Method for analyzing and predicting pneumatic conveying airflow nonlinear signal based on machine learning

Abstract

The invention relates to a method for analyzing and predicting a pneumatic conveying airflow nonlinear signal based on machine learning, which adopts a method of combining nonlinear dynamic analysis and machine learning in a pneumatic conveying system, and the nonlinear dynamic analysis method can perform nonlinear dynamic feature extraction on an electric signal acquired and converted by an acoustic emission sensor. The recurrent neural network can process sequence data, can capture dynamic characteristics in a time sequence, and uses data collected by the acoustic emission sensor as a main analysis object to predict and analyze important parameters such as the conveying solid-gas ratio and the system pressure drop in the pneumatic conveying system; and proper operation parameters under the optimization target needing to be achieved are determined through dynamic optimization of the parameters, so that the conveying system intelligently and finely controls the air flow and the fluctuation range of the high-pressure air flow, the conveying energy consumption and the fluctuation quantity of the air flow are reduced, and it is guaranteed that the conveying system is in the optimal working state.

Description

Technical Field

[0001] The present invention relates to the field of pneumatic conveying, and in particular to a method for predicting nonlinear signals of pneumatic conveying airflow based on machine learning analysis. Background Art

[0002] Pneumatic transportation is a common method of material transportation. In recent years, it has been widely used in the transportation of powdery and granular materials such as grain, flour, salt and molding sand.

[0003] The traditional pneumatic conveying system includes a silo, a silo pump, and a conveying pipeline. The silo pump is a shell structure, and a feed port and a discharge port are respectively arranged above and below the silo pump. The discharge port of the silo is connected to the feed port of the silo pump, and the conveying pipeline is connected to the discharge port of the silo pump. The pressurized air pipe is connected to the inside of the silo pump and is used to pressurize the inside of the silo pump. The working process of the pneumatic conveying system mainly includes four stages. The first is the feeding stage. The discharge port of the silo is opened, and the material in the silo falls freely into the silo pump. When the material in the pump silo reaches a certain height, the discharge port of the silo is closed. The second is the fluidization and pressurization stage. The pressurized pipeline is passed with gas from the bottom of the silo pump to fluidize the material and increase the internal pressure of the silo pump. Finally, there is the conveying stage. The pressure in the silo pump rises to a certain level, the discharge port of the silo pump is opened, and the material enters the conveying pipeline. The air flowing in the conveying pipeline drives the material to move and complete the material conveying.

[0004] Pneumatic conveying has the advantages of being clean, environmentally friendly, highly adaptable, highly efficient and highly automated. However, on the other hand, it also faces problems such as high energy consumption due to large gas volume, severe wear of materials and pipelines, high conveying pressure due to high fluctuations in gas consumption, and system safety caused by frequent opening and closing of pipelines. Intelligent automatic control is an effective means to solve such problems. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a method for predicting nonlinear signals of pneumatic conveying airflow based on machine learning analysis.

[0006] The technical solution of the present invention is: a method for predicting nonlinear signals of pneumatic conveying airflow based on machine learning analysis, comprising the following steps:

[0007] Parameter Input

[0008] ① Input system parameters, including temperature, humidity, particle characteristics, pipeline layout, pipeline length, and system mechanical device configuration, and then input operating parameters, including air flow velocity, material mass flow, and pipeline inlet and outlet pressure;

[0009] Data collection and preprocessing

[0010] ② Analyze the gas mass flow rate through the gas flow meter data, analyze the material mass flow rate and pipeline pressure drop through the weighing sensor and pressure sensor data, and then collect the acoustic signal of the acoustic emission sensor, and then remove the noise and outliers from the obtained data signal, and perform signal processing such as filtering and normalization;

[0011] ③ Extraction of nonlinear dynamic features: converting the collision signal in the pipeline measured by the acoustic emission sensor during pneumatic conveying into an electrical signal, and selecting appropriate time delay (τ) and embedding dimension (m) to reconstruct the phase space. The time delay (τ) refers to the time interval used to connect the data points in the same time series to form a multidimensional vector when constructing a vector, and the embedding dimension (m) refers to the dimension of the vector used to describe the system state during the phase space reconstruction process.

[0012] Data storage and nonlinear dynamics analysis

[0013] ④ Store the data every 5 seconds in the input and output databases, and then perform nonlinear dynamic analysis on the data in the input and output databases. The calculation method of the relevant parameters in the nonlinear dynamic analysis method is as follows:

[0014] Lyapunov exponent LE

[0015]

[0016] where λ(i) is the maximum Lyapunov exponent at time delay i; k max and k min are the minimum and maximum time delays, respectively; k is the parameter for adjusting the control input weights in model predictive control; dt is the time step; ∥Y i+k -Y s+k ∥ / ∥Y i -Y s ∥ is the distance between point i and its adjacent point s in each stage;

[0017] Approximate Entropy AE

[0018] AE=Φ m -Φ m+1

[0019]

[0020] Where r is the threshold radius; Φ m and Φ m+1 are statistical functions calculated for dimensions m and m+1 respectively; Θ is the Heaviside function; the Heaviside function under dimension m is as follows:

[0021]

[0022] Recursion rate RR

[0023]

[0024] Building a Neural Network

[0025] ⑤ The neural network model includes an input layer, a hidden layer and an output layer. The input layer of the neural network model is the nonlinear dynamic characteristic parameters and measurement data, the output layer is the transport solid-gas ratio and system pressure drop, and the hidden layer is a new feature created by combining different features of the input layer;

[0026] ⑥ Establish a recurrent neural network RNN. In RNN, the output of each neuron depends not only on the input of the current time step, but also on the output of the previous time step. This recursive connection enables RNN to maintain state, thereby processing time series data. The training of RNN involves forward propagation and back propagation. In forward propagation, the input sequence passes through the network time step by time, and the output and loss of each time step are calculated. In back propagation, the gradient of the loss function with respect to the network parameters is calculated and then propagated back through the network to update the weights and bias terms;

[0027] Neuron output formula:

[0028] h t =f(W ih ·x t +W hh ·h t-1 +b h )

[0029] Among them, h t is the state of the hidden layer at time step t; x t is the input of the input layer at time step t; W ih is the weight matrix input to the hidden layer; W hh is the recursive connection weight matrix of the hidden layer itself; h t-1 is the state of the hidden layer at the previous time step t-1; b h is the bias term of the hidden layer; f is the ReLU activation function, f(x) = max(0,x);

[0030] Loss Function

[0031]

[0032] Where L is the value of the loss function; y i is the true distribution of the target category; are the log odds (logits) predicted by the model;

[0033] ⑦ Deploy the trained model to the actual pneumatic conveying system for real-time monitoring, prediction and optimization control. Adjust the operating parameters according to the model output, including adjusting the air flow velocity and material flow rate. Continuously optimize the model based on the feedback from the system operation and new data to adapt to system changes and improve prediction accuracy. Adjust the model structure or reselect features based on the comparison results to improve prediction accuracy.

[0034] Preferably, the model is predicted and controlled by selecting an appropriate cost function weight through the model predictive control method, the operating parameters of the input pneumatic conveying system are dynamically adjusted, and the optimal model is judged for parameter output. The cost function is calculated as follows:

[0035] J(x,u)=∑(xr) T Q(xr)+∑(uu prev ) T R(uu prev )+∑u T Su

[0036] Where x is the system state vector; u is the control input vector; r is the reference state vector; u prev is the control input at the previous moment; Q is the state deviation weight matrix; R is the control deviation weight matrix; S is the control input weight matrix.

[0037] Preferably, in each control cycle, the future behavior of the system is predicted based on the current system state and the prediction model, so as to calculate the optimal control input to minimize the cost function, and dynamically adjust the operating parameters of the pneumatic conveying system based on whether the predicted output parameters are tending to be optimal. If it is predicted that the output parameters are tending to be optimal, the parameter library storage is optimized, and the optimized input and output parameter database corresponding to the conveying capacity and the minimum conveying energy consumption is set, and then the input parameter comparison is performed, and the input parameter adjustment step is determined according to the database comparison result, so as to realize the dynamic adjustment of the operating parameter input; if it is predicted that the output parameters are not tending to be optimal, the input parameter comparison is performed, and the input parameter adjustment step is determined according to the database comparison result, so as to realize the dynamic adjustment of the operating parameter input.

[0038] Preferably, the data set after nonlinear dynamics analysis is divided into a training set, a validation set and a test set. The training set data is used to train the neural network, and the network weights are adjusted by the back propagation algorithm to minimize the difference between the predicted output and the actual output. The validation set data is used to adjust the model parameters, including the learning rate, batch size, number of network layers and number of neurons, to prevent overfitting.

[0039] Preferably, the model is analyzed and optimized, and the performance of the model is evaluated on a previously determined test set of acoustic signals based on good acoustic emission sensors. The input operating parameters are dynamically tuned according to the comparison results, and the optimized nonlinear index parameters are predicted by a neural network to obtain optimized prediction results such as solid-gas ratio and system pressure drop, and the comparison reference test set is dynamically updated.

[0040] Preferably, the phase space reconstruction is a method of extracting system dynamic characteristics from time series data, which is based on time-delay coordinate embedding technology to convert one-dimensional time series data into points in high-dimensional phase space in order to better analyze the dynamic behavior of the system.

[0041] The beneficial technical effects of the present invention are:

[0042] (1) The present invention adopts a method combining nonlinear dynamic analysis and machine learning in the pneumatic conveying system, and uses the data collected by the acoustic emission sensor as the main analysis object to predict and analyze the important parameters of the pneumatic conveying system, such as the solid-gas ratio and the system pressure drop. The appropriate operating parameters are determined under the required optimization target through dynamic optimization of the parameters, so as to realize the intelligent and refined control of the gas volume and fluctuation range of the high-pressure airflow by the conveying system, reduce the conveying energy consumption and the fluctuation of the airflow, improve the safety of the system conveying, and ensure that the conveying system is in the best working state.

[0043] (2) The nonlinear dynamic analysis method of the present invention can extract nonlinear dynamic features from the electrical signals converted after being collected by the acoustic emission sensor to determine the nonlinear dynamic related parameters related thereto. These parameters can be high-level features extracted from the original data to enhance the performance of the neural network model, wherein the data of the test set based on good acoustic emission sensor signals obtained under experimental conditions can dynamically analyze and optimize the accuracy of the neural network model prediction.

[0044] (3) The machine learning method of the present invention adopts a recurrent neural network, which can process sequence data and has a memory function. It can capture the dynamic characteristics in the time series, and uses nonlinear dynamic characteristic parameters and some measurement data as its input layer. The conveying solid-gas ratio and system pressure drop as its output layer can better reflect the conveying capacity and energy consumption of the pneumatic conveying system. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is the overall logic schematic diagram of the present invention;

[0046] Figure 2 It is a schematic diagram of the network for application of the present invention;

[0047] Figure 3It is a schematic diagram of the method for combining nonlinear dynamic analysis and neural network of the present invention. DETAILED DESCRIPTION

[0048] Embodiment 1, see attached Figure 1-3 , a method for predicting nonlinear signals of pneumatic conveying airflow based on machine learning analysis, the steps are as follows:

[0049] Parameter Input

[0050] ① Input system parameters, including temperature, humidity, particle characteristics, pipeline layout, pipeline length, and system mechanical device configuration, and then input operating parameters, including air flow velocity, material mass flow, and pipeline inlet and outlet pressure;

[0051] Data collection and preprocessing

[0052] ② Analyze the gas mass flow rate through the gas flow meter data, analyze the material mass flow rate and pipeline pressure drop through the weighing sensor and pressure sensor data, and then collect the acoustic signal of the acoustic emission sensor. The advantage of this sensor is that it can be used in pneumatic conveying. Non-invasive measurement can be used to avoid affecting the flow pattern in the pipeline. Then, the obtained data signal is de-noised and outliers are removed, and signal processing such as filtering and normalization is performed;

[0053] The good acoustic emission sensor signals obtained under the experimental state are preprocessed to obtain the three nonlinear analysis index parameters under this state, and the association between the nonlinear index and the parameters such as the conveying solid-gas ratio and the system pressure drop is established. These are used as the test set data to analyze and optimize the correctness of the model prediction.

[0054] ③ Extraction of nonlinear dynamic features: convert the collision signal in the pipeline measured by the acoustic emission sensor during pneumatic conveying into an electrical signal, and select appropriate time delay (τ) and embedding dimension (m) to reconstruct the phase space, where time delay (τ) refers to the time interval used to connect data points in the same time series to form a multidimensional vector when constructing a vector. The selection of time delay is crucial to capturing the intrinsic dynamics of the system. Embedding dimension (m) refers to the dimension of the vector used to describe the state of the system during phase space reconstruction. Phase space reconstruction is a method of extracting system dynamic features from time series data. It is based on time delay coordinate embedding technology to convert one-dimensional time series data into points in high-dimensional phase space in order to better analyze the dynamic behavior of the system.

[0055] Data storage and nonlinear dynamics analysis

[0056] ④ Store the data every 5 seconds in the input and output databases, and then perform nonlinear dynamic analysis on the data in the input and output databases. The calculation method of the relevant parameters in the nonlinear dynamic analysis method is as follows:

[0057] The Lyapunov exponent LE can evaluate the degree of chaos in a system. It is a quantitative indicator of how sensitive a dynamic system is to initial conditions, and helps identify the stability and predictability of a system. It describes the rate of divergence or convergence of adjacent trajectories in phase space. If all exponents are negative, the trajectories converge, indicating stability. On the contrary, a positive exponent indicates divergence and instability, i.e., small initial differences can lead to large differences in long-term behavior.

[0058]

[0059] where λ(i) is the maximum Lyapunov exponent at time delay i; k max and k min are the minimum and maximum time delays, respectively; k is the parameter for adjusting the control input weights in model predictive control; dt is the time step; ∥Y i+k -Y s+k ∥ / ∥Y i -Y s ∥ is the distance between point i and its adjacent point s in each stage;

[0060] Approximate entropy AE is a measure of the complexity of time series data. It is used to evaluate the randomness and unpredictability of data. It is based on comparing the frequency of similar patterns in time series and calculating the complexity of patterns under different embedding dimensions. Lower approximate entropy indicates more predictable behavior, while higher ones are more complex.

[0061] AE=Φ m -Φ m+1

[0062]

[0063] Where r is the threshold radius; Φ m and Φ m+1 are statistical functions calculated for dimensions m and m+1 respectively; Θ is the Heaviside function; the Heaviside function under dimension m is as follows:

[0064]

[0065] Recurrence Rate RR,Recurrence Rate RR is used to analyze the repetitive pattern of states in a dynamic system. Recurrence Rate RP is calculated through a recurrence plot, which is a graphical tool used to visualize repetitive states or periodic behavior in time series data.

[0066]

[0067] The recurrence rate (RR) is the ratio of the number of repeated points to the total number of points.

[0068] Building a Neural Network

[0069] ⑤ The data set after nonlinear dynamic analysis is divided into training set, validation set and test set. The training set data is used to train the neural network, and the network weights are adjusted through the back propagation algorithm to minimize the difference between the predicted output and the actual output. The validation set data is used to adjust the model parameters, including learning rate, batch size, number of network layers and number of neurons, to prevent overfitting; then the model is analyzed and optimized, and the performance of the model is evaluated on the previously determined test set based on the acoustic signal of a good acoustic emission sensor. The input operation parameters are dynamically tuned according to the comparison results, and the optimized nonlinear indicator parameters are predicted by the neural network to obtain the optimized solid-gas ratio, system pressure drop and other prediction results, and the comparison reference test set is dynamically updated.

[0070] The neural network model includes an input layer, a hidden layer and an output layer. The input layer of the neural network model is nonlinear dynamic characteristic parameters and measurement data, the output layer is the conveying solid-gas ratio and system pressure drop, and the hidden layer is a new feature created by combining different features of the input layer. These new features may be more predictive for the output. The number of hidden layers depends on the complexity of the pneumatic conveying system pipeline.

[0071] ⑥ Establish a recurrent neural network RNN. In RNN, the output of each neuron depends not only on the input of the current time step, but also on the output of the previous time step. This recursive connection enables RNN to maintain state, thereby processing time series data. The training of RNN involves forward propagation and back propagation. In forward propagation, the input sequence passes through the network time step by time, and the output and loss of each time step are calculated. In back propagation, the gradient of the loss function with respect to the network parameters is calculated and then propagated back through the network to update the weights and bias terms;

[0072] Neuron output formula:

[0073] h t =f(W ih ·x t +W hh ·h t-1 +b h )

[0074] Among them, h t is the state of the hidden layer at time step t; x t is the input of the input layer at time step t; W ih is the weight matrix input to the hidden layer; W hhis the recursive connection weight matrix of the hidden layer itself; h t-1 is the state of the hidden layer at the previous time step t-1; b h is the bias term of the hidden layer; f is the ReLU activation function, f(x) = max(0,x);

[0075] Loss function, the purpose of the loss function is to quantify the difference between the model prediction and the true value. Ideally, the value of the loss function should be as small as possible. The loss function of this neural network chooses cross entropy loss, which can predict whether the system state is stable.

[0076]

[0077] Where L is the value of the loss function; y i is the true distribution of the target category (usually one-hot encoding); are the log odds (logits) predicted by the model;

[0078] ⑦ Deploy the trained model to the actual pneumatic conveying system for real-time monitoring, prediction and optimization control. Adjust the operating parameters according to the model output, including adjusting the air flow velocity and material flow rate. Continuously optimize the model based on the feedback from the system operation and new data to adapt to system changes and improve prediction accuracy. Adjust the model structure or reselect features based on the comparison results to improve prediction accuracy.

[0079] The model is predicted and controlled by selecting the appropriate cost function weight through the model predictive control method, the operating parameters of the input pneumatic conveying system are dynamically adjusted, and the optimal model is judged for parameter output. The cost function is calculated as follows:

[0080] J(x,u)=∑(xr) T Q(xr)+∑(uu prev ) T R(uu prev )+∑u T Su

[0081] Where x is the system state vector; u is the control input vector; r is the reference state vector; u prev is the control input at the previous moment; Q is the state deviation weight matrix; R is the control deviation weight matrix; S is the control input weight matrix.

[0082] In each control cycle, the future behavior of the system is predicted based on the current system state and the prediction model, so as to calculate the optimal control input to minimize the cost function, and dynamically adjust the operating parameters of the pneumatic conveying system according to whether the predicted output parameters are tending to be optimal. If it is predicted that the output parameters are tending to be optimal, the parameter library storage is optimized, and the optimized input and output parameter database corresponding to the conveying capacity and the minimum conveying energy consumption is set. Then, the input parameter comparison is performed, and the input parameter adjustment step is determined according to the database comparison result, so as to realize the dynamic adjustment of the operating parameter input; if it is predicted that the output parameters are not tending to be optimal, the input parameter comparison is performed, and the input parameter adjustment step is determined according to the database comparison result, so as to realize the dynamic adjustment of the operating parameter input.

Claims

1. A method for predicting nonlinear signals of pneumatic conveying airflow based on machine learning analysis, Its characteristics include the following steps: Parameter Input ① Input system parameters, including temperature, humidity, particle characteristics, pipeline layout, pipeline length, and system mechanical device configuration, and then input operating parameters, including air flow velocity, material mass flow, and pipeline inlet and outlet pressure; Data collection and preprocessing ② Analyze the gas mass flow rate through the gas flow meter data, analyze the material mass flow rate and pipeline pressure drop through the weighing sensor and pressure sensor data, and then collect the acoustic signal of the acoustic emission sensor, and then remove the noise and outliers from the obtained data signal, and perform signal processing such as filtering and normalization; ③ Extraction of nonlinear dynamic features: converting the collision signal in the pipeline measured by the acoustic emission sensor during pneumatic conveying into an electrical signal, and selecting appropriate time delay (τ) and embedding dimension (m) to reconstruct the phase space. The time delay (τ) refers to the time interval used to connect the data points in the same time series to form a multidimensional vector when constructing a vector, and the embedding dimension (m) refers to the dimension of the vector used to describe the system state during the phase space reconstruction process. Data storage and nonlinear dynamics analysis ④ Store the data every 5 seconds in the input and output databases, and then perform nonlinear dynamic analysis on the data in the input and output databases. The calculation method of the relevant parameters in the nonlinear dynamic analysis method is as follows: Lyapunov exponent LE where λ(i) is the maximum Lyapunov exponent at time delay i; k max and k min are the minimum and maximum time delays, respectively; k is the parameter for adjusting the control input weights in model predictive control; dt is the time step; ∥Y i+k -Y s+k ∥ / ∥Y i -Y s ∥ is the distance between point i and its adjacent point s in each stage; Approximate Entropy AE AE=Φ m -Φ m+1 Where r is the threshold radius; Φ m and Φ m+1 are statistical functions calculated for dimensions m and m+1 respectively; Θ is the Heaviside function; the Heaviside function under dimension m is as follows: Recursion rate RR Building a Neural Network ⑤ The neural network model includes an input layer, a hidden layer and an output layer. The input layer of the neural network model is the nonlinear dynamic characteristic parameters and measurement data, the output layer is the transport solid-gas ratio and system pressure drop, and the hidden layer is a new feature created by combining different features of the input layer; ⑥ Establish a recurrent neural network RNN. In RNN, the output of each neuron depends not only on the input of the current time step, but also on the output of the previous time step. This recursive connection enables RNN to maintain state, thereby processing time series data. The training of RNN involves forward propagation and back propagation. In forward propagation, the input sequence passes through the network time step by time, and the output and loss of each time step are calculated. In back propagation, the gradient of the loss function with respect to the network parameters is calculated and then propagated back through the network to update the weights and bias terms; Neuron output formula: h t =f(W ih ·x t +W hh ·h t-1 +b h ) Among them, h t is the state of the hidden layer at time step t; x t is the input of the input layer at time step t; W ih is the weight matrix input to the hidden layer; W hh is the recursive connection weight matrix of the hidden layer itself; h t-1 is the state of the hidden layer at the previous time step t-1; b h is the bias term of the hidden layer; f is the ReLU activation function, f(x) = max(0,x); Loss Function Where L is the value of the loss function; y i is the true distribution of the target category; are the log odds (logits) predicted by the model; ⑦ Deploy the trained model to the actual pneumatic conveying system for real-time monitoring, prediction and optimization control. Adjust the operating parameters according to the model output, including adjusting the air flow velocity and material flow rate. Continuously optimize the model based on the feedback from the system operation and new data to adapt to system changes and improve prediction accuracy. Adjust the model structure or reselect features based on the comparison results to improve prediction accuracy.

2. The method for predicting nonlinear signals of pneumatic conveying airflow based on machine learning analysis according to claim 1, characterized in that: The model is predicted and controlled by selecting the appropriate cost function weight through the model predictive control method, the operating parameters of the input pneumatic conveying system are dynamically adjusted, and the optimal model is judged for parameter output. The cost function is calculated as follows: J(x,u)=∑(xr) T Q(xr)+∑(u-uprev) T R(u-uprev)+∑u T Su Where x is the system state vector; u is the control input vector; r is the reference state vector; u prev is the control input at the previous moment; Q is the state deviation weight matrix; R is the control deviation weight matrix; S is the control input weight matrix.

3. The method for predicting nonlinear signals of pneumatic conveying airflow based on machine learning analysis according to claim 2, characterized in that: In each control cycle, the future behavior of the system is predicted based on the current system state and the prediction model, so as to calculate the optimal control input to minimize the cost function, and dynamically adjust the operating parameters of the pneumatic conveying system according to whether the predicted output parameters are tending to be optimal. If it is predicted that the output parameters are tending to be optimal, the parameter library storage is optimized, and the optimized input and output parameter database corresponding to the conveying capacity and the minimum conveying energy consumption is set. Then, the input parameter comparison is performed, and the input parameter adjustment step is determined according to the database comparison result, so as to realize the dynamic adjustment of the operating parameter input; if it is predicted that the output parameters are not tending to be optimal, the input parameter comparison is performed, and the input parameter adjustment step is determined according to the database comparison result, so as to realize the dynamic adjustment of the operating parameter input.

4. The method for predicting nonlinear signals of pneumatic conveying airflow based on machine learning analysis according to claim 1, characterized in that: The data set after nonlinear dynamics analysis is divided into training set, validation set and test set. The training set data is used to train the neural network, and the network weights are adjusted through the back propagation algorithm to minimize the difference between the predicted output and the actual output. The validation set data is used to adjust the model parameters, including learning rate, batch size, number of network layers and number of neurons, to prevent overfitting.

5. The method for predicting nonlinear signals of pneumatic conveying airflow based on machine learning analysis according to claim 4, characterized in that: The model is analyzed and optimized, and its performance is evaluated on a previously determined test set of acoustic signals based on good acoustic emission sensors. The input operating parameters are dynamically tuned according to the comparison results, and the optimized nonlinear index parameters are predicted through a neural network to obtain the optimized prediction results such as solid-gas ratio and system pressure drop, and the comparison reference test set is dynamically updated.

6. The method for predicting nonlinear signals of pneumatic conveying airflow based on machine learning analysis according to claim 1, characterized in that: The phase space reconstruction is a method for extracting system dynamic characteristics from time series data. It converts one-dimensional time series data into points in a high-dimensional phase space based on time-delay coordinate embedding technology to better analyze the dynamic behavior of the system.

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