and comparison with other empirical models
CN111310968A (en) LSTM neural network circulation hydrological forecasting method based on mutual information
CN109472110A (en) A kind of aero-engine remaining life prediction technique based on LSTM network and ARIMA model
CN110648014A (en) Regional wind power prediction method and system based on space-time quantile regression
Chen et al. Probabilistic forecasting of drought: a hidden Markov model aggregated with the RCP 8.5 precipitation projection
CN111144644A (en) Short-term wind speed prediction method based on variation variance Gaussian process regression
Wang et al. Bayesian approaches for evaluating wind‐resistant performance of long‐span bridges using structural health monitoring data
CN115907131B (en) Method and system for constructing electric heating load prediction model in northern area
CN114757096B (en) Bridge temperature prediction method, device, equipment and medium based on NARX neural network
CN116451514A (en) Bridge structure state evaluation method and device and electronic equipment
CN115081269B (en) Bridge thermal boundary condition prediction method, device and medium based on hybrid input neural network model
CN116845874A (en) Short-term prediction method and device for power load
Mao et al. Automated Bayesian operational modal analysis of the long-span bridge using machine-learning algorithms
Bilgili et al. Time-series prediction of hourly atmospheric pressure using ANFIS and LSTM approaches
CN110852415B (en) Vegetation index prediction method, system and equipment based on neural network algorithm
CN113988415B (en) Medium-and-long-term power load prediction method
Lu et al. Structural response estimation method based on particle swarm optimisation/support vector machine and response correlation characteristics
Huang et al. A decomposition‐based multi‐time dimension long short‐term memory model for short‐term electric load forecasting
Carrara et al. Deep learning for structural health monitoring: An application to heritage structures
CN118017482A (en) Flexible climbing capacity demand analysis method based on prediction error feature extraction
CN113866391A (en) Deep learning model prediction factor interpretation method and application thereof in soil water content prediction
CN113591957A (en) Wind power output short-term rolling prediction and correction method based on LSTM and Markov chain
CN113408183A (en) Vehicle base short-term composite prediction method based on prediction model
CN116960962A (en) Mid-long term area load prediction method for cross-area data fusion

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant