Method for predicting exhaust gas temperature after engine cleaning by migrating process neural network

Abstract

The present invention relates to a method for predicting the exhaust temperature after engine cleaning by a migrating process neural network. A TPNN model is provided, and the TPNN includes a mapping method between variables and the EGTM and a mapping method between variables. The feature is that for the mapping method between data parameters and the EGTM, a linear fitting method is adopted to establish the corresponding relationship between all variables and EGTM data, and forward and inverse solutions are realized. Among them, the data before water washing is linearly fitted, and the value at ti of the linear function is taken as VBW, the pre-water washing time CSN and the water washing cycle ΔCSN; the data after water washing is linearly fitted, the difference between the value at ti of the linear function and VBW is taken as INC, and the slope of the linear function is taken as DR; a migrating process neural network is used as the mapping model between the variables before and after water washing, and the model adopts a migration technique to learn the initial framework from the data of the same type of engine and migrate it to the target engine data for training.

Description

Technical Field:

[0001] The present invention relates to the technical field of aero-engine exhaust gas temperature monitoring, and specifically relates to a method for predicting the exhaust gas temperature after engine washing by a Transfer Process Neural Networks (hereinafter referred to as TPNN), which can solve the problem of difficultly accurately predicting the trend of data mutation caused by washing in the traditional technology. Background Art:

[0002] After an aero-engine has been running for a long time, dirt in the air deposits on the surface of the engine blades. While promoting blade pitting, the fouling of the blades reduces the compressor air flow rate, resulting in a reduction in thrust. To compensate for the thrust, the engine increases fuel consumption, causing the exhaust gas temperature (EGT) to rise and the engine life to decrease. Due to the low level of air flow, the increased fuel cannot be fully burned, leading to an increase in the emission of polluting gases by the engine.

[0003] In response to the theme of "energy conservation and emission reduction" pursued by the aviation industry and to meet the airworthiness requirements of the engine, it is necessary to wash the engine. Engine washing refers to cleaning the gas path of the in-service engine. Engine washing can remove blade fouling, restore air flow rate and thrust. Therefore, it can reduce fuel consumption and EGT, prevent blade pitting, and extend the engine life. Therefore, engine washing has been widely emphasized and applied in various countries around the world. The engine washing work is listed as a mandatory item in the maintenance regulations.

[0004] Currently, airlines copy the regular washing plan provided by the manufacturer without adjusting the washing plan according to local conditions. The washing cycle in the manufacturer's plan is longer than the actual washing cycle required by the local engines. Therefore, the local engines are often not washed in time. Figure 1 This is a photo of the engine interior taken with a borescope during the investigation at the Beijing maintenance base. There is a lot of dirt adhering to the compressor blades, which proves that the engine has not been washed in time.

[0005] The washing effect is difficult to directly measure with indicators. However, since engine washing can reduce EGT, the washing effect can be evaluated by observing EGT. By predicting the washing effect, it is possible to determine whether the upcoming washing timing is appropriate and whether repair is needed. This helps to extend the engine service life, reduce the emission of polluting gases, and thus improve the economic benefits of airlines.

[0006] The prediction of the EGT margin (EGTM) after water washing can be used to estimate the water washing effect. Usually, airlines use EGTM instead of EGT as a reference for the water washing effect. EGTM refers to the difference between the EGT red line value of the engine and the exhaust gas temperature when the engine takes off at full thrust at the flat power temperature. Since the calculation of EGTM excludes the interference of factors such as noise, it can reflect the water washing effect of the engine better than EGT.

[0007] EGTM will increase significantly after the water washing of aero engines. Figure 2 (a) Taking points to represent EGTM, it shows that EGTM continued to decline before water washing, had a step after water washing, and then continued to decline. By accurately predicting the change of EGTM after water washing, airlines can not only evaluate the duration of the water washing effect according to the prediction results, but also evaluate the reduction of polluting gases in the engine after water washing, providing data support for engine emission control and environmental impact assessment.

[0008] However, such research faces a challenge that traditional methods cannot accurately predict the change of EGTM after water washing. As Figure 2 (a) shows, traditional methods achieve prediction by extending the current data trend, making the data predicted by traditional methods have a continuous trend with the previous data. Traditional methods are only applicable to time series data without the influence of mutation factors. Related research uses methods such as Long Short-Term Memory (LSTM) and kernel Extreme Learning Machine (KELM) to predict engine data. The model required by airlines can accurately predict the data mutation that will occur after water washing when the engine is not water washed, and its prediction effect is as Figure 2 (b) shows. Traditional prediction methods are difficult to predict the mutations that occur in the later data. Therefore, the method currently adopted in the engineering front line is to refer to the increase of EGTM after monthly water washing in history.

[0009] Another challenge is that the number of cleaning times during the in-service period of the engine is small, which increases the prediction difficulty. Although water washing significantly improves EGT and effectively extends the engine life, according to the current water washing plan, during the in-service period of 3000 flight cycles of the engine, the average water washing cycle is more than 300 cycles. Therefore, the number of water washings during the in-service period is less than 10 times. Moreover, in reality, relevant maintenance records are often missing, so the average number of records that can be collected from each engine is only 5. Therefore, the prediction of aero engine data after water washing is a typical small sample prediction task. Summary of the Invention:

[0010] In view of the disadvantages and deficiencies existing in the prior art, in order to accurately predict the change of EGTM after water washing and provide guarantee for the evaluation of the duration of water washing effect and environmental impact in subsequent processing, a method for predicting the exhaust temperature of an engine after cleaning by TPNN is proposed.

[0011] The present invention is achieved by the following measures:

[0012] A method for predicting the exhaust temperature of an engine after cleaning by TPNN, provided with a TPNN model. TPNN includes a mapping method between variables and EGTM and a mapping method between variables. It is characterized in that, for the mapping method between data parameters and EGTM, a linear fitting method is adopted to establish the corresponding relationship between all variables and EGTM data, and forward and inverse solutions are realized. Among them, the data before water washing is linearly fitted, and the value at ti of the linear function is taken as VBW, the advance water washing time CSN and the water washing cycle ΔCSN; the data after water washing is linearly fitted, and the difference between the value at ti of the linear function and VBW is taken as INC, and the slope of the linear function is taken as DR; for the mapping method between variables [VBW, CSN, ΔCSN] and [DR, INC], a transfer process neural network is used as the mapping model of variables before and after water washing. The model adopts transfer technology to learn the initial framework from the data of engines of the same type and transfer it to the data of the target engine for training; among them, the CSN is the flight cycle, which is the total number of cycles of the engine from factory to the current; ΔCSN is when the engine is water washed multiple times, the water washing interval is represented by the flight cycle, denoted as ΔCSN; INC is set that when the current water washing times is i and the water washing time is t i ,t i The sudden change of the EGTM after that is called the step amount INC; DR is the decay rate of EGTM. The EGTM after water washing is linearly fitted, and the slope of the fitted straight line is called the decay rate DR of EGTM; VBW is the EGTM value of the engine before water washing. The mapping method between EGTM and data parameters of the present invention includes the following contents:

[0013] Let x be the EGTM data after water washing to be predicted, let the number of flight cycles be t, and the water washing time be, then x is expressed by formula (1): x = DR×(t - t i ) + INC + VBW, t > t i (1),

[0014] In formula (1), [DR, INC] is mapped from [VBW, CSN, ΔCSN], [VBW, CSN, ΔCSN] is obtained from the data before ti. The transfer process neural network is called h, and let θ be the model parameter, representing the weights and biases in the transfer process neural network. The transfer process neural network h is expressed as:

[0015] [DR, INC] = h(VBW, CSN, ΔCSN|θ) (2),

[0016] The model parameter θ is trained from [DR, INC] and [VBW, CSN, ΔCSN] extracted from sample data and maintenance records, and the training process of θ is expressed as:

[0017]

[0018] Let the EGTM data in the sample be X = {x1, x2, x3, ……, x n}, where n is the total amount of data; the number of water washes is {1, 2, …, i, … k}, and k is the total number of water washes; the time points of the water wash records are: T washing = {t1, t2, …, t i , …, t k}, then according to T washing X is divided into k + 1 groups of data:

[0019]

[0020] If the water wash time is characterized by the number of flight cycles, for the i-th water wash, CSN is the total number of flight cycles at the current water wash, and ΔCSN is the number of flight cycles between two water wash events, then there is:

[0021] CSN i = t i

[0022] ΔCSN i = t i - t (i-1) (5);

[0023] Perform linear fitting on the data before water wash, and take the value at the water wash point of the fitting function as VBW;

[0024] For the i-th water wash, the data before water wash is expressed as X(i) = {x t(i－1)+1 , x t(i－1)+2 , ……, x ti－1}, let the parameters of the linear fitting function be b i , a i , then there is:

[0025] X(i) = b i + a i × t, t = {t (i-1) + 1, t (i-1) + 2,..., t i - 1} (6)

[0026] Use the data X(i) to fit b i , ai , we get:

[0027]

[0028]

[0029] where card(·) refers to the number of elements in X(i), and thus the VBW for the i-th water wash i can be calculated by Equation (8):

[0030] VBW i = b i + a i ×(ti - 1) (8),

[0031] DR and INC in the data sample are obtained from the change curves of the engine EGTM data after water wash;

[0032] Subtract the engine EGTM data value VBW before water wash for each group of data in Equation (4) respectively, and we have:

[0033]

[0034] [DR, INC] is linearly fitted from the data in Equation (9). For the i-th water wash, the data parameters DR i and INC i are fitted with the data of X(i + 1) as:

[0035]

[0036]

[0037] The transfer process neural network TPNN of the present invention is composed of process neurons. The neuron includes three parts: weighting, integration, and excitation. Suppose the time interval for sample acquisition is [0, T], then the input of the process neuron in the hidden layer is:

[0038]

[0039] In the formula: w(t) is the weight function between the process neuron in the hidden layer and the input. The output of the process neuron in the hidden layer is:

[0040] out = g(net + θ1) (12)

[0041] In the formula: θ1 is the bias of the process neuron in the hidden layer, g(·) is the excitation function of the process neuron in the hidden layer, and is set as the Sigmoid function; the excitation function f(·) of the output layer is a linear function, that is, f(z) = z. Finally, the expression of this transfer process neural network is:

[0042]

[0043] where: x i —— an input vector of length L, which is the i-th input unit of the input layer;

[0044] w i —— the weight vector connecting the j-th neuron in the hidden layer and the i-th input unit in the input layer;

[0045] v j —— the weight value connecting the j-th neuron in the hidden layer and the output neuron;

[0046] θ2 —— the bias of the output layer;

[0047] The data extracted according to the washing records is: data = [X:(ΔCSN, CSN, VBW), Y:(DR, INC)]. For engines with incomplete washing records, the source domain S1 = {S1, S2, …, Si, …|Si = [data1, data2, …]} is defined; for engines with complete washing records, the source domain S2 = {S1, S2, …, Si, …|Si = [data1, data2, …]} is defined; for the target engine of the prediction task, the target domain G = {G1, G2|G = [data1, data2, …]} is defined;

[0048] To ensure that the data has a similar distribution, the same type of engine is collected for the source domains S1, S2 and the target domain G. Therefore, these data have a similar distribution. In fact, most of the engine data has the problem of incomplete records. Therefore, the sample size of H1 will be much larger than that of S2 and G;

[0049] Use the samples of the source domain S1 to train the TPNN model. The optimization task is:

[0050] loss = ∑(y - f(x))2 / n(14),

[0051] Transfer the trained model parameters w and v to the new model. Then use the samples of the source domain S2 to train the new model for the second transfer, and use the samples of the target domain G to train. The relatively small data of S2 and G may cause overfitting problems. To prevent this problem, set the optimization tasks for S2 and G as:

[0052] loss = ∑(y - f(x))2 / n + λ∑|w| / n + λ∑|v| / n + λ∑w2 / n + λ∑v2 / n (15);

[0054] In the design of the hidden layer structure of TPNN, let: n in be the number of nodes in the input layer, n hidden be the number of nodes in the hidden layer, nout is the number of nodes in the output layer; the number of nodes in the hidden layer of the process neural network is determined by Equation (16): The above model has a dual output, so n out = 2, n in = 3, n hidden ≈ 3.

[0055] The present invention further designs a new backpropagation learning algorithm based on orthogonal basis expansion for the TPNN. According to the Weierstrass approximation theorem, for any ε > 0, there exists a polynomial function P(t) such that Equation (17) holds:

[0056]

[0057] Given a set of orthonormal basis functions in the input space of the TPNN: b1(t), b2(t), ……, b ∞ (t), given a as the expansion coefficient, the component function x(t) of the i-th in the input vector of the network can be expanded as:

[0058]

[0059] To make the orthogonal basis closest to the original time series, choose to perform Schmidt orthogonalization on x i (t) to generate the orthonormal basis b l (t):

[0060] b1′(t) = x i1 (t)

[0061]

[0062]

[0063] For any ε > 0, there exists a sufficiently large constant L0 such that for any L > L0, there is:

[0064]

[0065] At this time, Equation (18) can be expressed as:

[0066]

[0067] Among them, a il can be calculated as:

[0068]

[0069] Similarly, w i (t) can also be expanded under b1(t), b2(t), ……, b ∞ (t) as:

[0070]

[0071] Substituting Equation (21) and Equation (23) into Equation (13), we get:

[0072]

[0073] Since b1(t), b2(t), ……, b ∞ (t) are mutually orthogonal, we have:

[0074]

[0075] Therefore, Equation (24) can be simplified to:

[0076]

[0077] From this derivation process, the optimization rules of the neural network are:

[0078]

[0079]

[0080]

[0081]

[0082] The present invention proposes a TPNN prediction method for predicting the EGTM after water washing. First, the EGTM before water washing is mapped to data parameters (water washing interval, water washing time, current state); then, using the data parameter mapping model, the data parameters after water washing (data increase amount, data decline trend) are generated from the data parameters of the data before water washing; finally, the data parameters after water washing are mapped to the EGTM data after water washing. Taking the data of the CFM56-5B aero-engine as a sample, the proposed model is compared with LSTM, XGBoost, and KELM in terms of performance, and the results verify that the prediction method guided by maintenance records can accurately predict the EGTM after water washing. Description of the Drawings:

[0083] Attached Figure 1 is a photo of the engine interior.

[0084] Attached Figure 2 is the prediction effect diagram of the traditional model, where (a) the traditional model is only an extension of the data trend, and (b) the expected prediction effect of the airline.

[0085] Attached Figure 3It is the change of the EGTM data of the CFM56-5B engine after water wash, showing the characteristics related to engine cleaning, where DR and INC are the EGTM data characteristics before cleaning, and VBW, CSN, and ΔCSN are the characteristics after cleaning.

[0086] Appendix Figure 4 It is the process of modeling and prediction of the neural network guided by maintenance records.

[0087] Appendix Figure 5 It is the structure diagram of the TPNN model.

[0088] Appendix Figure 6 It is the schematic diagram of the structure of the neurons of the process neural network.

[0089] Appendix Figure 7 It is the schematic diagram of the backpropagation structure of the TPNN.

[0090] Appendix Figure 8 It is the schematic diagram of the exhaust gas temperature measurement points of an aeroengine.

[0091] Appendix Figure 9 It is the prediction results of the EGTM of the samples by all four methods in the embodiments of the present invention.

[0092] Appendix Figure 10 It is the residual situation of the data parameter prediction method based on the TPNN in the present invention. 10(a) is the residual normal probability plot, and 10(b) is the residual histogram.

[0093] Appendix Figure 11 It is the prediction effects of two methods, where 11(a) is the prediction effect of the decay rate DR, and 11(b) is the prediction effect of the step size INC. Specific implementation manner:

[0094] Embodiment 1:

[0095] In order to achieve accurate prediction of the change of EGTM after water wash and provide guarantee for the evaluation of the duration of the water wash effect and environmental impact in subsequent research, the present invention proposes a TPNN model. The model includes the mapping method between variables and EGTM and the mapping method between variables.

[0096] First, the variables involved are introduced. Figure 3 It shows the change of the EGTM data of the CFM56-5B engine after water wash, and the corresponding time scale is characterized by flight cycles.

[0097] The variable names related to the change of EGTM after engine water wash are introduced as follows:

[0098] The A.CSN. flight cycle is the total number of cycles of the engine from factory to the current time, called (Cycle Since New, CSN). Therefore Figure 3 the water wash time involved in is the CSN of the engine during water wash.

[0099] B. ΔCSN. When the engine is water washed multiple times, the water wash interval can also be expressed by flight cycles, denoted as ΔCSN.

[0100] C. INC. Let the current number of water washes be i and the water wash time be ti. From Figure 3 it shows that there is an obvious mutation in EGTM after ti, and this obvious mutation is called the step amount (Increment, INC).

[0101] D. DR. In order to obtain the INC point with a relatively small computational complexity, the EGTM after water wash is linearly fitted. The slope of the fitted straight line is called the decreasing rate (Decreasing Rate, DR) of EGTM.

[0102] E. VBW. Figure 3 The VBW in is the value of the engine EGTM before water wash (Value Before Washing, VBW).

[0103] For the mapping method of data parameters and EGTM, the present invention adopts a linear fitting method to establish the corresponding relationship between all variables and EGTM data, and realizes forward and inverse solutions. Specifically, the present invention linearly fits the data before water wash, and takes the value at t i of the linear function as VBW, the advance water wash time CSN and the water wash cycle ΔCSN; linearly fits the data after water wash, and takes the difference between the value at t i of the linear function and VBW as INC, and takes the slope of the linear function as DR.

[0104] For the mapping method between variables [VBW, CSN, ΔCSN] and [DR, INC], in the case of a small number of samples extracted from a single engine, the present invention proposes a transfer process neural network as a mapping model for variables before and after water wash. The model uses transfer technology to learn the initial framework from the data of other engines of the same type and transfers it to the target engine data for training. The process of modeling and prediction of the neural network guided by maintenance records is as Figure 4 shown.

[0105] Among them, the mapping method of EGTM and data parameters is as follows:

[0106] Let x be the EGTM data after water wash to be predicted, let the number of flight cycles be t, and the water wash time be, then x is expressed by the formula:

[0107] x = DR×(t - t i ) + INC + VBW, t > t i (1)

[0108] In Equation (1), [DR, INC] can be obtained by mapping [VBW, CSN, ΔCSN], and [VBW, CSN, ΔCSN] is obtained from the data before ti. The migration process neural network mentioned in Section 2.1 is called h. Let θ be the model parameters, representing the weights and biases in the migration process neural network. The migration process neural network h can be expressed as:

[0109] [DR, INC] = h(VBW, CSN, ΔCSN|θ) (2)

[0110] The model parameters θ can be trained from [DR, INC] and [VBW, CSN, ΔCSN] extracted from the sample data and maintenance records. The training process of θ can be expressed as:

[0111]

[0112] Let the EGTM data in the sample be X = {x1, x2, x3, ……, xn}, where n is the total amount of data; the number of water washings is {1, 2, …, i, … k}, and k is the total number of water washings; the time points of the water washing records are: Twashing = {t1, t2, …, ti, …, tk}. Then X can be divided into k + 1 groups of data according to Twashing:

[0113]

[0114] If the water washing time is characterized by the number of flight cycles, for the i-th water washing, CSN is the total number of flight cycles at the current water washing, and ΔCSN is the number of flight cycles between two water washing events. There is:

[0115] CSN i = t i

[0116] ΔCSN i = t i - t (i-1) (5)

[0117] The acquisition of VBW is shown by Figure 3 . Since there are a large number of outliers in the EGTM data, it is inaccurate to use the EGTM value before water washing as VBW. In the present invention, the data before water washing is linearly fitted, and the value at the water washing point of the fitting function is taken as VBW.

[0118] For the i-th water washing, the data before water washing is expressed as X(i) = {x t(i－1)+1 , x t(i－1)+2 , ……, xti－1 Let the parameters of the linear fitting function be b i and a i , then we have:

[0119] X(i) = b i + a i × t, t = {t (i-1) + 1, t (i-1) + 2,..., t i - 1} (6)

[0120] Use the data X(i) to fit b i and a i , and we can get:

[0121]

[0122]

[0123] where card(·) refers to the number of elements of X(i).

[0124] Thus, the VBWi for the i-th water wash can be calculated by Equation (8):

[0125] VBW i = b i + a i × (ti - 1) (8)

[0126] The DR and INC in the data sample can be obtained by the method shown Figure 3 . Figure 3 The dashed line in is the fitting function of the EGTM data after water wash. The intersection point of the dashed line and the water wash time (vertical line) is the EGTM value after water wash, and the difference between this value and VBW is INC. The slope of the dashed line is DR.

[0127] Subtract the VBW, the engine EGTM data value before water wash for each group of data in Equation (4), and we have:

[0128]

[0129] [DR, INC] is linearly fitted from the data in Equation (9). For the i-th water wash, the data parameters DRi and INCi can be fitted with the data of X(i + 1) as:

[0130]

[0131]

[0132] The present invention proposes TPNN to realize the mapping of [VBW, CSN, ΔCSN] and [DR, INC], that is, for the problem of small samples, transfer learning is combined with PNN to form a TPNN model, which makes up for the insufficient training of PNN. For the problem that the traditional backpropagation algorithm is not applicable, a learning method based on orthogonal basis expansion is designed for TPNN.

[0133] The topological structure of the TPNN model described in the present invention consists of Figure 5 As shown, the collected data includes complete and incomplete records. The problem is that there is little complete data to support model learning, and the present invention solves it by using the method of transfer learning. First, the basic framework of the model is trained with incomplete data, and then the model is fine-tuned with complete data. This enables the model to make full use of the knowledge of incomplete data, that is, to ensure accuracy and prevent overfitting.

[0134] TPNN is composed of process neurons, which include three parts: weighting, integration, and excitation. The neurons of the process neural network are as Figure 6 shown:

[0135] Let the time interval of sample collection be [0, T], then the input of the process neuron in the hidden layer is:

[0136]

[0137] In the formula: w(t) is the weight function between the process neuron in the hidden layer and the input. The output of the process neuron in the hidden layer is:

[0138] out = g(net + θ1) (12)

[0139] In the formula: θ1 is the bias of the process neuron in the hidden layer, and g(·) is the activation function of the process neuron in the hidden layer, which is set as the Sigmoid function.

[0140] The activation function f(·) of the output layer is a linear function, that is, f(z) = z. Finally, the expression of this transfer process neural network is:

[0141]

[0142] In the formula: x i —— An input vector of length L, which is the i-th input unit of the input layer;

[0143] w i —— The weight vector connecting the j-th neuron in the hidden layer and the i-th input unit of the input layer;

[0144] v j —— The weight value connecting the j-th neuron in the hidden layer and the output neuron;

[0145] θ2——Bias of the output layer.

[0146] The data extracted from the washing records is: data = [X: (ΔCSN, CSN, VBW), Y: (DR, INC)]. For engines with incomplete washing records, the source domain S1 = {S1, S2, …, Si, …|Si = [data1, data2, …]} is defined; for engines with complete washing records, the source domain S2 = {S1, S2, …, Si, …|Si = [data1, data2, …]} is defined; for the target engine of the prediction task, the target domain G = {G1, G2|G = [data1, data2, …]} is defined.

[0147] To ensure that the data has a similar distribution, the same model of engines is collected for the source domains S1, S2 and the target domain G, so these data have a similar distribution. In fact, most of the engine data has the problem of incomplete records, so the sample size of H1 will be much larger than that of S2 and G.

[0148] Use the samples of the source domain S1 to train the TPNN model. The optimization task is:

[0149] loss = ∑(y - f(x)) 2 / n(14)

[0150] Transfer the trained model parameters w and v to the new model. Then use the samples of the source domain S2 to train the new model. Conduct the second transfer and use the samples of the target domain G to train. The relatively small data of S2 and G may lead to overfitting problems. To prevent this problem, set the optimization tasks for S2 and G as:

[0151] loss = ∑(y - f(x)) 2 / n + λ∑|w| / n + λ∑|v| / n + λ∑w 2 / n + λ∑v 2 / n(15)

[0152] The hidden layer structure of the TPNN is the key point of the network structure design. Let: nin be the number of input layer nodes, nhidden be the number of hidden layer nodes, and nout be the number of output layer nodes. According to the reference [], the number of hidden layer nodes of the process neural network is determined by Equation (16):

[0153]

[0154] In the present invention, the model has a dual output, so n out = 2, n in = 3, n hidden ≈ 3.

[0155] TPNN Learning Method Based on Orthogonal Basis Expansion

[0156] Since there is an integral link in TPNN, it is difficult to use the traditional backpropagation algorithm when calculating the gradient, making the calculation very complex. Therefore, the present invention designs a new backpropagation learning algorithm for TPNN based on orthogonal basis expansion. According to the Weierstrass approximation theorem [], for any ε>0, there exists a polynomial function P(t) such that Equation (17) holds:

[0157]

[0158] Therefore, in the input space of TPNN, a set of orthonormal basis functions is given: b1(t), b2(t), ……, b∞(t). Given a as the expansion coefficient, the component function x(t) of the i-th in the input vector of the network can be expanded as:

[0159]

[0160] In order to make the orthogonal basis closest to the original time series, the present invention selects to perform Schmidt orthogonalization on xi(t) to generate the orthonormal basis b l (t):

[0161] b1′(t) = x i1 (t)

[0162]

[0163]

[0164] For any ε>0, there exists a sufficiently large constant L0 such that for any L>L0, there is:

[0165]

[0166] At this time, Equation (18) can be expressed as:

[0167]

[0168] Among them, ail can be calculated as:

[0169]

[0170] Similarly, w i (t) can also be expanded under b1(t), b2(t), ……, b ∞ (t) as:

[0171]

[0172] Substitute Equation (21) and Equation (23) into Equation (13), and we get:

[0173]

[0174] Since b1(t), b2(t), ……, b ∞ (t) are mutually orthogonal, we have:

[0175]

[0176] Therefore, Equation (24) can be simplified to:

[0177]

[0178] According to the chain rule, the backpropagation method of Equation (26) can be represented by Figure 7 as follows:

[0179] From this, the optimization rules of the process neural network can be derived as:

[0180]

[0181]

[0182]

[0183]

[0184] Next, the performance of the present invention will be compared and analyzed in combination with experiments. The data in the present invention is collected from a CFM56-5B type aeroengine, which is widely used in aircraft such as Boeing 737, Airbus A320, Airbus A340-200 / 300, and KC-135. The EGTM data is from the inlet temperature of the high-pressure turbine of the engine, Figure 8 which is the exhaust gas temperature measurement point of the aeroengine.

[0185] The data required for the research are maintenance records and the corresponding EGTM data. In this example, the EGTM data parameters [DR, INC, VBW, CSN, ΔCSN] before and after water washing are collected from 33 engines. However, there is a problem that the water washing records are incomplete for the data collected from 31 engines, and only 2 engines have complete water washing records. There are a total of 10 water washing records, but the EGTM data is incomplete and cannot cover all water washing records. Therefore, only the data parameters of the first 9 water washing records can be extracted and are shown in Table 1.

[0186] Table 1 EGTM data parameters before and after water washing

[0187]

[0188] Verification of the effectiveness of the mapping between EGTM and data parameters: The TPNN model combines the maintenance records to map the EGTM data into data parameters, and then predicts the data parameters with the TPNN model, and then calculates the washed EGTM data. In order to reflect the effectiveness of this method, the present invention compares this method with the XGBoost, LSTM and KELM methods.

[0189] The above four methods are used to predict the EGTM of the CFM56-5B engine after water washing in 2016. The present invention uses the first few groups of data as target domain samples and predicts the last group of data. The errors of RMSE, MSE and MAE are compared in Table 2.

[0190] Table 2 Data prediction errors of each model

[0191]

[0192] Figure 9 The prediction results of EGTM for samples by all four methods are given in Figure 1. The figure contains the real data of EGTM and the prediction data of all prediction methods.

[0193] From Table 2 and Figure 9 In the example, although the output of LSTM shows a step, it shows a large error. This reflects that the cumulative effect of the long-term prediction error of the LSTM model leads to a large error in the later period. Each water wash means that the working condition of the engine system changes. The LSTM model trained with data under the previous working conditions cannot accurately predict the data parameters of the system under the new working conditions.

[0194] The outputs of XGBoost and KELM are close to a straight line, and the step amount after water washing is not predicted. This shows that XGBoost and KELM can only expand the trend of previous data to predict future data, and cannot mine the impact of water washing events on data. At the same time, this also reflects that the long-term prediction ability of XGBoost and KELM is weak.

[0195] The TPNN model can evaluate the trend of the engine's EGTM data over a larger time span, which has important reference value for formulating long-term engine maintenance plans.

[0196] The residual normal probability plot and residual histogram are tools used to verify whether the neural network guided by the maintenance record is accurate. The residual normal probability plot is also used to test the normal distribution law of the residual. Under normal circumstances, the normal probability plot is a straight line, which is Figure 10 (a) shows that the data points are approximately close to the straight line, and it can be seen that the data points approximately obey the normal distribution.

[0197] The residual histogram is given by Figure 10(as shown in (b)). The residual histogram is used to reflect the distribution of residuals. As can be seen from the figure, the residual distribution basically conforms to normality. The residuals are basically distributed within horizontal bands of equal width on both sides, so the model fits the data well. It can be seen that the neural network guided by maintenance records has a good fit.

[0198] The effectiveness verification of the data parameter mapping method based on TPNN in this example is as follows:

[0199] TPNN is a transfer process neural network algorithm for data parameter prediction. Using the data in Table 1 as test data and other collected data as training data, the TPNN model is trained using a transfer learning training strategy. The mean relative errors (Mean Relative Error, MAE) of the KELM method, LSTM method, and TPNN proposed in this invention for predicting [DR, INC] are given in Table 3, where the bold numbers represent the optimal results of the prediction methods for single parameter prediction. In addition, Figure 11 The prediction results of the three methods for [DR, INC] are given.

[0200] Table 3 Feature prediction errors of each model

[0201]

[0202] LSTM has a large error, so Figure 11 the curve of LSTM is not fully shown in. The reason is that the LSTM model contains many parameters, so it cannot be well trained in the case of insufficient data. In this task, the input node x = 3, the output node y = 2, and the hidden layer node h = 3. The number of parameters contained in the LSTM model can be calculated as:

[0203] 4×((x + h)×h + y×h) = 4×((3 + 3)×3 + 2×3) = 96 (28)

[0204] However, the total number of samples in the target domain and source domain in this prediction task is only 281, which is not enough to train the LSTM model. Therefore, LSTM is difficult to predict well.

[0205] Figure 11 In, the output of the kernel extreme learning machine is close to a straight line and cannot effectively reflect the trend of the real data. The reason is that the kernel extreme learning machine is suitable for predicting linear data, while the engine is a highly nonlinear system, so the prediction effect is not good.

[0206] The data predicted by the TPNN proposed in the present invention is in good agreement with the real data. The TPNN model is an extension of the neural network in the time domain and has the ability to predict time series like LSTM. The TPNN model requires fewer samples than LSTM, can obtain sufficient prior knowledge from the source domain, and avoids the problem of overfitting using the loss function during training in the target domain. Therefore, the TPNN model in the present invention is most suitable for the data parameter prediction model.

[0207] The present invention proposes a TPNN prediction method for predicting the EGTM after water washing. First, the EGTM before water washing is mapped into data parameters (water washing interval, water washing time, current state); then, using the data parameter mapping model, the data parameters after water washing (data increase amount, data decline trend) are generated from the data parameters of the data before water washing; finally, the data parameters after water washing are mapped into the EGTM data after water washing. Taking the data of the CFM56-5B type aeroengine as a sample, the performance of the proposed model is compared with LSTM, XGBoost, and KELM. The results verify that the prediction method guided by the maintenance record can accurately predict the EGTM after water washing. The technical solution recorded in the present invention is not only applicable to the prediction of data after water washing, but also applicable to applications such as the prediction of data after repair.

Claims

1. A method for predicting the exhaust gas temperature after engine cleaning using a transfer process neural network, which is provided with a transfer process neural network model TPNN. The TPNN includes a mapping method between variables and the EGT margin EGTM and a mapping method between variables, and is characterized in that, The mapping method of EGTM and data parameters includes the following: Let x be the EGTM data after washing to be predicted, let the number of flight cycles be t, and the washing time be t i , then x is expressed by Equation (1): x = DR×(t - t i ), + INC + VBW, t > t i (1), [DR, INC] in formula (1) is mapped from [VBW, CSN, ΔCSN], and [VBW, CSN, ΔCSN] is obtained from the data before t i The CSN is the flight cycle, which is the total number of cycles of the engine from factory to the current time; ΔCSN is the interval between water washes when the engine is washed multiple times, expressed in flight cycles, denoted as ΔCSN; INC is set that the current number of water washes is i and the water wash time is t i , t i The mutation of the EGTM after t is called the step amount INC; DR is the decay rate of the EGTM. The EGTM after water wash is linearly fitted, and the slope of the fitted straight line is called the decay rate DR of the EGTM; VBW is the engine EGTM value before water washing; The migration process neural network is called h, and let θ be the model parameters, representing the weights and biases in the migration process neural network. The migration process neural network h is expressed as: [DR, INC] = h(VBW, CSN, ΔCSN|θ) (2), and the model parameters θ are obtained by training [DR, INC] and [VBW, CSN, ΔCSN] extracted from sample data and maintenance records. The training process of θ is expressed as: Let the EGTM data in the sample be \(X = \{x_1, x_2, x_3, \ldots, x\) n \}, where \(n\) is the total amount of data; the number of washing times is \(\{1, 2, \ldots, i, \ldots, k\}\), and \(k\) is the total number of washing times; the time points of the washing records are: T washing = {t1, t2, …, t i , …, t k}, then according to T washing divide X into k + 1 groups of data: If the water washing time is characterized by the number of flight cycles, for the i-th water washing, CSN is the total number of flight cycles at the current water washing, and ΔCSN is the number of flight cycles between two water washing events. There is: Perform linear fitting on the data before water washing, and take the value at the water washing point of the fitting function as VBW; for the i-th water washing, the data before water washing is expressed as X(i) = {x t(i－1)+1 , x t(i－1)+2 , ……, x ti－1}, assuming the parameters of the linear fitting function are b i and a i , then we have: X(i) = b i + a i × t, t = {t (i-1) + 1, t (i-1) + 2,..., t i - 1}(6), Fitting b using data X(i) i and a i , we get: where card(·) refers to the number of elements of X(i), and thus the VBW of the i-th water wash i can be calculated by Equation (8): VBW i = b i + a i × (t i - 1)(8), DR and INC in the data samples are obtained from the change curve of the engine EGTM data after water washing. By subtracting the engine EGTM data value VBW before water washing for each group of data in Equation (4), there is: [DR, INC] is obtained by linearly fitting the data in Equation (9). For the i-th water wash, the data parameters are DR i and INC i Fitted with the data of X(i + 1) as:

2. The method for predicting the exhaust temperature after engine cleaning by a migration process neural network according to claim 1, wherein TPNN is composed of process neurons. A neuron includes three parts: weighting, integration, and excitation. Let the time interval for sample collection be [0, T]. Then the input of the process neuron in the hidden layer is: In the formula: w(t) is the weight function between the process neuron in the hidden layer and the input. The output of the process neuron in the hidden layer is: out = g(net + θ1)(12) In the formula: θ1 is the bias of the process neuron in the hidden layer, and g(·) is the excitation function of the process neuron in the hidden layer, which is set as the Sigmoid function; the excitation function f(·) of the output layer is a linear function, that is, f(z) = z. Finally, the expression of this migration process neural network is: where: x i is an input vector of length L and is the i-th input unit of the input layer; w i is the weight vector connecting the j-th neuron in the hidden layer to the i-th input unit in the input layer; v j is the weight for connecting the j-th neuron in the hidden layer and the output neuron; θ2 is the bias of the output layer; The data extracted according to the water washing records is: data = [X:(ΔCSN, CSN, VBW), Y:(DR, INC)]. For engines with incomplete water washing records, the source domain S1 = {S1, S2, …, Si, …|Si = [data1, data2, …]}; for engines with complete water washing records, the source domain S2 = {S1, S2, …, Si, …|Si = [data1, data2, …]}; for the target engine of the prediction task, the target domain G = {G1, G2|G = [data1, data2, …]}; To ensure that the data has a similar distribution, the same type of engine is collected for the source domains S1, S2 and the target domain G. Therefore, these data have a similar distribution. In fact, most engine data has the problem of incomplete records. Therefore, the number of samples in H1 will be much larger than that in S2 and G; Use the samples in the source domain S1 to train the TPNN model. The optimization task is: loss = ∑(y-f(x)) 2 / n (14), Migrate the trained model parameters w and v to the new model. Then use the samples in the source domain S2 to train the new model for the second migration, and use the samples in the target domain G for training. The relatively small data in S2 and G may cause overfitting problems. To prevent this problem, set the optimization tasks for S2 and G as: loss = ∑(y - f(x)) 2 / n + λ∑|w| / n + λ∑|v| / n + λ∑w 2 / n + λ∑v 2 / n(15); In the hidden layer structure design of TPNN, let: n in be the number of nodes in the input layer, n hidden be the number of nodes in the hidden layer, n out be the number of nodes in the output layer; the number of hidden layer nodes of the process neural network is determined by Equation (16): The above model has dual outputs, so n out = 2, n in = 3, n hidden ≈ 3.

3. A method for predicting the exhaust temperature after engine cleaning by a migration process neural network according to claim 2, characterized in that, It also includes a new backpropagation learning algorithm based on orthogonal basis expansion. According to the Weierstrass approximation theorem, for any ε > 0, there exists a polynomial function P(t) such that Equation (17) holds: Given a set of orthonormal basis functions in the input space of TPNN: b1(t), b2(t), ……, b ∞ (t), given a as the expansion coefficient, the component function x(t) of the i-th in the input vector of the network can be expanded as: To make the orthogonal basis closest to the original time series, choose to perform Schmidt orthogonalization on x i (t) to generate the orthonormal basis b l (t): b1′(t) = x i1 (t) For any ε > 0, there exists a sufficiently large constant L0 such that for any L > L0, we have: At this time, Equation (18) can be expressed as: where a il can be calculated as: Similarly, w i (t) can also be expanded under b1(t), b2(t), ……, b ∞ (t) as follows: Substituting Equation (21) and Equation (23) into Equation (13), we get: Since b1(t), b2(t), ……, b ∞ (t) are mutually orthogonal, we have: Therefore, Equation (24) can be simplified to: From this derivation process, the optimization rule of the neural network is:

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