CN114254416A - Soil stress-strain relation determination method based on long-term and short-term memory deep learning - Google Patents
Soil stress-strain relation determination method based on long-term and short-term memory deep learning Download PDFInfo
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Abstract
The invention discloses a soil stress-strain relation determining method based on long-term and short-term memory deep learning, which comprises the following steps of: preparing soil body samples with different physical and mechanical parameters, acquiring strain data of the different soil body samples under a specified stress loading step, establishing an original data set of stress strain, and performing normalization processing to obtain a normalized data set; establishing a four-layer LSTM deep learning network; determining an initial weight matrix and a vector of the LSTM deep learning network; inputting the training set into an LSTM deep learning network, updating a weight matrix by using a modified A dam momentum gradient descent algorithm, and determining a cost function value J; and repeating the iteration until the cost function J of the LSTM deep learning network is smaller than a preset value x or reaches a preset iteration training time Iter. By adopting the method, the stress-strain relationship of different soil bodies under different confining pressure conditions can be rapidly and accurately predicted, and the method has important significance for guiding actual engineering. The method is simple, practical, convenient to popularize and high in application value.
Description
Technical Field
The invention relates to the field of soil constitutive relation, in particular to a soil stress-strain relation determination method based on long-term and short-term memory deep learning.
Background
The soil body is a carrier of geotechnical infrastructure, determines the nonlinear mechanical response of the soil body under the load condition, and has important significance for the design and construction of the infrastructure. Due to the complex internal structure and various components of the soil body, the soil body has complex nonlinear deformation characteristics under the action of external load. The mathematical model for determining the nonlinear mechanical behavior of the soil body and describing the nonlinear mechanical behavior of the soil body at present is called a constitutive model. According to different research methods, the soil constitutive model can be divided into a traditional theoretical model and a neural network constitutive model. The traditional constitutive model generally regards soil as a continuous medium, approximately describes the nonlinear stress-strain relationship of the soil based on various idealized assumptions, and deviates from the actual stress-strain behavior of the soil more or less; under specific conditions, specific stress-strain behaviors of a certain soil body can be well described, for example, a modified Cambridge model can describe shear expansion of sand, but cannot describe creep characteristics of clay; in order to enable the model to describe more soil nonlinear characteristics, the advanced constitutive model increases characteristic parameters of the model, and the characteristic parameters have no clear physical significance, so that the difficulty of parameter calibration is caused, the problem of parameter optimization is caused, and the problem of geotechnical engineering is better solved. The neural network method is a data driving method, the nonlinear stress-strain characteristic of the soil body is directly extracted from the stress-strain data of the soil body, and the method is simple, strong in universality and easy to popularize.
The search of documents in the prior art finds that the existing neural network method for researching the soil constitutive model mainly comprises a feedforward neural network, a feedback neural network and an embedded neural network. The stress-strain characteristic of the sandy soil is learned by adopting a feed-forward type neural network method in a text of 'elastic-plastic constitutive model research of a neural network of sandy soil under different stress paths' published by 'rock-soil mechanics' in 2004; in the article of 'simulation of sandstone mechanical characteristics under dry-wet cycle action and neural network of constitutive model' published in 'rock-soil mechanics' in 2013, the Li Ke steel describes stress-strain relationship of sandstone by adopting a feedforward neural network; hasharah is equal to the stress-strain characteristic of the Soil body in the shear test in the text of A New Triaxial application Impulse non-deformation Shearing for Deep Learning of Soil Behavior published in Geotechnical Testing Journal in 2019, and an embedded neural network is adopted to research the stress-strain characteristic of the Soil body in the shear test. However, the time-related characteristics of the soil stress-strain behavior are not considered in the methods, and the influence of the historical stress-strain on the current stress-strain cannot be described, so that the result has larger deviation. At present, no neural network stress-strain determination method capable of considering the long-term time characteristic of stress-strain exists.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a soil stress-strain relationship determination method based on long-short term memory deep learning, which overcomes the defects that a theoretical model adopts various assumptions, the universality is poor and the high-level model parameter calibration is difficult, overcomes the defect that the traditional neural network method does not consider the time-related characteristics of the soil stress-strain behavior, and adopts the long-short term memory LSTM deep learning technology to extract and determine the nonlinear relationship between stress and strain from experimental data.
In order to solve the technical problem, the invention provides a soil stress-strain relationship determination method based on long-term and short-term memory deep learning, which comprises the following steps:
s1: preparing soil body samples with different physical mechanical parameters, wherein the physical mechanical parameters comprise compression index lambda, rebound index kappa, porosity e and strength parameter M of the soil body.
Preferably, the soil sample is a cylindrical soil test sample with the height-diameter ratio of 2-2.5.
S2: and using a triaxial compression test to obtain strain data of different soil body samples under a specified stress loading step, and establishing an original data set of stress strain.
Preferably, theThree-axis compression experimentMeans that: a triaxial compression instrument is adopted, and under the action of the pressure around a given triaxial pressure chamber, the axial additional pressure is continuously increased until the sample is sheared and damaged.
Preferably, the original data set is a set of original stress-strain data samples under all loading conditions, and is divided into a training set and a testing set;
preferably, the original stress-strain data sample is sequence data with a time length of t, which is composed of soil body parameters, stress and strain corresponding to t continuous stress loading steps, and the data in a single time step is divided into input data and label data.
Preferably, the training set refers to: and selecting a certain proportion of stress-strain data samples in the stress-strain data set.
Preferably, the test set refers to: stress-strain data samples in the stress-strain data set other than the training set.
More preferably, the input data refers to: physical and mechanical parameters and stress of the soil body sample;
more preferably, the tag data is: strain of soil mass sample.
S3: and carrying out normalization processing on the original data set to obtain a normalized data set.
Preferably, the normalization processing means: carrying out non-dimensionalization on the stress-strain data samples, dividing the physical mechanical parameters, stress and strain of all the stress-strain data samples by the product of the maximum value of the respective absolute value and the scaling factor A, and mapping all the data to a (0, 1) range, wherein the normalization formula is as shown in the formula (1);
wherein x is a physical mechanical parameter, stress and strain, xnormThe normalized physical mechanical parameters, stress and strain are obtained;
more preferably, the value of the scaling factor A is between 1 and 2.
Preferably, the normalized data set refers to: carrying out normalization processing on the original data set to obtain a data set;
s4: establishing a four-layer LSTM deep learning network by using Octave, and determining the number N of nodes of a hidden layerhActivating a function and a cost function J, and determining an initial weight matrix and a vector;
preferably, the Octave refers to: an open source data processing software;
preferably, the four-layer LSTM deep learning model is: the deep learning model is composed of an input layer, an LSTM unit hidden layer, a full-connection hidden layer and an output layer, and the weights of adjacent time steps are always the same by utilizing the function of learning or forgetting historical information of the LSTM unit in the time dimension;
preferably, the number of hidden layer nodes NhThe method comprises the following steps: number of nodes, N, in LSTM cell hidden layer and fully-connected hidden layerhSatisfies formula (2):
Nh＝a×Nc+b×Nv (2)
wherein N iscThe number of constant variables, N, that do not change with time in the input data, which are stress-strain data samplesvThe number of variable variables which change along with time in input data of a stress-strain data sample is a constant variable coefficient which is generally 2, and b is a variable coefficient which is generally 5;
preferably, the activation function is: nonlinear mapping functions in LSTM deep learning network nodes are generally sigmoid functions and hyperbolic tangent functions;
preferably, the cost function J refers to: the function for measuring the difference between the output data of the output layer of the LSTM deep learning network and the label data of the data sample is generally a root mean square error cost function, and meets the formula (3):
where n is the number of data samples and m is the stress strain per data sampleNumber of data pairs, yo kiOutput data for the LSTM model at the ith time step of the kth data sample, ykiIs the label data of the ith time step of the kth data sample, wherein lambda is L2 regular coefficient, and wjIs the jth weight in the model, NwIs the weight number of the LSTM model, alpha is the scaling factor, when log | ykiI < 0, α ═ 1, when log | yki|＞0，α＝0.1。
More preferably, the input layer refers to: inputting data samples into a data layer of the LSTM deep learning model, wherein the number of nodes of the input layer is equal to the number of variables of input data, and the input data of the input layer is directly used as output data of the layer and is input into an LSTM unit hidden layer;
more preferably, the LSTM unit hiding layer refers to: a data layer consisting of LSTM unit nodes, the number of nodes of the hidden layer is NhThe input data is the output data of the input layer, and the output data is input to the full-connection hidden layer;
more preferably, the fully-connected hidden layer refers to: a data layer consisting of fully connected node units, the number of nodes of the hidden layer being NhThe input data is the output data of the LSTM unit hiding layer, and the output data is input to the output layer;
more preferably, the output layer refers to: the data layer is composed of output unit nodes, the number of the output layer nodes is 1, the input of the output layer nodes is output data of a full-connection hidden layer, and the output data is output data of an LSTM model.
More preferably, the LSTM unit node refers to: the method comprises the steps that unit nodes connected in a time dimension exist, and LSTM unit output data of the next time step are calculated by utilizing input data of the previous time step and output data of the LSTM unit of the previous time step;
more preferably, the fully-connected node unit refers to: a node unit conforming to a fully connected nonlinear mapping relationship;
more preferably, the output layer node means: the node unit accords with the nonlinear mapping relation of the output layer, and the output data of the node unit of the output layer is output;
s5: and determining an initial weight matrix and a vector of the LSTM deep learning network.
Preferably, the initial weight matrix and the vector refer to: the initial weight matrix and vector of the preset LSTM model satisfy the formula (4):
wherein U is uniformly distributed, Wl，Rl，blIs the weight matrix and offset vector of the l-th layer, NlThe number of nodes of the L-th layer of data layer of the LSTM model is shown, and L is the layer number of the recurrent neural network. .
S6: inputting the training set into an LSTM deep learning network, updating a weight matrix by using a modified Adam momentum gradient descent algorithm, and determining a cost function value J; .
Preferably, the calculation process of the modified Adam momentum gradient descent algorithm is as follows:
a) and (3) specifying optimization parameters: momentum exponential decay parameter beta1And beta2Defaults to 0.9 and 0.999, and a coefficient ε is 10－8Designating a step length alpha, initializing a first order momentum m0Second order momentum v0The sum time step t is 0, the weight parameter of the previous iteration step is thetat－1；
b) Calculating weight parameter gradient gt，
c) Calculating the first order momentum mt，mt＝β1mt-1+(1-β1)gt；
d) Calculating a second order momentum vt，vt＝β2vt-1+(1-β2)gt 2；
e) Calculating a first order momentum correction term
f) Calculating a second order momentum correction term
g) Calculating updated weight parameter thetat，
Wherein, the thetat－1The weight matrix and the vector referring to the last iteration step of the LSTM model, thetatRefers to the updated weight matrix and vector.
S7: and repeating the iteration S6 until the cost function J of the LSTM deep learning network is smaller than the preset value χ or reaches the preset iteration training times Iter.
The invention has the following beneficial effects: the invention adopts long-short term memory LSTM deep learning technology, extracts and determines the nonlinear relation of stress and strain from experimental data, and can consider the time-dependent characteristic of the stress-strain behavior of the soil body. The method is simple, practical, convenient to popularize and high in application value.
Drawings
FIG. 1 is a three-dimensional structure diagram of an LSTM deep learning network according to an embodiment of the present invention;
FIG. 2 is a flow chart of soil stress-strain relationship determination based on the LSTM deep learning method according to an embodiment of the present invention;
fig. 3 is a soil stress-strain relationship determined based on the LSTM deep learning method according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings.
The stress-strain behavior of a certain soil body under different confining pressure conditions conforms to the modified cambridge model.
As shown in fig. 1 to fig. 3, the present embodiment provides a method for determining a soil stress-strain relationship based on long-term and short-term memory deep learning, where the method is implemented by the following steps:
step one, preparing soil body samples with different physical and mechanical parameters.
In this embodiment, a numerical test method is adopted to establish 29 numerical soil samples, and the value ranges of the physical and mechanical parameters are as follows: the compression index lambda of the soil body is respectively 0.06, 0.09, 0.1, 0.12 and 0.15; a rebound index kappa of 0.1 lambda, a porosity e of 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8; the intensity parameter M is 1;
and step two, acquiring strain data of different soil body samples under a series of specified stress loading steps by utilizing a triaxial compression test, and establishing an original data set of stress strain.
In the embodiment, a triaxial compression test is utilized to apply 30-60 strain loading steps to 29 soil samples under 127 different confining pressures within the pressure range of 10-900 kPa, and the strain epsilon is different in different axesaGenerating 127 stress-strain data samples with different time lengths (30-60 time steps) according to the corresponding partial stress q, and forming an original data set, wherein the training set comprises 100 stress-strain data samples, the testing set comprises 27 stress-strain data sets, the input data of the samples are 4 variables, namely an initial porosity ratio e, a compression index lambda and a confining pressure sigma respectively3And axial strain εaThe label data is bias stress q;
and step three, carrying out normalization processing on the original data set to obtain a normalized data set.
In this embodiment, the normalization process satisfies formula (1), and all data are mapped to the range of (0, 1) to obtain a normalized data set;
step four, establishing a four-layer LSTM deep learning network based on Octave, and determining the number N of nodes of a hidden layerhAn activation function and a cost function J.
In the embodiment, Octave open-source software is adopted to construct four layers of LSTM deep learning networks, namely an input layer, an LSTM unit hidden layer, a full-connection hidden layer and an output layer; number of hidden layer nodes NhCalculated according to the formula (2), the number of the cells is 11:
Nh＝a×Nc+b×Nv＝2×3+5×1＝11 (2)
in this embodiment, the activation function is a sigmoid function and a hyperbolic tangent function;
in this embodiment, the cost function J adopts a root mean square error cost function, and satisfies formula (3):
in this embodiment, the number of nodes of the input layer is equal to the variable number of input data, and is 4 nodes, and the input data of the input layer is directly input to the LSTM unit hidden layer as the output data of the layer;
in this embodiment, the number of nodes of the LSTM unit hidden layer is 11, the input data thereof is the output data of the input layer, and the output data thereof is input to the full-connection hidden layer;
in this embodiment, the number of nodes of the fully-connected hidden layer is 11, the input data of the fully-connected hidden layer is the output data of the LSTM unit hidden layer, and the output data of the fully-connected hidden layer is input to the output layer;
in this embodiment, the number of the output layer nodes is 1, the input of the output layer nodes is output data of a fully connected hidden layer, and the output data is output data of an LSTM model, that is, predicted bias stress.
In this embodiment, the LSTM unit node is a unit node having a connection in a time dimension, and calculates LSTM unit output data of a next time step by using input data of a previous time step and output data of an LSTM unit of the previous time step;
and step five, determining an initial weight matrix and a vector of the LSTM deep learning network.
In this embodiment, the initial weight matrix and the vector satisfy formula (4):
and step six, inputting the training set into an LSTM deep learning network, updating the weight matrix by using a modified Adam momentum gradient descent algorithm, and determining a cost function value J.
In this embodiment, the calculation process of the modified Adam momentum gradient descent algorithm is as follows:
a) and (3) specifying optimization parameters: momentum exponential decay parameter beta1And beta2Defaults to 0.9 and 0.999, and a coefficient ε is 10－8Designating a step length alpha, initializing a first order momentum m0Second order momentum v0The sum time step t is 0, the weight parameter of the previous iteration step is thetat－1；
b) Calculating weight parameter gradient gt，
c) Calculating the first order momentum mt，mt＝β1mt-1+(1-β1)gt；
d) Calculating a second order momentum vt，vt＝β2vt-1+(1-β2)gt 2；
e) Calculating a first order momentum correction term
f) Calculating a second order momentum correction term
g) Calculating updated weight parameter thetat，
Wherein, the thetat－1The weight matrix and the vector referring to the last iteration step of the LSTM model, thetatRefers to the updated weight matrix and vector.
And step seven, repeating the iteration of the sixth step until the LSTM deep learning model reaches 3000 times of preset iterative training.
In this example, 27 sets of stress-strain data samples were determined using a trained LSTM deep learning network, and the results are shown in fig. 3. The mean square error of the LSTM deep learning network in the training set is only 0.0064, and the mean square relative error is only 0.074; the mean square error in the test set was only 0.0045 and the relative mean square error was only 0.058.
The method for determining the soil stress-strain relationship of the long-term and short-term memory deep learning can quickly and accurately predict the stress-strain relationship of different soil bodies under different confining pressure conditions, and has important significance for guiding actual engineering. The method is simple, practical, convenient to popularize and high in application value.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.
Claims (9)
1. A soil stress-strain relation determining method based on long-term and short-term memory deep learning is characterized by comprising the following steps:
s1: preparing soil body samples with different physical and mechanical parameters;
s2: using a triaxial compression test to obtain strain data of different soil body samples under a specified stress loading step, and establishing an original data set of stress strain;
s3: carrying out normalization processing on the original data set to obtain a normalized data set;
s4: establishing a four-layer LSTM deep learning network by using Octave, and determining the number N of nodes of a hidden layerhActivating a function and a cost function J, and determining an initial weight matrix and a vector;
s5: determining an initial weight matrix and a vector of the LSTM deep learning network;
s6: inputting the training set into an LSTM deep learning network, updating a weight matrix by using a modified Adam momentum gradient descent algorithm, and determining a cost function value J;
s7: and repeating the iteration S6 until the cost function J of the LSTM deep learning network is smaller than the preset value χ or reaches the preset iteration training times Iter.
2. The method for determining soil stress-strain relationship based on long-short term memory deep learning of claim 1, wherein in step S1, the physical and mechanical parameters include compression index λ, rebound index κ, porosity e, and strength parameter M of the soil; the soil body sample is a cylindrical soil body test sample with the ratio of height to diameter of 2-2.5.
3. The method for determining soil stress-strain relationship based on long-short term memory deep learning of claim 1, wherein in step S2, the original data set is a set of original stress-strain data samples under all loading conditions, and is divided into a training set and a testing set; the original stress-strain data sample consists of soil body parameters, stress and strain corresponding to t continuous stress loading steps.
4. The soil stress-strain relationship determination method based on long-short term memory deep learning of claim 1, wherein the four-layer LSTM deep learning network is a deep learning model composed of an input layer, an LSTM unit hidden layer, a full-connection hidden layer and an output layer.
5. The soil stress-strain relationship determination method based on long-short term memory deep learning as claimed in claim 4,wherein the number of hidden layer nodes NhFor the number of nodes, N, in the LSTM unit hidden layer and the fully-connected hidden layerhSatisfies the formula:
Nh＝a×Nc+b×Nv
wherein N iscThe number of constant variables, N, that do not change with time in the input data, which are stress-strain data samplesvThe number of variable variables which change with time in the input data of the stress strain data sample is a, a is a constant variable coefficient, and b is a variable coefficient.
6. The method for determining soil stress-strain relationship based on long-short term memory deep learning of claim 5, wherein the activation function is a nonlinear mapping function in LSTM deep learning network nodes.
7. The method for determining soil stress-strain relationship based on long-short term memory deep learning of claim 6, wherein the cost function J is a function for measuring the difference between the output data of the output layer of the LSTM deep learning network and the label data of the data sample,
where n is the number of data samples, m is the number of stress-strain data pairs per data sample, yo kiOutput data for the LSTM model at the ith time step of the kth data sample, ykiThe label data of the ith time step of the kth data sample is L2 regular coefficient, wjIs the jth weight in the model, NwIs the weight number of the LSTM model, alpha is the scaling factor, when log | ykiI < 0, α ═ 1, when log | yki|＞0，α＝0.1。
8. The method for determining soil stress-strain relationship based on long-short term memory deep learning of claim 1, wherein the initial weight matrix and vector are initial weight matrix and vector of a predetermined LSTM model, and the method of initial weight matrix and vector satisfies a formula
Wherein U is uniformly distributed, Wl，Rl，blIs the weight matrix and offset vector of the l-th layer, NlThe number of nodes of the L-th layer of data layer of the LSTM model is shown, and L is the layer number of the recurrent neural network. .
9. The method for determining soil stress-strain relationship based on long-short term memory deep learning of claim 1, wherein the calculation process of the modified Adam momentum gradient descent algorithm is as follows:
a) and (3) specifying optimization parameters: momentum exponential decay parameter beta1And beta2Defaults to 0.9 and 0.999, and a coefficient ε is 10－8Designating a step length alpha, initializing a first order momentum m0Second order momentum v0The sum time step t is 0, the weight parameter of the previous iteration step is thetat－1；
b) Calculating weight parameter gradient gt，gt＝▽θft(θt-1)；
c) Calculating the first order momentum mt，mt＝β1mt-1+(1-β1)gt；
d) Calculating a second order momentum vt，vt＝β2vt-1+(1-β2)gt 2；
e) Calculating a first order momentum correction term
f) Calculating a second order momentum correction term
g) Calculating updated weight parameter thetat，
Wherein, the thetat－1The weight matrix and the vector referring to the last iteration step of the LSTM model, thetatRefers to the updated weight matrix and vector.
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