CN114708927A - High-temperature alloy fatigue performance prediction method based on grey prediction and LSTM - Google Patents

High-temperature alloy fatigue performance prediction method based on grey prediction and LSTM Download PDF

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CN114708927A
CN114708927A CN202210258972.5A CN202210258972A CN114708927A CN 114708927 A CN114708927 A CN 114708927A CN 202210258972 A CN202210258972 A CN 202210258972A CN 114708927 A CN114708927 A CN 114708927A
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黄渭清
李冬伟
刘金祥
左正兴
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Beijing Institute of Technology BIT
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Abstract

The invention aims to solve the problems of high cost and low reliability of a prediction result in the prior art, and provides a high-temperature alloy fatigue life prediction method based on grey prediction and an LSTM neural network; the method comprises the steps of firstly predicting the damage factors of the high-temperature alloy of a very small amount of samples of a time sequence at equal intervals by utilizing gray prediction, then fitting a test value with a predicted value by utilizing a least square method to obtain a fitting function of the time sequence and the damage factors, namely obtaining the damage factors at any time, selecting the damage factors at fixed time intervals, calculating the fatigue life of the time sequence through a damage-life relation, and training by taking the damage factors and the fatigue life of the time sequence as a data set of an LSTM neural network. The LSTM neural network can be used as a time series neural network prediction model based on damage information to predict the fatigue life of the high-temperature alloy damaged in time series. Under the condition of not needing to carry out a large number of tests and simulations, a small amount of sample data can be used for predicting the fatigue life related to the time series, and the maintenance cost of the component is greatly reduced.

Description

High-temperature alloy fatigue performance prediction method based on grey prediction and LSTM
Technical Field
The invention relates to a gray prediction and LSTM (localized surface plasmon resonance) based high-temperature alloy fatigue performance prediction method, in particular to a directional solidification high-temperature alloy fatigue performance prediction method based on gray prediction and LSTM long-time neural network, belonging to the related field of directional solidification high-temperature alloy.
Background
The directionally solidified high-temperature alloy is often used on turbine blades of hot-end parts of aircraft engines due to the excellent performance of the directionally solidified high-temperature alloy, the service environment of the turbine blades is very harsh, and the blades bear long-term mechanical load at high temperature, so that the blade materials have microstructure morphology evolution related to time, and the microstructure morphology evolution is called as micro-damage in the service stage. The microscopic damage obviously reduces the mechanical property of the blade material and influences the service life of the material, thereby influencing the safe operation and service life of the aeroengine. Therefore, attention is paid to how to predict material properties quickly and accurately. Because the sampling work of the material in the service process is difficult to carry out, the sample size of test data is small, and the performance of the material is difficult to be accurately predicted by using a small amount of data.
Commonly used methods for predicting material properties are empirical formulas and finite element methods. The method for establishing the life prediction empirical formula needs a large number of mechanical tests, and then test data are analyzed to establish a prediction model. The method has high test cost. The finite element method is also a commonly used effective method for predicting material performance, however, the finite element method often cannot be well fitted with engineering practice, so that the reliability of the prediction result is low.
Disclosure of Invention
The invention aims to solve the problems of high prediction cost and low reliability in the prior art, and provides a high-temperature alloy service life prediction method based on gray prediction and an LSTM neural network; the method comprises the steps of firstly predicting the damage factors of the high-temperature alloy of a very small amount of samples of a time sequence at equal intervals by utilizing gray prediction, then fitting a test value with a predicted value by utilizing a least square method to obtain a fitting function of the time sequence and the damage factors, namely obtaining the damage factors at any time, selecting the damage factors at fixed time intervals, calculating the fatigue life of the time sequence through a damage-life relation, and training by taking the damage factors and the fatigue life of the time sequence as a data set of an LSTM neural network. The LSTM neural network can be used as a time series neural network prediction model based on damage information to predict the time series related performance of the superalloy. The fatigue life prediction related to the time series can be carried out by using a very small amount of sample data under the condition of not carrying out a large amount of tests and simulations.
The purpose of the invention is realized by the following technical scheme.
A high-temperature alloy fatigue life prediction method based on gray prediction and LSTM comprises the following steps:
step one, acquiring a data set: and constructing a data set of microstructure damage information parameters and mechanical property test data of the alloy to be predicted. The micro-tissue damage information parameters include: the volume fraction, the carbides and the topological close arrangement of the gamma 'strengthening phase, the gamma matrix phase and the gamma' strengthening phase are equal; the mechanical property test data comprises: fatigue life, yield strength, fatigue strength, and tensile strength.
Step two, constructing a grey prediction model: the GM (1, 1) model was constructed according to the Gray systems theory.
S21 known elements raw sequence data:
X(0)＝(x(0)(1)，x(0)(2)，x(0)(3)，...，x(0)(n))
wherein X(0)Represents the original sequence, and x(0)(k) More than or equal to 0, k is 1, 2. The accumulation of the raw sequence data generates a sequence as follows:
X(1)＝(x(1)(1)，x(1)(2)，x(1)(3)，...，x(1)(n))
wherein X(1)Represents a generation sequence, and
Figure BDA0003539456490000021
X(1)the close-proximity mean generation sequence of (1) is:
Z(1)＝(z(1)(2)，z(1)(3)，...，z(1)(n))
wherein Z(1)Generating a sequence for the close-proximity mean, an
z(1)(k)＝0.5x(1)(k)+0.5x(1)(k-1)，k＝1，2，…，n
S22, establishing a gray differential equation model of GM (1, 1):
x(0)(k)+az(1)(k)＝c
wherein a is a development coefficient, and c is a gray effect amount.
S23
Figure BDA0003539456490000022
For the parameter vector to be estimated, i.e.
Figure BDA0003539456490000023
The least-squares estimation parameter column of the gray differential equation satisfies
Figure BDA0003539456490000024
Wherein B is a mean sequence vector, Y is a constant phase vector, and the following are respectively:
Figure BDA0003539456490000025
s24 builds a whitening equation for the gray differential equation:
Figure BDA0003539456490000026
the solution to the whitening equation is a time response function, and is:
Figure BDA0003539456490000027
s25, subtracting and restoring to obtain a gray prediction model:
Figure BDA0003539456490000031
and thirdly, predicting the micro-tissue damage factor based on the time sequence according to the grey prediction model to obtain a future time prediction value of the same time interval.
And step four, fitting the test values in the data set in the step one and the predicted values obtained in the step three by using a least square method to obtain a fitting function.
And step five, calculating the damage factor value at any time by using the fitting function obtained in the step four. Giving time sequence intervals to obtain a damage factor value of each time interval point, and obtaining a damage factor data set related to the time sequence; and calculating the fatigue life corresponding to each time point by using the relation between the damage factors and the fatigue life.
And step six, constructing an LSTM neural network prediction model. The model is composed of a memory storage unit, the memory storage unit, namely a memory cell, is regulated and controlled by an updating gate, a forgetting gate and an output gate, and data propagation of an input data set is controlled by a gate control unit.
S61 loads the data set: and D, respectively inputting and outputting the damage factor value and the fatigue life value in the step V, and predicting the fatigue life by using an LSTM neural network.
S62 construction of an LSTM neural network prediction model based on a Keras framework:
forget the door: forgetting useless memory accumulated at the past t-1 moment, namely deleting useless information in the damage information,
ft＝σ(Wxfxt+Whfht-1+bf)
in the formula, x is an input data set of LSTM, h is a state value, W is a weight matrix, b is a bias matrix, sigma represents an activation function sigmoid, and f is a forgetting gate.
And (3) updating a door: updating the new content at the time t, retaining the related knowledge in the damage information in the memory cell, updating the information in the memory cell,
it＝σ(Wxixt+Whiht-1+bi)
gt＝tanh(Wxgxt+Whght-1+bg)
where i and g are two function operations for updating the gate, tanh represents the activation function tanh.
Memory storage unit (i.e. memory cell): at each time step of the LSTM, there is a memory cell that gives the LSTM the selective memory function, so that the LSTM has the ability to freely select what is memorized within each time step.
ct＝ct-1⊙ft+gt⊙it
Wherein [ ] is the Hadamard product, and c is the memory cell.
An output gate: and calculating by using useful knowledge at the time t to obtain:
Ot＝σ(Wxoxt+Whoht-1+bo)
mt＝tanh(ct)
ht＝ot⊙mt
yt＝Wghht+bg
wherein O is an output gate, m is the tanh calculation of the memory cell and the output gate, m can convert the useful memory content in the memory cell into output, and y is an output value, namely the predicted value of the alloy performance.
S63, compiling LSTM neural network prediction model, defining average absolute error as loss function:
Figure BDA0003539456490000041
in the formula yiTo predict value, xiAre true values.
And seventhly, predicting the fatigue life of the directionally solidified high-temperature alloy relevant to the time sequence by using the constructed LSTM neural network.
Advantageous effects
1. The grey prediction model has the advantages of short-term prediction and few-sample-volume prediction, belongs to a time series statistical model, and can effectively predict the future development trend of the few-sample-volume data related to the time sequence obtained by the high-temperature alloy material sample.
2. The directional solidification high-temperature alloy material used on the hot end component of the engine is not easy to sample in the service period, and the test difficulty is high, so the cost for carrying out the mechanical property test on the material is high. The invention predicts the service life of the material by utilizing the established neural network prediction model based on small sample size, and can greatly reduce the test cost, the material cost and the maintenance cost of the turbine blade.
3. The LSTM neural network model established by using the expanded data can predict the service life of the micro-tissue damage at any time based on the time sequence, thereby greatly improving the service life prediction efficiency of the service material.
4. The short-term prediction and few-sample prediction advantages of the gray prediction model are combined with the nonlinear prediction advantages of the LSTM neural network, and the accuracy of life prediction can be improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a graph comparing predicted values and experimental values for a gray prediction model.
FIG. 3 is a graph based on predicted versus experimental values for the LSTM neural network.
Detailed Description
Embodiments of the present invention are described in further detail below with reference to the drawings and examples.
A method for predicting the fatigue life of directionally solidified high-temperature alloy based on gray prediction and LSTM is disclosed, and the specific flow is shown in figure 1, and comprises the following steps:
step one, acquiring a data set. Acquiring a microstructure damage information and fatigue life data information base of the directionally solidified high-temperature alloy; the microstructure damage information of the high-temperature alloy is obtained by laboratory electron microscope observation and picture analysis software analysis, and the fatigue life data is obtained by mechanical property tests. The micro-tissue damage information parameters include: the size of the gamma 'strengthening phase, the size of the gamma matrix phase, the volume fraction of the gamma' strengthening phase, carbides and topological close packing are equal; the mechanical property test data comprises: fatigue life, yield strength, fatigue strength, tensile strength, and the like. The pretreatment condition of the microstructure of the high-temperature alloy material is set based on the turbine blade overhaul time and the actual working condition. The time nodes of the pre-damage are respectively 0h, 300h, 600h, 900h and 1200h, so that four groups of micro-tissue damage information data and fatigue life data are obtained. Wherein the damage information of each time point is defined as a damage factor Di，0≤DiLess than or equal to 1, and the fatigue life of each time point is NfiIn this case, i represents a time point. Corresponding a group of injury factors D at each time pointiAnd fatigue life NfiIn this example, the test values total 5 sets of data, { D }1，D2，D3，D4，D5And { N }f1，Nf2，Nf3，Nf4，Nf5}。
Step two, constructing a gray prediction model: constructing GM (1, 1) model according to grey system theory
S21 known elements raw sequence data:
X(0)＝(x(0)(1)，x(0)(2)，x(0)(3)，…，x(0)(n))
wherein X(0)Represents the original sequence, and x(0)(k) More than or equal to 0, k is 1, 2. The accumulation of the raw sequence data generates a sequence as follows:
X(1)＝(x(1)(1)，x(1)(2)，x(1)(3)，…，x(1)(n))
wherein X(1)Represents a generation sequence, and
Figure BDA0003539456490000051
X(1)the close-proximity mean generation sequence of (1) is:
Z(1)＝(z(1)(2)，z(1)(3)，...，z(1)(n))
wherein Z(1)Generating a sequence for the close-proximity mean, an
z(1)(k)＝0.5x(1)(k)+0.5x(1)(k-1)，k＝1，2，…，n
S22, establishing a gray differential equation model of GM (1, 1):
x(0)(k)+az(1)(k)＝c
wherein a is a development coefficient, and c is a gray effect amount.
S23
Figure BDA0003539456490000052
For the parameter vector to be estimated, i.e.
Figure BDA0003539456490000053
The least-squares estimation parameter column of the gray differential equation satisfies
Figure BDA0003539456490000054
Wherein B is a mean sequence vector, Y is a constant phase vector, and the following are respectively:
Figure BDA0003539456490000055
s24 builds a whitening equation for the gray differential equation:
Figure BDA0003539456490000061
the solution to the whitening equation is a time response function, and is:
Figure BDA0003539456490000062
s25, subtracting and restoring to obtain a gray prediction model:
Figure BDA0003539456490000063
step three, according to the grey prediction model established in the step two, the micro-tissue damage factor D is subjected toiAnd (6) performing prediction. D corresponding to 0h, 300h and 600h of pre-damage obtained by test1、D2、D3The damage factors under 900h and 1200h are predicted by 3 groups of test values, and the prediction result and the test value are shown in figure 2.
Step four, fitting 5 groups of damage factors of the predicted values and the test values of the grey prediction model with corresponding time parameters, and obtaining an optimal fitting function by using a least square method, wherein the optimal fitting function is shown as the following formula:
y＝y0-aexp(-x/b)
wherein x and y are time and injury factors, respectively, y0Has a fitting value of 0.9254, and the fitting values for parameters a and b are-0.9288 and 1036.74, respectively.
And step five, obtaining the damage factor at any moment by using the fitting function obtained in the step four. Given a time series h1，h2，...，h900A lesion factor may be calculated every 1h, resulting in 900 time-series correlated sets of lesion factor data { D }1，D2，...，D900Calculating the corresponding life of each time point by using the relation between the damage factor and the fatigue life, namely { N }f1，Nf2，...，Nf900And obtaining 900 groups of fatigue life data sets. The relation between the damage factor and the fatigue lifeExpressed as:
D＝a(Nf)b
where parameters a and b were curve fitted to 0.4438 and-0.034, respectively.
And step six, constructing an LSTM neural network prediction model. The model is composed of a memory storage unit, the memory storage unit, namely a memory cell, is regulated and controlled by an updating gate, a forgetting gate and an output gate, and data propagation of an input data set is controlled by a gate control unit.
S61 loads the data set: and (5) respectively taking the damage factors and the fatigue life in the step five as the input and the output of the neural network to train the neural network, wherein 900 groups of data are used, and the LSTM neural network is used for predicting the fatigue life of the last 20 h.
S62, constructing an LSTM neural network prediction model based on a Keras framework:
forget the door: forgetting useless memory accumulated at the past t-1 moment, namely deleting useless information in the damage information,
ft＝σ(Wxfxt+Whfht-1+bf)
where x is the input data set of LSTM, h is the state, W is the weight matrix, b is the bias matrix, σ represents the activation function sigmoid, and f is the forgetting gate.
And (4) updating the door: updating the new content at the time t, retaining the related knowledge in the damage information in the memory cell, updating the information in the memory cell,
it＝σ(Wxixt+Whiht-1+bi)
gt＝tanh(Wxgxt+Whght-1+bg)
where i and g are two function operations for updating the gate, tanh represents the activation function tanh.
Memory storage unit (i.e. memory cell): at each time step of the LSTM, there is a memory cell that gives the LSTM the selective memory function, so that the LSTM has the ability to freely select what is memorized within each time step.
ct＝ct-1⊙ft+gt⊙it
Wherein [ ] is the Hadamard product, and c is the memory cell.
An output gate: calculating by using useful knowledge at t moment to obtain output
Ot＝σ(Wxoxt+Whoht-1+bo)
mt＝tanh(ct)
ht＝ot⊙mt
yt＝Wghht+bg
Wherein O is an output gate, m is the tanh calculation of the memory cell and the output gate, m can convert the useful memory content in the memory cell into output, and y is an output value, namely the predicted value of the fatigue life.
S63, compiling LSTM neural network prediction model, defining average absolute error as loss function:
Figure BDA0003539456490000071
in the formula yiTo predict value, xiAre true values.
And seventhly, predicting the service life of the directionally solidified superalloy related to the time sequence by using the constructed LSTM neural network. And (5) training and predicting the front 880 group data set in the step five in the constructed LSTM neural network model, predicting the life of 20h in the future, wherein the prediction result is shown in fig. 3.
According to the error value calculation formula in step S63, the average absolute error MAE of the predicted value is calculated to be 0.0164, and it can be seen from the figure that the variation tendency of the predicted value calculated using the model is consistent with the test value, and the predicted value approaches the test value. According to the invention, the time sequence prediction is carried out on test data by utilizing the gray prediction, the function fitting is carried out on the predicted value and the test value to obtain a damage factor data set, the service life data set is obtained according to the damage-service life relation, the damage factor data set and the service life data set are respectively used as the input and the output of an LSTM neural network model for training, and finally, the model capable of predicting the time sequence-related fatigue life of the high-temperature alloy is obtained.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (1)

1. A high-temperature alloy fatigue life prediction method based on gray prediction and LSTM comprises the following steps:
step one, acquiring a data set: constructing a data set of microstructure damage information parameters and mechanical property test data of the alloy to be predicted; the micro-tissue damage information parameters include: the volume fraction, carbide and topological close packing of the gamma 'strengthening phase, the gamma matrix phase and the gamma' strengthening phase are equal; the mechanical property test data comprises: fatigue life, yield strength, fatigue strength, and tensile strength;
step two, constructing a gray prediction model: constructing a GM (1, 1) model according to a grey system theory;
s21 known elements raw sequence data:
X(0)＝(x(0)(1)，x(0)(2)，x(0)(3)，...，x(0)(n))
wherein X(0)Represents the original sequence, and x(0)(k) More than or equal to 0, k-1, 2., n; the accumulation of the raw sequence data generates a sequence as follows:
X(1)＝(x(1)(1)，x(1)(2)，x(1)(3)，…，x(1)(n))
wherein X(1)Represents a generation sequence, and
Figure FDA0003539456480000011
X(1)the close-proximity mean generation sequence of (1) is:
Z(1)＝(z(1)(2)，z(1)(3)，...，z(1)(n))
wherein Z(1)Generating a sequence for the close-proximity mean, an
z(1)(k)＝0.5x(1)(k)+0.5x(1)(k-1)，k＝1，2，…，n
S22, establishing a gray differential equation model of GM (1, 1):
x(0)(k)+az(1)(k)＝c
wherein a is a development coefficient, and c is a gray effect amount;
S23
Figure FDA0003539456480000012
for the parameter vector to be estimated, i.e.
Figure FDA0003539456480000013
The least-squares estimation parameter column of the gray differential equation satisfies
Figure FDA0003539456480000014
Wherein B is a mean sequence vector, Y is a constant phase vector, and the following are respectively:
Figure FDA0003539456480000015
s24 builds a whitening equation for the gray differential equation:
Figure FDA0003539456480000021
the solution to the whitening equation is a time response function, as:
Figure FDA0003539456480000022
s25, subtracting and restoring to obtain a gray prediction model:
Figure FDA0003539456480000023
thirdly, forecasting the micro-tissue damage factor based on the time sequence according to the grey forecasting model to obtain a future time forecasting value under the same time interval;
step four, fitting the test values in the data set obtained in the step one and the predicted values obtained in the step three by using a least square method to obtain a fitting function;
step five, obtaining a damage factor value at any time by using the fitting function obtained in the step four; giving time sequence intervals to obtain a damage factor value of each time interval point, and obtaining a damage factor data set related to the time sequence; calculating the fatigue life corresponding to each time point by using the relationship between the damage factors and the fatigue life;
constructing an LSTM neural network prediction model; the model is composed of a memory storage unit, the memory storage unit is regulated and controlled through an updating gate, a forgetting gate and an output gate, namely a memory cell, and the gate control unit controls data transmission of an input data set;
s61 loads the data set: respectively taking the damage factor value and the fatigue life value in the step five as input and output, and predicting the fatigue life by using an LSTM (least squares metric) long-time memory neural network;
s62 construction of an LSTM neural network prediction model based on a Keras framework:
forget the door: forgets to delete useless memory accumulated at the past t-1 moment, namely deletes useless information in the damage information,
ft＝σ(Wxfxt+Whfht-1+bf)
in the formula, x is an input data set of LSTM, h is a state value, W is a weight matrix, b is a bias matrix, sigma represents an activation function sigmoid, and f is a forgetting gate;
and (3) updating a door: updating the new content at the time t, keeping the knowledge related to the damage information in the memory cell, updating the information in the memory cell,
it＝σ(Wxixt+Whiht-1+bi)
gt＝tanh(Wxgxt+Whght-1+bg)
wherein i and g are two function operations of the update gate, and tanh represents an activation function tanh;
memory storage unit (i.e. memory cell): in each time step of the LSTM, a memory cell is provided, and the LSTM is given a selective memory function, so that the LSTM can freely select the content memorized in each time step;
ct＝ct-1⊙ft+gl⊙it
wherein [ ] is Hadamard product, and c is memory cell;
an output gate: and calculating by using useful knowledge at the time t to obtain:
Ot＝σ(Wxoxt+Whoht-1+bo)
mt＝tanh(ct)
ht＝ot⊙mt
yt＝Wghht+bg
wherein O is an output gate, m is the tanh calculation of the memory cell and the output gate, m can convert useful memory contents in the memory cell into output, and y is an output value, namely an alloy performance predicted value;
s63, compiling LSTM neural network prediction model, defining average absolute error as loss function:
Figure FDA0003539456480000031
wherein y isiTo predict value, xiAre true values.
And seventhly, predicting the fatigue life of the directionally solidified high-temperature alloy relevant to the time sequence by using the constructed LSTM neural network.
CN202210258972.5A 2022-03-09 2022-03-09 High-temperature alloy fatigue performance prediction method based on grey prediction and LSTM Pending CN114708927A (en)

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