A dual spark plug engine system and a control method thereof

By combining a dual spark plug design with a swirl premixing chamber and multi-sensor monitoring, the problem of unstable combustion in traditional engines has been solved, resulting in more efficient combustion and lower emissions, thus improving engine performance.

CN119712340BActive Publication Date: 2026-02-24GUANGXI UNIV
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Patent Information

Application Number
CN202411788402.2
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-12-06
Publication Date
2026-02-24
Estimated Expiration
2044-12-06

AI Technical Summary

Technical Problem

Traditional single-spark plug engines suffer from problems such as long flame propagation distance, long combustion time, uneven air-fuel mixture, incomplete combustion, low thermal efficiency, and high emissions. Furthermore, they lack real-time monitoring and feedback of combustion chamber temperature and pressure, leading to unstable combustion and increased emissions.

Method used

It adopts a dual spark plug design, combined with a swirl premixing chamber and multi-sensor monitoring. The BP neural network controls the spark plug ignition timing and fuel injection quantity in the combustion chamber. Temperature sensors, pressure sensors and camshaft sensors are used to monitor the combustion chamber status in real time, and the combustion process is optimized in conjunction with the electronic control unit.

Benefits of technology

It improves fuel combustion efficiency, shortens combustion time, reduces misfire rate and knock tendency, lowers emissions and fuel consumption, and enhances engine power, economy and safety.

✦ Generated by Eureka AI based on patent content.

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Abstract

The application discloses a double spark plug engine system and a control method thereof, and belongs to the technical field of engines, and solves the technical problems of long flame propagation distance and long combustion time of a single spark plug ignition mode. The system comprises a body, an electronic control unit, a piston arranged in the body, a cylinder cover arranged at the top of the body, a combustion chamber formed between the cylinder cover and the piston, a front spark plug and a rear spark plug arranged on the cylinder cover on the two sides of the combustion chamber, an oil injector arranged on the cylinder cover on the side of the rear spark plug, a vortex pre-mixing chamber arranged on the cylinder cover at the front end of the oil injector, a nozzle arranged on the vortex pre-mixing chamber, and an air inlet channel arranged on the cylinder cover on the side of the oil injector and communicated with the vortex pre-mixing chamber. The cylinder cover on the two sides of the combustion chamber is further respectively provided with a temperature sensor and a pressure sensor. The front spark plug and the rear spark plug are cooperatively arranged to shorten the propagation distance of the flame and reduce the combustion time.
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Description

Technical Field

[0001] This invention relates to the field of engine technology, and more specifically, to a dual-spark plug engine system and its control method. Background Technology

[0002] Currently, the thermal efficiency conversion of gasoline engines remains a challenge, with most gasoline engines achieving a maximum thermal efficiency of only around 40%. Most research on engine performance focuses primarily on single influencing factors such as intake / exhaust port location, combustion chamber structure, spark plug placement and ignition timing, compression ratio, and fuel performance.

[0003] Traditional single-spark plug ignition systems result in a longer flame propagation distance and combustion time. Traditional direct injection engines have shorter fuel-air mixing times, leading to uneven mixture distribution within the combustion chamber and potential for localized overly rich or lean mixtures. Furthermore, traditional engines lack real-time monitoring and feedback of combustion chamber temperature and pressure, making it impossible to precisely control the injection quantity and ignition timing of the injectors and spark plugs based on different operating conditions and fuel properties. The traditional method of using a single camshaft position sensor to determine ignition timing suffers from high uncertainty, poor accuracy, and unstable ignition timing. All of these factors contribute to incomplete and unstable combustion of the air-fuel mixture within the combustion chamber, resulting in a large amount of unburned gas and soot, leading to reduced thermal efficiency and increased emissions. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to address the above-mentioned shortcomings of the prior art. The objective of the present invention is to provide a dual spark plug engine system.

[0005] The second objective of this invention is to provide a control method for a dual-spark plug engine system.

[0006] To achieve the aforementioned objective, the present invention provides a dual-spark plug engine system, comprising an engine block and an electronic control unit. The engine block contains a piston, and a cylinder head is located on the top of the engine block. A combustion chamber is formed between the cylinder head and the piston. A front spark plug and a rear spark plug are respectively located on the cylinder heads on both sides of the combustion chamber. An injector is located on the cylinder head on the side of the rear spark plug. A swirl premixing chamber is located on the cylinder head at the front end of the injector, and a nozzle is located in the swirl premixing chamber. An intake passage communicating with the swirl premixing chamber is located on the cylinder head on the side of the injector. Temperature sensors and pressure sensors are also respectively located on the cylinder heads on both sides of the combustion chamber. The electronic control unit is electrically connected to the front spark plug, the rear spark plug, the injector, the temperature sensor, the pressure sensor, and a camshaft position sensor of the engine.

[0007] As a further improvement, the center lines of the front spark plug, the rear spark plug, the nozzle, and the cylinder bore are located on the same plane.

[0008] Furthermore, the angle between the centerline of the front spark plug and the centerline of the cylinder bore is 55° to 65°.

[0009] Furthermore, the angle between the centerline of the rear spark plug and the centerline of the cylinder bore is 20-30°.

[0010] Furthermore, the angle between the centerline of the nozzle and the centerline of the cylinder bore is 65-70°.

[0011] Furthermore, the angle between the air intake and the fuel injector is 20-30°.

[0012] Furthermore, the vortex premixing chamber has a spherical structure, the top of the piston has a groove structure, the groove structure is high in the middle and low on the periphery, and the cylinder head directly above the piston has a conical groove structure.

[0013] Furthermore, the temperature sensor is located on one side of the front spark plug, and the pressure sensor is located on one side of the rear spark plug.

[0014] To achieve the second objective mentioned above, the present invention provides a control method for a dual spark plug engine system, comprising the following steps:

[0015] Step 1. Establish a BP neural network. The input parameters of the BP neural network include temperature, pressure, and cam phase. The output parameters of the BP neural network include spark plug usage, front spark plug ignition timing signal, rear spark plug ignition timing signal, and fuel injection quantity.

[0016] Step 2. Train the BP neural network based on the historical data of the temperature sensor, pressure sensor, and camshaft position sensor to obtain a control model, and run the control model in the electronic control unit;

[0017] Step 3. The electronic control unit obtains the current temperature, current pressure and current camshaft phase information in the combustion chamber through the temperature sensor, pressure sensor and camshaft position sensor respectively, and inputs them into the control model to obtain the optimal predicted spark plug usage, predicted front spark plug ignition timing signal, predicted rear spark plug ignition timing signal and predicted fuel injection quantity.

[0018] Step 4. The electronic control unit controls the operation of the front spark plug, the rear spark plug, and the fuel injector respectively based on the predicted spark plug usage, the predicted front spark plug ignition timing signal, the predicted rear spark plug ignition timing signal, and the predicted fuel injection quantity.

[0019] As a further improvement, the BP neural network comprises a three-layer structure: an input layer, a hidden layer, and an output layer;

[0020] The input layer mainly receives the output signals from the temperature sensor, pressure sensor, and camshaft position sensor after they have been processed by the electronic control unit.

[0021] The output layer mainly outputs the spark plug usage, the front spark plug ignition timing signal, the rear spark plug ignition timing signal, and the fuel injection quantity;

[0022] The hidden layer extracts data features based on nonlinear transformations, and the number of nodes in the hidden layer is calculated using an empirical formula based on the number of nodes in the input and output layers.

[0023]

[0024] Where h represents the number of neurons in the hidden layer, m and n represent the number of nodes in the input layer and output layer, respectively, and a is a constant from 1 to 10; according to equation (1), the number of nodes in the hidden layer is determined to be 8;

[0025] Forward propagation: Network initialization, the weights from the input layer to the hidden layer are ω. ij The threshold for hidden layer nodes is a. j The weights from the hidden layer to the output layer are ω. jk The threshold value for the output layer nodes is b. k The learning efficiency is η, and it is applied to ω respectively. ij a j ω jk b k Assign random values ​​within the range of [-1, 1], and select the Tanh function as the activation function for the hidden layer;

[0026]

[0027] Choose any set of input samples X = (x1, x2, ..., xn) n ), calculate the input I of the j-th node in the hidden layer. j With output O j :

[0028]

[0029] Output layer output calculation:

[0030]

[0031] Backpropagation of error: The backpropagation process improves the accuracy of the network by continuously adjusting the weights and thresholds. To ensure that the algorithm does not get stuck in local minima, logistic regression is used as the loss function, and the expected output of the output layer is Y. kThe error E of the output layer:

[0032]

[0033] To minimize the error E, the gradient descent method is used to correct the weights along the steepest descent direction of the sum of squared errors. Let the updated weights of the hidden layer and the output layer be... The weights of the input layer and the hidden layer are

[0034] Weight correction from hidden layer to output layer:

[0035]

[0036] Weight adjustment from input layer to hidden layer:

[0037]

[0038] The threshold updates for the hidden layer and the output layer are as follows:

[0039]

[0040]

[0041] Through multiple iterations, the difference between the actual output and the expected output is continuously reduced. The training process ends when the difference in error between two consecutive iterations is less than a specified value.

[0042] Beneficial effects

[0043] Compared with the prior art, the advantages of this invention are as follows:

[0044] 1. The dual spark plug design of this invention can significantly improve fuel combustion efficiency within a reasonable ignition energy range. By having two spark plugs ignite the air-fuel mixture in stages, two flame fronts are formed, accelerating flame propagation efficiency, shortening combustion time, reducing misfire rate and knocking tendency, achieving more complete combustion, and reducing emissions and fuel consumption. At the same time, this design reduces the ignition energy requirement, ensuring the spark plugs' utilization rate under different operating conditions and extending their service life.

[0045] 2. The present invention designs a spherical vortex premixing chamber with the intake manifold installed at an angle of 20-30° to the injector. This ensures that high-concentration fuel does not remain around the intake port. The intake manifold forces the gas into the vortex premixing chamber at high speed, forming a high-speed vortex with the fuel injected by the injector. This improves the effect of guiding the fuel and air along the spherical wall. The vortex premixing chamber enables the gas and gasoline to achieve sufficient initial mixing and atomization, reducing the problem of insufficient fuel mixing in the combustion chamber.

[0046] 3. In this invention, the fuel injected from the vortex premixing chamber enters the combustion chamber at an angle of 65° to 70° with the cylinder bore centerline. This facilitates the full entry of the initially mixed fuel into the combustion chamber, where it is further atomized and mixed with air by the ω-shaped piston surface and cylinder wall surface. Furthermore, this alignment with the spark plug's ignition direction further promotes disturbance and complete combustion throughout the combustion chamber mixer. This improves fuel combustion efficiency, increases engine power, and ensures the engine's performance, economy, and emissions performance.

[0047] 4. This invention utilizes temperature sensors, pressure sensors, and camshaft sensors to monitor the temperature, pressure, and camshaft phase information within the combustion chamber in real time. This information is fed back to the Electronic Control Unit (ECU). The ECU preprocesses this information, including normalization, noise reduction, and feature selection, before inputting it into a trained neural network model. This model adjusts the fuel injection quantity and spark plug ignition timing based on different operating conditions and fuel strategies, ensuring complete combustion of the air-fuel mixture within the combustion chamber, reducing fuel waste and pollutant emissions, and improving engine safety and reliability. This multi-sensor data fusion technology offers advantages such as good fault tolerance, high precision, rapid processing capabilities, and strong complementarity. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the structure of the present invention;

[0049] Figure 2 This is the control flowchart of the present invention;

[0050] Figure 3 This is a schematic diagram of the control model of the present invention.

[0051] The components are: 1-engine block, 2-piston, 3-cylinder head, 4-front spark plug, 5-temperature sensor, 6-rear spark plug, 7-injector, 8-swirl premixing chamber, 9-intake manifold, 10-pressure sensor, 11-combustion chamber, 12-nozzle. Detailed Implementation

[0052] The present invention will be further described below with reference to specific embodiments shown in the accompanying drawings.

[0053] See Figures 1-3A dual-spark plug engine system includes an engine block 1 and an electronic control unit (ECU). The engine block 1 houses a piston 2, and a cylinder head 3 is located on top of the engine block 1, forming a combustion chamber 11 between the cylinder head 3 and the piston 2. A front spark plug 5 and a rear spark plug 6 are respectively located on the cylinder head 3 on both sides of the combustion chamber 11. An injector 7 is located on the cylinder head 3 on the side of the rear spark plug 6. A swirl premixing chamber 8 is located at the front end of the injector 7, and a nozzle 12 is located in the swirl premixing chamber 8. An intake passage 9 communicating with the swirl premixing chamber 8 is located on the cylinder head 3 on the side of the injector 7. A temperature sensor 4 and a pressure sensor 10 are also respectively located on the cylinder head 3 on both sides of the combustion chamber 11. The ECU is electrically connected to the front spark plug 5, the rear spark plug 6, the injector 7, the temperature sensor 4, the pressure sensor 10, and the engine camshaft position sensor.

[0054] In this embodiment, the centerlines of the front spark plug 5, the rear spark plug 6, the nozzle 12, and the cylinder bore are located on the same plane. The angle between the centerline of the front spark plug 5 and the cylinder bore centerline is 55-65°, the angle between the centerline of the rear spark plug 6 and the cylinder bore centerline is 20-30°, the angle between the centerline of the nozzle 12 and the cylinder bore centerline is 65-70°, and the angle between the intake manifold 9 and the fuel injector 7 is 20-30°.

[0055] The vortex premixing chamber 8 has a spherical structure, and the top of the piston 2 has a groove structure. The groove structure is high in the middle and low on the outside, that is, the cross-section of the groove structure is ω-shaped. The cylinder head 3 directly above the piston 2 has a conical groove structure, which is conducive to guiding the flow and further secondary mixing and atomization of air.

[0056] Temperature sensor 4 is located on one side of front spark plug 5, and pressure sensor 10 is located on one side of rear spark plug 6.

[0057] The system's working process is as follows:

[0058] 1) The fuel injector 7 injects fuel into the swirl premixing chamber 8, while the intake manifold 9 injects gas into the swirl premixing chamber 8, thereby achieving the initial mixing and atomization of gasoline and air in the swirl premixing chamber 8.

[0059] 2) The fuel after initial mixing and atomization is injected into the combustion chamber 11 through the nozzle 12 of the vortex premixing chamber 8, while air is introduced through the intake valve to mix with the fuel after initial mixing and atomization for a second time.

[0060] 3) Temperature sensor 4, high pressure sensor 10 and camshaft position sensor measure the current temperature, pressure and cam phase information in the combustion chamber and feed the measured signals back to the electronic control unit.

[0061] 4) The electronic control unit processes the collected signals and determines the spark plug energy, number of spark plugs, and spark plug ignition time required for ignition by converting and fusing the signals. The front spark plug 5 and the rear spark plug 6 ignite in stages to ensure complete combustion of the fuel in the combustion chamber. That is, the front spark plug 5 ignites first and the rear spark plug 6 ignites later.

[0062] To effectively improve fuel combustion efficiency, the present invention also provides a control method for a dual spark plug engine system, comprising the following steps:

[0063] Step 1. Establish a BP neural network. The input parameters of the BP neural network include temperature, pressure and cam phase. The output parameters of the BP neural network include spark plug usage, front spark plug ignition timing signal, rear spark plug ignition timing signal and fuel injection quantity.

[0064] Step 2. Train a BP neural network based on historical data from temperature sensor 4, pressure sensor 10, and camshaft position sensor to obtain a control model, and run the control model in the electronic control unit;

[0065] Step 3. The electronic control unit obtains the current temperature, current pressure and current cam phase information in the combustion chamber 11 through the temperature sensor 4, pressure sensor 10 and camshaft position sensor respectively, and inputs them into the control model to obtain the optimal predicted spark plug usage, predicted front spark plug ignition timing signal, predicted rear spark plug ignition timing signal and predicted fuel injection quantity.

[0066] Step 4. The electronic control unit controls the operation of the front spark plug 5, the rear spark plug 6 and the fuel injector 7 respectively based on the predicted spark plug usage, the predicted front spark plug ignition timing signal, the predicted rear spark plug ignition timing signal and the predicted fuel injection quantity.

[0067] A BP neural network consists of three layers: an input layer, a hidden layer, and an output layer.

[0068] The input layer mainly receives the output signals from the temperature sensor 4, pressure sensor 10, and camshaft position sensor after they have been processed by the electronic control unit.

[0069] The output layer mainly outputs the spark plug usage, the front spark plug ignition timing signal, the rear spark plug ignition timing signal, and the fuel injection quantity.

[0070] The hidden layer extracts data features based on nonlinear transformations. The number of nodes in the hidden layer is calculated using an empirical formula based on the number of nodes in the input and output layers.

[0071]

[0072] Where h represents the number of neurons in the hidden layer, m and n represent the number of nodes in the input and output layers, respectively, and a is a constant from 1 to 10; according to equation (1), the number of nodes in the hidden layer is determined to be 8. The network topology is as follows: Figure 3 As shown.

[0073] 1) Forward propagation of signal:

[0074] Network initialization, the weights from the input layer to the hidden layer are ω. ij The threshold for hidden layer nodes is a. j The weights from the hidden layer to the output layer are ω. jk The threshold value for the output layer nodes is b. k The learning efficiency is η, and it is applied to ω respectively. ij a j ω jk b k Assign random values ​​within the range [-1, 1]. Choose the Tanh function as the activation function for the hidden layer.

[0075]

[0076] Choose any set of input samples X = (x1, x2, ..., xn) n ), calculate the input I of the j-th node in the hidden layer. j With output O j .

[0077]

[0078] Output layer output calculation:

[0079]

[0080] 2) Backpropagation of error:

[0081] The error backpropagation process improves the network's accuracy by continuously adjusting the weights and thresholds. To prevent the algorithm from getting stuck in local minima, logistic regression is used as the loss function, and the expected output of the output layer is Y. k The error e of the output layer:

[0082]

[0083] To minimize the error e, the gradient descent method is used to correct the weights along the steepest descent direction of the sum of squared errors. Let the updated weights of the hidden layer and the output layer be... The weights of the input layer and the hidden layer are

[0084] Weight correction from hidden layer to output layer:

[0085]

[0086] Weight adjustment from input layer to hidden layer:

[0087]

[0088] The threshold updates for the hidden layer and the output layer are as follows:

[0089]

[0090] Through multiple iterations, the difference between the actual output and the expected output is continuously reduced. The training process ends when the difference in error between two consecutive iterations is less than a specified value.

[0091] In this invention, the front spark plug 5, rear spark plug 6, and nozzle 12 are all positioned towards the cylinder centerline. The ignition timing of the front spark plug 5 and rear spark plug 6 is determined by the electronic control unit, which facilitates fuel ignition in the center of the combustion chamber and minimizes the flame propagation distance. The principle behind this design is to optimize the air-fuel mixture distribution and flame propagation path within the combustion chamber by utilizing the installation position and angle of the spark plugs and injectors. This ensures that the ignition direction of the spark plugs corresponds to the injection direction of the injectors, thereby forming a central ignition zone. Simultaneously, the flame front spreads outwards from both spark plugs, shortening the flame propagation distance and reducing combustion time. This allows for a higher compression ratio, improving combustion efficiency and engine performance while reducing emissions and fuel consumption.

[0092] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make several modifications and improvements without departing from the structure of the present invention, and these will not affect the effectiveness of the implementation of the present invention or the practicality of the patent.

Claims

1. A dual-spark plug engine system, comprising an engine block (1) and an electronic control unit, wherein a piston (2) is disposed within the engine block (1), and a cylinder head (3) is disposed on the top of the engine block (1), wherein a combustion chamber (11) is formed between the cylinder head (3) and the piston (2), characterized in that, The cylinder heads (3) on both sides of the combustion chamber (11) are respectively provided with a front spark plug (5) and a rear spark plug (6). The cylinder head (3) on the side of the rear spark plug (6) is provided with an injector (7). The cylinder head (3) at the front end of the injector (7) is provided with a swirl premixing chamber (8). The swirl premixing chamber (8) is provided with a nozzle (12). The cylinder head (3) on the side of the injector (7) is provided with an intake passage (9) that connects to the swirl premixing chamber (8). The cylinder heads (3) on both sides of the combustion chamber (11) are also respectively provided with a temperature sensor (4) and a pressure sensor (10). The electronic control unit is electrically connected to the front spark plug (5), the rear spark plug (6), the injector (7), the temperature sensor (4), the pressure sensor (10), and the engine camshaft position sensor. The center lines of the front spark plug (5), the rear spark plug (6), the nozzle (12), and the cylinder bore are located on the same plane; The angle between the centerline of the front spark plug (5) and the centerline of the cylinder bore is 55-65°.

2. The dual spark plug engine system according to claim 1, characterized in that, The angle between the centerline of the rear spark plug (6) and the centerline of the cylinder bore is 20-30°.

3. The dual spark plug engine system according to claim 1, characterized in that, The angle between the centerline of the nozzle (12) and the centerline of the cylinder bore is 65-70°.

4. A dual spark plug engine system according to claim 1, characterized in that, The angle between the air intake (9) and the fuel injector (7) is 20-30°.

5. A dual spark plug engine system according to claim 1, characterized in that, The vortex premixing chamber (8) has a spherical structure, the top of the piston (2) has a groove structure, the groove structure is high in the middle and low on the periphery, and the cylinder head (3) directly above the piston (2) has a conical groove structure.

6. A dual spark plug engine system according to claim 1, characterized in that, The temperature sensor (4) is located on one side of the front spark plug (5), and the pressure sensor (10) is located on one side of the rear spark plug (6).

7. A control method for an engine system with dual spark plugs as described in claim 1, characterized in that, Includes the following steps: Step 1. Establish a BP neural network. The input parameters of the BP neural network include temperature, pressure, and cam phase. The output parameters of the BP neural network include spark plug usage, front spark plug ignition timing signal, rear spark plug ignition timing signal, and fuel injection quantity. Step 2. Train the BP neural network based on the historical data of the temperature sensor (4), pressure sensor (10) and camshaft position sensor to obtain a control model, and run the control model in the electronic control unit; Step 3. The electronic control unit obtains the current temperature, current pressure and current cam phase information in the combustion chamber (11) through the temperature sensor (4), pressure sensor (10) and camshaft position sensor respectively, and inputs them into the control model to obtain the optimal predicted spark plug usage, predicted front spark plug ignition timing signal, predicted rear spark plug ignition timing signal and predicted fuel injection quantity. Step 4. The electronic control unit controls the operation of the front spark plug (5), the rear spark plug (6) and the fuel injector (7) according to the predicted spark plug usage, the predicted front spark plug ignition timing signal, the predicted rear spark plug ignition timing signal and the predicted fuel injection quantity.

8. The control method for a dual spark plug engine system according to claim 7, characterized in that, The BP neural network consists of three layers: an input layer, a hidden layer, and an output layer. The input layer mainly receives the output signals from the temperature sensor (4), pressure sensor (10), and camshaft position sensor after they have been processed by the electronic control unit. The output layer mainly outputs the spark plug usage, the front spark plug ignition timing signal, the rear spark plug ignition timing signal, and the fuel injection quantity; The hidden layer extracts data features based on nonlinear transformations, and the number of nodes in the hidden layer is calculated using an empirical formula based on the number of nodes in the input and output layers. (1) in, This represents the number of neurons in the hidden layer. and These represent the number of nodes in the input and output layers, respectively. It is a constant from 1 to 10; according to equation (1), the number of nodes in the hidden layer is determined to be 8; Forward propagation of the signal: Network initialization, the weights from the input layer to the hidden layer are... The threshold for hidden layer nodes is The weights from the hidden layer to the output layer are: The threshold value for output layer nodes is Learning efficiency is , respectively , , , Assign random values ​​within the range of [-1, 1], and select the Tanh function as the activation function for the hidden layer; (2) Select any set of input samples Calculate the hidden layer 1 j Input of each node With output : (3) (4) Output layer output calculation: (5) Backpropagation: The backpropagation process improves network accuracy by continuously adjusting weights and thresholds. To prevent the algorithm from getting stuck in local minima, logistic regression is used as the loss function, and the expected output of the output layer is... Error of the output layer : (6) To minimize error The gradient descent method is used to correct the weights along the steepest descent direction of the sum of squared errors. Let the updated weights of the hidden layer and the output layer be... The input layer and hidden layer weights are ; Weight correction from hidden layer to output layer: (7) (8) Weight adjustment from input layer to hidden layer: (9) (10) The threshold updates for the hidden layer and the output layer are as follows: (11) (12) (13) (14) Through multiple iterations, the difference between the actual output and the expected output is continuously reduced. The training process ends when the difference in error between two consecutive iterations is less than a specified value.

Citation Information

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