CN116341383A - Tail flame temperature prediction method based on embedded physical mechanism model integration - Google Patents
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Abstract
The invention provides a tail flame temperature prediction method based on embedded physical mechanism model integration. Acquiring enough data under test conditions of good weather and uniform illumination, including combustion chamber pressure, nozzle throat diameter, tail flame temperature and the like, wherein the tail flame temperature is measured by a precise instrument; dividing the total data into data sets for model training, verification and testing; further constructing two tail flame temperature prediction models embedded with physical mechanisms, training and verifying, wherein the tail flame temperature is used as the output of the models, and the other parameters are used as the input; and finally, integrating the trained model, and carrying out predictive analysis on data in the test set to prove the effectiveness and reliability of the model. The model designed by the invention can effectively restrict the model to predict the evolution rule of the tail flame temperature through embedding a physical mechanism, fully utilizes the complementary advantages of regression modeling and operator learning, establishes the nonlinear relation between parameters such as the combustion chamber pressure and the tail flame temperature, and improves the prediction precision.
Description
Technical Field
The invention relates to a temperature prediction method, in particular to a tail flame temperature prediction method based on embedded physical mechanism model integration.
Background
The traditional precise temperature measuring instrument is interfered by external complex environmental factors such as weather, illumination, vibration and the like, so that the accuracy and reliability of the acquired tail flame temperature are greatly reduced. In general, in addition to temperature parameters, solid rocket engine test tests generally measure parameters such as pressure of a combustion chamber, throat diameter of a spray pipe, drug loading and the like which are less disturbed by external environment, and the parameters have close relation with tail flame temperature. Therefore, modeling the correlation between the multi-sensor parameters and the tail flame temperature is an effective means for digitally simulating the temperature measurement of the alternative instrument. The tail flame temperature prediction technology aims at predicting the tail flame temperature through multiple sensor parameters such as pressure and the like.
At present, the main stream tail flame temperature prediction is mainly realized through a numerical simulation model or a machine learning model. For example, "modeling and analyzing the temperature field characteristics of the tail flame of the solid rocket engine [ J ]. Sensor and microsystem, 2023,42 (01): 10-13+18" discloses a numerical simulation model of the tail flame flow field based on COMSOL Multiphysics software. The result of the method shows that the larger the ignition dose, the larger the working pressure and the larger the area of the generated high-temperature area under the premise of ensuring the structural integrity of the grain. But this method is computationally intensive and time consuming. The time consumption problem of the numerical simulation model is effectively relieved based on the machine learning model, for example, a propellant temperature prediction method based on least square fitting is disclosed in 'application of linear regression analysis to liquid rocket propellant temperature prediction [ J ]. Missile and space carrying technology 2020, no.372 (01): 43-47'. The accuracy of the method is verified by regression and example analysis. However, the linear regression method is difficult to model nonlinear correlation between parameters such as the pressure of a combustion chamber of the solid rocket engine and the temperature of the tail flame, ignores an inherent physical mechanism of temperature increase and decrease in different combustion stages, and cannot adapt to a dynamic and changeable test environment.
Disclosure of Invention
Technical problem to be solved by the invention
The invention provides an integrated tail flame temperature prediction method based on an embedded physical mechanism model, which aims to solve the problems that the existing solid rocket engine tail flame temperature prediction model is large in calculated amount and time-consuming, nonlinear correlation between parameters such as combustion chamber pressure and nozzle throat diameter and tail flame temperature is difficult to model, and the internal physical mechanism of temperature increase and decrease in different combustion stages is ignored.
In order to solve the technical problems, the invention adopts the technical proposal
A tail flame temperature prediction method based on embedded physical mechanism model integration comprises the following steps:
s1: acquiring and constructing a data set, acquiring tail flame temperature values at a plurality of moments in a plurality of areas by adopting a precise instrument, acquiring model parameters, environment parameters and other test parameters by utilizing equipment, and dividing the acquired data into training, verifying and testing data sets;
s2: constructing a network model embedded with a physical mechanism, and constructing a neural network model capable of learning an explicit physical mechanism, namely a model a; constructing a depth operator model capable of modeling an implicit physical mechanism, namely a model b, wherein various parameters are used as the input of the model, the tail flame temperature is used as the output of the model, the model a adopts a multi-layer perceptron to construct a network, and the input data of the model a uses X a ＝[t,p t ,p max ,p avg ,F t ,F max ,M,d i ,d o ,p env ,T env ,H env ]The output is the temperature values of 4 different areas of the tail flame at the moment t
Network mouldThe input layer may be denoted->
Wherein->
As output variable of input layer, f relu (. Cndot.) represents the ReLU activation function, (. Cndot.)>
And->
The hidden layer contains k stages, the computational iteration process can be expressed as +.>
1.ltoreq.i.ltoreq.k, wherein>
And->
Respectively representing the weight and bias of the hidden layer, i.e. the number of hidden layer nodes is n, and the output layer can be represented as T through the calculation of the hidden layer a ＝f relu (W o T Y 5 +b o ) Wherein->
And->
Respectively representing output layer weights and biases; the model b consists of three sub-networks, including a main network and two branch networks, wherein the construction of each sub-network is consistent with that of the model a, and the multi-layer perceptron is adopted to construct the hidden layer structure which is the same as that of the model a;
s3: model training and evaluation, wherein the training part of the data set constructed by the S1 is input into two models constructed by the S2 to respectively train, wherein the model a adopts the loss guided by a physical mechanism and the mean square error loss to carry out joint training, and the mean square error loss can be represented by the following formula
Wherein,,
indicating that the s-th model is at time t j Temperature true value of the i-th zone, r s The number of data representing a corresponding model of the input model, u represents the number of models,
the loss of physical mechanism guidance is calculated as follows
Where sign (·) represents the sign function, then the total loss function for model a training is
Where λ is the physical guided loss balance coefficient, unlike model a, model b describes the special structure of multiple sub-network combinations through S2 to achieve implicit physical modeling, which uses only mean square error loss training, i.e
S4: model test and integration, the model with the best performance on the test set in the training process is reserved, the reserved model a and model b are integrated, and the final temperature predicted value is obtained by weighting and summing the outputs of the two models, which is expressed by the following formula
T it ＝αT ait +(1-α)T bit 0＜α＜1,i∈{1,2,3,4}
Wherein T is it And (3) representing the temperature predicted value of the integrated model in the ith region of the tail flame at the moment t, wherein alpha is a weighting coefficient.
Further, the specific construction process of the S2 model b is as follows:
s21, constructing a backbone network m (phi): x for inputting backbone network m ＝[t,m,d i ,d o ,p env ,T env ,H env ]The representation, output is
The network input layer may be expressed as
Wherein the method comprises the steps of
And->
Respectively representing the weight and bias of the input layer of the backbone network, and then +.>
The input hidden layer performs forward computation to obtain +.>
The output layer transformation is carried out to obtain the output g of the main network, which can be expressed by the following formula,
wherein the method comprises the steps of
And->
Respectively representing the weight and the bias of the output layer of the backbone network;
s22, constructing a branch network B 1 (Φ): branch network B 1 The input of (1) is the combustion chamber pressure value acquired in the test start-stop time, and the test starting time is assumed to be t 0 =0, test end time t e Branch network B 1 The input of (a) can be expressed as
Wherein->
To be t in the test start-stop time i The combustion chamber pressure value at the moment, the input p represents the pressure change process during the test, the sampling moment is calculated, the pressure value is obtained,
where N represents the number of sampling points, and N has a limited but sufficient value, so that the branch network B 1 Can be expressed as an input layer of (a)
Wherein the method comprises the steps of
And->
Respectively represent branch networks B 1 Input layer weights and offsets of (2) and then will +.>
The input hidden layer forward direction is calculated to obtain +.>
Finally->
Obtaining a branch network B through transformation 1 Output of +.>
S23, constructing a branch network B 2 (Φ): branch network B 2 And branch network B 1 Is the same in structure, branch network B 2 The input of the test is the thrust value acquired in the test start-stop time and the branch network B 1 By sampling the thrust values in the test start-stop time in a limited but sufficient manner, the test start-stop time is taken as a branch network B 2 The output of the last branch network is denoted as
S24, combining sub-network output: first rearranging the output of the backbone network
Remodelling into
The outputs of the backbone network and the two branch networks are then combined as follows,
T b ＝g′ T (h*q)/2，
wherein the method comprises the steps of
The output of model b is shown as the temperature predictions for the four different regions of the tail flame at time t.
Further, the precise instrument adopted in the step S1 is a thermal infrared imager or a multispectral thermometer.
Further, the S1 model parameter comprises an initial throat diameter d of the engine spray pipe i Outer diameter d of outlet o And charge quality M, the environmental parameters include test environmental barometric pressure p env Temperature T env And humidity H env The test parameters include a test process combustion chamber pressure curve p (t), a thrust curve F (t), and a maximum pressure p max Average pressure p avg Maximum thrust F max 。
Further, the S3 model training optimizer employs Adam.
Further, the mean square error between the predicted temperature value and the true temperature value in S3 is used to evaluate the accuracy of the model, and the learning rate is adjusted by analyzing the prediction accuracy and the loss change rule of the model on the verification set in the training process, and the hidden layer number and the neuron node number of each sub-network of the model a and the model b.
The beneficial effects of the invention are as follows: the designed tail flame temperature prediction method integrates two depth models embedded with physical mechanisms, one model is trained through physical guiding loss, and explicit physical association between parameters such as combustion chamber pressure, engine thrust and the like and tail flame temperature can be learned; a model realizes operator learning through a multi-branch network structure, and can model an implicit physical mechanism among multiple sensor parameters; because complex equations in the numerical model and strong nonlinear fitting capacity of the depth model are not needed to be solved, the accuracy, the robustness and the instantaneity of tail flame temperature prediction are effectively improved through integration of the two models.
Drawings
FIG. 1 is a flow chart of a tail flame temperature prediction method based on embedded physical mechanism model integration of the invention;
Detailed Description
The invention provides a tail flame temperature prediction method based on embedded physical mechanism model integration. Firstly, acquiring enough data under test conditions of good weather and uniform illumination, including combustion chamber pressure, nozzle throat diameter, tail flame temperature and the like, wherein the tail flame temperature is measured by a precise instrument; dividing all data into data sets for model training, verification and testing; further constructing two tail flame temperature prediction models embedded with physical mechanisms, training and verifying, wherein the tail flame temperature is used as the output of the models, and the other parameters are used as the input; and finally, integrating the trained model, and carrying out predictive analysis on data in the test set to prove the effectiveness and reliability of the model. The model designed by the invention can effectively restrict the model to predict the evolution rule of the tail flame temperature through embedding a physical mechanism, fully utilizes the complementary advantages of regression modeling and operator learning, establishes the nonlinear relation between parameters such as the combustion chamber pressure and the tail flame temperature, and improves the prediction precision.
A tail flame temperature prediction method based on embedded physical mechanism model integration comprises the following steps:
s1, collecting and constructing a data set: firstly, under the good test environment condition, adopting a thermal infrared imager or a multispectral thermometer and other precise instruments to acquire tail flame temperature values at a plurality of areas and at a plurality of moments, and simultaneously utilizing equipment to acquire model parameters, environment parameters and other test parameters, wherein the model parameters comprise the initial throat diameter d of an engine spray pipe i Outer diameter d of outlet o And charge quality M, the environmental parameters include test environmental barometric pressure p env Temperature T env And humidity H env The test parameters include a test process combustion chamber pressure curve p (t), a thrust curve F (t), and a maximum pressure p max Average pressure p avg Maximum thrust F max The method comprises the steps of carrying out a first treatment on the surface of the Then dividing the collected data into training, verifying and testing data sets;
s2, constructing a network model of an embedded physical mechanism: and constructing a neural network model capable of learning an explicit physical mechanism, and constructing a depth operator model capable of modeling an implicit physical mechanism, wherein various parameters are used as the input of the model, and the tail flame temperature is used as the output of the model. For simplicity of description, the two models are denoted as model a and model b, respectively.
The neural network model capable of learning explicit physical mechanism, namely model a, adopts multilayer perceptron to construct network, and uses X for input data a ＝[t,p t ,p max ,p avg ,F t ,F max ,M,d i ,d o ,p env ,T env ,H env ]The output is the temperature values of 4 different areas of the tail flame at the moment t
The network model input layer may be expressed as
Y 0 ＝f relu (W 0 T X a +b 0 )，
Wherein the method comprises the steps of
As output variable of input layer, f relu (. Cndot.) represents the ReLU activation function, (. Cndot.)>
And
input layer weights and biases, respectively. The hidden layer contains k stages, and the computational iteration process can be expressed as
Y i ＝f relu (W i T Y i-1 +b i )1≤i≤k，
Wherein the method comprises the steps of
And->
The hidden layer weights and offsets are represented, respectively, i.e. the number of hidden layer nodes is n. Through the calculation of the hidden layer, the output layer can be expressed as
T a ＝f relu (W o T Y 5 +b o )，
Wherein the method comprises the steps of
And->
Respectively representing output layer weights and offsets.
The depth operator network capable of modeling the implicit physical mechanism, namely a model b, consists of three sub-networks, and specifically comprises a main network and two branch networks. The construction of each sub-network is consistent with the model a, and the multi-layer perceptron is adopted to construct the hidden layer, and the hidden layer structure is the same as that of the model a. The specific construction process of the model b is as follows:
s21, constructing a backbone network m (phi): x for inputting backbone network m ＝[t,m,d i ,d o ,p env ,T env ,H env ]The representation, output is
The network input layer may be expressed as
Wherein the method comprises the steps of
And->
Representing backbone network input layer weights and biases, respectively. Then will->
The input hidden layer performs forward computation to obtain +.>
The output layer transformation is carried out to obtain the output g of the main network, which can be expressed by the following formula,
wherein the method comprises the steps of
And->
Respectively representing backbone network output layer weights and biases.
S22, constructing a branch network B 1 (Φ): branch network B 1 The input of (2) is the combustion chamber pressure value collected during the test start-stop time. Let the test start time be t 0 =0, test end time t e Branch network B 1 The input of (a) can be expressed as
Wherein->
To be t in the test start-stop time i Combustion chamber pressure value at time. In order for the input p to be sufficient to represent the course of the pressure change during the test, the sampling instant is calculated and the pressure value is obtained as follows,
where N represents the number of sampling points, and N has a limited but sufficient value. Thus branch network B 1 Can be expressed as an input layer of (a)
Wherein the method comprises the steps of
And->
Respectively represent branch networks B 1 Input layer weights and offsets of (a). Then will->
Input hidden layer forward meterCalculated->
Finally->
Obtaining a branch network B through transformation 1 Output of +.>
S23, constructing a branch network B 2 (Φ): branch network B 2 And branch network B 1 Is the same in structure except that the branched network B 2 The input of (2) is the thrust value collected during the start-stop time of the test. And branch network B 1 By sampling the thrust values in the test start-stop time in a limited but sufficient manner, the test start-stop time is taken as a branch network B 2 Is input to the computer. The output of the last branch network is recorded as
S24, combining sub-network output: first rearranging the output of the backbone network
Remodelling into
The outputs of the backbone network and the two branch networks are then combined as follows,
T b ＝g′ T (h*q)/2，
wherein the method comprises the steps of
The output of model b is shown as the temperature predictions for the four different regions of the tail flame at time t.
S3, model training and evaluation: the training part of the data set constructed in the step 1 is input into two models constructed in the step S2 to be trained respectively, wherein a model a adopts the loss guided by a physical mechanism and the mean square error loss to carry out joint training, and the mean square error loss can be represented by the following formula
Wherein the method comprises the steps of
Indicating that the s-th model is at time t j The temperature true value of the i-th area, r represents the number of data corresponding to one model of the input model, and u represents the number of models. The loss of physical mechanism guidance is calculated as follows
Wherein sign (·) represents the sign function. The total loss function for model a training is then
Where λ is the physical pilot loss balance coefficient. Unlike model a, model b describes the special structure of the multiple sub-network combinations through step 2 to achieve implicit physical modeling, which uses only mean square error loss training, i.e
In addition, the model training optimizer employs Adam. The mean square error between the predicted temperature value and the true temperature value is used to evaluate the accuracy of the model. And the learning rate is adjusted by analyzing the prediction precision and loss change rule of the model on the verification set in the training process, and super parameters such as the hidden layer number and the neuron node number of each sub-network of the model a and the model b are adjusted.
S4, model test and integration: firstly, reserving a model with the best performance on a test set in the training process, then integrating the reserved model a and the reserved model b, and obtaining a final temperature predicted value by weighting and summing the outputs of the two models, wherein the final temperature predicted value is represented by the following formula
Wherein T is it And (3) representing the temperature predicted value of the integrated model in the ith region of the tail flame at the moment t, wherein alpha is a weighting coefficient.
The invention will be further illustrated with reference to the following figures and examples, which include but are not limited to the following examples.
As shown in fig. 1, the invention provides a tail flame temperature prediction method integrated by embedding a physical mechanism model, which comprises the following specific implementation processes:
step one: acquiring and constructing a dataset
Firstly, under the good test environment condition, adopting a thermal infrared imager or a multispectral thermometer and other precise instruments to obtain tail flame temperature values of a plurality of areas at a plurality of moments, and simultaneously utilizing a plurality of sensors or equipment to collect model parameters, environment parameters and other test parameters, wherein the model parameters comprise the initial throat diameter d of an engine spray pipe i Outer diameter d of outlet o And charge quality M, the environmental parameters include test environmental barometric pressure p env Temperature T env And humidity H env The test parameters include a test process combustion chamber pressure curve p (t), a thrust curve F (t), and a maximum pressure p max Average pressure p avg Maximum thrust F max The method comprises the steps of carrying out a first treatment on the surface of the Then dividing the collected data into training, verifying and testing data sets;
step two: construction of an embedded physical mechanism model
The invention constructs two depth models for embedding physical mechanisms. Firstly, a neural network model capable of learning an explicit physical mechanism is constructed, then a depth operator model capable of modeling an implicit physical mechanism is constructed, wherein the tail flame temperature is used as the output of the model, and the rest parameters are used as the input of the model. For simplicity of description, the two models are denoted as model a and model b, respectively.
(1) Neural network model capable of learning explicit physical mechanism
The neural network model capable of learning explicit physical mechanism, namely model a, adopts multilayer perceptron to construct network, and uses X for input data a ＝[t,p t ,p max ,p avg ,F t ,F max ,M,d i ,d o ,p env ,T env ,H env ]The output is the temperature values of 4 different areas of the tail flame at the moment t
The network model input layer may be expressed as
Y 0 ＝f relu (W 0 T X a +b 0 )，
Wherein the method comprises the steps of
As output variable of input layer, f relu (. Cndot.) represents the ReLU activation function, (. Cndot.)>
And
input layer weights and biases, respectively. The hidden layer contains k stages, and the computational iteration process can be expressed as
Wherein the method comprises the steps of
And->
The hidden layer weights and offsets are represented, respectively, i.e. the number of hidden layer nodes is n. Through hidden layersThe computation, output layer may be expressed as
T a ＝f relu (W o T Y 5 +b o )，
Wherein the method comprises the steps of
And->
Respectively representing output layer weights and biases;
(2) Depth operator model capable of modeling implicit physical mechanism
The depth operator network capable of modeling the implicit physical mechanism, namely a model b, consists of three sub-networks, and specifically comprises a main network and two branch networks. The construction of each sub-network is consistent with the model a, and the multi-layer perceptron is adopted to construct the hidden layer, and the hidden layer structure is the same as that of the model a. The specific construction process of the model b is as follows:
step 1), constructing a backbone network m (phi): x for inputting backbone network m ＝[t,m,d i ,d o ,p env ,T env ,H env ]The representation, output is
The network input layer may be expressed as
Wherein the method comprises the steps of
And->
Representing backbone network input layer weights and biases, respectively. Then will->
Input hidden layer forward computationObtain->
The output layer transformation is carried out to obtain the output g of the main network, which can be expressed by the following formula,
wherein the method comprises the steps of
And->
Respectively representing the weight and the bias of the output layer of the backbone network;
step 2), constructing a branch network B 1 (Φ): branch network B 1 The input of (2) is the combustion chamber pressure value collected during the test start-stop time. Let the test start time be t 0 =0, test end time t e Branch network B 1 The input of (a) can be expressed as
Wherein->
To be t in the test start-stop time i Combustion chamber pressure value at time. In order for the input p to be sufficient to represent the course of the pressure change during the test, the sampling instant is calculated and the pressure value is obtained as follows,
where N represents the number of sampling points, and N has a limited but sufficient value. Thus branch network B 1 Can be expressed as an input layer of (a)
Wherein the method comprises the steps of
And->
Respectively represent branch networks B 1 Input layer weights and offsets of (a). Then will->
The input hidden layer forward direction is calculated to obtain +.>
Finally->
Obtaining a branch network B through transformation 1 Output of +.>
Step 3), constructing a branch network B 2 (Φ): branch network B 2 And branch network B 1 Is the same in structure except that the branched network B 2 The input of (2) is the thrust value collected during the start-stop time of the test. And branch network B 1 By sampling the thrust values in the test start-stop time in a limited but sufficient manner, the test start-stop time is taken as a branch network B 2 Is input to the computer. The output of the last branch network is recorded as
Step 4), combining the sub-network outputs: first rearranging the output of the backbone network
Remodelling into
The backbone network and the two are then aligned according to the followingOutput of the branch network is combined and calculated, T b ＝g ′T (h*q)/2
Wherein the method comprises the steps of
The output of the model b is represented as the temperature predicted values of the tail flame in four different areas at the time t;
step three: model training and evaluation
The training part of the data set constructed in the step 1 is input into the two models constructed in the step 2 to be trained respectively, wherein the model a adopts the loss guided by a physical mechanism and the mean square error loss to carry out joint training, and the mean square error loss can be represented by the following formula
Wherein the method comprises the steps of
Indicating that the s-th model is at time t j The temperature true value of the i-th area, r represents the number of data corresponding to one model of the input model, and u represents the number of models. The loss of physical mechanism guidance is calculated as follows
Wherein sign (·) represents the sign function. The total loss function for model a training is then
Where λ is the physical pilot loss balance coefficient. Unlike model a, model b describes multiple by step 2The special structure of the sub-network combination realizes implicit physical modeling, which only adopts mean square error loss training, namely
In addition, the model training optimizer employs Adam. The root mean square error between the predicted temperature value and the true temperature value is used to evaluate the accuracy of the model. The learning rate is adjusted by analyzing the prediction precision and loss change rule of the model on the verification set in the training process, and super parameters such as the hidden layer number and the neuron node number of each sub-network of the model a and the model b are adjusted;
step four: model testing and integration
Firstly, reserving a model with the best performance on a test set in the training process, then integrating the reserved model a and the reserved model b, and obtaining a final temperature predicted value by weighting and summing the outputs of the two models, wherein the final temperature predicted value is represented by the following formula
Wherein T is it And (3) representing the temperature predicted value of the integrated model in the ith region of the tail flame at the moment t, wherein alpha is a weighting coefficient.
To verify the validity of the present invention, the CPU is provided with
And (3) performing simulation experiments on i7-6800K 3.40GHz CPU, NVIDIAGeForce GTX 1080GPU and Ubuntu operating systems by using Python software and PyTorch deep learning frameworks, wherein the data set adopted in the experiments is the data set constructed in the step (1) of the invention. All models in the experiment are trained by adopting an Adam optimizer, and 256 groups of data are input in each iteration. The initial learning rate is set to 0.01, and the learning rate is reduced by half every 50 rounds until the training is stopped for 1000 rounds, and meanwhile, the model with the best performance in the training process is saved for subsequent comparison. The neural network model capable of learning the explicit physical mechanism is denoted as a model 1, the depth operator model capable of modeling the implicit physical mechanism is denoted as a model 2, and the integration of the two models is denoted as a model 3. With RMSE asThe evaluation index shows the effect of the different methods, the smaller the RMSE value is, the better the algorithm effect is, and the results are shown in table 1 and table 2.
Table 1 comparison of experimental results of different algorithms on datasets
Table 2 comparison of experimental results of 3 methods proposed by the present invention on data sets
Claims (6)
1. The tail flame temperature prediction method based on embedded physical mechanism model integration is characterized by comprising the following steps:
s1: acquiring and constructing a data set, acquiring tail flame temperature values at a plurality of moments in a plurality of areas by adopting a precise instrument, acquiring model parameters, environment parameters and other test parameters by utilizing equipment, and dividing the acquired data into training, verifying and testing data sets;
s2: constructing a network model embedded with a physical mechanism, and constructing a neural network model capable of learning an explicit physical mechanism, namely a model a; constructing a depth operator model capable of modeling an implicit physical mechanism, namely a model b, wherein various parameters are used as the input of the model, the tail flame temperature is used as the output of the model, the model a adopts a multi-layer perceptron to construct a network, and the input data of the model a uses X a ＝[t,p t ,p max ,p avg ,F t ,F max ,M,d i ,d o ,p env ,T env ,H env ]The output is the temperature values of 4 different areas of the tail flame at the moment t
The network model input layer may be expressed as +.>
Wherein->
As output variable of input layer, f relu (. Cndot.) represents the ReLU activation function, (. Cndot.)>
And->
The hidden layer contains k stages, and the iterative process of computation can be expressed as Y i ＝f relu (W i T Y i-1 +b i ) 1.ltoreq.i.ltoreq.k, where
And->
Respectively representing the weight and bias of the hidden layer, i.e. the number of hidden layer nodes is n, and the output layer can be represented as T through the calculation of the hidden layer a ＝f relu (W o T Y 5 +b o ) Wherein->
And->
Respectively representing output layer weights and biases; the model b consists of three sub-networks, including a main network and two branch networks, wherein the construction of each sub-network is consistent with that of the model a, and the multi-layer perceptron is adopted to construct the hidden layer structure which is the same as that of the model a;
s3: model training and evaluation, wherein the training part of the data set constructed by the S1 is input into two models constructed by the S2 to respectively train, wherein the model a adopts the loss guided by a physical mechanism and the mean square error loss to carry out joint training, and the mean square error loss can be represented by the following formula
Wherein,,
indicating that the s-th model is at time t j Temperature true value of the i-th zone, r s The number of data representing a corresponding model of the input model, u represents the number of models,
the loss of physical mechanism guidance is calculated as follows
Where sign (·) represents the sign function, then the total loss function for model a training is
Where λ is the physical guided loss balance coefficient, unlike model a, model b describes the special structure of multiple sub-network combinations through S2 to achieve implicit physical modeling, which uses only mean square error loss training, i.e
S4: model test and integration, the model with the best performance on the test set in the training process is reserved, the reserved model a and model b are integrated, and the final temperature predicted value is obtained by weighting and summing the outputs of the two models, which is expressed by the following formula
T it ＝αT ait +(1-α)T bit 0＜α＜1,i∈{1,2,3,4}
Wherein T is it And (3) representing the temperature predicted value of the integrated model in the ith region of the tail flame at the moment t, wherein alpha is a weighting coefficient.
2. The tail flame temperature prediction method based on embedded physical mechanism model integration according to claim 1, wherein the specific construction process of the S2 model b is as follows:
s21, constructing a backbone network m (phi): x for inputting backbone network m ＝[t,m,d i ,d o ,p env ,T env ,H env ]The representation, output is
The network input layer may be expressed as
Wherein the method comprises the steps of
And->
Respectively representing the weight and bias of the input layer of the backbone network, and then +.>
The input hidden layer performs forward computation to obtain +.>
The output layer transformation is carried out to obtain the output g of the main network, which can be expressed by the following formula,
wherein the method comprises the steps of
And->
Respectively representing the weight and the bias of the output layer of the backbone network;
s22, constructing a branch network B 1 (Φ): branch network B 1 The input of (1) is the combustion chamber pressure value acquired in the test start-stop time, and the test starting time is assumed to be t 0 =0, test end time t e Branch network B 1 The input of (a) can be expressed as
Wherein->
To be t in the test start-stop time i The combustion chamber pressure value at the moment, the input p represents the pressure change process during the test, the sampling moment is calculated, the pressure value is obtained,
where N represents the number of sampling points, and N has a limited but sufficient value, so that the branch network B 1 Can be expressed as an input layer of (a)
Wherein the method comprises the steps of
And->
Respectively represent branch networks B 1 Input layer weights and offsets of (2) and then will +.>
The input hidden layer forward direction is calculated to obtain +.>
Finally->
Obtaining a branch network B through transformation 1 Output of +.>
S23, constructing a branch network B 2 (Φ): branch network B 2 And branch network B 1 Is the same in structure, branch network B 2 The input of the test is the thrust value acquired in the test start-stop time and the branch network B 1 By sampling the thrust values in the test start-stop time in a limited but sufficient manner, the test start-stop time is taken as a branch network B 2 The output of the last branch network is denoted as
S24, combining sub-network output: first rearranging the output of the backbone network
Remodelling into
The outputs of the backbone network and the two branch networks are then combined as follows,
T b ＝g′ T (h*q)/2，
wherein the method comprises the steps of
The output of model b is shown as the temperature predictions for the four different regions of the tail flame at time t.
3. The method for predicting the tail flame temperature based on embedded physical mechanism model integration according to claim 1, wherein the method comprises the following steps: the model a constructed by the S2 is trained by combining the physical guiding loss and the MSE loss of the S3 design.
4. The method for predicting the tail flame temperature based on embedded physical mechanism model integration according to claim 1, wherein the method comprises the following steps: the S1 model parameter comprises the initial throat diameter d of the engine spray pipe i Outer diameter d of outlet o And charge quality M, the environmental parameters include test environmental barometric pressure p env Temperature T env And humidity H env The test parameters include a test process combustion chamber pressure curve p (t), a thrust curve F (t), and a maximum pressure p max Average pressure p avg Maximum thrust F max 。
5. The method for predicting the tail flame temperature based on embedded physical mechanism model integration according to claim 1, wherein the method comprises the following steps: the predicted temperature value of the S4 is a weighted average of the predicted temperature values of the model a and the model b.
6. The method for predicting the tail flame temperature based on embedded physical mechanism model integration according to claim 1, wherein the method comprises the following steps: the root mean square error between the predicted temperature value and the true temperature value of the model a and the model b constructed in the S2 is used for evaluating the accuracy of the model, and the learning rate is adjusted by analyzing the prediction accuracy and the loss change rule of the model on the verification set in the training process, and the hidden layer number and the neuron node number of each sub-network of the model a and the model b.
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