Miniature sawtooth generation method based on artificial intelligence optimization algorithm

Abstract

The invention discloses a miniature sawtooth generation method based on an artificial intelligence optimization algorithm, and the method comprises the following steps: S1, initializing a generation parameter, and mapping the generation parameter to a high-dimensional complex field; s2, selecting and configuring an algorithm, and optimizing parameters by constructing a target function in a high-dimensional complex field; s3, constructing a neural morphology calculation system, processing the optimized parameters through a neural network and a complex modulation activation function, and generating a preliminary miniature sawtooth waveform; s4, error evaluation is carried out, an error signal is converted from a time domain to a frequency domain for weighted analysis and optimization, and key frequency band parameters are identified and adjusted; s5, adaptively adjusting the issuing frequency and synaptic weight of the neural network, generating parameters through continuous optimization, and circularly adjusting the waveform; and S6, outputting the optimized micro sawtooth waveform. According to the invention, high-precision and high-stability micro sawtooth waveform generation is realized, and the method is suitable for signal processing and application in a complex environment.

Description

Technical Field

[0001] The present invention relates to the fields of signal processing and artificial intelligence optimization, and in particular to a micro-sawtooth generation method based on an artificial intelligence optimization algorithm. Background Art

[0002] The defects of the prior art are as follows:

[0003] 1. The wide application of sawtooth waveforms and the limitations of existing technologies. In modern electronic and communication technologies, sawtooth waveforms are widely used in various signal processing, control systems, electronic equipment and image processing fields due to their unique periodicity and linearity. Especially in high-precision signal generation and control systems, micro-sawtooth waveforms have become the key to signal modulation, timing control and pulse width modulation applications due to their short period and rapid changes. Existing sawtooth waveform generation methods have multiple technical challenges, especially in application scenarios that require high precision and high stability. These challenges are particularly prominent.

[0004] 2. The shortcomings of traditional sawtooth waveform generation methods. Traditional sawtooth waveform generation methods are mainly based on a combination of analog circuits and digital circuits. These methods usually use capacitor charging and discharging circuits, crystal oscillators or digital counters to achieve sawtooth waveform generation. These methods have significant limitations in accuracy, stability and controllability. The sawtooth waveform generated by analog circuits is susceptible to temperature drift, device aging and electromagnetic interference, resulting in waveform distortion, frequency drift and amplitude changes. Although digital circuits can achieve relatively stable waveform output through counting and storage, in high-frequency applications, clock jitter, quantization errors and limited sampling rates can seriously affect the accuracy and resolution of the waveform.

[0005] 3. The flexibility of existing technologies in complex applications. Existing sawtooth waveform generation methods lack sufficient flexibility when facing complex application requirements. In communication systems, different modulation methods have different requirements for waveform linearity, frequency response, and phase noise, and traditional methods are usually unable to flexibly adjust these parameters without sacrificing other performance indicators. Especially in high-bandwidth communication systems, the generated sawtooth waveform is required to have extremely low phase noise and high-frequency stability, and existing technologies are difficult to meet these stringent performance requirements.

[0006] 4. Potential and challenges of artificial intelligence optimization algorithms. With the rapid development of artificial intelligence and machine learning technologies, artificial intelligence optimization algorithms have shown great potential in the field of signal processing. Artificial intelligence optimization algorithms can find the global optimal solution in a complex multidimensional parameter space by simulating and learning the evolutionary process or neural network structure in nature, thereby optimizing various parameters in the signal generation process. Although artificial intelligence optimization algorithms have powerful problem-solving capabilities in theory, they still face many challenges in the specific application of sawtooth waveform generation.

[0007] 5. Limitations of artificial intelligence optimization algorithms in practical applications. Existing artificial intelligence optimization algorithms often need to deal with highly nonlinear and multimodal optimization problems when facing actual physical systems. The objective functions of these problems may contain multiple local extreme points, making it easy for the optimization process to fall into local optimal solutions and difficult to find global optimal solutions. In addition, existing optimization algorithms usually rely on a large amount of training data and computing resources, but in actual engineering applications, it may be very difficult to obtain enough high-quality training data, especially in the field of high-frequency signal processing and precision control. The acquisition cost of experimental data is high and the cycle is long, which further limits the practical application of artificial intelligence optimization algorithms.

[0008] 6. Computational efficiency issues in high-dimensional parameter spaces. Existing artificial intelligence optimization algorithms are often severely limited in computational efficiency when processing high-dimensional parameter spaces. The complex sawtooth waveform generation process involves the joint optimization of multiple parameters, including frequency, amplitude, phase, and waveform smoothness. Traditional optimization algorithms often face the problem of a sharp increase in computational complexity in high-dimensional parameter spaces, resulting in a time-consuming and inefficient optimization process that is difficult to meet the needs of real-time signal processing.

[0009] 7. Adaptability and robustness in dynamic environments. Existing technologies lack sufficient adaptability and robustness when dealing with dynamically changing application environments. In practical applications, the generation of sawtooth waveforms often requires real-time adjustment of generation parameters according to different external environments and application requirements. In wireless communication systems, changes in the signal propagation environment and changes in device status may require real-time adjustment of the frequency and phase response of the sawtooth waveform. Existing artificial intelligence optimization algorithms are usually trained offline, making it difficult to respond to environmental changes in real time and lack the ability to adaptively adjust. This lag makes it difficult for existing methods to maintain the accuracy and stability of waveform generation in rapidly changing application scenarios.

[0010] Summary of limitations of existing technologies,In summary, existing sawtooth waveform generation technologies have many shortcomings,whether in analog circuits, digital circuits, or in the application of artificial intelligence optimization algorithms.,These technologies are difficult to meet the requirements of high precision, high stability and high flexibility at the same time,especially in the face of complex and changing application environments,the limitations of existing technologies are more obvious.

[0011] Therefore, how to provide a micro-sawtooth generation method based on an artificial intelligence optimization algorithm is an urgent problem that technicians in this field need to solve. Summary of the invention

[0012] One purpose of the present invention is to propose a method for generating micro-sawtooth waveforms based on an artificial intelligence optimization algorithm. The present invention combines advanced artificial intelligence technology with complex mathematical models to optimize various parameters in the signal generation process, and describes in detail the algorithm in signal processing and generation, which has the advantages of high precision, high stability and strong adaptability. By introducing an artificial intelligence optimization algorithm, the present invention can significantly improve the generation quality of micro-sawtooth waveforms and is suitable for various high-demand practical application scenarios.

[0013] A method for generating micro-sawtooth based on an artificial intelligence optimization algorithm according to an embodiment of the present invention comprises the following steps:

[0014] S1, initialize the generation parameters, set the initial values ​​of frequency, amplitude, phase and waveform smoothness;

[0015] S2. Select and configure an artificial intelligence optimization algorithm, which includes a genetic algorithm, a particle swarm optimization algorithm, or other optimization algorithms based on machine learning, to optimize initial parameters;

[0016] S3. Construct a neuromorphic computing system, which consists of a multi-layer neural network and a complex modulation matrix. The optimized parameter combination is processed through the nonlinear activation function and the complex modulation activation function in the neural network to generate a preliminary micro-sawtooth waveform.

[0017] S4, calculating the difference between the generated waveform and the target waveform through real-time error evaluation, and converting the error signal into the frequency domain for weighted analysis and optimization;

[0018] S5. According to the weighted error analysis results, the firing frequency and synaptic weight of the neuron are adaptively adjusted, and the generation parameters are further optimized through the artificial intelligence optimization algorithm. By repeatedly converting the time domain and frequency domain of the signal, the waveform is continuously adjusted in a cycle until the generated waveform meets the predetermined accuracy requirements;

[0019] S6. Output an optimized micro-sawtooth waveform and process it through a filter based on non-trivial topological space and multiple complex number field transformations to optimize the waveform's anti-interference ability and stability.

[0020] Optionally, the S2 specifically includes:

[0021] S21. In the initial stage, construct an objective function, where the objective function includes frequency optimization, amplitude optimization, phase adjustment, and waveform smoothness optimization, and map these objectives to a high-dimensional complex domain space:

[0022]

[0023] Among them, z is the signal generation parameter vector in the complex domain, including frequency f, amplitude A, phase and the complex number representation of the waveform smoothness σ, Ψ k (z) represents the potential function associated with the kth target, w k is the weight of each target, β k and γ k is the control coefficient, N(z) represents the nonlinear operation matrix in the complex domain;

[0024] S22. Generate an initial population. Each individual in the population represents a parameter combination.

[0025] S23, optimize the population through quantum state evolution operations, using non-Hermitian Hamiltonian quantum operators To update the quantum state, the updated state is expressed as:

[0026]

[0027] Among them, |ψ i represents the current quantum state, is a non-Hermitian Hamiltonian operator, and the quantum state is introduced to describe the state of each individual in the population, and Δt is the time step;

[0028] S23, parameter z i Perform adaptive mutation operation and optimize parameters:

[0029]

[0030] Among them, ⊕ represents the complex domain convolution operation, has a mean of zero and a variance of σ 2 Non-Gaussian complex noise;

[0031] S24, select the optimal solution through fitness evaluation, perform nonlinear hierarchical screening on the parameter combination, retain the solution with the highest fitness and output the final optimized parameter z *, including the frequency f * , amplitude A * , Phase and waveform smoothness σ * .

[0032] Optionally, the S3 specifically includes:

[0033] S31, combine the optimized parameters A network of neurons input into a neuromorphic computing system;

[0034] S32, the output signal y of each neuron i (t) is processed by multiple complex modulation activation functions. The complexity of the multiple complex modulation activation function is reflected in its combination of complex modulation matrix and nonlinear amplification mechanism:

[0035]

[0036] Among them, y i (t) is the output signal of the i-th neuron at the current time t, σ(·) is a nonlinear activation function that adjusts the output characteristics of the neuron, and α i is the modulation coefficient of the i-th neuron, which controls the amplification effect of the input signal. Re(·) represents the real part of the complex number. * is the optimized complex parameter combination, including the frequency f * , amplitude A * , Phase and waveform smoothness σ * , e iωt is the phase factor related to time t and modulation frequency ω, M i is the complex modulation matrix, which controls the transformation of the signal in the complex domain. is based on the complex parameter z * and phase offset The sine function of , H is the complex magnification matrix, 1+|N·z * | 2 is the normalization factor of the signal, N is a complex matrix used for nonlinear control of signal amplification, ω ij represents the synaptic weight from the jth neuron to the ith neuron, Q j is the complex transformation matrix, which controls the response characteristics of the signal under time delay. Δt is the time delay factor, which determines the time difference of signal transmission between neurons.

[0037] S33, the signal y output by each layer of neurons i (t) Performing a complex domain fractional Fourier transform to convert the signal from the time domain to the frequency domain, optimizing the frequency domain characteristics of the signal, and reconstructing and optimizing the waveform by analyzing the frequency domain characteristics;

[0038] S34, based on frequency domain analysis and waveform reconstruction, adjust the synaptic weight ω through multiple iterations ij and complex modulation matrix parameters to optimize signal transmission in neural networks;

[0039] S34. In the process of waveform generation, the following complex spectrum modulation and adaptive smoothing processing formula are used to further optimize the frequency domain signal:

[0040]

[0041] in, is the frequency domain signal after smoothing and second-order derivative modulation, f is the frequency variable, F(y i (f)) is the output signal y from the neuron i (t) The Fourier transform result converted to the frequency domain, f0 is the center frequency, indicating the main frequency component of the signal, σ f is the standard deviation of the frequency, which determines the width of the spectrum smoothing, is a Gaussian function used for spectrum smoothing, P(f) is a frequency domain modulation function used to control the modulation effect of the frequency response, and R(t) is a phase modulation function that gives the signal additional phase complexity. Represents the second-order derivative of frequency f, capturing the characteristics of spectrum changes;

[0042] S35, through the inverse fractional Fourier transform, the optimized frequency domain signal Converting back to the time domain generates the optimized miniature sawtooth waveform x(t).

[0043] Optionally, the S4 step specifically includes:

[0044] S41, after generating the preliminary micro sawtooth waveform x(t), perform an error evaluation on it to evaluate the accuracy of the generated waveform, and compare x(t) with the preset ideal target waveform x ideal (t), calculate the difference and generate an error signal;

[0045] S42, error signal x ideal The difference between x(t) and x(t) is not obvious or difficult to analyze in the time domain. The error is converted from the time domain to the frequency domain for analysis.

[0046] S43, analyzing the energy density of the error signal in the frequency domain;

[0047] S44, weighting the error energy density, and highlighting the frequency range that has a greater impact on the final waveform quality during the optimization process;

[0048] S45. According to the weighted error analysis results, adjust the parameter combination of waveform generation, and feed these adjustments back to the optimization algorithm.

[0049] Optionally, the S5 specifically includes:

[0050] S51, based on the error evaluation and preliminary parameter adjustment in S44, further optimize the generated micro sawtooth waveform x(t), and re-evaluate the adjusted parameter combination z * , the optimized waveform gradually approaches the target waveform;

[0051] S52. Use the adaptive adjustment mechanism to fine-tune the synaptic weights ω in the neuronal network ij , optimize the signal transmission process between neurons;

[0052] S53, converting the adjusted signal to the frequency domain again through the complex domain Fourier transform, analyzing the spectrum characteristics of the signal in the frequency domain, and identifying the frequency components that have a great impact on the waveform quality;

[0053] S54, according to the result of the frequency domain analysis, updating the time domain expression x(t) of the generated waveform, optimizing and reducing the difference between the waveform and the target waveform;

[0054] S55. For errors that still exist within a specific frequency range, continue to fine-tune the synaptic weights ω in the neural network through multiple iterations. ij and the associated parameter combination z * ;

[0055] S56, converting the optimized signal from the frequency domain back to the time domain, and performing a final error evaluation, so that the optimized generated micro sawtooth waveform x(t) meets the predetermined accuracy and quality requirements.

[0056] Optionally, the S6 specifically includes:

[0057] S61, inputting the optimized waveform x(t) into a filter based on a non-trivial topological space for processing, wherein the filter optimizes the anti-interference ability and diversity of the signal by utilizing the characteristics of the non-trivial topological structure;

[0058] S62. A nonlinear transformation formula based on multiple complex number fields is used to perform amplitude modulation on the signal:

[0059]

[0060] Among them, x modulated (t) is the modulated signal, which represents the output after complex number domain transformation, x topo(t) is the signal after non-trivial topology filtering, which is the basis of modulation. i is the imaginary unit, which is used to realize the complex modulation part of the signal. D(t) is the time-dependent complex modulation function, which controls the modulation intensity of the signal over time. It is a multiple complex number operator, which is used to perform nonlinear transformation on the signal in the complex number domain and increase the structural complexity of the signal. κ and ∈ are nonlinear modulation parameters, which control the intensity of signal modulation and the nonlinear response curve respectively.

[0061] S63. Perform phase correction on the modulated signal. The phase correction is based on quantum group theory and is implemented by using the R matrix of the quantum group and the trace operation of the matrix, thereby optimizing the phase drift problem that may occur in the traditional method:

[0062]

[0063] in, is the corrected signal phase, the result after quantum group entanglement correction, Tr(·) represents the matrix trace operation, which is used to extract the key phase information in quantum group entanglement. is the R matrix of the quantum group, which is responsible for describing the entanglement phenomenon of the signal during the phase correction process. P(·) is the phase correction operator, which finely adjusts the phase of the signal.

[0064] S64. After phase correction, the signal enters the frequency domain optimization processing stage based on non-Abelian statistics, and the signal is optimized through an adaptive topological quantum field filter:

[0065]

[0066] Among them, X final (f) is the signal after frequency domain optimization processing, which is the frequency domain expression of the final output signal. m (f) is a topological filter function based on non-Abelian statistics, which is used to optimize the characteristics of frequency domain signals. * represents non-Abelian convolution operation, which enhances the complexity of the signal in the frequency domain. is a tensor product operation, which is used to describe the interaction between frequency domain signals and topological structures. m (f) is the adaptive tuning function, which adjusts the response of the signal at different frequencies;

[0067] S65, converts the optimized signal in the frequency domain back to the time domain through inverse transformation to generate the final micro sawtooth waveform X final (t).

[0068] Beneficial Effects

[0069] Through the micro-sawtooth generation method based on artificial intelligence optimization algorithm proposed in the present invention, compared with the existing technology, the present invention achieves significant technical improvement and multiple advantages in practical applications.

[0070] First, the present invention overcomes the temperature drift, device aging, and electromagnetic interference problems faced by traditional analog circuits and digital circuits when generating sawtooth waveforms. By introducing artificial intelligence optimization algorithms and complex mathematical models, the generation accuracy and stability of sawtooth waveforms are significantly improved. In the signal generation process, the present invention makes full use of multi-dimensional complex number fields, non-commutative algebra, and cutting-edge mathematical tools of quantum group theory to achieve precise control of frequency, amplitude, phase, and waveform smoothness, solving the problems of waveform distortion, frequency drift, and phase noise in the prior art.

[0071] Secondly, the present invention realizes adaptive optimization and real-time adjustment of signal generation by constructing a neuromorphic computing system. The combination of the neural network and synaptic weights enables the system to respond to changes in the external environment in real time and dynamically adjust the signal generation parameters based on error evaluation. This adaptability not only improves the robustness of waveform generation, but also enables the system to maintain high accuracy and high stability in rapidly changing application scenarios.

[0072] In addition, the artificial intelligence optimization algorithm of the present invention can operate efficiently in a high-dimensional parameter space, avoiding the problem that traditional optimization algorithms are prone to falling into local optimal solutions and low computational efficiency. Through genetic algorithms, particle swarm optimization algorithms or other optimization algorithms based on machine learning, the present invention can find the global optimal solution in complex multimodal optimization problems, greatly improving the efficiency and accuracy of the signal generation process.

[0073] In general, the method proposed in the present invention significantly improves the generation quality of micro-sawtooth waveforms, and has the advantages of high precision, high stability, strong adaptability and high efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0075] Figure 1 A summary diagram of a method for generating micro-sawtooth based on an artificial intelligence optimization algorithm proposed by the present invention;

[0076] Figure 2 The figure of claim 2 of the method for generating micro-sawtooth based on artificial intelligence optimization algorithm proposed by the present invention;

[0077] Figure 3The present invention provides a method for generating micro-sawtooths based on an artificial intelligence optimization algorithm, as shown in claim 3. DETAILED DESCRIPTION

[0078] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

[0079] refer to Figure 1-3 , a micro-sawtooth generation method based on artificial intelligence optimization algorithm, comprising the following steps:

[0080] S1, initialize the generation parameters, set the initial values ​​of frequency, amplitude, phase and waveform smoothness;

[0081] S2. Select and configure an artificial intelligence optimization algorithm, which includes a genetic algorithm, a particle swarm optimization algorithm, or other optimization algorithms based on machine learning, to optimize initial parameters;

[0082] S3. Construct a neuromorphic computing system, which consists of a multi-layer neural network and a complex modulation matrix. The optimized parameter combination is processed through the nonlinear activation function and the complex modulation activation function in the neural network to generate a preliminary micro-sawtooth waveform.

[0083] S4, calculating the difference between the generated waveform and the target waveform through real-time error evaluation, and converting the error signal into the frequency domain for weighted analysis and optimization;

[0084] S5. According to the weighted error analysis results, the firing frequency and synaptic weight of the neuron are adaptively adjusted, and the generation parameters are further optimized through the artificial intelligence optimization algorithm. By repeatedly converting the time domain and frequency domain of the signal, the waveform is continuously adjusted in a cycle until the generated waveform meets the predetermined accuracy requirements;

[0085] S6. Output an optimized micro-sawtooth waveform and process it through a filter based on non-trivial topological space and multiple complex number field transformations to optimize the waveform's anti-interference ability and stability.

[0086] In this implementation, S2 specifically includes:

[0087] S21. In the initial stage, construct an objective function, where the objective function includes frequency optimization, amplitude optimization, phase adjustment, and waveform smoothness optimization, and map these objectives to a high-dimensional complex domain space:

[0088]

[0089] Among them, z is the signal generation parameter vector in the complex domain, including frequency f, amplitude A, phase and the complex number representation of the waveform smoothness σ, Ψ k (z) represents the potential function associated with the kth target, w k is the weight of each target, β k and γ k is the control coefficient, N(z) represents the nonlinear operation matrix in the complex domain;

[0090] S22. Generate an initial population. Each individual in the population represents a parameter combination.

[0091] S23, optimize the population through quantum state evolution operations, using non-Hermitian Hamiltonian quantum operators To update the quantum state, the updated state is expressed as:

[0092]

[0093] Among them, |ψ i represents the current quantum state, is a non-Hermitian Hamiltonian operator, and the quantum state is introduced to describe the state of each individual in the population, and Δt is the time step;

[0094] S23, parameter z i Perform adaptive mutation operation and optimize parameters:

[0095]

[0096] Among them, ⊕ represents the complex domain convolution operation, has a mean of zero and a variance of σ 2 Non-Gaussian complex noise;

[0097] S24, select the optimal solution through fitness evaluation, perform nonlinear hierarchical screening on the parameter combination, retain the solution with the highest fitness and output the final optimized parameter z * , including the frequency f * , amplitude A * , Phase and waveform smoothness σ * .

[0098] In this implementation, S3 specifically includes:

[0099] S31, combine the optimized parameters A network of neurons input into a neuromorphic computing system;

[0100] S32, the output signal y of each neuron i(t) is processed by multiple complex modulation activation functions. The complexity of the multiple complex modulation activation function is reflected in its combination of complex modulation matrix and nonlinear amplification mechanism:

[0101]

[0102] Among them, y i (t) is the output signal of the i-th neuron at the current time t, σ(·) is a nonlinear activation function that adjusts the output characteristics of the neuron, and α i is the modulation coefficient of the i-th neuron, which controls the amplification effect of the input signal. Re(·) represents the real part of the complex number. * is the optimized complex parameter combination, including the frequency f * , amplitude A * , Phase and waveform smoothness σ * , e iωt is the phase factor related to time t and modulation frequency ω, M i is the complex modulation matrix, which controls the transformation of the signal in the complex domain. is based on the complex parameter z * and phase offset The sine function of , H is the complex magnification matrix, 1+|N·z * | 2 is the normalization factor of the signal, N is a complex matrix used for nonlinear control of signal amplification, ω ij represents the synaptic weight from the jth neuron to the ith neuron, Q j is the complex transformation matrix, which controls the response characteristics of the signal under time delay. Δt is the time delay factor, which determines the time difference of signal transmission between neurons.

[0103] S33, the signal y output by each layer of neurons i (t) Performing a complex domain fractional Fourier transform to convert the signal from the time domain to the frequency domain, optimizing the frequency domain characteristics of the signal, and reconstructing and optimizing the waveform by analyzing the frequency domain characteristics;

[0104] S34, based on frequency domain analysis and waveform reconstruction, adjust the synaptic weight ω through multiple iterations ij and complex modulation matrix parameters to optimize signal transmission in neural networks;

[0105] S34. In the process of waveform generation, the following complex spectrum modulation and adaptive smoothing processing formula are used to further optimize the frequency domain signal:

[0106]

[0107] in, is the frequency domain signal after smoothing and second-order derivative modulation, f is the frequency variable, F(y i (f)) is the output signal y from the neuron i (t) The Fourier transform result converted to the frequency domain, f0 is the center frequency, indicating the main frequency component of the signal, σ f is the standard deviation of the frequency, which determines the width of the spectrum smoothing, is a Gaussian function used for spectrum smoothing, P(f) is a frequency domain modulation function used to control the modulation effect of the frequency response, and R(f) is a phase modulation function that gives the signal additional phase complexity. Represents the second-order derivative of frequency f, capturing the characteristics of spectrum changes;

[0108] S35, through the inverse fractional Fourier transform, the optimized frequency domain signal Converting back to the time domain generates the optimized miniature sawtooth waveform x(t).

[0109] In this implementation manner, the S4 step specifically includes:

[0110] S41, after generating the preliminary micro sawtooth waveform x(t), perform an error evaluation on it to evaluate the accuracy of the generated waveform, and compare x(t) with the preset ideal target waveform x ideal (t), calculate the difference and generate an error signal;

[0111] S42, error signal x ideal The difference between x(t) and x(t) is not obvious or difficult to analyze in the time domain. The error is converted from the time domain to the frequency domain for analysis.

[0112] S43, analyzing the energy density of the error signal in the frequency domain;

[0113] S44, weighting the error energy density, and highlighting the frequency range that has a greater impact on the final waveform quality during the optimization process;

[0114] S45. According to the weighted error analysis results, adjust the parameter combination of waveform generation, and feed these adjustments back to the optimization algorithm.

[0115] In this implementation manner, S5 specifically includes:

[0116] S51, based on the error evaluation and preliminary parameter adjustment in S44, further optimize the generated micro sawtooth waveform x(t), and re-evaluate the adjusted parameter combination z * , the optimized waveform gradually approaches the target waveform;

[0117] S52. Use the adaptive adjustment mechanism to fine-tune the synaptic weights ω in the neuronal network ij, optimize the signal transmission process between neurons;

[0118] S53, converting the adjusted signal to the frequency domain again through the complex domain Fourier transform, analyzing the spectrum characteristics of the signal in the frequency domain, and identifying the frequency components that have a great impact on the waveform quality;

[0119] S54, according to the result of the frequency domain analysis, updating the time domain expression x(t) of the generated waveform, optimizing and reducing the difference between the waveform and the target waveform;

[0120] S55. For errors that still exist within a specific frequency range, continue to fine-tune the synaptic weights ω in the neural network through multiple iterations. ij and the associated parameter combination z * ;

[0121] S56, converting the optimized signal from the frequency domain back to the time domain, and performing a final error evaluation, so that the optimized generated micro sawtooth waveform x(t) meets the predetermined accuracy and quality requirements.

[0122] In this implementation manner, S6 specifically includes:

[0123] S61, inputting the optimized waveform x(t) into a filter based on a non-trivial topological space for processing, wherein the filter optimizes the anti-interference ability and diversity of the signal by utilizing the characteristics of the non-trivial topological structure;

[0124] S62. A nonlinear transformation formula based on multiple complex number fields is used to perform amplitude modulation on the signal:

[0125]

[0126] Among them, x modulated (t) is the modulated signal, which represents the output after complex number domain transformation, x topo (t) is the signal after non-trivial topology filtering, which is the basis of modulation. i is the imaginary unit, which is used to realize the complex modulation part of the signal. D(t) is the time-dependent complex modulation function, which controls the modulation intensity of the signal over time. It is a multiple complex number operator, which is used to perform nonlinear transformation on the signal in the complex number domain to increase the structural complexity of the signal. k and ∈ are nonlinear modulation parameters, which control the intensity of signal modulation and the nonlinear response curve respectively.

[0127] S63. Perform phase correction on the modulated signal. The phase correction is based on quantum group theory and is implemented by using the R matrix of the quantum group and the trace operation of the matrix, thereby optimizing the phase drift problem that may occur in the traditional method:

[0128]

[0129] in, is the corrected signal phase, the result after quantum group entanglement correction, Tr(·) represents the trace operation of the matrix, which is used to extract the key phase information in the quantum group entanglement. is the R matrix of the quantum group, which is responsible for describing the entanglement phenomenon of the signal during the phase correction process. P(·) is the phase correction operator, which finely adjusts the phase of the signal.

[0130] S64. After phase correction, the signal enters the frequency domain optimization processing stage based on non-Abelian statistics, and the signal is optimized through an adaptive topological quantum field filter:

[0131]

[0132] Among them, X final (f) is the signal after frequency domain optimization processing, which is the frequency domain expression of the final output signal. m (f) is a topological filter function based on non-Abelian statistics, which is used to optimize the characteristics of frequency domain signals. ★ represents non-Abelian convolution operation, which enhances the complexity of the signal in the frequency domain. is a tensor product operation, which is used to describe the interaction between frequency domain signals and topological structures. m (f) is the adaptive tuning function, which adjusts the response of the signal at different frequencies;

[0133] S65, converts the optimized signal in the frequency domain back to the time domain through inverse transformation to generate the final micro sawtooth waveform X final (t).

[0134] Example

[0135] In order to verify the feasibility of the present invention in implementation, the present invention was applied to a high-precision measuring instrument R&D company in a certain city, where the research team is developing a high-performance measuring instrument for industrial automation control. One of the core technologies of this instrument is to use a micro-sawtooth waveform to drive its sensors and control systems to achieve precise control of industrial equipment. However, in the traditional sawtooth waveform generation process, the team found that the existing methods had obvious distortion, frequency drift and phase instability problems when facing interference, noise and temperature changes in industrial environments. These problems directly lead to serious deficiencies in the accuracy and reliability of the measuring instrument. In order to solve these problems, the team decided to adopt the micro-sawtooth generation method based on the artificial intelligence optimization algorithm proposed in the present invention to improve the accuracy and stability of the waveform, thereby improving the overall performance of the instrument.

[0136] In this application scenario, the research team used the method of the present invention to generate a high-precision micro-sawtooth waveform and applied it to industrial measurement instruments according to the following steps:

[0137] The team initialized the parameters for sawtooth waveform generation based on the working requirements of the measuring instrument. The frequency was set to 100kHz to meet the instrument's requirements for high-frequency signals; the initial values ​​of amplitude, phase, and waveform smoothness were adjusted based on the signal characteristics in the actual application environment to ensure that the generated waveform can achieve the expected effect in actual operation.

[0138] The team selected and configured an AI optimization algorithm suitable for this application scenario. The particle swarm optimization algorithm was selected to optimize the initial parameters. The goal is to find the optimal parameter combination through the optimization process so that the generated waveform can maintain high accuracy and high stability under different working conditions. The advantage of the particle swarm algorithm is that it can converge quickly in a complex parameter space, thereby improving the optimization efficiency.

[0139] Based on the optimized parameters, the team built a neuromorphic computing system to further optimize the waveform generation process. The system simulates the working mode of biological neural networks, generating preliminary sawtooth waveforms through pulse communication between neurons and signal transmission and weighting of synapses. In this process, the firing frequency of neurons and synaptic weights can be dynamically adjusted according to real-time changes in the external environment to maintain the stability of the waveform.

[0140] The generated preliminary sawtooth waveform was subjected to real-time error evaluation in the working environment of the actual measuring instrument. The system obtained the error value by calculating the difference between the generated waveform and the preset ideal waveform. Based on these error values, the neuromorphic computing system adaptively adjusted the firing frequency and synaptic weights of the neurons, and further optimized the generation parameters through artificial intelligence optimization algorithms. The cyclic adjustment process continues until the error of the waveform is controlled within the predetermined accuracy range.

[0141] After the optimization process is completed, the system outputs an optimized micro sawtooth waveform. This waveform is used in the core drive part of the measuring instrument to ensure that the instrument can continue to work stably in different industrial environments. The generated waveform is not only highly accurate, but also has extremely high anti-interference ability, which can effectively deal with electromagnetic interference and temperature fluctuations in industrial environments.

[0142] An industrial automation laboratory in a certain city conducted a three-month test. The test environment included a standard laboratory environment, an industrial production workshop, and an outdoor high temperature and high humidity environment to ensure the comprehensiveness and reliability of the test results. The experiment mainly measured the frequency stability, phase noise, waveform distortion, and signal quality SNR of the waveform.

[0143] Table 1: Experimental data comparison table

[0144]

[0145] The @ symbol means "measured at a certain frequency offset." Specifically, "Phase noise dBc / Hz@1kHz" means that the phase noise is measured at a 1kHz offset from the carrier frequency.

[0146] Experimental results show that the micro-sawtooth generation method of the present invention is significantly superior to the traditional method in various environments. Specifically, in terms of frequency stability, the frequency drift of the present invention in a standard laboratory environment, an industrial production workshop and an outdoor high temperature and high humidity environment is reduced to ±0.05kHz, ±0.1kHz and ±0.15kHz, respectively, which is a significant improvement compared to the ±0.3kHz, ±0.5kHz and ±0.7kHz of the traditional method; in terms of phase noise level, the phase noise of the present invention in different environments is increased to 102dBc / Hz, 95dBc / Hz and 90dBc / Hz, respectively, which is a significant improvement compared to the 90dBc / Hz, 85dBc / Hz and 80dBc / Hz of the traditional method; in terms of waveform distortion, the distortion of the present invention in each environment is 0.4%, 0.8% and 1.0%, respectively, which is much lower than the 1.5%, 2.5% and 3.0% of the traditional method; in terms of signal quality SNR, the SNR of the present invention in different environments is 55dB, 50dB and 48dB, respectively, which is significantly better than the 45dB, 40dB and 35dB of the traditional method. These data fully demonstrate the superiority of the present invention in various key technical indicators.

[0147] Results analysis shows that the method of the present invention is significantly superior to the traditional sawtooth waveform generation method in multiple key technical indicators. In particular, the present invention has shown extremely high performance in terms of frequency stability, phase noise and waveform distortion. In particular, in harsh industrial environments, the present invention can still maintain stable signal output, greatly improving the accuracy and reliability of the measuring instrument.

[0148] In summary, the present invention, by introducing artificial intelligence optimization algorithms and neuromorphic computing systems, not only solves many problems in traditional sawtooth waveform generation methods, but also demonstrates extremely high stability and adaptability in practical applications, and is suitable for various types of high-precision and high-stability industrial automation control systems.

[0149] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for generating micro-sawtooth based on artificial intelligence optimization algorithm, characterized in that: The steps include: S1, initialize the generation parameters, set the initial values ​​of frequency, amplitude, phase and waveform smoothness; S2. Select and configure an artificial intelligence optimization algorithm, which includes a genetic algorithm and a particle swarm optimization algorithm, and optimize initial parameters; S3. Construct a neuromorphic computing system, which consists of a multi-layer neural network and a complex modulation matrix. The optimized parameter combination is processed through the nonlinear activation function and the complex modulation activation function in the neural network to generate a preliminary micro-sawtooth waveform. S4, calculating the difference between the generated waveform and the target waveform through real-time error evaluation, and converting the error signal into the frequency domain for weighted analysis and optimization; S5. According to the weighted error analysis results, the firing frequency and synaptic weight of the neuron are adaptively adjusted, and the generation parameters are further optimized through the artificial intelligence optimization algorithm. By repeatedly converting the time domain and frequency domain of the signal, the waveform is continuously adjusted in a cycle until the generated waveform meets the predetermined accuracy requirements; S6. Output an optimized micro-sawtooth waveform and process it through a filter based on non-trivial topological space and multiple complex number field transformations to optimize the waveform's anti-interference ability and stability.

2. The micro-sawtooth generation method based on artificial intelligence optimization algorithm according to claim 1 is characterized in that: The S2 specifically includes: S21. In the initial stage, construct an objective function, where the objective function includes frequency optimization, amplitude optimization, phase adjustment, and waveform smoothness optimization, and map the target to a high-dimensional complex domain space: Among them, z is the signal generation parameter vector in the complex domain, including frequency f, amplitude A, phase and the complex number representation of the waveform smoothness σ, Ψ k z represents the potential function associated with the kth target, w k is the weight of each target, β k and γ k is the control coefficient, Nz represents the nonlinear operation matrix in the complex domain; S22. Generate an initial population. Each individual in the population represents a parameter combination. S23, optimize the population through quantum state evolution operations, using non-Hermitian Hamiltonian quantum operators To update the quantum state: Among them, |ψ i represents the current quantum state, is a non-Hermitian Hamiltonian operator, and the quantum state is introduced to describe the state of each individual in the population, and Δt is the time step; S23, parameter z i Perform adaptive mutation operation and optimize parameters: in, represents the complex domain convolution operation, has a mean of zero and a variance of σ 2 Non-Gaussian complex noise; S24, select the optimal solution through fitness evaluation, perform nonlinear hierarchical screening on the parameter combination, retain the solution with the highest fitness and output the final optimized parameter z * , including the frequency f * , amplitude A * , Phase and waveform smoothness σ * .

3. The micro-sawtooth generation method based on artificial intelligence optimization algorithm according to claim 1 is characterized in that: The S3 specifically includes: S31, combine the optimized parameters A network of neurons input into a neuromorphic computing system; S32, the output signal y of each neuron i (t) is processed by multiple complex modulation activation functions. The complexity of the multiple complex modulation activation function is reflected in its combination of complex modulation matrix and nonlinear amplification mechanism: Among them, y i (t) is the output signal of the i-th neuron at the current time t, σ(·) is a nonlinear activation function that adjusts the output characteristics of the neuron, and α i is the modulation coefficient of the i-th neuron, which controls the amplification effect of the input signal. Re(·) represents the real part of the complex number. * is the optimized complex parameter combination, including the frequency f * , amplitude A * , Phase and waveform smoothness σ * , e iωt is the phase factor related to time t and modulation frequency ω, M i is the complex modulation matrix, which controls the transformation of the signal in the complex domain. is based on the complex parameter z * and phase offset The sine function of , H is the complex magnification matrix, 1+|N·z * | 2 is the normalization factor of the signal, N is a complex matrix used for nonlinear control of signal amplification, ω ij represents the synaptic weight from the jth neuron to the ith neuron, Q j is the complex transformation matrix, which controls the response characteristics of the signal under time delay. Δt is the time delay factor, which determines the time difference of signal transmission between neurons. S33, the signal y output by each layer of neurons i (t) performing a complex domain fractional Fourier transform to convert the signal from the time domain to the frequency domain, optimizing the frequency domain characteristics of the signal, and reconstructing and optimizing the waveform by analyzing the frequency domain characteristics; S34, based on frequency domain analysis and waveform reconstruction, adjust the synaptic weight ω through multiple iterations ij and complex modulation matrix parameters to optimize signal transmission in neural networks; S34. In the process of waveform generation, complex spectrum modulation and adaptive smoothing processing formula are used to further optimize the frequency domain signal: in, is the frequency domain signal after smoothing and second-order derivative modulation, f is the frequency variable, F(y i (f)) is the output signal y from the neuron i (t) The Fourier transform result converted to the frequency domain, f0 is the center frequency, indicating the main frequency component of the signal, σ f is the standard deviation of the frequency, which determines the width of the spectrum smoothing, is a Gaussian function used for spectrum smoothing, P(f) is a frequency domain modulation function used to control the modulation effect of the frequency response, and R(f) is a phase modulation function that gives the signal additional phase complexity. Represents the second-order derivative of frequency f, capturing the characteristics of spectrum changes; S35, through the inverse fractional Fourier transform, the optimized frequency domain signal Converting back to the time domain generates the optimized miniature sawtooth waveform x(t).

4. The method for generating micro-sawtooth based on artificial intelligence optimization algorithm according to claim 1, characterized in that: The S4 step specifically includes: S41, after generating the preliminary micro sawtooth waveform x(t), perform an error evaluation on it to evaluate the accuracy of the generated waveform, and compare x(t) with the preset ideal target waveform x ideal (t), calculate the difference and generate an error signal; S42, error signal x ideal The difference between x(t) and x(t) is not obvious or difficult to analyze in the time domain. The error is converted from the time domain to the frequency domain for analysis. S43, analyzing the energy density of the error signal in the frequency domain; S44, weighting the error energy density, and highlighting the frequency range that has a greater impact on the final waveform quality during the optimization process; S45. According to the weighted error analysis results, adjust the parameter combination of waveform generation, and feed these adjustments back to the optimization algorithm.

5. The method for generating micro-sawtooth based on artificial intelligence optimization algorithm according to claim 1, characterized in that: The S5 specifically includes: S5 1. Based on the error evaluation and preliminary parameter adjustment in S44, the generated micro-sawtooth waveform x(t) is further optimized, and the adjusted parameter combination z* is re-evaluated, so that the optimized waveform gradually approaches the target waveform; S52. Use the adaptive adjustment mechanism to fine-tune the synaptic weights ω in the neuronal network ij , optimize the signal transmission process between neurons; S53, converting the adjusted signal to the frequency domain again through the complex domain Fourier transform, analyzing the spectrum characteristics of the signal in the frequency domain, and identifying the frequency components that have a great impact on the waveform quality; S54, according to the result of the frequency domain analysis, updating the time domain expression x(t) of the generated waveform, optimizing and reducing the difference between the waveform and the target waveform; S55. For errors that still exist within a specific frequency range, continue to fine-tune the synaptic weights ω in the neural network through multiple iterations. ij and the associated parameter combination z * ; S56, converting the optimized signal from the frequency domain back to the time domain, and performing a final error evaluation, so that the optimized generated micro sawtooth waveform x(t) meets the predetermined accuracy and quality requirements.

6. The method for generating micro-sawtooth based on artificial intelligence optimization algorithm according to claim 1, characterized in that: The S6 specifically includes: S61, inputting the optimized waveform x(t) into a filter based on a non-trivial topological space for processing, wherein the filter optimizes the anti-interference ability and diversity of the signal by utilizing the characteristics of the non-trivial topological structure; S62. A nonlinear transformation formula based on multiple complex number fields is used to perform amplitude modulation on the signal: Among them, x modulated (t) is the modulated signal, which represents the output after complex number domain transformation, x topo (t) is the signal after non-trivial topology filtering, which is the basis of modulation. i is the imaginary unit, which is used to realize the complex modulation part of the signal. D(t) is the time-dependent complex modulation function, which controls the modulation intensity of the signal over time. is a multiple complex number operator, which is used to perform nonlinear transformation on the signal in the complex number domain and increase the structural complexity of the signal. κ and ∈ are nonlinear modulation parameters, which control the intensity of signal modulation and the nonlinear response curve respectively. S63. Perform phase correction on the modulated signal. The phase correction is based on quantum group theory and is implemented by using the R matrix of the quantum group and the trace operation of the matrix, thereby optimizing the phase drift problem that may occur in the traditional method: in, is the corrected signal phase, the result after quantum group entanglement correction, Tr(·) represents the trace operation of the matrix, which is used to extract the key phase information in the quantum group entanglement. is the R matrix of the quantum group, which is responsible for describing the entanglement phenomenon of the signal during the phase correction process. P(.) is the phase correction operator, which finely adjusts the phase of the signal. S64. After phase correction, the signal enters the frequency domain optimization processing stage based on non-Abelian statistics, and the signal is optimized through an adaptive topological quantum field filter: Among them, X final (f) is the signal after frequency domain optimization processing, which is the frequency domain expression of the final output signal. m (f) is a topological filter function based on non-Abelian statistics, which is used to optimize the characteristics of frequency domain signals. ★ represents non-Abelian convolution operation, which enhances the complexity of the signal in the frequency domain. is a tensor product operation, which is used to describe the interaction between frequency domain signals and topological structures. m (f) is the adaptive tuning function, which adjusts the response of the signal at different frequencies; S65, converts the optimized signal in the frequency domain back to the time domain through inverse transformation to generate the final micro sawtooth waveform X final (t).

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