Grey prediction and lstm based fatigue performance prediction method for superalloys

Abstract

The application aims at solving the problems of high cost and low reliability of the existing technology, and provides a high-temperature alloy fatigue life prediction method based on grey prediction and LSTM neural network; the high-temperature alloy damage factor of a small amount of samples of equal interval time sequence is predicted by using the grey prediction, then the test value and the prediction value are fitted by using the least square method, the fitting function of the time sequence and the damage factor is obtained, the damage factor at any time is obtained, the damage factor at a fixed time interval is selected, the fatigue life at the time interval sequence is calculated through the damage-life relationship, and the damage factor and the fatigue life at the time sequence are taken as a data set of the LSTM neural network for training. The LSTM neural network can be used as a time sequence neural network prediction model based on damage information to predict the high-temperature alloy fatigue life of the time sequence damage. Without a large number of tests and simulations, a small amount of sample data can be used for fatigue life prediction related to time sequence, so that the maintenance cost of the component is greatly reduced.

Description

Technical Field

[0001] This invention relates to a method for predicting the fatigue properties of high-temperature alloys based on grey prediction and LSTM, and particularly to a method for predicting the fatigue properties of directionally solidified high-temperature alloys based on grey prediction and LSTM long short-time neural networks, belonging to the related field of directionally solidified high-temperature alloys. Background Technology

[0002] Directional solidification superalloys are frequently used in turbine blades, hot-end components of aero-engines, due to their superior properties. Turbine blades operate in extremely harsh environments, enduring prolonged mechanical loads at high temperatures. This leads to time-dependent evolution of the blade material's microstructure, termed microdamage during service. Microdamage significantly reduces the mechanical properties of the blade material, affecting its service life and consequently impacting the safe operation and service life of the aero-engine. Therefore, the rapid and accurate prediction of material properties is receiving increasing attention. However, due to the difficulty of sampling materials during service and the limited sample size of experimental data, it is challenging to accurately predict material properties using limited data.

[0003] Commonly used methods for predicting material properties include empirical formulas and the finite element method (FEM). Establishing empirical formulas for life prediction requires extensive mechanical testing, followed by analysis of the experimental data to build a predictive model. This method is costly. The FEM is also a commonly used and effective method for predicting material properties; however, it often fails to accurately reflect engineering realities, resulting in lower reliability of its predictions. Summary of the Invention

[0004] The purpose of this invention is to address the problems of high prediction costs and low reliability in existing technologies by providing a high-temperature alloy life prediction method based on grey prediction and LSTM neural networks. This invention first uses grey prediction to predict the damage factors of high-temperature alloys from a very small number of samples in an equally spaced time series. Then, using the least squares method, the experimental values ​​are fitted to the predicted values ​​to obtain a fitting function between the time series and the damage factors, thus obtaining the damage factors at any given time. By selecting the damage factors at a fixed time interval, the fatigue life of this time interval series is calculated using the damage-life relationship. The damage factors and fatigue life of this time series are then used as the dataset for training an LSTM neural network. This LSTM neural network can serve as a time-series neural network prediction model based on damage information to predict time-related high-temperature alloy properties. Time-series-related fatigue life prediction can be performed using a very small amount of sample data without requiring extensive experiments and simulations.

[0005] The objective of this invention is achieved through the following technical solution.

[0006] A method for predicting the fatigue life of high-temperature alloys based on grey prediction and LSTM includes the following steps:

[0007] Step 1, Dataset Acquisition: Construct a dataset containing microstructural damage information parameters and mechanical property test data of the alloy to be predicted. The microstructural damage information parameters include: γ′ strengthening phase, γ matrix phase, γ′ strengthening phase volume fraction, carbides, and topologically close-packed phases, etc.; the mechanical property test data includes: fatigue life, yield strength, fatigue strength, and tensile strength.

[0008] Step 2, Construction of the grey prediction model: Based on grey system theory, construct the GM(1,1) model.

[0009] S21: Original sequence data of known elements:

[0010] X (0) =(x (0) (1), x (0) (2), x (0) (3), ..., x (0) (n))

[0011] Where X (0) Denotes the original sequence, and x (0) (k)≥0, k=1,2,...,n. The cumulative sequence generated from the original sequence data is:

[0012] X (1) =(x (1) (1), x (1) (2), x (1) (3), ..., x (1) (n))

[0013] Where X (1) Indicates the generated sequence, and

[0014]

[0015] X (1) The nearest neighbor mean generation sequence is:

[0016] Z (1) =(z (1) (2), z (1) (3), ..., z (1) (n))

[0017] Z (1) Generate a sequence that is immediately adjacent to the mean, and

[0018] z (1) (k)=0.5x (1) (k)+0.5x (1)(k-1), k = 1, 2, ..., n

[0019] S22 establishes the grey differential equation model of GM(1,1):

[0020] x (0) (k)+az (1) (k)=c

[0021] Where a is the development coefficient and c is the gray action quantity.

[0022] S23 The vector of parameters to be estimated, i.e. Then the least squares estimated parameter sequence of the grey differential equation satisfies

[0023]

[0024] Where B is the mean sequence vector and Y is the constant phase vector, respectively:

[0025]

[0026] S24 establishes the whitening equation for the gray differential equation:

[0027]

[0028] The solution to the whitening equation is a time response function, which is:

[0029]

[0030] S25 cumulative subtraction restoration yields the grey prediction model:

[0031]

[0032] Step 3: Based on the grey prediction model, perform time series-based prediction of micro-tissue damage factors to obtain future time prediction values ​​for the same time interval.

[0033] Step four: Using the least squares method, fit the experimental values ​​in the dataset from step one and the predicted values ​​obtained in step three to obtain the fitting function.

[0034] Step 5: Using the fitting function obtained in Step 4, calculate the damage factor value at any time. Given a time series interval, obtain the damage factor value at each time interval, thus obtaining the time series-related damage factor dataset; calculate the fatigue life corresponding to each time point using the relationship between the damage factor and fatigue life.

[0035] Step six: Construction of the LSTM neural network prediction model. This model consists of memory storage units, which are regulated by update gates, forget gates, and output gates. The data propagation of the input dataset is controlled by gating units.

[0036] S61 Load Dataset: The damage factor value and fatigue life value from step five are used as input and output, respectively, and the fatigue life is predicted using an LSTM neural network.

[0037] S62 builds an LSTM neural network prediction model based on the Keras framework:

[0038] Forget gate: Forgetting useless memories accumulated at time t-1 in the past, that is, deleting useless information from damaged information.

[0039] f t =σ(W xf x t +W hf h t-1 +b f )

[0040] In the formula, x is the input dataset of LSTM, h is the state value, W is the weight matrix, b is the bias matrix, σ represents the activation function sigmoid, and f is the forget gate.

[0041] Update gate: Updates the new content at time t, retains relevant knowledge from the damage information in the memory cell, and updates the information within the memory cell.

[0042] i t =σ(W xi x t +W hi h t-1 +b i )

[0043] g t =tanh(W xg x t +W hg h t-1 +b g )

[0044] In the formula, i and g are the two function operations of the update gate, and tanh represents the activation function tanh.

[0045] Memory storage unit (i.e., memory cell): There is a memory cell in each time step of LSTM, which gives LSTM the ability to select memory, allowing LSTM to freely select the content to be memorized in each time step.

[0046] c t =c t-1 ⊙ft +g t ⊙i t

[0047] Where ⊙ represents the Hadamard product and c represents a memory cell.

[0048] Output gate: Using the useful knowledge at time t, we calculate and obtain:

[0049] O t =σ(W xo x t +W ho h t-1 +b o )

[0050] m t =tanh(c t )

[0051] h t =o t ⊙m t

[0052] y t =W g h ht +b g

[0053] In the formula, O is the output gate, m is the tanh calculation between the memory cell and the output gate, m can convert the useful memory content in the memory cell into the output, and y is the output value, i.e. the predicted value of alloy performance.

[0054] S63 compiles LSTM neural network prediction models, defining the mean absolute error as the loss function:

[0055]

[0056] In the formula y i For the predicted value, x i This is the actual value.

[0057] Step 7: Use the constructed LSTM neural network to predict the fatigue life of time-dependent directional solidification superalloys.

[0058] Beneficial effects

[0059] 1. The grey prediction model has the advantages of short-term prediction and prediction with very small sample size. It belongs to the time series statistical model and can effectively predict the future development trend of time-related data with very small sample size obtained from high-temperature alloy material samples.

[0060] 2. Directionally solidified high-temperature alloys used on engine hot-end components are difficult to sample during their service life, making testing challenging and resulting in high costs for mechanical property testing. This invention utilizes a neural network prediction model based on a small sample size to predict material life, which can significantly reduce testing costs, material costs, and turbine blade maintenance costs.

[0061] 3. The LSTM neural network model established using the expanded data can predict the lifetime of materials based on time-series micro-tissue damage at any time, thus greatly improving the lifetime prediction efficiency of materials in service.

[0062] 4. The advantages of grey prediction models in short-term and few-sample prediction, combined with the nonlinear prediction advantages of LSTM neural networks, can improve the accuracy of lifespan prediction. Attached Figure Description

[0063] Figure 1 The method flowchart of the present invention.

[0064] Figure 2 A comparison chart of predicted and experimental values ​​from the grey prediction model.

[0065] Figure 3 A comparison chart of predicted and experimental values ​​based on an LSTM neural network. Detailed Implementation

[0066] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0067] A method for predicting the fatigue life of directionally solidified superalloys based on grey prediction and LSTM is described in the following process: Figure 1 As shown, it includes the following steps:

[0068] Step 1: Data Acquisition. A database of microstructure damage information and fatigue life data for directionally solidified superalloys was acquired. The microstructure damage information was obtained through laboratory electron microscopy observation and image analysis software, while the fatigue life data was obtained through mechanical property tests. Microstructure damage parameters include: γ′ strengthening phase size, γ matrix phase size, γ′ strengthening phase volume fraction, carbides, and topologically close-packed phases, etc. The mechanical property test data includes: fatigue life, yield strength, fatigue strength, and tensile strength, etc. The pre-damage treatment conditions for the superalloy microstructure were set based on the turbine blade overhaul time and actual operating conditions. The pre-damage time nodes were set at 0h, 300h, 600h, 900h, and 1200h, resulting in four sets of microstructure damage information data and fatigue life data. The damage information at each time point was defined as the damage factor D. i , 0≤D i ≤1, fatigue life at each time point is determined by Nfi Let i represent a time point. Each time point corresponds to a set of damage factors D. i and fatigue life N fi In this embodiment, there are a total of 5 sets of experimental data, namely {D1, D2, D3, D4, D5} and {N}. f1 N f2 N f3 N f4 N f5}

[0069] Step 2, Construction of the grey prediction model: Based on grey system theory, construct the GM(1,1) model.

[0070] S21: Original sequence data of known elements:

[0071] X (0) =(x (0) (1), x (0) (2), x (0) (3), ..., x (0) (n))

[0072] Where X (0) Denotes the original sequence, and x (0) (k)≥0, k=1,2,...,n. The cumulative sequence generated from the original sequence data is:

[0073] X (1) =(x (1) (1), x (1) (2), x (1) (3), ..., x (1) (n))

[0074] Where X (1) Indicates the generated sequence, and

[0075]

[0076] X (1) The nearest neighbor mean generation sequence is:

[0077] Z (1) =(z (1) (2), z (1) (3), ..., z (1) (n))

[0078] Z (1) Generate a sequence that is immediately adjacent to the mean, and

[0079] z (1) (k)=0.5x (1) (k)+0.5x (1) (k-1), k = 1, 2, ..., n

[0080] S22 establishes the grey differential equation model of GM(1,1):

[0081] x (0) (k)+az (1) (k)=c

[0082] Where a is the development coefficient and c is the gray action quantity.

[0083] S23 The vector of parameters to be estimated, i.e. Then the least squares estimated parameter sequence of the grey differential equation satisfies

[0084]

[0085] Where B is the mean sequence vector and Y is the constant phase vector, respectively:

[0086]

[0087] S24 establishes the whitening equation for the gray differential equation:

[0088]

[0089] The solution to the whitening equation is a time response function, which is:

[0090]

[0091] S25 cumulative subtraction restoration yields the grey prediction model:

[0092]

[0093] Step 3: Based on the grey prediction model established in Step 2, analyze the micro-tissue damage factor D. i Prediction was performed. Using the three sets of experimental values ​​(D1, D2, and D3) corresponding to pre-damage at 0h, 300h, and 600h, the damage factors at 900h and 1200h were predicted. The prediction results were compared with the experimental values. Figure 2 As shown.

[0094] Step four: Fit the five sets of damage factors (predicted and experimental values ​​from the grey prediction model) to the corresponding time parameters, and use the least squares method to obtain the best fitting function, as shown in the following formula:

[0095] y = y0 - aexp(-x / b)

[0096] In the formula, x and y are time and damage factor, respectively, the fitted value of y0 is 0.9254, and the fitted values ​​of parameters a and b are -0.9288 and 1036.74, respectively.

[0097] Step 5: Using the fitting function obtained in Step 4, the damage factor at any given time can be obtained. Given a time series {h1, h2, ..., h...} 900} = {1, 2, ..., 900}h, and a damage factor can be calculated every 1 hour, thus obtaining a dataset of 900 time-series related damage factors {D1, D2, ..., D...} 900}, using the relationship between damage factors and fatigue life, the corresponding life at each time point is calculated, i.e., {N} f1 N f2 , ..., N f900}, resulting in a fatigue life dataset of 900 sets. The relationship between the damage factor and fatigue life is expressed as:

[0098] D = a(N) f ) b

[0099] The parameters a and b, after curve fitting, are 0.4438 and -0.034, respectively.

[0100] Step six: Construction of the LSTM neural network prediction model. This model consists of memory storage units, which are regulated by update gates, forget gates, and output gates. The data propagation of the input dataset is controlled by gating units.

[0101] S61 Load Dataset: Train the neural network by using the damage factor and fatigue life from step five as the input and output of the neural network, respectively. A total of 900 sets of data are used, and the LSTM neural network is used to predict the fatigue life in the last 20 hours.

[0102] S62 builds an LSTM neural network prediction model based on the Keras framework:

[0103] Forget gate: Forgetting useless memories accumulated at time t-1 in the past, that is, deleting useless information from damaged information.

[0104] f t =σ(W xf x t +W hf h t-1 +b f )

[0105] In the formula, x is the input dataset 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 forget gate.

[0106] Update gate: Updates the new content at time t, retains relevant knowledge from the damage information in the memory cell, and updates the information within the memory cell.

[0107] i t =σ(W xi x t +W hi h t-1 +b i )

[0108] g t =tanh(W xg x t +W hg h t-1 +b g )

[0109] In the formula, i and g are the two function operations of the update gate, and tanh represents the activation function tanh.

[0110] Memory storage unit (i.e., memory cell): There is a memory cell in each time step of LSTM, which gives LSTM the ability to select memory, allowing LSTM to freely select the content to be memorized in each time step.

[0111] c t =c t-1 ⊙f t +g t ⊙i t

[0112] Where ⊙ represents the Hadamard product and c represents a memory cell.

[0113] Output gate: Calculates the output using the knowledge available at time t.

[0114] O t =σ(W xo x t +W ho h t-1 +b o )

[0115] m t =tanh(c t )

[0116] h t =o t ⊙m t

[0117] y t =W gh h t +b g

[0118] In the formula, O is the output gate, m is the tanh calculation between the memory cell and the output gate, m can convert the useful memory content in the memory cell into the output, and y is the output value, which is the fatigue life prediction value.

[0119] S63 compiles LSTM neural network prediction models, defining the mean absolute error as the loss function:

[0120]

[0121] In the formula y i For the predicted value, x i This is the actual value.

[0122] Step 7: Predict the lifetime of time-dependent directional solidification superalloys using the constructed LSTM neural network. Train and predict the lifetime over the next 20 hours using the first 880 datasets from Step 5 within the constructed LSTM neural network model. The prediction results are as follows: Figure 3 As shown.

[0123] According to the error calculation formula in step S63, the mean absolute error (MAE) of the predicted value is calculated to be 0.0164. Furthermore, the graph shows that the trend of the predicted value calculated using the model is consistent with the experimental value, and the predicted value is close to the experimental value. This invention utilizes grey prediction to perform time-series prediction on experimental data, performs function fitting between the predicted and experimental values ​​to obtain a damage factor dataset, and obtains a life dataset based on the damage-life relationship. The damage factor dataset and life dataset are used as the input and output of an LSTM neural network model for training, respectively, ultimately resulting in a model that can predict the fatigue life of time-related high-temperature alloys.

[0124] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting the fatigue life of high-temperature alloys based on grey prediction and LSTM, comprising the following steps: Step 1, Data Acquisition: Construct a dataset of microstructure damage information parameters and mechanical property test data of the alloy to be predicted; The microstructural damage information parameters include: γ′ reinforcing phase, γ matrix phase, γ′ reinforcing phase volume fraction, carbides, and topologically close-packed phases, etc.; the mechanical property test data include: fatigue life, yield strength, fatigue strength, and tensile strength. Step 2, Construction of the grey prediction model: Based on grey system theory, construct the GM(1,1) model; S21: Original sequence data of known elements: X (0) =(x (0) (1),x (0) (2),x (0) (3),...,x (0) (n)) Where X (0) Denotes the original sequence, and x (0) (k)≥0, k=1,2,...,n; the cumulative sequence generated from the original sequence data is: X (1) =(x (1) (1),x (1) (2),x (1) (3),...,x (1) (n)) Where X (1) Indicates the generated sequence, and X (1) The nearest neighbor mean generation sequence is: WITH (1) =(of (1) (2),with (1) (3),...,with (1) (n)) Z (1) Generate a sequence that is immediately adjacent to the mean, and With (1) (k)=0.5x (1) (k)+0.5x (1) (k-1),k=1,2,...,n S22 establishes the grey differential equation model of GM(1,1): x (0) (k)+az (1) (k)=c Where a is the development coefficient and c is the grey effect quantity; S23 The vector of parameters to be estimated, i.e. Then the least squares estimated parameter sequence of the grey differential equation satisfies Where B is the mean sequence vector and Y is the constant phase vector, respectively: S24 establishes the whitening equation for the gray differential equation: The solution to the whitening equation is a time response function, which is: S25 cumulative subtraction restoration yields the grey prediction model: Step 3: Based on the grey prediction model, perform time series-based prediction of micro-tissue damage factors to obtain future time prediction values ​​under the same time interval; Step 4: Using the least squares method, fit the experimental values ​​in the dataset obtained in Step 1 and the predicted values ​​obtained in Step 3 to obtain the fitting function; Step 5: Using the fitting function obtained in Step 4, the damage factor value at any time is obtained; given the time series interval, the damage factor value at each time interval is obtained, that is, the time series-related damage factor dataset is obtained; using the relationship between damage factor and fatigue life, the fatigue life corresponding to each time point is calculated. Step 6: Construction of the LSTM neural network prediction model; This model consists of memory storage units, which are regulated by update gates, forget gates and output gates, i.e. memory cells, and the data propagation of the input dataset is controlled by gating units; S61 Load Dataset: Take the damage factor value and fatigue life value from step five as input and output respectively, and use the LSTM long short time memory neural network to predict the fatigue life. S62 builds an LSTM neural network prediction model based on the Keras framework: Forget gate: Forgetting useless memories accumulated at time t-1 in the past, that is, deleting useless information from damaged information. f t =σ(W xf x t +W hf h t-1 +b f ) In the formula, x is the input dataset of LSTM, h is the state value, W is the weight matrix, b is the bias matrix, σ represents the activation function sigmoid, and f is the forget gate; Update gate: Updates the new content at time t, retains relevant knowledge from the damage information in the memory cell, and updates the information within the memory cell. i t =σ(W xi x t +W hi h t-1 +b i ) g t =tanh(W xg x t +W hg h t-1 +b g ) In the formula, i and g are the two function operations of the update gate, and tanh represents the activation function tanh; Memory storage unit: In each time step of LSTM, there is a memory cell, which gives LSTM the ability to select memory, allowing LSTM to freely select the content to be memorized in each time step; c t =c t-1 ☉f t +g t ☉i t Where ⊙ represents the Hadamard product and c represents the memory cell; Output gate: Using the useful knowledge at time t, we calculate and obtain: O t =σ(W xo x t +W ho h t-1 +b o ) m t = tanh(c t ) h t =o t ☉m t y t =W gh h t +b g In the formula, O is the output gate, m is the tanh calculation between the memory cell and the output gate, m can convert the useful memory content in the memory cell into the output, and y is the output value, i.e. the predicted value of alloy performance. S63 compiles LSTM neural network prediction models, defining the mean absolute error as the loss function: Where y i For the predicted value, x i The actual value; Step 7: Use the constructed LSTM neural network to predict the fatigue life of time-dependent directional solidification superalloys.

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