Fuzzy machine learning transient optimization method for dynamic calibration of MEMS accelerometer

Abstract

The application provides a fuzzy machine learning transient optimization method for dynamic calibration of a MEMS accelerometer, comprising the following steps: step 1, constructing a MEMS accelerometer response model; step 2, constructing a memory neural network and designing a fuzzy back propagation learning rule; step 3, introducing a fuzzy rule trigger time mechanism for transient process analysis; step 4, transient induced Zeno phenomenon and transient optimization; and step 5, dynamic calibration verification. The application combines the accelerometer response characteristics, introduces a Caputo fractional differential model to study the system memory and convolution correlation characteristics, solves the problems of ignoring the system history state, transient induced Zeno phenomenon and modeling distortion in the traditional machine learning, can accurately match the dynamic response process of the MEMS accelerometer, and greatly improves the dynamic calibration precision.

Description

Technical Field

[0001] This invention belongs to the field of fuzzy machine learning technology, specifically relating to a fuzzy machine learning transient optimization method for dynamic calibration of MEMS accelerometers. Background Technology

[0002] MEMS accelerometers are core sensing devices in inertial navigation and microelectromechanical systems (MEMS), and their calibration accuracy directly determines the overall measurement performance of the system. The calibration process essentially involves establishing a sensor input-output mapping model and completing model parameter identification and error compensation. From a system characteristic perspective, the output of any real system is the convolution result of the input signal and the system response; MEMS accelerometers also follow this rule. Therefore, accelerometer calibration must be combined with its inherent response characteristics to truly reflect its actual performance under dynamic conditions and achieve high-precision, high-robust dynamic calibration.

[0003] Machine learning has been widely applied in the modeling of complex dynamic systems. It can learn features and adaptively identify model parameters using sensor input and output data, providing a reliable technical means for the dynamic calibration of MEMS accelerometers. The core implementation process is as follows: a neural network propagates the input signal forward to obtain a predicted output. This predicted output is compared with the actual output of the MEMS accelerometer to construct an error signal. Then, based on this error signal, the weight parameters of the neural network are iteratively corrected in reverse, thereby achieving high-precision modeling of the MEMS accelerometer and providing solid support for subsequent fault diagnosis, state prediction, and control optimization.

[0004] Error-backward iterative learning rules are a core component of machine learning techniques. Fuzzy control technology, due to its advantages of not relying on a precise system model and achieving arbitrary precision approximation of nonlinear systems, is widely used in the field of dynamic system control. Introducing fuzzy control technology into the design of error-backward iterative learning rules, through a series of processes such as constructing a fuzzy rule base, establishing membership functions based on error signals, performing fuzzy inference, and completing defuzzification, a fuzzy-based error-backward iterative learning mechanism can be formed, thereby realizing fuzzy machine learning. This technology has become an important research direction in the field of machine learning.

[0005] The core of using fuzzy machine learning for dynamic calibration of MEMS accelerometers is to synchronize the output of the fuzzy neural network with the actual output of the MEMS accelerometer, thereby completing the parameter identification of the MEMS accelerometer's input-output model. It is important to note that because MEMS accelerometers possess inherent response characteristics (i.e., the ability to remember historical inputs), only by enabling the fuzzy neural network to reproduce this memory characteristic can we ensure that its output remains synchronized with the MEMS accelerometer output under any input, accurately reproducing the MEMS accelerometer's response characteristics, achieving high-standard dynamic modeling, and laying the foundation for subsequent dynamic calibration optimization.

[0006] However, considering the memory characteristics of MEMS accelerometers, when using fuzzy machine learning for iterative identification of system parameters, the iterative changes in system parameters during parameter updates via error backpropagation will induce transient oscillations in the fuzzy machine learning output according to the convolution duality principle. These transient oscillations will further propagate to the calibration process of the MEMS accelerometer, causing calibration signal oscillations. In severe cases, this can even lead to divergence in the calibration process, significantly reducing calibration accuracy and stability, making it difficult to meet the dynamic calibration requirements of high-precision MEMS accelerometers. This problem has not yet been effectively solved. Summary of the Invention

[0007] Purpose of the invention: The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing a fuzzy machine learning transient optimization method for dynamic calibration of MEMS accelerometers. By combining the response characteristics of the research object, a memory neural network is constructed, a fuzzy backpropagation learning rule is designed, and by combining the memory characteristics and the backpropagation learning rule, the transient process of machine learning is analyzed, the fuzzy backpropagation learning parameters are optimized, false triggering and Zeno's phenomenon are avoided, the fuzzy learning transient is optimized, and the accuracy of dynamic calibration is improved. The overall technical route of this invention is as follows: Research on the response characteristics of MEMS accelerometers → Construction of a memory neural network → Design of fuzzy backpropagation learning rules → Analysis of machine learning transient processes (combining memory characteristics and backpropagation learning rules) → Optimization of fuzzy backpropagation learning parameters → Suppression of false triggering and Zeno's phenomenon → Fuzzy learning transient optimization → Dynamic calibration and verification. The method specifically includes the following steps: Step 1: Construct a MEMS accelerometer response model; Step 2: Construct a memory neural network and design fuzzy backpropagation learning rules; Step 3: Introduce a fuzzy rule-triggered time mechanism for transient process analysis; Step 4: Transient induction of Zeno phenomenon and transient optimization, establishing a dynamic model of MEMS accelerometer; Step 5, dynamic calibration and verification.

[0008] Step 1 includes the following steps: Step 1.1: Construct an autonomous system model based on the response characteristics of the MEMS accelerometer; Step 1.2: Introduce basis vectors to linearize the nonlinear function.

[0009] Step 1.1 includes: MEMS accelerometer response characteristics Represented as: (1), in The constant coefficient, This indicates the decay characteristics of the system's impulse response over time. An autonomous system is represented as: (2), in Indicates the input signal of the MEMS accelerometer, symbol This represents the convolution operation. It's about state variables. Nonlinear functions; A constant representing the decay of the reaction over time; In formula (2), the model is transformed into a fractional-order autonomous model: (3), in Represents the state variables Caputo fractional derivative, It's about state variables. Nonlinear functions.

[0010] Step 1.2 includes: converting the nonlinear function... Linearization: (4), in yes Nonlinear functions in Projected coordinates in the coordinate system express Transpose of; The linearized impulse response model of the autonomous system is obtained as follows: (5).

[0011] Step 2 includes the following steps: Step 2.1, Construct a machine learning neural network: (6), Will exist Projection in coordinate system: ; It is a nonlinear function exist Projected coordinates in the base coordinate system; Step 2.2, construct the identification error model; Establish a dynamic calibration machine learning error model based on parameter identification error: (7), in, This represents the machine learning error, which is the difference between the output of the MEMS accelerometer and the output of the fuzzy neural network. Error of state variables at time t ; Time parameter identification error ; when , Parameter identification was achieved in time; Step 2.3, Construct iterative learning rules for unknown parameters: (8), in This is the backpropagation function; Further results were obtained: (9), in, Representing nonlinear functions The fractional derivative is used to obtain the inverse iterative learning rule. Machine learning is performed based on historical dynamics; Step 2.4: Integrate the unknown parameters and state variables together to form a new neural network, and obtain the relationship between error and parameter iteration: (10) Define a new vector Rearrange the formulas in steps 2.2 and 2.3: (11), in Indicates by The new vector formed The fractional derivative; Simplified formula (11): (12) in, , Let the first new vector be obtained according to formula (10). This is the second new vector obtained according to formula (10).

[0012] Step 3 includes the following steps: Step 3.1: Establish a fuzzy inference rule base, construct membership functions, perform fuzzy inference, and obtain a fuzzy controller; Construct fuzzy sets, fuzzy inference rule bases, and fuzzy membership functions; Fuzzy rules: If satisfy ,So satisfy , ; in , These represent the fuzzy set corresponding to the error and the fuzzy set corresponding to fuzzy backpropagation, respectively. It comes from machine learning errors. It is a reverse learning rule; This represents the nth dimension component of the machine learning error; Constructing fuzzy membership functions , By utilizing fuzzy inference and center-average defuzzification, a fuzzy learning controller is obtained. : (13); Step 3.2: Introduce fuzzy event triggering time and construct a piecewise continuous function for the fuzzy learning controller; remember For the start time, For the k-th fuzzy event trigger time, the corresponding fuzzy learning controller is represented as: (14) in Time period ~ The fuzzy learning controller function within; Step 3.3, connect the fuzzy controller and the fuzzy neural network using piecewise continuous functions. express: (15) in The backpropagation function represents the occurrence of the i-th fuzzy event; ; Using the unit step function at time t ,get: (16) (17); Step 3.4: Combining the relationship between fractional integrals and convolution, analyze the transient process of fuzzy machine learning output one by one.

[0013] The machine learning error is obtained from fractional-order operations: (18) in Represents the gamma function. It is a function of time t; Segment-by-segment analysis of the fuzzy learning controller output: analyze Output: (19) in Indicates in Learning error under the influence of [the system / mechanism]; (20) Indicates in Under the influence of this effect, the steady-state output of machine learning error, (twenty one), Indicates in Transient output of machine learning error under the influence of [the system / mechanism]; analyze Output: (twenty two), in Indicates in Learning error under the influence of action; (twenty three), (twenty four), analyze Output: (25) in Indicates in Learning error under the influence of action; (26) (27) get : (28) in, ; .

[0014] Step 4 includes the following steps: Step 4.1, Transient-induced Zeno phenomenon analysis, constructing constraints to avoid Zeno phenomenon: within the transient oscillation range, fuzzy events are not triggered; Step 4.2, construct machine learning stability constraints: based on fractional Lyapunov stability theory, calculate the stability parameter constraints in formula (17) in step 3.3; Step 4.3: Establish constraints for fuzzy machine learning; The intersection of the parameter constraints obtained in steps 4.1 and 4.2 is the fuzzy machine learning parameter constraint. If the intersection is not empty, proceed with the next steps; otherwise, the adopted fuzzy machine learning scheme is not feasible. Step 4.4: Optimize the iteration rules for fuzzy machine learning parameters; Based on the constraints established in step 4.3, the fuzzy machine learning parameters are optimized using the particle swarm optimization search algorithm.

[0015] Step 5 includes the following steps: Step 5.1: Using the Adams algorithm, write a simulation program for the memory neural network; Step 5.2: Fix the fractional order, change the fuzzy machine learning parameters, and simulate to verify the relationship between the transient process and the control parameters; Step 5.3: Fix the machine learning parameters, change the fraction order, and verify the relationship between the transient process and the memory features of the memory neural network; Step 5.4: Optimize the learning parameters of the particle swarm optimization to optimize the machine learning process; Step 5.5: Apply the calibrated MEMS accelerometer to robot pose control and navigation to verify the accuracy and performance of dynamic calibration.

[0016] The present invention also provides an electronic device, including a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method.

[0017] The present invention also provides a storage medium storing a computer program or instructions that, when the computer program or instructions are run on a computer, execute the steps of the method described.

[0018] This invention combines the response characteristics of MEMS accelerometers and employs a Caputo fractional-order model to construct a memory neural network, characterizing the system's convolutional memory features. It designs fuzzy backpropagation learning rules, introduces a fuzzy event triggering time mechanism, and rigorously decomposes the machine learning output into steady-state and transient terms, revealing the source of transient oscillations. It constructs non-triggering constraints in the transient interval to suppress Zeno's phenomenon, and uses fractional-order Lyapunov stability theory to determine stable constraints. Finally, it optimizes the fuzzy learning parameters using a particle swarm optimization algorithm, achieving smooth and rapid convergence of the learning process. This invention can accurately reproduce the system's memory characteristics, effectively suppress transient oscillations and false triggering, reduce hardware overhead, and improve the dynamic calibration accuracy and convergence robustness of MEMS accelerometers. The resulting technology can also be widely applied to complex industrial system modeling, intelligent control, fault diagnosis, and power system transient analysis, demonstrating outstanding creativity and engineering practicality.

[0019] The present invention has the following beneficial effects: The present invention combines the response characteristics of accelerometers and introduces the Caputo fractional differential model to study the memory and convolutional related characteristics of the system, which solves the problems of traditional machine learning ignoring the historical state of the system and modeling distortion. It can accurately match the dynamic response process of MEMS accelerometers and greatly improve the dynamic calibration accuracy.

[0020] This invention reveals the source of transient oscillations at the mechanistic level and achieves controllable transient processes: By using piecewise continuous functions and convolutional integrals, it introduces fuzzy event triggering time for the first time, strictly decomposes the output of fuzzy machine learning into steady-state and transient terms, and clarifies that transient oscillations are jointly caused by historical inputs and parameter iterations. This enables analyzable, predictable, and suppressable transient behavior, fundamentally solving the problems of oscillations and unstable convergence in the learning process, and optimizing the dynamic calibration process.

[0021] Effectively suppressing false triggering and Zeno's phenomenon, reducing system hardware overhead: This invention proposes a transient interval non-triggering constraint mechanism to avoid misjudging transient oscillations as learning errors and frequently triggering fuzzy rules, significantly reducing the number of controller actions, communication bandwidth usage and storage consumption, eliminating Zeno's phenomenon, reducing device switching losses, and extending equipment lifespan.

[0022] Balancing learning stability and convergence speed, and optimizing dynamic performance: This invention combines fractional-order Lyapunov stability theory with particle swarm optimization algorithm to dynamically optimize fuzzy learning parameters within the stable feasible region, enabling machine learning to converge faster and be more robust, thus solving the shortcomings of traditional methods such as large oscillations, slow convergence, and easy divergence.

[0023] High degree of technological integration, strong versatility and engineering applicability: This invention organically combines fractional memory characteristics, fuzzy reasoning, event triggering mechanism and dynamic optimization to form a complete closed-loop scheme for dynamic calibration of accelerometers. The resulting technology can also be applied to scenarios such as dynamic modeling of complex industrial systems, intelligent control, fault diagnosis, and robotics. It has strong practicality and wide applicability.

[0024] Simulation and theory are unified, and the method is reproducible and verifiable: This invention uses the Adams prediction and correction algorithm for simulation, which is theoretically rigorous, numerically stable, and the results are reproducible. It provides a standardized process for algorithm performance verification, which is convenient for academic research and engineering promotion. Attached Figure Description

[0025] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention in the above and other aspects will become clearer.

[0026] Figure 1 The simulation diagram shows the error oscillation of dynamic calibration fuzzy machine learning with a fractional order of 0.4 and a trigger threshold of 0.3.

[0027] Figure 2 The trigger threshold is set to 0.3 for the fractional order, and the trigger time for fuzzy machine learning is dynamically calibrated.

[0028] Figure 3 The simulation diagram shows the error oscillation of dynamic calibration fuzzy machine learning with a fractional order of 0.4 and a trigger threshold of 0.1.

[0029] Figure 4 The trigger threshold is set to 0.1 for the fractional order, and the trigger time for fuzzy machine learning is dynamically calibrated.

[0030] Figure 5 The simulation diagram shows the error oscillation of dynamic calibration fuzzy machine learning with a fractional order of 0.95 and a trigger threshold of 0.3.

[0031] Figure 6 A schematic diagram illustrating the dynamic calibration of fuzzy machine learning trigger time with a fractional order of 0.95 and a trigger threshold of 0.3.

[0032] Figure 7 The simulation diagram shows the error oscillation of dynamic calibration fuzzy machine learning with a fractional order of 0.95 and a trigger threshold of 0.1.

[0033] Figure 8 A schematic diagram illustrating the dynamic calibration of fuzzy machine learning trigger time with a fractional order of 0.95 and a trigger threshold of 0.1. Detailed Implementation

[0034] This invention provides a fuzzy machine learning transient optimization method for dynamic calibration of MEMS accelerometers, comprising the following steps: Step 1: Construct a MEMS accelerometer response model; Step 2: Construct a memory neural network and design fuzzy backpropagation learning rules; Step 3: Introduce a fuzzy rule-triggered time mechanism for transient process analysis; Step 4: Fuzzy learning transient optimization to establish a dynamic model of the MEMS (Micro-Electro-Mechanical System) accelerometer; Step 5, dynamic calibration and verification.

[0035] Step 1 includes the following steps: Step 1.1: Construct an autonomous system model based on the response characteristics of the MEMS accelerometer: From a system perspective, every system has its own impulse response. Generally, the response characteristics of MEMS accelerometers... Represented as: (1), in The constant coefficient, This indicates the decay characteristics of the system's impulse response over time; A typical autonomous system is represented as: (2), in Indicates the input signal of the MEMS accelerometer, symbol This represents the convolution operation. It's about state variables. Nonlinear functions; A constant representing the decay of the reaction over time; In formula (2), the model is transformed into a fractional-order autonomous model: (3), in Represents the state variables Caputo fractional derivative, It's about state variables. Nonlinear functions.

[0036] It can be regarded as the output of the accelerometer sensor. Formula (3) establishes the input and output model of MEMS accelerometer.

[0037] Note: The model in formula (2) and the model in formula (3) can be converted to each other according to the definition of Caputo fractional order.

[0038] Step 1.2: Introduce basis vectors to linearize the nonlinear function; nonlinear functions Linearization: (4), yes Nonlinear functions in Projected coordinates in the coordinate system express Transpose of; By combining the system impulse response, the MEMS accelerometer system model is transformed into a fractional-order differential model, which fits the system response characteristics and the feature of being correlated with the input throughout the entire process.

[0039] The linearized impulse response model of the autonomous system is obtained as follows: (5).

[0040] Step 2 includes the following steps: Step 2.1, Construct a machine learning neural network: (6), Will exist Projection in coordinate system: ; It is a nonlinear function exist Projected coordinates in the base coordinate system; Step 2.2, construct the identification error model; Establish a dynamic calibration machine learning error model based on parameter identification error: (7), in, This represents the machine learning error, which is the difference between the output of the MEMS accelerometer and the output of the fuzzy neural network. Error of state variables at time t ; Time parameter identification error ; when , Parameter identification was achieved in time; Step 2.3, Construct iterative learning rules for unknown parameters: (8), in This is the backpropagation function.

[0041] Further results were obtained: (9), in, Representing nonlinear functions The fractional derivative is used to obtain the inverse iterative learning rule. Machine learning is performed based on historical dynamics.

[0042] Step 2.4: Integrate the unknown parameters and state variables together to form a new neural network, and obtain the relationship between error and parameter iteration: (10) Define a new vector Rearrange the formulas in steps 2.2 and 2.3: (11), in Indicates by The new vector formed The fractional derivative; Simplified formula (11): (12) in, , The new vector obtained according to formula (10) Let be the new vector obtained according to formula (10).

[0043] Step 3 includes the following steps: Step 3.1: Establish a fuzzy inference rule base, construct membership functions, perform fuzzy inference, and obtain a fuzzy controller; Construct fuzzy sets, fuzzy inference rule bases, and fuzzy membership functions; Fuzzy rules: If satisfy ,So satisfy , ; in , These represent the fuzzy set corresponding to the error and the fuzzy set corresponding to fuzzy backpropagation, respectively. It comes from machine learning errors. It is a reverse learning rule; This represents the nth dimension component of the machine learning error; Constructing fuzzy membership functions , By utilizing fuzzy inference and center-average defuzzification, a fuzzy learning controller is obtained. : (13); Step 3.2: Introduce fuzzy event triggering time and construct a piecewise continuous function for the fuzzy learning controller; remember For the start time, For the k-th fuzzy event trigger time, the corresponding fuzzy learning controller is represented as: (14) in Time period ~ The fuzzy learning controller function within; Step 3.3, connect the fuzzy controller and the fuzzy neural network using piecewise continuous functions. express: (15) in The backpropagation function represents the occurrence of the i-th fuzzy event; ; Using the unit step function at time t ,get: (16) (17); Step 3.4: Combining the relationship between fractional integrals and convolution, analyze the transient process of fuzzy machine learning output one by one.

[0044] The machine learning error is obtained from fractional-order operations: (18) in Represents the gamma function. It is a function of time t; Segment-by-segment analysis of the fuzzy learning controller output: 1) Analysis Output: (19) in Indicates in Learning error under the influence of [the system / mechanism]; (20) Indicates in Under the influence of this effect, the steady-state output of machine learning error, (twenty one), Indicates in Transient output of machine learning error under the influence of [the system / mechanism]; 2) Analysis Output: (twenty two), in Indicates in Learning error under the influence of [the system / mechanism]; (twenty three), (twenty four), 3) Analysis Output: (25) in Indicates in Learning error under the influence of [the system / mechanism]; (26) (27) get : (28) in, This part is constant; This part is the transient state formed by the learning inputs from each iteration.

[0045] Note: This transient response reflects the transient oscillations of the output error under each learning iteration. These oscillations include not only the machine learning error oscillations of the MEMS accelerometer dynamic calibration but also the parameter identification oscillations. These transient oscillations are often overlooked in existing research, potentially leading to them being mistakenly studied as machine learning errors, causing frequent triggering of machine learning and resulting in the Zeno phenomenon; they may also reduce machine learning speed or even cause convergence failure and divergence.

[0046] Step 4 includes the following steps: Step 4.1: Transient induced Zeno phenomenon analysis, constructing constraints to avoid Zeno phenomenon.

[0047] As shown in formula (28) in step 3.4, the transient process is generated by the historical input. The current input cannot be changed. The next fuzzy event should not be triggered within the transient oscillation range. Otherwise, after one trigger, due to the transient state, the fuzzy event triggering condition is met again instantly, causing the fuzzy mechanism to be triggered frequently, resulting in the Zeno phenomenon. This not only increases the system hardware overhead, but also, due to frequent triggering, naturally leads to the continuous generation of transient oscillations, which may even become higher and higher, causing machine learning to diverge.

[0048] To avoid the Zeno phenomenon, a fuzzy mechanism constraint can be obtained based on transient oscillations: that is, within the range of transient oscillations, fuzzy events are not triggered.

[0049] Step 4.2: Construct machine learning stability constraints.

[0050] Although fuzzy event triggering will induce transients, for physically realizable systems in nature, the transients converge over time, and the system stability is constrained by the steady-state portion.

[0051] According to the fractional Lyapunov stability theory, the stability parameter constraint conditions in formula (17) in step 3.3 can be calculated.

[0052] Step 4.3: Establish fuzzy machine learning constraints.

[0053] Fuzzy machine learning systems must satisfy both stability and convergence conditions while avoiding Zeno's phenomenon. The intersection of the parameter constraints obtained in steps 4.1 and 4.2 constitutes the fuzzy machine learning parameter constraints.

[0054] If the intersection is not empty, proceed with the next steps. Otherwise, the fuzzy machine learning scheme used by this system is not feasible and requires further investigation.

[0055] Step 4.4: Optimize the iteration rules for fuzzy machine learning parameters; Based on the constraints established in step 4.3, the particle swarm optimization search algorithm is used to optimize the fuzzy machine learning parameters, reduce oscillations, optimize transient performance, improve the speed of fuzzy machine learning, and make machine learning more stable and faster.

[0056] Step 5 includes the following steps: Step 5.1: Use the Adams algorithm to write a simulation program for the memory neural network.

[0057] Step 5.2: Fix the fractional order, change the fuzzy machine learning parameters, and simulate to verify the relationship between the transient process (including transient oscillations and fuzzy event triggering time) and the control parameters.

[0058] Step 5.3: Fix the machine learning parameters, change the fraction order, and verify the relationship between transient processes (including transient oscillations and fuzzy event trigger times) and memory features of the memory neural network.

[0059] Step 5.4: Optimize the learning parameters of the particle swarm optimization to optimize the machine learning process.

[0060] Step 5.5: Apply the calibrated MEMS accelerometer to fields such as robot pose control and navigation to verify the accuracy and performance of dynamic calibration.

[0061] In one specific embodiment of the present invention, the parameters of the memory learning neural network are set as follows: , Among the symbols Represents the Kronecker product; Represents a 6th-order identity matrix; matrix , matrix , It is a 2-order identity matrix.

[0062] Based on the output error, fuzzy machine learning rules were designed. The fractional order of the MEMS accelerometer model was set to 0.4 and 0.95 respectively (representing different memory characteristics, i.e. response characteristics) for simulation to verify the dynamic calibration transient oscillation and trigger time of the same system under different fuzzy rules, and the transient oscillation and trigger time of different system responses under the same fuzzy rule.

[0063] To highlight the impact of the rules, this embodiment uses the same reasoning, only changing the trigger threshold of the fuzzy rules.

[0064] When the fractional order is 0.4, simulations are performed with different trigger threshold values.

[0065] The trigger threshold is set to 0.3, and the simulation results for learning error and fuzzy learning trigger time are as follows: Figure 1 and Figure 2 As shown.

[0066] When the fractional order is 0.4, simulations are performed with different trigger threshold values.

[0067] The trigger threshold is set to 0.1. The simulation results for learning error and fuzzy learning trigger time are as follows: Figure 3 and Figure 4 As shown.

[0068] Comparing the two scenarios, it can be seen that as the threshold decreases, the triggering time interval increases significantly, leading to frequent triggering and an increase in the transient oscillation frequency.

[0069] When the fractional order is 0.95, simulations are performed with different values ​​for the trigger threshold.

[0070] The trigger threshold is set to 0.3, and the simulation results for learning error and fuzzy learning trigger time are as follows: Figure 5 and Figure 6 As shown.

[0071] When the fractional order is 0.95, simulations are performed with different values ​​for the trigger threshold.

[0072] The trigger threshold is set to 0.1. The simulation results for learning error and fuzzy learning trigger time are as follows: Figure 7 and Figure 8 As shown.

[0073] Comparing the two scenarios, it can be seen that as the threshold decreases, the triggering time interval increases significantly, leading to frequent triggering and an increase in the transient oscillation frequency.

[0074] Simulation results show that when the fractional order is 0.95, the transient oscillations are less pronounced than when it is 0.4, and the triggering intervals for fuzzy events become increasingly longer. This indicates that transient oscillations are closely related to memory characteristics (system response characteristics), and that transient oscillations will affect the triggering mechanism. Therefore, it is necessary to study machine learning transient oscillations in conjunction with system response characteristics and formulate corresponding machine learning schemes.

[0075] This invention provides a fuzzy machine learning transient optimization method for dynamic calibration of MEMS accelerometers. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A fuzzy machine learning transient optimization method for dynamic calibration of MEMS accelerometers, characterized in that, Includes the following steps: Step 1: Construct a MEMS accelerometer response model; Step 2: Construct a memory neural network and design fuzzy backpropagation learning rules; Step 3: Introduce a fuzzy rule-triggered time mechanism for transient process analysis; Step 4: Transient induction of Zeno phenomenon and transient optimization, establishing a dynamic model of MEMS accelerometer; Step 5, dynamic calibration and verification.

2. The method according to claim 1, characterized in that, Step 1 includes the following steps: Step 1.1: Construct an autonomous system model based on the response characteristics of the MEMS accelerometer; Step 1.2: Introduce basis vectors to linearize the nonlinear function.

3. The method according to claim 2, characterized in that, Step 1.1 includes: MEMS accelerometer response characteristics Represented as: （1）， in The constant coefficient, This indicates the decay characteristics of the system's impulse response over time. An autonomous system is represented as: （2）， in Indicates the input signal of the MEMS accelerometer, symbol This represents the convolution operation. It's about state variables. Nonlinear functions; A constant representing the decay of the reaction over time; In formula (2), the model is transformed into a fractional-order autonomous model: （3）， in Represents the state variables Caputo fractional derivative, It's about state variables. Nonlinear functions.

4. The method according to claim 3, characterized in that, Step 1.2 includes: converting the nonlinear function... Linearization: （4）， in yes Nonlinear functions in Projected coordinates in the coordinate system express Transpose of; The linearized impulse response model of the autonomous system is obtained as follows: （5）。 5. The method according to claim 4, characterized in that, Step 2 includes the following steps: Step 2.1, Construct a machine learning neural network: （6） ， Will exist Projection in coordinate system: ; It is a nonlinear function exist Projected coordinates in the base coordinate system; Step 2.2, construct the identification error model; Establish a dynamic calibration machine learning error model based on parameter identification error: （7）， in, Indicates machine learning error; Error of state variables at time t ; Time parameter identification error ; when , Parameter identification was achieved in time; Step 2.3, Construct iterative learning rules for unknown parameters: （8）， in This is the backpropagation function; Further results were obtained: （9）， in, Representing nonlinear functions The fractional derivative is used to obtain the inverse iterative learning rule. Machine learning is performed based on historical dynamics; Step 2.4: Integrate the unknown parameters and state variables together to form a new neural network, and obtain the relationship between error and parameter iteration: （10）， Define a new vector Rearrange the formulas in steps 2.2 and 2.3: （11）， in Indicates by The new vector formed The fractional derivative; Simplified formula (11): （12）， in, ， Let the first new vector be obtained according to formula (10). This is the second new vector obtained according to formula (10).

6. The method according to claim 5, characterized in that, Step 3 includes the following steps: Step 3.1: Establish a fuzzy inference rule base, construct membership functions, perform fuzzy inference, and obtain a fuzzy controller; Construct fuzzy sets, fuzzy inference rule bases, and fuzzy membership functions; Fuzzy rules: If satisfy ,So satisfy , ; in , These represent the fuzzy set corresponding to the error and the fuzzy set corresponding to fuzzy backpropagation, respectively. It comes from machine learning errors. It is a reverse learning rule; This represents the nth dimension component of the machine learning error; Constructing fuzzy membership functions , By utilizing fuzzy inference and center-average defuzzification, a fuzzy learning controller is obtained. : （13）； Step 3.2: Introduce fuzzy event triggering time and construct a piecewise continuous function for the fuzzy learning controller; remember For the start time, For the k-th fuzzy event trigger time, the corresponding fuzzy learning controller is represented as: （14）， in Time period ~ The fuzzy learning controller function within; Step 3.3, connect the fuzzy controller and the fuzzy neural network using piecewise continuous functions. express: （15）， in The backpropagation function represents the occurrence of the i-th fuzzy event; ; Using the unit step function at time t ,get: （16）， （17）； Step 3.4: Combining the relationship between fractional integrals and convolution, analyze the transient process of fuzzy machine learning output one by one; The machine learning error is obtained from fractional-order operations: （18）， in Represents the gamma function. It is a function of time t; Segment-by-segment analysis of the fuzzy learning controller output: analyze Output: （19）， in Indicates in Learning error under the influence of [the system / mechanism]; （20）， Indicates in Under the influence of this effect, the steady-state output of machine learning error, （21）， Indicates in The transient output of machine learning error under the influence of [the system / mechanics]. analyze Output: （22）， in Indicates in Learning error under the influence of action; （23）， （24）， analyze Output: （25）， in Indicates in Learning error under the influence of action; （26）， （27）， get : （28）， in, ； 。 7. The method according to claim 6, characterized in that, Step 4 includes the following steps: Step 4.1, Transient-induced Zeno phenomenon analysis, constructing constraints to avoid Zeno phenomenon: within the transient oscillation range, fuzzy events are not triggered; Step 4.2, construct machine learning stability constraints: based on fractional Lyapunov stability theory, calculate the stability parameter constraints in formula (17) in step 3.3; Step 4.3: Establish constraints for fuzzy machine learning; The intersection of the parameter constraints obtained in steps 4.1 and 4.2 is the fuzzy machine learning parameter constraint. If the intersection is not empty, proceed with the subsequent steps; otherwise, the adopted fuzzy machine learning scheme is not feasible. Step 4.4: Optimize the iteration rules for fuzzy machine learning parameters; Based on the constraints established in step 4.3, the fuzzy machine learning parameters are optimized using the particle swarm optimization search algorithm.

8. The method according to claim 7, characterized in that, Step 5 includes the following steps: Step 5.1: Using the Adams algorithm, write a simulation program for the memory neural network; Step 5.2: Fix the fractional order, change the fuzzy machine learning parameters, and simulate to verify the relationship between the transient process and the control parameters; Step 5.3: Fix the machine learning parameters, change the fraction order, and verify the relationship between the transient process and the memory features of the memory neural network; Step 5.4: Optimize the learning parameters of the particle swarm optimization to optimize the machine learning process; Step 5.5: Apply the calibrated MEMS accelerometer to robot pose control and navigation to verify the accuracy and performance of dynamic calibration.

9. An electronic device, characterized in that, It includes a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method as described in any one of claims 1 to 8.

10. A storage medium, characterized in that, It stores a computer program or instructions that, when run on a computer, perform the steps of the method as described in any one of claims 1 to 8.

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