Active vibration reduction control method based on adaptive neural fuzzy inference system

Abstract

An active vibration reduction control method based on a self-adaptive neural fuzzy inference system belongs to the technical field of vibration isolation control, and comprises the following steps: constructing a system model and carrying out data acquisition; designing an ANFIS model based on the state variable of the platform; the ANFIS model automatically adjusts parameters of the fuzzy membership function through experimental data training; training the ANFIS model based on a mixed learning algorithm; the displacement and the speed of the platform are obtained in real time through a sensor and input into the ANFIS model, and real-time active vibration reduction control is achieved. Displacement and speed data of the platform are collected in real time and input to the ANFIS model, so that the system can dynamically calculate control signals, quickly respond to vibration changes, effectively suppress vibration, reduce the vibration amplitude of the system and guarantee the stability of the platform. Through a feedback loop of the sensor and the control system, the system can automatically adjust the control signal at any time according to the actual vibration state of the platform.

Description

Technical Field

[0001] The present invention belongs to the technical field of vibration isolation control, and in particular relates to an active vibration reduction control method based on an adaptive neural fuzzy inference system. Background Art

[0002] In recent years, the Adaptive Neuro-Fuzzy Inference System (ANFIS), as an intelligent control method, has garnered widespread attention due to its integration of fuzzy logic and neural networks. It has shown significant potential, particularly in multivariable control and nonlinear modeling of complex systems. ANFIS utilizes fuzzy rules to classify system states and uses neural networks for adaptive parameter learning. It predicts the system's future dynamics in real time and outputs precise control signals, effectively reducing vibration impacts and enhancing system robustness, enabling superior vibration reduction in complex environments.

[0003] This paper proposes a quasi-zero-stiffness active vibration reduction method for air-bearing supports based on an adaptive neural-fuzzy inference system (ANFIS). The method is suitable for suppressing low-frequency vibrations in precision manufacturing and optical measurement equipment. Leveraging the low stiffness and high load characteristics of air-bearing supports, displacement and velocity are used as inputs to the ANFIS model. System modeling and frequency response identification are performed in conjunction with experimental data. Control signals are generated through adaptive learning to control the voice coil motor in real time to suppress vibrations. The ANFIS model is trained using a hybrid learning algorithm. The least squares method is used to optimize output weights in the forward propagation phase, and the gradient descent method is used to adjust the fuzzy membership functions in the backward propagation phase. Experimental results show that this method significantly improves vibration reduction in the 0.5-70 Hz frequency range and can stably support the operation of precision equipment in complex environments. Summary of the Invention

[0004] The purpose of this section is to summarize some aspects of the embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the abstract and title of this application to avoid obscuring the purpose of this section, the abstract and the title of the invention, and such simplifications or omissions should not be used to limit the scope of the present invention.

[0005] In view of the above or existing problems of active vibration reduction control methods based on adaptive neural fuzzy inference systems, the present invention is proposed.

[0006] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0007] An embodiment of the present invention provides an active vibration reduction control method based on an adaptive neural fuzzy inference system, comprising: constructing a system model and collecting data; designing an ANFIS model based on the state variables of a platform; automatically adjusting the parameters of the fuzzy membership function of the ANFIS model through experimental data training; training the ANFIS model based on a hybrid learning algorithm; and using sensors to obtain the displacement and velocity of the platform in real time, inputting the data into the ANFIS model to achieve real-time active vibration reduction control.

[0008] As a preferred solution of the active vibration reduction control method based on the adaptive neural fuzzy inference system of the present invention, the method of constructing a system model and collecting data includes:

[0009] Obtain the platform displacement through the sensor and speed As the input variable of the system, it reflects the current state of the vibration system. The voice coil motor generates the corresponding braking force F according to the control signal to offset the vibration force exerted on the platform, thereby constructing the dynamic model of the system to determine the input-output relationship.

[0010] As a preferred solution of the active vibration reduction control method based on the adaptive neural fuzzy inference system of the present invention, the dynamic model is used to describe the dynamic behavior of the platform vibration system, and the equation is as follows:

[0011]

[0012] Where M is the system's equivalent mass matrix, which determines the system's response strength to external vibrations; C is the damping coefficient, which characterizes the system's damping effect; K is the stiffness coefficient, which determines the system's ability to resist deformation; and F(t) is the control force generated by the voice coil motor, which is used to offset the platform's vibration.

[0013] As a preferred solution of the active vibration reduction control method based on the adaptive neural fuzzy inference system of the present invention, wherein: the ANFIS model is designed based on the state variables of the platform, including:

[0014] Through the nonlinear mapping of fuzzy logic rules and the adaptive ability of neural networks, the control signal of the system is generated. The ANFIS model uses the displacement of the platform and speed As input variable, the output variable is the control signal.

[0015] As a preferred solution of the active vibration reduction control method based on the adaptive neural fuzzy inference system of the present invention, wherein: the ANFIS model is designed based on the state variables of the platform, and further includes:

[0016] The input state is defined by fuzzy processing and fuzzy membership function. The membership function uses the generalized Bell function, which is expressed as:

[0017]

[0018] Among them, μ(x) is the input state of the input data x, a is the width parameter, which controls the stretching degree of the membership function; b is the shape parameter, which adjusts the curve shape of the membership function; c is the center parameter, which determines the position of the membership function.

[0019] As a preferred solution of the active vibration reduction control method based on the adaptive neural fuzzy inference system of the present invention, the ANFIS model automatically adjusts the parameters of the fuzzy membership function through experimental data training, including:

[0020] Multiple fuzzy rules R i Composed of ANFIS model, each rule is based on the input variables and The fuzzy state generates the control output, and the fuzzy rules are as follows:

[0021]

[0022] Among them, Ai and Bi represent the fuzzy sets of input variables; U represents the control signal of the voice coil motor.

[0023] As a preferred solution of the active vibration reduction control method based on the adaptive neural fuzzy inference system of the present invention, the activation value of each rule is derived according to the fuzzy rules:

[0024]

[0025] Among them, ω i Indicates the degree of rule activation, μA i (x) represents the membership of the input x(t) to the fuzzy set Ai, μBi(x) represents the membership of the input x(t) to the fuzzy set B i The degree of membership;

[0026] Perform weighted average defuzzification on the fuzzy result and output the final control signal:

[0027]

[0028] Among them, f i Represents the output of the i-th fuzzy rule, N represents the total number of rules, i=1, 2, 3,…, N.

[0029] As a preferred solution of the active vibration reduction control method based on the adaptive neural fuzzy inference system of the present invention, the training of the ANFIS model based on the hybrid learning algorithm includes:

[0030] In the forward propagation stage, the least squares method is used to optimize the linear combination weights of the output to minimize the error between the model output and the actual value. The ANFIS output layer is a linear combination of activated fuzzy rules, and its calculation formula is:

[0031]

[0032] Among them, U is the control signal of the voice coil motor, w n is the weight of the fuzzy rule; f n is the nth fuzzy rule output, n=1, 2, 3, ..., N; f1 is the first model rule output, f2 is the second model rule output, w1 and w2 are the corresponding weights;

[0033] The goal of the least squares method is to adjust w i Minimize the error, which is defined as:

[0034]

[0035] Among them, E is the error, m is the number of samples, k represents the number from the 1st to the mth sample, is the predicted output value, is the actual output value; in the back propagation stage, the gradient descent method is used to update the parameters of the fuzzy membership function. By adjusting the shape and position of the membership function, the output of the model is close to the response of the actual system. The update formula is as follows:

[0036]

[0037]

[0038]

[0039] Where η is the learning rate, , , are the updated system parameters, , , The current system parameters.

[0040] As a preferred solution of the active vibration reduction control method based on the adaptive neural fuzzy inference system of the present invention, wherein: the training of the ANFIS model based on the hybrid learning algorithm further includes:

[0041] Define the error function of the system, assuming that e(t) is the error at time step t, and calculate it as follows:

[0042]

[0043] Among them, y(t) is the actual output value at time t, y desired (t) is the expected output value at time t;

[0044] Calculate the rate of change of the error, that is, the gradient of the error Δe(t):

[0045]

[0046] If the error rate of change is large, the system state changes, and the adjustment is accelerated by increasing the learning rate; if the error change is small, the system tends to be stable, and the learning rate is reduced;

[0047] Gradually reduce the learning rate based on the error value or error rate of change, as follows:

[0048]

[0049] Among them, η(t) is the learning rate at time t, η0 is the initial learning rate, and λ is the adjustment factor;

[0050] Use the dynamically adjusted learning rate to update the weights and parameters of the neural network, and use the gradient descent method to update the weights.

[0051] As a preferred embodiment of the active vibration reduction control method based on the adaptive neural fuzzy inference system of the present invention, the method uses sensors to obtain the displacement and velocity of the platform in real time and inputs them into the ANFIS model to achieve real-time active vibration reduction control, including:

[0052] The ANFIS model uses a combination of fuzzy logic and neural networks to calculate corresponding control signals based on historical data and real-time inputs. The control signals drive actuators such as voice coil motors to generate reverse forces to offset the vibration of the platform.

[0053] The beneficial effects of the present invention are as follows: By collecting the platform's displacement and velocity data in real time and inputting it into the ANFIS model, the system can dynamically calculate control signals, rapidly respond to vibration changes, effectively suppress vibrations, and reduce the system's vibration amplitude, thereby ensuring the stability of the platform. The ANFIS model combines the advantages of fuzzy logic and neural networks, automatically adjusting control rules based on different vibration states. It has strong adaptability and robustness, and can handle complex vibration problems in different environments and operating conditions. The feedback loop between the sensor and the control system ensures that the system can automatically adjust the control signal according to the actual vibration state of the platform at any time, achieving continuous and stable active vibration reduction control. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0055] Figure 1 This is the ANFIS control flow chart of the active vibration reduction device.

[0056] Figure 2 ANFIS training error changes with training rounds.

[0057] Figure 3 Comparison chart between actual output and ANFIS predicted output (time domain).

[0058] Figure 4 Comparison diagram of the autopower spectrum density between the actual output and the ANFIS predicted output.

[0059] Figure 5 This is the displacement response diagram before vibration suppression (ANFIS control).

[0060] Figure 6 is the displacement response diagram after vibration suppression (ANFIS control).

[0061] Figure 7 Comparison of maximum displacement before and after vibration suppression (ANIFS control). DETAILED DESCRIPTION

[0062] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0063] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0064] Secondly, the term "one embodiment" or "embodiment" herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in various places throughout this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive of other embodiments.

[0065] Example 1

[0066] Reference Figure 1, is an embodiment of the present invention, which provides an active vibration reduction control method based on an adaptive neural fuzzy inference system, comprising:

[0067] S1: By building a system model and collecting data.

[0068] Preferably, the displacement of the platform is obtained by a sensor and speed As the input variable of the system, it reflects the current state of the vibration system. The voice coil motor generates a corresponding braking force F according to the control signal to offset the vibration force on the platform, thus building a dynamic model of the system to determine the input-output relationship.

[0069] Furthermore, the dynamic model is used to describe the dynamic behavior of the platform vibration system, and the equation is as follows:

[0070]

[0071] Where M is the system's equivalent mass matrix, which determines the system's response strength to external vibrations; C is the damping coefficient, which characterizes the system's damping effect; K is the stiffness coefficient, which determines the system's ability to resist deformation; and F(t) is the control force generated by the voice coil motor, which is used to offset the platform's vibration.

[0072] S2: Design the ANFIS model based on the platform’s state variables.

[0073] Preferably, nonlinear mapping is performed through fuzzy logic rules and the adaptive ability of neural networks to generate the control signal of the system. The ANFIS model selects the displacement of the platform. and speed As input variable, the output variable is the control signal.

[0074] Preferably, the input state is defined by fuzzification processing and fuzzy membership function, and the membership function is a generalized Bell-type function, which is expressed as:

[0075]

[0076] Among them, μ(x) is the input state of the input data x, a is the width parameter, which controls the stretching degree of the membership function; b is the shape parameter, which adjusts the curve shape of the membership function; c is the center parameter, which determines the position of the membership function.

[0077] Furthermore, the ANFIS model contains multiple fuzzy rules, each of which generates a corresponding control signal based on the fuzzified state of the input (such as the membership of displacement and velocity). For example, the following two fuzzy rules are set:

[0078] Rule 1: If the displacement x(t) is large and the velocity v(t) is large, the output control signal U or I is large to generate a stronger reverse force;

[0079] Rule 2: If the displacement x(t) is small and the velocity v(t) is small, the output control signal U or I is small to generate a weaker reverse force;

[0080] For each rule, the output of the control signal F i It can be expressed by the fuzzy reasoning formula as follows:

[0081]

[0082] Among them, w i is the activation weight of the rule, which indicates the influence of the membership of the input variable on the rule. p, q, and r are the linear parameters of the model, which reflect the relationship between the input variable and the output control signal.

[0083] Ultimately, the control signal U or I is the weighted average of all rule outputs:

[0084]

[0085] In this way, the ANFIS model generates corresponding control signals based on real-time sensor data and adjusts the opposing force in real time to offset the vibration of the platform.

[0086] S3: The ANFIS model automatically adjusts the parameters of the fuzzy membership function through experimental data training.

[0087] Preferably, multiple fuzzy rules R i Composed of ANFIS model, each rule is based on the input variables and The fuzzy state generates the control output, and the fuzzy rules are as follows:

[0088]

[0089] Among them, Ai and Bi represent the fuzzy sets of input variables; U represents the control signal of the voice coil motor.

[0090] Preferably, based on the fuzzy rules, the activation value of each rule is derived:

[0091]

[0092] Among them, w i Indicates the degree of rule activation, μA i (x) represents the membership of the input x(t) to the fuzzy set Ai, μBi(x) represents the membership of the input x(t) to the fuzzy set B i The degree of membership;

[0093] Perform weighted average defuzzification on the fuzzy result and output the final control signal:

[0094]

[0095] Among them, U is the control signal of the voice coil motor, f i Represents the output of the i-th fuzzy rule, N represents the total number of rules, i=1, 2, 3,…, N.

[0096] Furthermore, suppose we have four fuzzy rules (N=4), which define different control signal outputs f i :

[0097] Rule 1: If the displacement is large and the velocity is large, the control signal is large (f1);

[0098] Rule 2: If the displacement is large and the velocity is small, the control signal is medium (f2);

[0099] Rule 3: If the displacement is small and the velocity is large, the control signal is medium (f3);

[0100] Rule 4: If the displacement is small and the velocity is small, the control signal is small (f4);

[0101] For a given input x(t) and v(t), calculate the activation value w for each rule i :

[0102] w1=μbig(x(t))⋅μbig(v(t))

[0103] w2=μlarge(x(t))⋅μsmall(v(t))

[0104] w3=μsmall(x(t))⋅μlarge(v(t))

[0105] w4=μsmall(x(t))⋅μsmall(v(t))

[0106] Assume that the membership degree obtained by the fuzzy membership function is:

[0107] μlarge(x(t))=0.8,μlarge(v(t))=0.7,μsmall(x(t))=0.2,μsmall(v(t))=0.3,

[0108] Then get the activation value of each rule:

[0109] w1=0.56, w2=0.8⋅0.3=0.24, w3=0.2⋅0.7=0.14, w4=0.2⋅0.3=0.06,

[0110] Next, calculate the fuzzy output f of each rule i, assuming the output of the rule is:

[0111] f1=0.9, f2=0.5, f3=0.5, f4=0.1;

[0112] The final control signal U is 0.7, which will be used to drive the voice coil motor to generate a braking force opposite to the vibration direction, thereby achieving the effect of active vibration reduction.

[0113] S4: Train the ANFIS model based on the hybrid learning algorithm.

[0114] Preferably, in the forward propagation stage, the least squares method is used to optimize the linear combination weights of the output to minimize the error between the model output and the actual value. The ANFIS output layer is a linear combination of activated fuzzy rules, and its calculation formula is:

[0115]

[0116] Among them, U is the control signal of the voice coil motor, w n is the weight of the fuzzy rule; f n is the nth fuzzy rule output, n=1, 2, 3, ..., N; f1 is the first model rule output, f2 is the second model rule output, w1 and w2 are the corresponding weights; the goal of the least squares method is to adjust w i Minimize the error, which is defined as:

[0117]

[0118] Where E is the error. The gradient descent method is used in the back propagation stage to update the parameters of the fuzzy membership function. By adjusting the shape and position of the membership function, the output of the model is made close to the response of the actual system. The update formula is as follows:

[0119]

[0120]

[0121]

[0122] Where η is the learning rate.

[0123] Preferably, the error function of the system is defined, assuming that e(t) is the error at time step t, and is calculated as follows:

[0124]

[0125] Among them, y(t) is the output value at the current moment, y desired (t) is the expected output value;

[0126] Calculate the rate of change of the error, that is, the gradient of the error:

[0127]

[0128] If the error rate of change is large, the system state changes, and the adjustment is accelerated by increasing the learning rate; if the error change is small, the system tends to be stable, and the learning rate is reduced;

[0129] Gradually reduce the learning rate based on the error value or error rate of change, as follows:

[0130]

[0131] Among them, η0 is the initial learning rate, λ is the adjustment factor, and e(t) is the current error;

[0132] Use the dynamically adjusted learning rate to update the weights and parameters of the neural network, and use the gradient descent method to update the weights:

[0133]

[0134] Among them, ∇ w E(t) is the gradient of the loss function.

[0135] Furthermore, assuming that there are N fuzzy rules Ri, the output of each rule is fi, and each rule has a weight wi, then the calculation formula of the ANFIS output layer is:

[0136]

[0137] Among them, wi is the weight of rule Ri, which indicates the activation degree of the rule; fi is the fuzzy output of rule Ri, which indicates the control signal generated by the rule;

[0138] In the least squares method, the goal is to adjust the weights wi to minimize the error. The error is defined as the difference between the model output U and the actual target value U target The differences between:

[0139]

[0140] Where E is the error function, which represents the square difference between the model output and the actual target value; U i is the output of the model, U target is the desired control signal;

[0141] To optimize the weights by minimizing the error, we take the partial derivative of the error function E with respect to the weight wi and update the weights:

[0142]

[0143] The weights can then be adjusted according to gradient descent:

[0144]

[0145] Where η is the learning rate.

[0146] Furthermore, the parameters a, b, and c of the membership function can be updated by the gradient descent method to minimize the output error. First, the error is defined as:

[0147]

[0148] Next, calculate the gradient of the error function with respect to the membership function parameters. For each parameter, calculate its derivative:

[0149]

[0150] Then, update the parameters of the membership function:

[0151]

[0152] Through the gradient update in the back-propagation phase, the parameters a, b, and c of the membership function will gradually be adjusted to the optimal values, so that the ANFIS model can fit the dynamic characteristics of the system more accurately and output more precise control signals.

[0153] Furthermore, set the target output y desired (t) is the expected state of the platform, and the error at the current moment is calculated as e(t)=y desired (t)-y(t);

[0154] Calculate the error rate of change:

[0155]

[0156] If the error changes significantly (e.g., de(t) / dt>ϵ, where ϵ is the set threshold), increase the learning rate.

[0157] The parameters of the ANFIS model are updated by the gradient descent method. During the updating process, the dynamically adjusted learning rate η(t) enables the model to quickly learn the correct control signal.

[0158] S5: Use sensors to obtain the platform's displacement and velocity in real time, input them into the ANFIS model, and implement real-time active vibration reduction control.

[0159] Preferably, the ANFIS model utilizes a combination of fuzzy logic and neural networks to calculate corresponding control signals based on historical data and real-time inputs. The control signals drive actuators such as voice coil motors to generate reverse forces to offset the vibration of the platform.

[0160] Furthermore, suppose this control system is applied to a platform to reduce the impact of platform vibration during flight. The platform is equipped with an accelerometer and a laser displacement sensor. These sensors are used to collect the platform's vibration displacement and velocity in real time. The sensor data is transmitted to the control system via wireless communication. The ANFIS model within the control system uses the real-time displacement and velocity data as input to calculate the control signal U(t). Based on the control signal, the voice coil motor generates a reverse force F(t) to offset the vibration caused by the external vibration source.

[0161] After several experiments and adjustments, the system can adjust the control signal in real time according to the vibration state of the platform, thereby achieving precise active vibration reduction control.

[0162] Example 2

[0163] Reference Figures 2 to 7 , which is another embodiment of the present invention.

[0164] Figure 2 The following plot shows the ANFIS training error changing with training epochs. The ANFIS model's training error decreased from approximately 0.17 in the initial epochs to below 0.1 by the end of training. Specifically, the training error dropped sharply during the first 20 training epochs, reaching a stable value near 0.1. Afterward, the fluctuations decreased and remained at a relatively low error level (close to 0.05). Quantitatively, the decrease in training error indicates that the model achieved over 70% error reduction after 100 epochs of training, demonstrating good convergence.

[0165] Figure 3 The following figure compares the actual output and the ANFIS predicted output (time domain). The actual output (red) and the ANFIS predicted output (dashed blue) are compared in the time domain. Although the figure shows a large number of points, the overall trend shows that the ANFIS predicted output closely tracks the fluctuations of the actual output, especially in high-frequency signal variations, where the two maintain a high degree of similarity. Comparing the numerical fluctuation range, the ANFIS predicted output fluctuates between -0.6 and 0.6, which is generally consistent with the actual output fluctuations.

[0166] Figure 4 The auto-power spectral density of the actual output and the ANFIS-predicted output in the frequency domain is displayed. The power spectral density of the actual output ranges from -26dB to -44dB, and the power spectral density of the ANFIS-predicted output is also close to this range, indicating that the ANFIS prediction can well maintain the frequency domain characteristics across different frequency bands. In particular, in the frequency range of 5Hz to 25Hz, the power spectral density of the ANFIS-predicted output and the actual output are almost identical, demonstrating the accuracy of the model within the main frequency band.

[0167] Figure 5 and Figure 7 The displacement response before and after vibration suppression under ANFIS control is shown. The amplitude is significantly reduced to between -0.2 m and 0.2 m, a 50% reduction. This demonstrates that ANFIS control significantly reduces the system's displacement response, demonstrating the control effect from a quantitative perspective.

[0168] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. An active vibration reduction control method based on an adaptive neural fuzzy inference system, characterized in that: include: By building a system model and collecting data; Design ANFIS model based on the platform's state variables; The ANFIS model automatically adjusts the parameters of the fuzzy membership function through experimental data training; Train the ANFIS model based on hybrid learning algorithm; The displacement and velocity of the platform are acquired in real time using sensors and input into the ANFIS model to achieve real-time active vibration reduction control.

2. The active vibration reduction control method based on the adaptive neural fuzzy inference system according to claim 1, characterized in that: The system model is constructed and data is collected, including: Obtain the platform displacement through the sensor and speed As the input variable of the system, it reflects the current state of the vibration system. The voice coil motor generates the corresponding braking force F according to the control signal to offset the vibration force exerted on the platform, so as to construct the dynamic model of the system and determine the input-output relationship.

3. The active vibration reduction control method based on the adaptive neural fuzzy inference system according to claim 2, characterized in that: The dynamic model is used to describe the dynamic behavior of the platform vibration system, and the equation is as follows: ； Among them, M is the equivalent mass matrix of the system, which determines the response intensity of the system to external vibration; C is the damping coefficient, which characterizes the damping effect of the system; K is the stiffness coefficient, which determines the system's anti-deformation ability; F(t) is the control force generated by the voice coil motor, which is used to offset the vibration of the platform.

4. The active vibration reduction control method based on the adaptive neural fuzzy inference system according to claim 1, characterized in that: The ANFIS model is designed based on the state variables of the platform, including: Through nonlinear mapping using fuzzy logic rules and the adaptive capabilities of neural networks, the control signal of the system is generated. The ANFIS model selects the displacement of the platform. and speed as input variable and the output variable is the control signal.

5. The active vibration reduction control method based on the adaptive neural fuzzy inference system according to claim 1, characterized in that: The design of the ANFIS model based on the state variables of the platform also includes: The input state is defined by fuzzy processing and fuzzy membership function. The membership function uses the generalized Bell function, and the expression is: ； Among them, μ(x) is the input state of the input data x, a is the width parameter, which controls the stretching degree of the membership function; b is the shape parameter, which adjusts the curve shape of the membership function; c is the center parameter, which determines the position of the membership function.

6. The active vibration reduction control method based on the adaptive neural fuzzy inference system according to claim 1, characterized in that: The ANFIS model automatically adjusts the parameters of the fuzzy membership function through experimental data training, including: Multiple fuzzy rules R i Composed of ANFIS model, each rule is based on the input variables and The fuzzy state generates the control output, and the fuzzy rules are as follows: ； Among them, Ai and Bi represent the fuzzy sets of input variables; U represents the control signal of the voice coil motor.

7. The active vibration reduction control method based on the adaptive neural fuzzy inference system according to claim 6, characterized in that: According to the fuzzy rules, the activation value of each rule is derived: ； Among them, ω i Indicates the degree of rule activation, μA i (x) represents the membership degree of the input x(t) to the fuzzy set Ai, μBi(x) means that the input x(t) belongs to the fuzzy set B i The degree of membership; Perform weighted average defuzzification on the fuzzy result and output the final control signal: ； Among them, f i represents the i-th fuzzy rule output, N represents the total number of rules, i=1, 2, 3,…, N.

8. The active vibration reduction control method based on the adaptive neural fuzzy inference system according to claim 1, characterized in that: The training of the ANFIS model based on the hybrid learning algorithm includes: In the forward propagation stage, the least squares method is used to optimize the linear combination weights of the output to minimize the error between the model output and the actual value. The ANFIS output layer is a linear combination of activated fuzzy rules, and its calculation formula is: ； Among them, U is the control signal of the voice coil motor, w n is the weight of the fuzzy rule; f n is the nth fuzzy rule output, n=1, 2, 3, ..., N; f1 is the first model rule output, f2 is the second model rule output, w1 and w2 are the corresponding weights; The goal of the least squares method is to adjust w i Minimize the error, which is defined as: ； Among them, E is the error, m is the number of samples, and k represents the number of samples from the 1st to the mth. is the predicted output value, is the actual output value; the gradient descent method is used in the back propagation stage to update the parameters of the fuzzy membership function. By adjusting the shape and position of the membership function, the output of the model is close to the response of the actual system. The update formula is as follows: ； ； ； Where η is the learning rate, , , is the updated system parameter, , , The current system parameters.

9. The active vibration reduction control method based on the adaptive neural fuzzy inference system according to claim 1, characterized in that: The training of the ANFIS model based on the hybrid learning algorithm further includes: Define the error function of the system, assuming that e(t) is the error at time step t, and calculate it in the following way: ； Among them, y(t) is the actual output value at time t, y desired (t) is the expected output value at time t; Calculate the rate of change of the error, that is, the gradient of the error Δe(t): ； If the error rate of change is large, the system state changes, and the adjustment is accelerated by increasing the learning rate; if the error change is small, the system tends to be stable, and the learning rate is reduced; Gradually reduce the learning rate based on the error value or error change rate as follows: ； Among them, η(t) is the learning rate at time t, η0 is the initial learning rate, and λ is the adjustment factor; Use the dynamically adjusted learning rate to update the weights and parameters of the neural network, and use the gradient descent method to update the weights.

10. The active vibration reduction control method based on the adaptive neural fuzzy inference system according to claim 1, characterized in that: The method uses sensors to obtain the displacement and velocity of the platform in real time and inputs them into the ANFIS model to achieve real-time active vibration reduction control, including: The ANFIS model uses a combination of fuzzy logic and neural networks to calculate corresponding control signals based on historical data and real-time inputs. The control signals drive actuators such as voice coil motors to generate reverse forces to offset the vibration of the platform.

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