CN114880734A - BP-LSTM-based steel-concrete combined bridge deck system temperature field and temperature effect prediction method - Google Patents
BP-LSTM-based steel-concrete combined bridge deck system temperature field and temperature effect prediction method Download PDFInfo
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Abstract
The invention discloses a BP-LSTM-based prediction method for a temperature field and a temperature effect of a steel-concrete combined bridge deck system, which comprises the following steps: a, acquiring a temperature field of a steel-concrete combined bridge deck system and a training data set for predicting a temperature effect; b, respectively training a BP network and an LSTM network by utilizing a training data set; c, fusing the BP network and the LSTM network obtained after training in the step B to obtain a BP-LSTM prediction model; d, acquiring an actual measurement input vector corresponding to the input feature set in the step A; and E, preprocessing the actually measured input vector and inputting the preprocessed actually measured input vector into a BP-LSTM prediction model to obtain a temperature field and temperature effect prediction result. The invention combines the advantages of BP network nonlinear mapping and the advantages of LSTM network overcoming long-term dependence, provides a new method for predicting the structure temperature field and temperature effect, has strong reconstruction and generalization capability and accurate prediction result, overcomes the problems of higher time and economic cost brought by traditional theoretical calculation, finite element method and field actual measurement, and has great application significance in the fields of structure calculation and health monitoring.
Description
Technical Field
The invention belongs to the technical field of structural health monitoring, and particularly relates to a BP-LSTM-based prediction method for a temperature field and a temperature effect of a steel-concrete combined bridge deck system.
Background
The space shape of the steel-concrete combined bridge deck system is complex, the properties of various materials are different, and the influence of the space temperature effect is more critical. In the field of structural health monitoring, a rapid real-time prediction method for a steel-concrete combined bridge deck system space temperature field and temperature effect is not available at home and abroad.
At present, there are two main methods for calculating the temperature field of the bridge structure:
one method is that a theory or finite element method is adopted for calculation according to corresponding specifications, for example, in 2007, Riding K A and other factors considering radiation, material thermodynamic parameters, sunlight shielding and the like provide a calculation method for a large-volume concrete temperature field; in 2014, yin and yang parameters are introduced, geometric constraint relation, constitutive relation and balance condition are introduced, the conversion cross section is integrated, and the electric calculation method based on the nonlinear temperature gradient of the conversion cross section is derived.
The defect that calculation is time-consuming due to huge data amount exists according to specifications or calculation by adopting a finite element method, and if a long-term temperature field or a temperature effect of a structure needs to be calculated, a common calculation platform is difficult to meet the requirements.
Secondly, the temperature distribution model is established by field actual measurement, wherein in 2013, statistical analysis is carried out on the basis of measured temperature data of the bridge superstructure, a corresponding rule of the temperature field distribution of the girder is given, and the temperature distribution model is established.
The field actual measurement can only measure the temperature of the structure, if the field actual measurement is carried out for a long time, the time and economic cost are higher, measuring points are generally sparse, the structure temperature field is difficult to reflect comprehensively, and the temperature effect cannot be tested directly.
The BP (Back propagation) network is the most widely applied artificial neural network structure at present, the BP network adopts a back propagation algorithm, consists of an input layer, a hidden layer and an output layer, any mapping relation can be described without corresponding equations, and the universal approximation theorem proposed by HORNIK and the like and CYBENKO in 1989 shows that: the feedforward neural network can fit a function with any complexity at any precision only by a single hidden layer and a limited number of neural units.
The LSTM (Long Short Term Memory networks) network is a chain network circulation structure proposed in 1997 by HOCHREITER and SCHMIDHUBER to solve the long-Term dependence problem of the general circulation neural network, and controls the network input through the input gate, forgets the gate control Memory unit and outputs the gate control network output.
Disclosure of Invention
The invention aims to provide a BP-LSTM-based temperature field and temperature effect prediction method for a steel-concrete combined bridge deck system, aiming at the defects of high hardware requirement and high time economic cost of the traditional temperature field and temperature effect prediction method for the steel-concrete combined bridge deck system, and the prediction of the temperature field and temperature effect of the steel-concrete combined bridge deck system is realized in a low-cost and high-efficiency mode.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a BP-LSTM-based prediction method for a temperature field and a temperature effect of a steel-concrete combined bridge deck system is characterized by comprising the following steps:
a, acquiring a training data set for predicting a temperature field and a temperature effect of a steel-concrete combined bridge deck system, wherein the training data set comprises an input feature set and an output feature set, the input feature set comprises a structural feature, a time feature and an environmental feature, and the output feature set comprises the temperature and the temperature effect;
b, training the BP network by using the training data set in the step A, and training the LSTM network by using the training data set in the step A;
step C, fusing the BP network and the LSTM network obtained after training in the step B to obtain a BP-LSTM prediction model;
step D, acquiring an actual measurement input vector corresponding to the input feature set in the step A;
and E, preprocessing the actually measured input vector and inputting the preprocessed actually measured input vector into the BP-LSTM prediction model to obtain a temperature field and temperature effect prediction result.
In a preferred embodiment, in step a, a training data set is obtained based on measured data in combination with a finite element method.
As a preferred mode, in the step C, a weighted average method is adopted to fuse the BP network and the LSTM network, and after multiple training, initial network parameters corresponding to the BP network and the LSTM network with the minimum loss function and the highest accuracy of the output feature set are stored to obtain a BP-LSTM prediction model.
As a preferable mode, the step E includes:
e1, preprocessing the actual measurement input vector, inputting the actual measurement input vector into a BP network in a BP-LSTM prediction model, and obtaining the output of the BP network;
e2, preprocessing the output of the BP network, inputting the preprocessed output into an LSTM network in a BP-LSTM prediction model, and obtaining the output of the LSTM network;
and E3, weighting the output of the BP network obtained in the step E1 and the output of the LSTM network obtained in the step E2 to obtain a temperature field and temperature effect prediction result.
Preferably, the preprocessing method comprises a Z-score data standardization processing method.
As a preferred mode, the output layer of the BP network uses an identity function as an activation function, and the hidden layer of the BP network uses a linear rectification function as an activation function.
As a preferred mode, the BP network employs a mean square error function as a loss function.
Preferably, the LSTM network uses a mean square error function incorporating a temporal weighting factor as a loss function.
Compared with the prior art, the invention has the following beneficial effects:
(1) the method realizes the nonlinear mapping from the structural characteristics, the time characteristics and the environmental characteristics to the structural temperature field and the temperature effect by utilizing the high dimensionality, nonlinearity and adaptivity of a deep learning algorithm from the angle of data driving, establishes a BP-LSTM-based prediction model of the temperature field and the temperature effect of the steel-concrete composite bridge deck system, takes the three-dimensional coordinates, the time sequence and the environmental temperature of each position of an actual structure as driving factors, and takes the structural temperature field and the temperature effect as responses to simulate the time-space change process of the structural temperature field and the temperature effect.
(2) The advantages of BP network nonlinear mapping and the advantages of the LSTM network overcoming long-term dependence are combined, a new method is provided for predicting the structure temperature field and the temperature effect, the built model is high in reconstruction and generalization capability, and the prediction result is accurate.
(3) The method solves the problems of higher time and economic cost brought by the traditional theoretical calculation, the finite element method and the field actual measurement, and has great application significance in the fields of structural calculation and health monitoring.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a diagram of a BP network structure according to an embodiment of the present invention.
Fig. 3 is a diagram of an LSTM network architecture according to an embodiment of the present invention.
Fig. 4 is a diagram of a BP-LSTM network architecture according to an embodiment of the present invention. Fig. 4(a) shows the structure of the BP-LSTM hybrid model in the training mode, and fig. 4(b) shows the structure of the BP-LSTM hybrid model in the prediction mode.
FIG. 5 is a diagram of training results according to an embodiment of the present invention. Fig. 5(a) is a scatter diagram of the temperature reconstruction value and the temperature target value, fig. 5(b) is a scatter diagram of the temperature effect reconstruction value and the temperature effect target value, fig. 5(c) is a comparison diagram of the temperature predicted value and the target value of the top 2349# node of the concrete, and fig. 5(d) is a comparison diagram of the temperature effect predicted value and the target value of the top 2349# node of the concrete.
FIG. 6 is a diagram of predicted results according to an embodiment of the present invention. Fig. 6(a) is a diagram showing a comparison between predicted values and actual values of the temperature effect of the top plate node, fig. 6(b) is a diagram showing a comparison between predicted values and actual values of the temperature effect of the bottom plate node, and fig. 6(c) is a diagram showing a comparison between predicted values and actual values of the temperature effect of the steel beam node.
FIG. 7 is a graph of accuracy comparisons of training the same dataset using BP network, LSTM network, and BP-LSTM fusion models, respectively. Fig. 7(a) is a temperature prediction comparison map of a partial time period at a certain node, and fig. 7(b) is a temperature stress prediction comparison map of a partial time period at a certain node.
Detailed Description
The invention is described in further detail below with reference to the following figures and embodiments:
the invention takes a steel-concrete combined bridge deck system as a research object.
As shown in figure 1, the BP-LSTM-based prediction method for the temperature field and the temperature effect of the steel-concrete combined bridge deck system comprises the following steps:
step one, performing thermal coupling calculation by compiling a Python program and combining a finite element method, and generating structural input characteristics and output characteristics in batches, wherein the structural input characteristics and the output characteristics form a data set for model training, and the structure of the training data set is shown as a formula (1).
The S is a node type and is divided into four types, namely an outer surface node (I), an inner node (II), a side steel beam node (III) and a middle steel beam node (IV); n is a node number; cx, Cz and Cy are components of the node coordinates in the x, z and y directions respectively; d is the distance between the node and each outer surface; i, judging whether the current node is in contact with a part formed by other materials, if so, taking-1, otherwise, taking-0; d is the number of days; t is a time sequence; t is the ambient temperature; t is t ni Is the temperature value of the node i at the time n; sigma ni For node i inThe temperature effect value at time n.
The input features comprise the coordinates of the positions of the structure and the spatial position relation of the structure and the key features of the change of the external environment temperature along with the time. In the traditional heat transfer science calculation, the heat flux density of each surface of the structure can be calculated according to the geography latitude and longitude, the coordinates of each position of the structure and the time information, further, the space temperature field calculation can be carried out according to the thermodynamic parameters of the material and the geometric information of the structure, namely, the structure temperature field can be calculated according to the structure characteristics, the time characteristics and the environmental characteristics through an explicit algorithm, and further, the structure temperature effect is calculated. However, considering that the conventional calculation method is large in calculation time consumption for the problem of the large geometric scale and time scale of the embodiment, the mapping relationship from the input features to the output features is considered to be simulated by using an efficient form of a neural network (since the embodiment is only directed at a single-seat bridge structure, the geographic latitude and longitude difference at each position of the single-seat bridge structure is negligible, the structural features are not considered).
Finite element calculations should cover typical time periods throughout the year, including high and low temperature times, and the time span should not be too short to make the resulting data set representative. In this embodiment, the finite element thermal coupling analysis is performed on 10 days each in 12 months in the whole year in 2012, and a data set is generated according to the result.
This step also includes the construction of temperature and temperature effect data sets. The temperature and the temperature effect can be calculated by adopting any finite element calculation software or self-programming, and the parameter calculation is realized by adopting Python and large universal finite element software Abaqus in the embodiment of the invention. Table 1 shows the partial data sets constructed in this example.
TABLE 1 nodal temperature and temperature Effect data set (partial data)
And step two, fusing the LSTM and the BP network of the deep learning method to establish a BP-LSTM fusion model. The model structure is shown in fig. 2, 3 and 4. Creation of import step oneThe BP-LSTM fusion model is trained. In FIG. 4, w B And w L Voting weight factors of the BP network and the LSTM network are respectively.
The method comprises the steps of constructing a neural network based on an open source deep learning frame Pythrch, establishing a data set read in the first step of the fusion network for training by utilizing the advantages of an LSTM network in a time sequence problem and combining with the strong fitting capacity of a BP network, realizing the output of two types of multidimensional vectors of temperature and temperature effect by inputting a matrix formed by structural features, time features and environmental features, realizing weighted voting on the BP network and the LSTM network by different weight factors respectively, and finally obtaining the output of a fusion model.
The BP network includes forward propagation of signals and back propagation of errors, as detailed below:
(1) for the input training samples, the weights ω and the offsets b are initialized.
(2) For each training sample x, a corresponding activation value a is set x,1 And executing:
forward propagation: for each L2, 3 x,l ＝ω l a x,l-1 +b l And a x,l ＝σ(z x,l )。
Output error delta x,L : computing vectors
Back propagation error:
for each L ═ L-1, L-2,.., 2, δ is calculated x,l ＝((ω l+1 ) T δ x,l+1 )⊙σ'(z x,l )。
(3) The gradient is decreased and the weights and biases are updated according to different optimization methods for each L-1, L-2.
In the formula, a x,l Value of activation function representing the l-th layer to which input value x corresponds, z x,l Representing weighted input, ω, of the l-th layer to which input value x corresponds l Represents the weight of the l-th layer, b l Represents the bias of the l-th layer, σ (x) being the activation function, δ x,L Representing input valuesx corresponds to the output error vector of the L-th layer,
partial derivative of each neuron activation function value of layer L corresponding to x for loss function C
The constructed vector.
The LSTM network algorithm is as follows:
(1) inputting a set of training samples, initializing weights omega, bias b and cell state C t 。
(2) The respective coefficients are calculated by each part of the LSTM network:
forget gate calculation memory attenuation coefficient f t ＝σ(ω f ·[h t-1 ,x t ]+b f )；
Input gate calculates current learning and memory attenuation coefficient i t ＝σ(ω i ·[h t-1 ,x t ]+b i ) Current memory of
And current cell status
The output gate calculates the attenuation coefficient o at the current moment t ＝σ(ω o ·[h t-1 ,x t ]+b o ) Output h t ＝o t *tanh(C t )。
(3) To output h t And inputting x at the next time t+1 And (3) repeating the process in the step (2) until the loss function value is lower than the expected value or the maximum iteration number is reached.
In the above algorithm, ω f 、ω t 、ω i 、ω o Weights of the forgetting gate, the input gate, the current memory gate and the output gate, respectively, b f 、b t 、b i 、b o Offsets of the forgetting gate, the input gate, the current memory gate and the output gate, x t As an input vector at the current time t, C t 、h t Are respectively at tThe network element of the moment outputs a vector.
In the training mode, respectively inputting a training data set to a BP network and an LSTM network, and importing initial parameters of the network with the best training effect into a prediction model; in the prediction mode, data are input into a BP network part after being preprocessed, calculation results of the BP network are input into an LSTM network after being preprocessed again, and finally weighting voting is carried out on BP output in the LSTM network to obtain a final prediction result.
This step also includes a data preprocessing method. Data normalization: the data set comprises a plurality of characteristics with different dimensions, such as node coordinates, environment temperature, day sequence, time sequence, stress and the like, and is standardized in order to avoid the occurrence of singular sample data, which causes overlong training time, gradient explosion or network convergence failure. Data normalization was performed using the Z-score method:
wherein, a i Is a normalized value, x i For individual observations, μ is the overall data mean and σ is the overall standard deviation.
The normalized data was replicated to generate a total of two identical samples, randomized to 70%: 15%: the proportion of 15 percent is divided into a training set, a verification set and a test set which are respectively used for training the BP network and the LSTM network.
The step also comprises setting an activation function and a loss function of the BP-LSTM model.
The activation function in the output layer adopts an identity function, the activation function of the hidden layer adopts a linear rectification function (ReLU), and the initial value of the linear rectification function uses a standard deviation of n when the number of nodes in the previous layer is n
A gaussian distribution of (a).
The loss function represents an "severity" indicator of network model performance, i.e., the degree of under-fit to the target data. For BP networks, the most common mean square error function (MSE) is chosen here as the loss function:
in the formula, C is a loss function, ω and b respectively represent a set of all weights and offsets in the network, n is the number of training data, σ (x) represents a network output value when input data is x, and T represents a vector composed of corresponding supervision data when input data is σ (x).
For the LSTM network, considering that the network input is a padded sequence of equal length, and the actual effective lengths of the sequences are different, it is obvious that here, weights are set for the sequences of different lengths, so as to avoid unreasonable adjustment of the network due to too small data size when inputting a short sequence. Here, a temporal weighting factor is introduced based on MSE, with the improved MSE as a loss function:
in the formula, the time weighting factor Δ t is tan (el) seq /l)，l seq And the effective length of the current training batch sequence is l, the total training data length is l, and e is a natural logarithm.
And step two, setting the hyper-parameters of the BP-LSTM model. Random deletion nodes (Dropout), small batches (Mini-Batch), Batch-Normalization (Batch-Normalization), and Early-Stopping techniques (Early-Stopping) are introduced in the training phase to achieve the optimized result of accuracy and overfitting rejection. An adaptive momentum estimation method (Adam) provided by KINGMA D in 2014 is adopted as an optimization method, a decision coefficient is used as a network output precision evaluation index, the two models are fused by adopting a weighted average method, and after multiple times of training, the network initial parameters with the minimum loss function value and the highest precision are stored to generate a BP-LSTM fusion model. The hyper-parameters are set as: learning rate lr being 0.001, Adam method primary momentum coefficient β 1 0.9, coefficient of second order momentum β 2 0.999, Batch size (Batch-size) 500, Dropout method neuron deletion ratio dr 0.25, BPThe network output weight w1 is 0.64, and the LSTM network output weight w2 is 0.36.
And step three, extracting a BP-LSTM model training result, and reserving initial parameters of the model with the highest precision to realize prediction of the temperature field and the temperature effect of the steel-concrete combined bridge deck system.
Using a determining coefficient R 2 Evaluating the training effect of the fusion model, and establishing the relation between the model predicted value y and the target value T in a linear regression mode:
in the formula, a and b are regression coefficients, SSR is regression square sum, and SST is total square sum.
The scatter plot of predicted values (reconstructed values) versus target values is shown in fig. 5, the regression coefficients a, b and the decision coefficients are shown in fig. 5, and the decision coefficients for both temperature and temperature effects exceed 0.92, indicating the higher reconstruction and generalization capability of the model.
And inputting feature data which does not participate in training for prediction by using the established BP-LSTM model. In this embodiment, the temperature field and the temperature effect of the steel-concrete composite bridge deck system in 2013, 1 month and 10 months without participating in the BP-LSTM model training are predicted, and the result is shown in fig. 6 (only the predicted values and the actual values of the temperature and the temperature effect in the odd month part of the concrete top plate, the concrete bottom plate and the steel beam part node are given in space). As can be seen from FIG. 6, the prediction result of the method is ideal, the difference between the structure temperature and the temperature effect and the actual measurement is not large, the trend that the structure temperature and the temperature effect change along with the temperature of the external environment in four seasons can be well reflected in each month, and the method has good performance.
In order to verify the superiority of the method, the same data set is trained by adopting the BP network and the LSTM network respectively, and the precision pair of the BP network and the LSTM network and the training result of the BP-LSTM fusion model is shown in the graph 7 and the table 2 (limited to space, only the prediction result of the node No. 3 in a part of the time period is given). It can be seen that the single BP network and single LSTM network predictions are not very different in time from the BP-LSTM network, but it is difficult to implement the embodimentAccurate prediction of temperature field and temperature effect of steel-concrete combined bridge deck system, single BP network and single LSTM network prediction determination coefficient R 2 Compared with BP-SLTM, the maximum reduction is 0.126, and the minimum reduction is 0.079. Therefore, compared with a single model, the fusion model provided by the invention has more excellent accuracy on the premise of not much different calculation time.
TABLE 2 BP, LSTM, BP-LSTM network prediction accuracy vs. elapsed time
In the table, a and b are regression coefficients, R 2 To determine the coefficients
The structure space temperature field and the temperature effect are calculated through thermal coupling by a traditional finite element method, the time lengths are respectively predicted to be 1 day, 10 days, 20 days and 30 days, the calculation result is output according to the frequency per hour, and the calculation time of the calculation result is compared with the calculation time of the BP-LSTM model on the same calculation platform, which is provided by the invention, and the calculation time is shown in a table 3. As can be seen from table 3, although the time consumed for constructing and expanding the data set is long, the time consumed for other steps is very small, and the time can be changed with the input data in the process of realizing the prediction, the traditional finite element method can be used for carrying out the thermal coupling calculation, although the prediction of the temperature field and the temperature effect of the structural space can be realized in the same way, the calculation time is unacceptable under the condition that the result is output only once per hour, the calculation time is exponentially increased when the input frequency is higher, the time required for predicting 30 days is up to 23 hours, and the long-time prediction is usually carried out according to the frequency of every 15 minutes or every 30 minutes in the actual structural health monitoring, so the cost is difficult to bear by adopting the finite element method, and the method has no actual feasibility. By adopting the BP-LSTM model, under the condition that the time consumption of data set construction and model training in the early stage is not considered, the time required for prediction is not more than 20s, the calculation efficiency is greatly improved, the calculation time consumption during output at higher frequency is far less than that of a finite element method, and the real-time prediction of the temperature field and the temperature effect of the steel-concrete combined bridge deck system can be considered to be realized.
TABLE 3 comparison of the computational efficiency of the conventional finite element method and the method of the present invention
The tests prove that the prediction result of the fusion model has certain difference with the actual result, but the prediction result has higher precision and stronger generalization capability, has more excellent performance compared with a single BP or LSTM network, has extremely high efficiency in second of calculation time on a common household calculation platform, and can realize the real-time prediction of the structure temperature field and the temperature effect.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (8)
1. A BP-LSTM-based prediction method for a temperature field and a temperature effect of a steel-concrete combined bridge deck system is characterized by comprising the following steps:
a, acquiring a training data set for predicting a temperature field and a temperature effect of a steel-concrete combined bridge deck system, wherein the training data set comprises an input feature set and an output feature set, the input feature set comprises a structural feature, a time feature and an environmental feature, and the output feature set comprises the temperature and the temperature effect;
b, training the BP network by using the training data set in the step A, and training the LSTM network by using the training data set in the step A;
step C, fusing the BP network and the LSTM network obtained after training in the step B to obtain a BP-LSTM prediction model;
step D, acquiring an actual measurement input vector corresponding to the input feature set in the step A;
and E, preprocessing the actually measured input vector and inputting the preprocessed actually measured input vector into the BP-LSTM prediction model to obtain a temperature field and temperature effect prediction result.
2. The BP-LSTM based steel and concrete composite bridge deck system temperature field and temperature effect prediction method according to claim 1, wherein in the step A, a training data set is obtained based on measured data and a finite element method.
3. The method for predicting the temperature field and the temperature effect of the steel-concrete combined bridge floor system based on the BP-LSTM according to claim 1, wherein in the step C, a weighted average method is adopted to fuse the BP network and the LSTM network, and after multiple training, initial network parameters corresponding to the BP network and the LSTM network with the minimum loss function and the highest output feature set precision are stored to obtain a BP-LSTM prediction model.
4. The BP-LSTM based steel and concrete composite bridge deck temperature field and temperature effect prediction method of claim 1, wherein the step E comprises:
e1, preprocessing the actual measurement input vector, inputting the actual measurement input vector into a BP network in a BP-LSTM prediction model, and obtaining the output of the BP network;
e2, preprocessing the output of the BP network, inputting the preprocessed output into an LSTM network in a BP-LSTM prediction model, and obtaining the output of the LSTM network;
and E3, weighting the output of the BP network obtained in the step E1 and the output of the LSTM network obtained in the step E2 to obtain a temperature field and temperature effect prediction result.
5. The BP-LSTM based steel-concrete composite bridge deck system temperature field and temperature effect prediction method according to claim 4, wherein the pre-processing method comprises a Z-score data standardization processing method.
6. The BP-LSTM-based steel-concrete composite bridge deck system temperature field and temperature effect prediction method according to claim 1, wherein an output layer of the BP network adopts an identity function as an activation function, and an implicit layer of the BP network adopts a linear rectification function as an activation function.
7. The BP-LSTM based steel and concrete composite bridge deck system temperature field and temperature effect prediction method of claim 1, wherein the BP network employs a mean square error function as a loss function.
8. The method for predicting the temperature field and temperature effect of the steel-concrete composite bridge deck system based on the BP-LSTM according to claim 1, wherein the LSTM network adopts a mean square error function with an introduced time weight factor as a loss function.
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