CN114611418A - Natural gas pipeline flow state prediction method - Google Patents

Natural gas pipeline flow state prediction method Download PDF

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CN114611418A
CN114611418A CN202111544230.0A CN202111544230A CN114611418A CN 114611418 A CN114611418 A CN 114611418A CN 202111544230 A CN202111544230 A CN 202111544230A CN 114611418 A CN114611418 A CN 114611418A
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石国赟
周园春
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Abstract

The invention discloses a natural gas pipeline flow state prediction method, which relates to the field of natural gas pipeline transportation. The method of the invention only needs one forward calculation. The flow state of the natural gas pipeline can be accurately predicted, and the calculated amount, the resource consumption and the prediction time are greatly reduced.

Description

Natural gas pipeline flow state prediction method
Technical Field
The invention relates to the field of natural gas pipeline transportation, and provides a method for predicting the natural gas flow state in a pipeline by combining a prediction model with physical information.
Background
At present, the flow state in the pipeline is obtained by a numerical simulation method on the basis of natural gas pipeline flow management, and the method needs one-step and one-step iterative solution and cannot directly obtain the flow state, so that the calculation amount is overlarge, the efficiency is low, and the method is difficult to be applied to increasing pipeline length and user requirements. In addition, if a general intelligent model is used to predict the pipeline flow, a large amount of on-site measured data or simulated data is required, which results in a limitation in practical application due to data acquisition.
Disclosure of Invention
The invention aims to provide a natural gas pipeline flow state prediction method, which is characterized in that a prediction model of a deep neural network is constructed, flow is simulated in a data driving mode, a flow differential equation is used as a loss function of model parameter optimization, the prediction model is optimized through learning, and the finally obtained intelligent prediction model is used for predicting the natural gas pipeline flow state.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a natural gas pipeline flow state prediction method comprises the following steps:
acquiring natural gas pipeline parameters: pipeline length, pipeline internal diameter and friction coefficient, and detect the natural gas fluid parameter in the pipeline: establishing a one-dimensional flow control equation of the natural gas pipe network according to the gas density, the gas velocity, the gas pressure and the gas temperature, wherein the one-dimensional flow control equation comprises a continuity equation, a momentum equation and a state equation;
selecting a pipeline length value, a gas velocity value, a gas pressure value and a gas density value of a boundary condition as characteristic quantities, introducing dimensionless quantities by using the characteristic quantities to express the pipeline length, the gas velocity, the gas pressure and the gas density, and carrying out dimensionless transformation on a continuous equation, a momentum equation and a state equation of the one-dimensional flow control equation;
constructing a prediction model of a full-connection deep neural network, wherein the full-connection deep neural network comprises an input layer, five hidden layers and an output layer, the input layer is a neuron representing the length of a pipeline, and the output layer is three neurons representing the gas speed, the gas pressure and the gas density; the activation function of the full-connection deep neural network adopts a hyperbolic tangent function;
constructing derivatives of output quantities to input quantities of a continuous equation, a momentum equation and a state equation which are non-dimensionalized to obtain three differential equations of the continuous equation, the momentum equation and the state equation, and constructing a model loss function for the three differential equations and the boundary conditions, wherein the model loss function is composed of weighting of a boundary condition loss function, a continuous equation loss function, a momentum equation loss function and a state equation loss function;
for the fully-connected deep neural network prediction model, an Adam optimization solver is adopted to pre-learn the boundary condition loss function, and the input quantity is any length value in the total pipeline length of the natural gas pipeline; and continuously learning by adopting an LBFGS optimization solver on the basis of the pre-learning to finally obtain an intelligent prediction model, and predicting the flow state of the natural gas pipeline by using the intelligent prediction model.
Preferably, the expression of the one-dimensional flow control equation is as follows:
the continuous equation:
Figure BDA0003415309790000021
the momentum equation:
Figure BDA0003415309790000022
the state equation is as follows:
p＝ρRgT；
wherein x is the length of the pipeline, ρ is the gas density, u is the gas velocity, p is the gas pressure, λ friction coefficient, D is the internal diameter of the pipeline, R is the gas velocitygGas constant, T is the gas temperature.
Preferably, the value of the length x of the pipe is chosen+Gas velocity value urGas pressure value prAnd gas density value ρrAs the characteristic quantity, a dimensionless quantity is set
Figure BDA0003415309790000023
The pipe length, gas velocity, gas pressure and gas density are then introduced into dimensionless quantities denoted x ═ x+X,u＝Uur,p＝Ppr,
Figure BDA0003415309790000024
Preferably, the expressions of the continuity equation, the momentum equation and the momentum equation of the non-dimensionalized one-dimensional flow control equation are:
Figure BDA0003415309790000025
Figure BDA0003415309790000026
Figure BDA0003415309790000027
preferably, the equation of state is derived
Figure BDA0003415309790000028
The expression of the dimensionless momentum equation is reduced to
Figure BDA0003415309790000029
Preferably, the number of neurons of 5 hidden layers is [100,200,300,200,100 ].
Preferably, the activation function employs a tanh function:
Figure BDA00034153097900000210
preferably, the expression of the output quantity of the deep neural network is as follows:
tanh(W5 tanh(W4 tanh(W3 tanh(W2 tanh(W1x+b1)+b2)+b3)+b4)+b5)；
where, tanh () is hyperbolic tangent function, and W, b are parameters.
Preferably, the derivatives of the output quantities to the input quantities are constructed for the non-dimensionalized continuous equations, momentum equations and state equations using automatic differentiation techniques provided by the open source deep learning framework; the three differential equation expressions of the continuous equation, the momentum equation and the state equation are obtained as follows:
Figure BDA0003415309790000031
Figure BDA0003415309790000032
Figure BDA0003415309790000033
preferably, the mean variance method is adopted to construct a model loss function, and the expression of the model loss function is MSE-wbMSEb+wcMSEc+wuMSEu+wpMSEp(ii) a Wherein w is a weight coefficient, MSEb、MSEc、MSEu、MSEpRespectively representing a boundary condition loss function, a continuous equation loss function, a momentum equation loss function and a state equation loss function;
the loss function for the mean variance of an arbitrary variable is expressed as
Figure BDA0003415309790000034
Wherein t ═ b, c, u, p, x ═ fc，fu，fpAnd boundary conditions of the deep neural network output; x is the number of0Is a target value for fc，fu，fp，x0Are all zero; for the boundary condition, x0Is a given value; and N is the training data volume.
The invention has the following beneficial effects:
compared with the traditional prediction method, the intelligent prediction model capable of predicting the flow state of the natural gas pipeline is obtained by solving the pipeline flow differential equation by using the deep learning model, and due to the introduced physical equation and the deep neural network, the dependence on actual measurement data is greatly reduced, the investment of measurement equipment is greatly reduced, and the management cost of natural gas management flow is reduced.
Drawings
Fig. 1 is a flow chart of a method for predicting a flow state of a natural gas pipeline according to an embodiment of the present invention.
Fig. 2 is a comparative graph of natural gas pipeline pressure distribution prediction using a conventional method and the method of the present invention.
FIG. 3 is a comparison graph of natural gas pipeline velocity profiles predicted using a conventional method and the method of the present invention.
Detailed Description
In order to make the aforementioned and other features and advantages of the invention more comprehensible, embodiments accompanied with figures are described in detail below.
The embodiment of the invention provides a method for predicting a flow state of a natural gas pipeline, which specifically comprises the following steps as shown in fig. 1:
1) acquiring natural gas pipeline parameters: pipeline length, pipeline internal diameter, friction coefficient etc to and detect and acquire the interior natural gas fluid parameter of pipeline: gas density, gas velocity, gas pressure, gas temperature, etc.; because the length of the pipeline is far greater than the diameter of the pipeline, a one-dimensional flow control equation is established according to the parameters, and comprises a continuous equation, a momentum equation and an ideal gas state equation:
the continuous equation:
Figure BDA0003415309790000041
the momentum equation:
Figure BDA0003415309790000042
the state equation is as follows:
p＝ρRgT (3)
wherein x is the length of the pipeline, ρ is the gas density, u is the gas velocity, p is the gas pressure, λ friction coefficient (constant), D is the inner diameter of the pipeline, R is the gas velocitygThe gas constant (287J/(kg. K)) and T are the gas temperature (288.15K).
2) SelectingCharacteristic amount: the characteristic length, the characteristic speed, the characteristic pressure and the characteristic density are used for calculating dimensionless quantity of the one-dimensional flow control equation. In this embodiment, the characteristic length x is selected+D (pipe inside diameter), characteristic speed urAt maximum or boundary flow rate, characteristic pressure prAs boundary pressure, characteristic density ρrFor boundary density and dimensionless quantity
Figure BDA0003415309790000043
Figure BDA0003415309790000044
The corresponding physical variable can be expressed as x ═ x using dimensionless quantities+X，u＝Uur，p＝ Ppr，
Figure BDA0003415309790000045
Note that: the selected characteristic quantity can be selected at will according to the actual situation, and the principle is to ensure the value of the dimensionless quantity to be between 0 and 1 as far as possible, but the value is not necessarily kept in the interval. The boundary values are directly given according to actual conditions, measurement is not needed, and in special cases, a characteristic quantity can be directly and artificially set for calculating the dimensionless quantity.
Substituting the physical variables represented by the dimensionless quantities into the one-dimensional flow control equation in step 1) to obtain a dimensionless one-dimensional flow control equation, which is:
Figure BDA0003415309790000046
Figure BDA0003415309790000047
Figure BDA0003415309790000048
in addition, the method can be obtained according to the state equation
Figure BDA0003415309790000049
Substituting equation (6) yields:
Figure BDA00034153097900000410
3) it can be seen from the above equation that the fluid flow state is represented by three variables, namely pressure, density, flow rate, which are all functions of the length of the pipe, so that the function can be learned through a neural network, thereby achieving the purpose of prediction. Therefore, a fully-connected deep neural network is constructed, and the input layer of the network is a neuron for expressing the length of the pipeline; the output layer is three neurons for expressing pressure, density and flow rate, 5 hidden layers are included between the input layer and the output layer, and the number of the neurons of the 5 hidden layers is [100,200,300,200 and 100 ]. The activation function adopts a hyperbolic tangent function:
Figure BDA0003415309790000051
the neural network output constructed according to the above parameters can be expressed by the following expression:
tanh(W5 tanh(W4 tanh(W3 tanh(W2 tanh(W1x+b1)+b2)+b3)+b4)+b5) (9)
the parameters W, b are needed to be adjusted by an optimization method, which is described below.
4) Before introducing the optimization method, an evaluation standard in deep neural network training learning needs to be constructed, so that a loss function of the neural network needs to be constructed. The derivative of the output quantity to the input quantity is constructed using an automatic differentiation technique provided by an open source deep learning framework (e.g., Tensorflow), and the following differential equations are established by combination:
Figure BDA0003415309790000052
Figure BDA0003415309790000053
Figure BDA0003415309790000054
the final result of the three differential equations is required to be 0, so that the model loss function can be constructed for the three differential equations and the boundary conditions by using the mean variance method as follows:
MSE＝wbMSEb+wcMSEc+wuMSEu+wpMSEp (13)
wherein w is weight coefficient (10-10000), MSEb、MSEc、MSEu、MSEpLoss functions representing boundary conditions, a continuity equation, a momentum equation, and a state equation, respectively, the loss function for the mean variance of an arbitrary variable is expressed as:
Figure BDA0003415309790000055
wherein t ═ b, c, u, p, x ═ fc，fu，fpAnd boundary conditions of the neural network output; x is the number of0Is a target value for fc，fu，fp， x0Are all zero; for the boundary condition, then x0Is a value given according to the actual situation; and N is the training data volume.
5) Firstly, utilizing Adam to optimize solver to carry out MSE on boundary condition loss functionbPre-learning is carried out, the input quantity is any length value in the total length of the pipeline, and the output quantity obtains a loss function MSE through the average variance of the boundary condition constructed in the step 4)bThe number of learning is usually about 10000; secondly, on the basis of pre-learning, the LBFGS optimization solver is used for continuing learning, and learning times are repeatedThe number is usually about 50000 times, and finally the W and b after training and adjustment are obtained, so that parameter values in the neural network constructed in the step 3) are determined, and a prediction model capable of predicting the flow state of the natural gas pipeline is obtained. In the step, corresponding functions in the Matlab or python of the computing software can be directly called to finish training.
The invention lists a specific application example as follows:
in this example, the natural gas pipeline has a length of 10m, an inner diameter D of 0.6m, a friction coefficient lambda of 300, and an inlet constant flow boundary of min1kg/s, constant pressure boundary at outlet pout＝105Pa. The discrete point N0 is 1000, and the number of training times is 10000,20000. The flow state of the natural gas pipeline is predicted by using the traditional method and the method provided by the invention, the predicted structures are compared, and the comparison result is shown in fig. 2 and fig. 3. The result comparison shows that the result obtained by the prediction method is basically coincident with the result obtained by the prediction of the traditional method, which shows that the flow state of the natural gas pipeline can be correctly solved by the method. Moreover, the traditional method needs to iterate for tens of thousands of times or even millions of times to obtain a correct result, but the method can obtain the same result by forward calculation only once through the trained intelligent prediction model, so that the calculation amount, the resource consumption and the prediction time are greatly reduced. In addition, the numerical solution algorithm of the traditional method can only obtain results by stepping from the inlet or the outlet of the pipeline, but the intelligent prediction model of the method can directly obtain the corresponding flow state by outputting the length of the pipeline, so that the method is more flexible and convenient to use. Therefore, compared with the traditional method, the method provided by the invention has the advantages that the efficiency and the flexibility are obviously improved.
According to the embodiment, the natural gas pipeline flow state prediction method provided by the invention simulates flow by a data-driven mode by constructing the deep learning model and fully utilizing the 'black box' characteristic of the prediction model. And then, the derivative of the output variable and the input variable of the prediction model is obtained by utilizing an automatic differential technology (a function derivative operation method realized by a computer), a flow differential equation is combined to be used as a loss function for optimizing model parameters, and the prediction model is learned by an LBFGS optimization algorithm to obtain a flow prediction model solution.
Although the present invention has been described with reference to the above embodiments, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (10)

1. A natural gas pipeline flow state prediction method is characterized by comprising the following steps:
acquiring natural gas pipeline parameters: pipeline length, pipeline internal diameter and friction coefficient to and the natural gas fluid parameter in the detection pipeline: the method comprises the following steps of (1) establishing a one-dimensional flow control equation of a natural gas pipe network according to the parameters, wherein the one-dimensional flow control equation comprises a continuous equation, a momentum equation and a state equation;
selecting a pipeline length value, a gas velocity value, a gas pressure value and a gas density value of a boundary condition as characteristic quantities, introducing dimensionless quantities by using the characteristic quantities to express the pipeline length, the gas velocity, the gas pressure and the gas density, and carrying out dimensionless transformation on a continuous equation, a momentum equation and a state equation of the one-dimensional flow control equation;
constructing a prediction model of a full-connection deep neural network, wherein the full-connection deep neural network comprises an input layer, five hidden layers and an output layer, the input layer is a neuron representing the length of a pipeline, and the output layer is three neurons representing gas speed, gas pressure and gas density; the activation function of the full-connection deep neural network adopts a hyperbolic tangent function;
constructing derivatives of output quantities to input quantities of a continuous equation, a momentum equation and a state equation which are non-dimensionalized to obtain three differential equations of the continuous equation, the momentum equation and the state equation, and constructing a model loss function for the three differential equations and the boundary conditions, wherein the model loss function is composed of weighting of a boundary condition loss function, a continuous equation loss function, a momentum equation loss function and a state equation loss function;
for the fully-connected deep neural network prediction model, an Adam optimization solver is adopted to pre-learn the boundary condition loss function, and the input quantity is any length value in the total pipeline length of the natural gas pipeline; and continuously learning by adopting an LBFGS optimization solver on the basis of the pre-learning to finally obtain an intelligent prediction model, and predicting the flow state of the natural gas pipeline by using the intelligent prediction model.
2. The method of claim 1, wherein the one-dimensional flow control equation is expressed as follows:
the continuous equation:
Figure FDA0003415309780000011
the momentum equation:
Figure FDA0003415309780000012
the state equation is as follows:
p＝ρRgT；
wherein x is the length of the pipeline, ρ is the gas density, u is the gas velocity, p is the gas pressure, λ friction coefficient, D is the internal diameter of the pipeline, R is the gas velocitygGas constant, T is the gas temperature.
3. The method of claim 2, wherein the pipe length value x is selected+Gas velocity value urGas pressure value prAnd gas density value ρrAs the characteristic quantity, a dimensionless quantity is set
Figure FDA0003415309780000013
The length of the pipeline is longDegree, gas velocity, gas pressure and gas density are introduced into dimensionless quantities expressed as x ═ x+X，u＝Uur，
Figure FDA0003415309780000021
4. The method of claim 3, wherein the equations of continuity, momentum, and momentum of the non-dimensionalized one-dimensional flow control equation are expressed as:
Figure FDA0003415309780000022
Figure FDA0003415309780000023
Figure FDA0003415309780000024
5. the method of claim 4, wherein the obtaining is based on an equation of state
Figure FDA0003415309780000025
The expression of the dimensionless momentum equation is reduced to
Figure FDA0003415309780000026
6. The method of claim 1, wherein the number of neurons in the 5 hidden layers is [100,200,300,200,100], respectively.
7. The method of claim 1, wherein the activation function employs a hyperbolic tangent function:
Figure FDA0003415309780000027
8. the method of claim 8, wherein the output of the deep neural network is expressed as:
tanh(W5 tanh(W4 tanh(W3 tanh(W2 tanh(W1x+b1)+b2)+b3)+b4)+b5)；
where tanh () is a hyperbolic tangent function and W, b are parameters.
9. The method of claim 5, wherein derivatives of the output quantities to the input quantities are constructed for the non-dimensionalized continuous equations, momentum equations, and state equations using an automatic differentiation technique provided by an open source deep learning framework; the three differential equation expressions of the continuous equation, the momentum equation and the state equation are obtained as follows:
Figure FDA0003415309780000028
Figure FDA0003415309780000029
Figure FDA00034153097800000210
10. the method of claim 9, wherein the model loss function is constructed using an average variance method, and the expression of the model loss function is MSE wbMSEb+wcMSEc+wuMSEu+wpMSEp(ii) a Wherein the content of the first and second substances,w is a weight coefficient, MSEb、MSEc、MSEu、MSEpRespectively representing a boundary condition loss function, a continuous equation loss function, a momentum equation loss function and a state equation loss function;
the loss function for the mean variance of an arbitrary variable is expressed as
Figure FDA00034153097800000211
Wherein t ═ b, c, u, p, x ═ fc，fu，fpAnd boundary conditions of the deep neural network output; x is the number of0Is a target value for fc，fu，fp，x0Are all zero; for the boundary condition, x0Is a given value; and N is the training data volume.
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