WO2024077642A1

WO2024077642A1 - Method for constructing quantum echo state network model for aero-engine fault early-warning

Info

Publication number: WO2024077642A1
Application number: PCT/CN2022/125541
Authority: WO
Inventors: 孙希明; 孙涛; 岳明达; 刘墨燃
Original assignee: 大连理工大学
Priority date: 2022-10-12
Filing date: 2022-10-17
Publication date: 2024-04-18
Also published as: CN115841067A

Abstract

A method for constructing a quantum echo state network model for an aero-engine fault early-warning. The method comprises: first, quantizing time series data of an aero-engine; then, using quantum state data as an input of a quantum network of a first layer and subjecting same to the action of a quantum recursive circuit, and then obtaining a probabilistic output by means of quantum measurement and transferring same to a reservoir of an echo state network of a second layer, so as to obtain a high-dimensional intermediate state; and finally, performing computation only once by using a least squares method, such that a weight matrix of an output layer can be obtained, thus completing network training. A trained quantum echo state network model is applied to aero-engine fault prediction, thereby providing relatively high-accuracy operation state prediction data of an engine at a future moment. In the present invention, a quantum controlled NOT gate is utilized to realize an entangled state, so as to approximately represent a possible coupling relationship between original input data, and a quantum rotation gate is set to be an adjustable parameter of a quantum network of a first layer, such that the distribution of data can be adjusted; moreover, an echo state network layer can exert the computational advantage of fast computation and completion of a final model with one-step training.

Description

A quantum echo state network model construction method for aero-engine fault warning

Technical Field

The present invention belongs to the technical field of aircraft engine fault prediction. By introducing quantum computing mechanism, a quantum echo state network model is designed to predict multiple operating state parameters of aircraft engines at future moments. Numerical simulation results show that the quantum echo state network model proposed in the present invention can effectively predict and diagnose whether an aircraft engine has a fault.

Background technique

With the development of aerospace industry, the safety and stability of aircraft in operation has become an important research topic. As the heart of aircraft, aircraft engines are the core components that are most prone to failure. Once a failure occurs, it will affect the performance of the aircraft at the least and cause the aircraft to be destroyed and people to die at the worst. Therefore, it is necessary to predict the possible types of engine failures in advance and take corresponding protection measures to ensure the reliable operation of the aircraft. Whether the operating state of the aircraft engine at a future moment can be accurately and efficiently predicted is crucial to the safety and stability of the entire flight process. Among the many failure problems of aircraft engines, surge failure, as one of the most common risk factors, will directly affect the performance of aircraft engines and pose a huge threat to the safety of aircraft. The effective way to solve this problem is to propose a data-driven model based on the previous surge failure data of aircraft engines, and then predict whether the engine will fail at a future moment, play an alarm role and take corresponding safety measures in time.

At present, there are several methods for predicting aircraft engine failures:

1) Analysis method based on fault tree.

This method mainly simulates the real-time data of the aircraft operation process from the perspective of fault monitoring, and uses the fault tree method to analyze and calculate the monitored data, and then determine the detailed cause of the fault. However, this fault tree-based analysis method requires that the person analyzing the fault must fully understand the object system being analyzed and be able to apply the analysis method familiarly, which leads to different fault tree analysis results given by different analysts. In addition, the calculation process of the fault tree is also very complicated, and it is difficult to accurately calculate the specific cause of the fault.

2) Analysis method based on least squares support vector machine.

This method uses the gas path parameters of the aircraft engine to establish a least squares support vector machine model to monitor the aircraft engine state. That is, according to the established model, the low-pressure rotor speed (n1), high-pressure rotor speed (n2) and tail nozzle outlet temperature (T6) of the aircraft engine are monitored, and the fault is analyzed by the relative error rate between the predicted value and the true value. However, it should be noted that the least squares support vector machine treats the data set as a vector mode, thus ignoring the natural relationship of mutual coupling and mutual influence between the data. In addition, if the data set is forcibly represented as a vector, the temporal correlation of the original data will be destroyed, which will inevitably produce large numerical errors.

Based on the above discussion, this paper proposes a new quantum echo state network model for aircraft engine fault prediction based on a data-driven approach. The model mainly includes two network layers. The output of the first layer of quantum heuristic neural network is transmitted to the reserve pool of the second layer of echo state network. After only one training, the final quantum echo state network model can effectively predict the operating status data of aircraft engines.

This patent is funded by the China Postdoctoral Science Foundation (2022TQ0179), the National Natural Science Foundation of China (61890920, 61890921) and the National Key R&D Program of China (2018YFB1700102).

Summary of the invention

The purpose of this invention is to design a quantum echo state network model that can be applied to aircraft engine fault prediction. Since aircraft engines are highly complex aerodynamic-thermodynamic-mechanical systems, the time series data they generate have strong temporal correlation, coupling and multimodal characteristics. Therefore, how to predict aircraft engine faults in a variable full envelope environment has always been a challenging problem.

In order to achieve the above object, the technical solution adopted by the present invention is:

A quantum echo state network model for aircraft engine fault warning. The present invention applies quantum computing theory to design a quantum circuit composed of a quantum rotation gate and a two-bit quantum controlled NOT gate, and constructs a first-layer quantum heuristic neural network as a pre-network for the second-layer echo state network. First, the time series data of the aircraft engine is quantized; then, the obtained quantum state data is used as the input of the first-layer quantum network, and after being acted upon by the quantum recursive circuit, a probabilistic output is obtained through quantum measurement, and then passed to the reserve pool of the second-layer echo state network to obtain a high-dimensional intermediate state; finally, the least squares method is used to obtain the output layer weight matrix with only one calculation, thus completing the network training. The trained quantum echo state network model can be applied to aircraft engine fault prediction to provide engine operating status prediction data with higher accuracy in the future. The specific steps are as follows:

Step 1: Select data sample features

First, multiple sets of sensors of the aircraft engine are used to collect various operating state data of the aircraft. Each type of data represents a sample feature variable, and its data form is a set of discrete time series data. The time series is recorded as: t = {1, 2, 3, ..., T}, where t is the sampling time and T is the last moment of sampling; then, data sample feature variables with a high degree of correlation with the occurrence of aircraft engine failure are selected from the various operating state data as the judgment criteria for fault prediction, such as ambient pressure, tail nozzle outlet temperature, engine combustion chamber temperature, etc. For example, after selecting n data sample feature variables, a total of n×T initial data { _xi (t)} are obtained through sensor collection, where i ranges from 1 to n, t ranges from 1 to T, and _xi (t) represents the value of the i-th data sample feature variable (such as tail nozzle outlet temperature) at time t.

Step 2: Initial data quantization

According to quantum computing theory, the input of the quantum circuit layer must be a quantum state, so the initial data { _xi (t)} collected in step 1 must be quantized to obtain quantum state data |ψ>＝a|0>+b|1>, where |ψ> represents a quantum state, |0>, |1> represent the two ground states of the binary quantum bit respectively, and a and b are the corresponding probability amplitudes. The physical meaning is: when quantum measuring the quantum state |ψ>, |0> will be observed with a probability of |a| ² , |1> will be observed with a probability of |b| ² , and |a| ² +|b| ² ＝1.

For a set of n-dimensional initial data [x ₁ (t), x ₂ (t), ..., x _n (t)] ^Τ collected at a certain time t, the initial data { _xi (t)} are first normalized according to formula (1), which is as follows:

Among them, x _i (t) and

They represent the initial data value and normalized data value of the i-th feature variable at time t, respectively.

The value range of belongs to [0,1];

represents the minimum value of the i-th characteristic variable in this group of time series, and j represents the time corresponding to the minimum value.

It represents the maximum value of the i-th characteristic variable in this group of time series, k represents the time corresponding to the maximum value, i＝1,2,...,n represents that i ranges from 1 to n, that is, all the time series data of n characteristic variables are normalized.

After normalizing the initial data, the probability amplitude in front of the quantum bit |1> is considered to represent the classical data information contained in the input quantum state. Then, the normalized data can be prepared into quantum state form data according to the quantization rule given by formula (2). Formula (2) is as follows:

Among them, | _xi (t)> represents the quantum state data prepared by the i-th characteristic variable at time t, _cosθi (t) and _sinθi (t) correspond to the probability amplitude of the quantum state | _xi (t)> before the binary quantum bit ground state |0> and |1>, respectively, and _θi (t) is obtained by

Taking the inverse sine gives.

Using formula (2), let i range from 1 to n, and thus obtain the quantum state data at time t |x ₁ (t)>, |x ₂ (t)>, ..., |x _n (t)>.

Step 3: Build a quantum circuit

The key to the advantages of quantum-inspired neural networks is how to construct the corresponding quantum circuits. Here is a quantum circuit construction method similar to the one in Figure 1, which only uses two basic types of quantum rotation gates and two-bit quantum controlled NOT gates. The specific description is as follows: First, n+1 quantum circuits are constructed. The input of the first n circuits (from top to bottom) at the initial time t=1 is the n quantum state data |x ₁ (1)>,|x ₂ (1)>,...,|x _n (1)> prepared in step 2; the n+1th quantum circuit is mainly used to calculate the output of the quantum circuit layer, and its input is an auxiliary quantum state |y(0)>, and its initial state defaults to |y(0)>＝|0>. The first n quantum states |x ₁ (1)>,|x ₂ (1)>,...,|x _n (1)> pass through a quantum rotation gate in turn, and then together with |y(0)> pass through n two-bit quantum controlled NOT gates from top to bottom. Note that a quantum rotation gate must be added in the n+1th quantum circuit to finally obtain |y(1)>. Then |x ₁ (2)>,|x ₂ (2)>,...,|x _n (2)>,|y(1)> are used as the n+1 quantum state inputs for the next time t=2, and recursive calculations are performed until t=T.

In the above quantum circuit, the quantum rotating gate that each quantum state input passes through is denoted as R(θ), and its matrix form is:

Where θ is the rotation angle, and its value range is [0,2π].

The two-bit quantum controlled NOT gate acting from top to bottom between every two adjacent quantum states is denoted as U _CN , and its matrix form is as follows:

Note that n+1 quantum rotating gates are used in common, so n+1 rotation angles need to be given in advance.

i＝1,2,...,n+1，where

As the parameters of the quantum network layer. At time t, the i-th quantum state input |x _i (t)> passes through the quantum rotation gate

The calculation formula is:

The specific calculation process of the above quantum circuit is given below: starting from time t=1, the above quantum circuit is used for recursive calculation. The input quantum state at time t=1 (from top to bottom) is |x ₁ (t ₁ )>,|x ₂ (t ₁ )>,...,|x _n (t ₁ )>,|y(t ₀ )>. After the entire quantum circuit is acted on once, the quantum state |y(1)> is used as the input of the auxiliary quantum state position at the next moment.

Considering the quantum circuit action at time t=r, the first n input quantum states pass through n quantum rotary gates, then pass through n quantum controlled NOT gates from top to bottom, and finally act on a quantum rotary gate at the circuit position where the auxiliary quantum state is located. The calculation formula for the output quantum state |y(t=r)> is:

in,

= y(r) ² represents the probability of the final quantum state of the position of the i-th row from top to bottom in the quantum circuit taking |1> when measured, i ranges from 1 to n; y(r) 2 represents the probability of the quantum state of the last row of auxiliary quantum states after passing through the controlled NOT gate when measured taking |1>. Note that the last row of quantum circuits must also be subjected to a rotating gate after passing through the controlled NOT gate.

Therefore, the output at time t=r is recorded as u(t _r ), which represents the probability of measuring |y(t=r)> and obtaining |1>. The calculation result is shown in formula (7):

According to formulas (6) and (7), recursive calculation is performed, and r is set from 1 to T. We can obtain a set of time series outputs u(t) = [u(t ₁ ), u(t ₂ ), ..., u(t _T )] ^Τ . Next, we take a new set of quantum rotating gate rotation angle parameters

i＝1,2,...,n+1, a new set of outputs can be obtained using the same quantum circuit. By randomly generating n sets of n+1 rotation angle parameters, n sets of T-dimensional output data can be obtained, which are recorded as the matrix U(t)＝[u ₁ (t),u ₂ (t),..., _un (t)].

Step 4: Build and train the quantum echo state network

As a new type of recursive neural network, echo state network is widely used in time series prediction due to its simple calculation mode (no need to solve the objective function gradient, only one linear regression is needed to complete the network training) and high stability. The echo state network consists of three parts: input layer, reservoir, and output layer. Its core structure is a randomly generated and unchanged reservoir.

The specific construction method of the quantum echo state network in the present invention is as follows: as shown in Figure 1, the output U(t) obtained by recursive calculation of the quantum network layer in step 3 is used as the input of the next layer of the echo state network, and the reserve pool of the echo state network is designed as a sparse network with multiple neurons, including a high-dimensional sparse reserve pool internal weight connection matrix W _res and an input layer connection matrix W _in for connecting U(t). The two matrices W _res and W _in are randomly generated and remain unchanged during the cyclic calculation process of the echo state network. In this way, when the low-dimensional data U(t) obtained by the quantum layer enters the echo state network, it will be projected into the sparse high-dimensional space, and complex and diverse nonlinear states will be generated in the reserve pool of the echo state network, thereby extracting more abundant and effective features and realizing the function of memorizing data. Finally, W _out is the output weight matrix to be trained, which needs to be trained by the training set data given in the actual problem.

The loop calculation in the echo state network layer can be described according to formula (8):

x(t)＝tanh( _Wres ·x(t-1)+ _Win ·U(t)), (8)

Where U(t) is the time series input, x(t) is the state of the reservoir, and its dimension is much larger than n. The initial state is set to x(0) = 0, and x(t) is recursively calculated according to formula (8), where tanh is the activation function, and W _res and W _in correspond to the internal weight connection matrix of the reservoir and the input layer connection matrix given above, respectively.

After the cyclic calculation, the output weight matrix W _out is trained according to the training set data in the actual problem. The training process only needs to use the least squares calculation in formula (9) once:

W _out =YX ^Τ (XX ^Τ ) ^-1 , (9)

Among them, X is the storage matrix of the reserve pool state, and Y is the time series matrix of the real sample data of the training set.

After W _out is obtained by formula (9), the entire quantum echo state network model training is completed. Applying the trained quantum echo state network model on the test set in the actual problem can be used to predict n parameter data at future moments.

Beneficial effects of the present invention:

The present invention uses quantum controlled NOT gates to realize entangled states to approximate the coupling relationship that may exist between the original input data. The quantum rotation gate is set as an adjustable parameter of the first layer of quantum network to adjust the distribution of data. The echo state network layer can take advantage of fast calculation and complete the calculation of the final model in one step of training. Numerical experiments have verified that the quantum echo state network model can accurately predict the state data of aircraft engines at future flight times.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a quantum echo state network model under the condition of characteristic variables of 3D data samples.

Figure 2 is a comparison diagram of the error between the predicted data and the real data on the training set, Figure 2(a) is a comparison diagram of the predicted data and the real data on the training set, and Figure 2(b) is a point-by-point error diagram between the real value and the predicted value on the training set.

Figure 3 is a comparison diagram of the error between the predicted data and the real data on the test set, Figure 3(a) is a comparison diagram of the predicted data and the real data on the test set, and Figure 3(b) is a point-by-point error diagram between the real value and the predicted value on the test set.

Detailed ways

The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

This embodiment is a quantum echo state network model for aircraft engine fault warning, which uses the 3D input quantum echo state network model in Figure 1 to predict the operating parameter data of the engine at a future time, including the following steps.

Step 1: Select data sample features

For the convenience of description, consider the numerical example of n = 3 sample feature variables. In the actual flight mission, it is found that when a fault occurs, the changes in ambient pressure, engine exhaust temperature and engine combustion chamber temperature are more obvious, indicating that these three feature variables are highly correlated with the occurrence of the fault, so the sample features are selected as the following three: ambient pressure, engine exhaust temperature, and engine combustion chamber temperature. The data comes from the actual flight mission of a certain type of aircraft engine. Multiple sensors are used for data collection. The sampling time interval is 0.1 seconds. The last moment of sampling is T = 60000. The total time series record is t = 1:60000. Time series data is collected for each sample feature, and a total of 3×60000 sample data is obtained for numerical experimental simulation.

Step 2: Divide the training set and test set and preprocess the data

The sample data obtained in step 1 is divided into a training set and a test set, wherein the selected training set time series data is t=40000:45000, and the test set time series data is t=46000:48000. The training set data is used to train the quantum echo state network model, and the test set data is used to verify the model prediction effect. After the training set and the test set are divided, the data in them need to be preprocessed. First, the initial data collected in step 1 is normalized according to formula (1), and then the quantum state input is prepared using the quantization rule described by formula (2). The preprocessing of the initial data is completed;

Step 3: Construction of quantum-inspired neural network layers

The training set data after quantization in step 2 is input into the first layer of quantum-inspired neural network, and n=3 groups of rotation angles are randomly generated. Table 1 shows three groups of different quantum rotating gate rotation angles using the rand command in MATLAB.

Table 1: Three sets of randomly generated quantum selective gate rotation angles

For each set of rotation angles, the quantum circuit shown in Figure 1 is constructed. Due to the lack of quantum computer hardware support, the calculation is performed using classical computer simulation, that is, the output U(t) of the quantum-inspired neural network layer is obtained by recursive calculation according to formulas (6) and (7);

Step 4: Train the quantum echo state network on the training set

The output U(t) obtained by the quantum-inspired neural network layer on the training set is used as the input of the second echo state network layer, and the relevant parameters in the reserve pool are randomly generated. The reserve pool dimension is selected as 100, that is, the input layer connection matrix W _in is a randomly generated matrix of 100×4, and the reserve pool internal weight connection matrix W _res is a randomly generated sparse matrix of 100×100. After adjusting the relevant parameters to optimize the network, the prediction step size is taken as 1, and the weight matrix W _out of the output layer is calculated using formula (9). The training is completed.

Figure 1 shows a quantum echo state network with a three-dimensional sample input. For the n-dimensional case, a similar generalization of the construction is sufficient. The quantum network part gives the quantum circuit through which the input quantum state passes, and shows the recursive action at the target quantum state. U(t) is the time series output obtained by the quantum layer, _Win and _Wres are high-dimensional matrices randomly generated in the echo state network reserve pool, and _Wout is the output weight matrix, which can be obtained through only one least squares training.

Step 5: Use the trained model to predict data and plot analysis

First, apply the trained model to the training set to obtain the predicted value. The training effect is judged by observing the error between the predicted value and the true value and then analyzed by drawing. Figure 2 shows the comparison of the predicted value and the true value obtained in the time series t = 40010:43010. It is found that the predicted value given by the model is very close to the real data. The mean square error between the predicted value and the true value obtained on the entire training set can be calculated to be 0.0053344, indicating that the training effect is very good and can be used for testing on the test set. Figure 2 (a) shows the data comparison of 3000 predicted values and true values on the training set. The solid line represents the true value on the training set, and the dotted line represents the predicted value given by the quantum echo state network model. Figure 2 (b) shows the error obtained by subtracting the predicted value from the true value at each time node.

Finally, the model is applied to the test set. The quantum state data on the test set obtained after preprocessing in step 2 is input into the trained quantum echo state network model in the form of Figure 1 to obtain the predicted value under the time series of t = 46000:48000. Figure 3 plots the error comparison between the predicted data given by the model and the real data under the time series of t = 46010:47010, and the mean square error is calculated to be 0.0065058, indicating that the prediction effect of the model is very good. Figure 3 (a) shows the data comparison of 1000 predicted values and real values on the test set. The solid line represents the real value on the test set, and the dotted line represents the predicted value given by the quantum echo state network model. Figure 3 (b) shows the error obtained by subtracting the predicted value from the real value at each time node.

The quantum echo state network model is applied to the prediction of aircraft engine faults. When the predicted value is very different from the actual value, it means that the engine may have a fault, thus achieving a fault warning function for the aircraft engine.

Implementation Results

1) As can be seen from Figure 2, using the quantum echo state network model to train once on the training set can achieve good prediction results. The deviation between the predicted value and the true value is very small, and the calculated mean square error is only 0.0053344.

2) As can be seen from Figure 3, the predicted values obtained by using the quantum echo state network to predict the test set are highly consistent with the true values, the deviation between the two is very small, and the calculated mean square error is only 0.0065058.

In summary, the numerical results of applying the quantum echo state network model to aero-engine data prediction show that the quantum echo state network can indeed exert quantum advantages and make the prediction results more accurate.

The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

A method for constructing a quantum echo state network model for early warning of aircraft engine faults, characterized in that it comprises the following steps:

Step 1: Select the data sample features of aircraft engines;

Step 2: quantize the initial data selected in step 1;

Step 3: Construct quantum circuit;

Step 4: Build and train the quantum echo state network template, apply the trained quantum echo state network model to aviation engine fault prediction, and provide the prediction data of engine operation status at future moments.
The method for constructing a quantum echo state network model for aircraft engine fault warning according to claim 1 is characterized in that it comprises the following steps:

Step 1: Select data sample features

Firstly, multiple groups of sensors of aircraft engines are used to collect various operating status data of aircraft. Each data represents a sample characteristic variable, and its data form is a set of discrete time series data. The time series is recorded as: t = {1, 2, 3, ..., T}, where t is the sampling time and T is the last moment of sampling. Then, data sample characteristic variables with a high degree of correlation with the occurrence of aircraft engine failure are selected from the various operating status data as the judgment criteria for fault prediction, including ambient pressure, tail nozzle outlet temperature, and engine combustion chamber temperature.

Step 2: Initial data quantization

The initial data { xi (t)} collected in step 1 is quantized to obtain quantum state data |ψ>＝a|0>+b|1>, where |ψ> represents a quantum state, |0>, |1> represent two ground states of binary quantum bits, a, b are corresponding probability amplitudes, and their physical meaning is: when quantum measurement is performed on the quantum state |ψ>, |0> will be observed with a probability of |a| 2 , |1> will be observed with a probability of |b| 2 , and |a| 2 +|b| 2 ＝1;

For a set of n-dimensional initial data [x 1 (t), x 2 (t), ..., x n (t)] Τ collected at a certain time t, firstly, the initial data { xi (t)} are normalized;

After normalizing the initial data, the probability amplitude in front of the quantum bit |1> is used to represent the classical data information contained in the input quantum state. According to the quantization rule given by formula (2), the normalized data is prepared into quantum state form data. Formula (2) is as follows:

Among them, | xi (t)> represents the quantum state data prepared by the i-th characteristic variable at time t, cosθi (t) and sinθi (t) correspond to the probability amplitude of the quantum state | xi (t)> before the binary quantum bit ground state |0> and |1>, respectively, and θi (t) is obtained by
Taking the inverse sine gives;

Using formula (2), let i range from 1 to n, and thus obtain the quantum state data at time t |x 1 (t)>, |x 2 (t)>, ..., |x n (t)>;

Step 3: Build a quantum circuit

First, construct n+1 quantum circuits. The input of the first n circuits at the initial time t=1 is the n quantum state data |x 1 (1)>,|x 2 (1)>,...,|x n (1)> prepared in step 2. The n+1th quantum circuit is mainly used to calculate the output of the quantum circuit layer. Its input is an auxiliary quantum state |y(0)>, and its initial state defaults to |y(0)>＝|0>. The first n quantum states |x 1 (1)>,|x 2 (1)>,...,|x n (1)> pass through a quantum rotation gate in turn, and then pass through n two-bit quantum controlled NOT gates from top to bottom together with |y(0)>. Note that a quantum rotation gate should be added to the n+1th quantum circuit to finally obtain |y(1)>, and then |x 1 (2)>,|x 2 (2)>,...,|x n (2)>,|y(1)> is used as the n+1 quantum state input at the next time t=2, and recursive calculation is performed until t=T;

In the above quantum circuit, the quantum rotation gate that each quantum state input passes through is denoted as R(θ), where θ is the rotation angle, and its value range is [0,2π]. The two-bit quantum controlled NOT gate acting from top to bottom between every two adjacent quantum states is denoted as U CN .

Since n+1 quantum rotating gates are shared, n+1 rotation angles need to be given first.
i＝1,2,...,n+1，where
As the parameters of the quantum network layer; at time t, the i-th quantum state input |x i (t)> passes through the quantum rotation gate
The calculation formula is:

The specific calculation process of the above quantum circuit is given below:

Starting from time t=1, the above quantum circuit is used for recursive calculation. The input quantum states at time t=1 are |x 1 (t 1 )>, |x 2 (t 1 )>, ..., |x n (t 1 )>, |y(t 0 )>. After the entire quantum circuit is acted upon once, the quantum state |y(1)> is used as the input of the auxiliary quantum state position at the next moment.

Considering the quantum circuit action at time t=r, the first n input quantum states pass through n quantum rotary gates, then pass through n quantum controlled NOT gates from top to bottom, and finally act on a quantum rotary gate at the circuit position where the auxiliary quantum state is located. The calculation formula for the output quantum state |y(t=r)> is:

in,
represents the probability of the final quantum state of the position of the i-th row from top to bottom in the quantum circuit taking |1> when measured, i ranges from 1 to n; y(r) 2 represents the probability of the quantum state of the last row of auxiliary quantum states after passing through the controlled NOT gate when measured taking |1>; the last row of quantum circuits will also be subjected to a rotating gate after passing through the controlled NOT gate
Therefore, the output at time t=r is recorded as u(t r ), which represents the probability of measuring |y(t=r)> and obtaining |1>. The calculation result is shown in formula (7):

According to formulas (6) and (7), recursive calculation is performed, and r is set from 1 to T. A set of time series outputs u(t) = [u(t 1 ), u(t 2 ), ..., u(t T )] Τ can be obtained. Next, a new set of quantum rotating gate rotation angle parameters is obtained:
i＝1,2,...,n+1, a new set of outputs can be obtained using the same quantum circuit. By randomly generating n sets of n+1 rotation angle parameters, n sets of T-dimensional output data can be obtained, which are recorded as the matrix U(t)＝[u 1 (t),u 2 (t),..., un (t)];

Step 4: Build and train the quantum echo state network

The quantum echo state network is composed of three parts: input layer, reserve pool and output layer. Its core structure is a randomly generated and unchanged reserve pool.

Build a quantum echo state network: Use the output U(t) obtained by recursive calculation of the quantum network layer in step 3 as the input of the next layer of echo state network, and design the reserve pool of the echo state network into a sparse network with multiple neurons, including a high-dimensional sparse reserve pool internal weight connection matrix W res and an input layer connection matrix W in used to connect U(t). The two matrices W res and W in are randomly generated and remain unchanged during the cyclic calculation process of the echo state network. When the low-dimensional data U(t) obtained by the quantum layer enters the echo state network, it will be projected into the sparse high-dimensional space and generate complex and diverse nonlinear states in the reserve pool of the echo state network, thereby extracting richer and more effective features and realizing the function of memorizing data. Finally, W out is the output weight matrix to be trained, which needs to be trained by the training set data given in the actual problem.

After the cyclic calculation, the output weight matrix W out is trained according to the training set data in the actual problem. The training process only needs to use the least squares calculation in formula (9) once:

W out =YX Τ (XX Τ ) -1 , (9)

Among them, X is the storage matrix of the reservoir state, and Y is the time series matrix of the real sample data of the training set;

After W out is obtained through formula (9), the entire quantum echo state network model training is completed; the trained quantum echo state network model is applied to the test set in the actual problem to predict the parameter data at the future time.
The method for constructing a quantum echo state network model for aircraft engine fault warning according to claim 1 is characterized in that in the step 4, the loop calculation in the quantum echo state network layer is described according to formula (8):

x(t)＝tanh( Wres ·x(t-1)+ Win ·U(t)), (8)

Where U(t) is the time series input, x(t) is the state of the reservoir, and its dimension is much larger than n. The initial state is set to x(0) = 0, and x(t) is recursively calculated according to formula (8), where tanh is the activation function, and W res and W in correspond to the internal weight connection matrix of the reservoir and the input layer connection matrix given above, respectively.