A high-precision analysis method for silicon resonance frequency

Abstract

The present invention provides a high-precision analysis method for silicon resonant frequency, and relates to the technical field of silicon resonant frequency analysis. The present invention obtains a theoretical frequency signal of a silicon resonator excitation power supply and an actual frequency signal of the excitation power supply, and performs fast Fourier transform to obtain a main frequency difference of a silicon resonator, extracts interference signal characteristics from the main frequency difference by establishing a main frequency analysis model, respectively obtains historical temperature, vibration, silicon resonant frequency data and interference signal characteristics of the silicon resonator, and forms a training data set of an ideal silicon resonant frequency under a standard environment, establishes a resonant frequency analysis model based on a neural network model, trains the model through the training data set, and further improves the analysis accuracy by constructing an optimization model of the analysis model, collects real-time interference characteristics of the power supply, temperature values ​​and vibration values ​​of the silicon resonator as inputs of the trained model, and outputs a high-precision silicon resonant analysis frequency.

Description

Technical Field

[0001] The invention relates to the technical field of silicon resonance frequency analysis, and in particular to a high-precision analysis method for silicon resonance frequency. Background Art

[0002] A silicon resonator is a micromechanical vibration system made of silicon material, which can be used as a frequency reference or sensor in electronic devices. Silicon resonators usually excite and detect vibrations through capacitance or piezoelectric effect. These devices are widely used in various technical fields due to their small size, high stability and low cost.

[0003] The resonant frequency is one of the core characteristics of silicon resonators, which directly affects the performance of the device. Accurate frequency ensures that the clock and signal processing functions in electronic devices work properly, while slight deviations in frequency can lead to performance degradation.

[0004] Although significant progress has been made in the design and manufacture of silicon resonators, accurately measuring and controlling their resonant frequency still faces many challenges. Temperature changes, tiny defects in the manufacturing process, and inhomogeneities in material properties can all affect the stability and accuracy of the frequency.

[0005] In the existing technology, the silicon resonant frequency is often compensated through temperature compensation algorithms, or interference is reduced through filters to improve the analysis accuracy of the silicon resonant frequency. However, the factors that affect the silicon resonator are mutually influential. Although the analysis accuracy can be improved to a certain extent by unilaterally analyzing a single factor, the improvement in accuracy is often limited.

[0006] The above information disclosed in this Background section is only for enhancement of understanding of the background of the present disclosure and therefore it may contain information that does not constitute the prior art that is already known to one of ordinary skill in the art. Summary of the invention

[0007] The object of the present invention is to provide a high-precision analysis method for silicon resonant frequency to solve the problems raised in the above background technology.

[0008] To achieve the above object, the present invention provides the following technical solutions:

[0009] A high-precision analysis method for silicon resonant frequency, the specific steps comprising:

[0010] Step 1: Obtain the historical theoretical frequency signal of the silicon resonator excitation power supply and the actual frequency signal of the excitation power supply, perform fast Fourier transform on the theoretical frequency signal and the actual frequency signal respectively, obtain the main frequency difference of the silicon resonator, establish a main frequency analysis model, and extract interference signal characteristics from the main frequency difference through the model;

[0011] Step 2: Under the same excitation power supply, obtain the silicon resonant frequency data of the silicon resonator under different temperature and vibration environments, and obtain the ideal silicon resonant frequency of the silicon resonator under the same excitation power supply in a standard environment, and stamp the interference characteristics of the power supply, the temperature value, vibration value and ideal silicon resonant frequency of the silicon resonator obtained at the same time with a timestamp to form a training data set;

[0012] Step 3: Establish a resonant frequency analysis model based on a neural network model, use the interference characteristics of the power supply, the temperature value and vibration value of the silicon resonator in the training data set as the input of the model, and the ideal silicon resonant frequency as the output of the model to train the model;

[0013] Step 4: By constructing an optimization model of the analytical model, by comparing the deviation between the output frequency and the theoretical frequency, the loss function of the neural network is set to further improve the analytical accuracy;

[0014] Step 5: Collect the real-time interference characteristics of the power supply, the temperature value and vibration value of the silicon resonator as the input of the trained model, and output the high-precision silicon resonance analysis frequency.

[0015] Furthermore, the specific steps of performing fast Fourier transform on the theoretical frequency signal and the actual frequency signal respectively to obtain the main frequency difference of the silicon resonator are:

[0016] Perform fast Fourier transform on the theoretical frequency signal and the actual frequency signal respectively, and convert the time domain signals of the theoretical frequency signal and the actual frequency signal into frequency domain signals. The specific calculation formula is:

[0017] in, is the frequency domain signal of the actual power supply frequency signal Quantity, is the frequency domain signal of the theoretical power frequency signal Quantity, is the time domain signal of the actual power frequency signal samples, The theoretical power frequency signal in the time domain is samples, is the total number of samples, Represents the frequency domain frequency components, ;

[0018] By comparing the frequency domain signals between the real-time power supply and the theoretical power supply signal, the main frequency difference is obtained. The specific calculation formula is: in, is the main frequency difference, is the frequency domain signal of the actual power supply frequency signal Quantity, is the frequency domain signal of the theoretical power frequency signal Quantity;

[0019] The specific calculation formula for establishing the main frequency analysis model and extracting the interference signal characteristics from the main frequency difference through the model is: in, is the interference signal characteristic, is the amplitude coefficient, is the model order.

[0020] Furthermore, the calculation formula of the training data set is:

[0021] in, is the training data set, for The temperature value at the moment, for The temperature value at the moment, for The interference signal characteristics at each moment, for The ideal silicon resonant frequency at the moment, is the data collection time, is the total number of samples, Is a positive integer.

[0022] Furthermore, the resonance frequency analysis model based on the neural network model is a long short-term memory neural network, and the neural network model includes an input gate, a forget gate and an output gate;

[0023] The equation of the forget gate is:

[0024] in, is the current switch state of the forget gate, represents the sigmoid function, is the forget gate weight, is the forget gate bias parameter, is the hidden state at the previous moment, Input switch for current data;

[0025] Determine how much of the unit state at the previous moment needs to be retained to the current moment;

[0026] The equation for the input gate is: in, is the current switch state of the input gate, represents the sigmoid function, is the input gate weight, is the input gate bias parameter, is the output hidden state of the previous moment, The interference characteristics of the power supply at the current moment, the temperature value and vibration value of the silicon resonator;

[0027] in, is the candidate cell state, To represent the hyperbolic tangent function, is the candidate cell weight, is the candidate cell state bias parameter, is the hidden state at the previous moment, Input switch for current data;

[0028] Determine how much of the network's input data needs to be saved to the unit state at the current moment;

[0029] The update equation is: in, is the current cell state, is the cell state at the previous moment;

[0030] The output gate equation is: in, is the current switch state of the output gate, represents the sigmoid function, is the output gate weight, is the output gate bias parameter, is the hidden state at the previous moment, Input switch for current data, is the ideal silicon resonant frequency at the current moment;

[0031] Controls how much of the current unit state needs to be output to the current output value;

[0032] Among them, the mathematical expressions of the sigmoid function and the hyperbolic tangent function are:

[0033] in, is the sigmoid function, Input for the sigmoid function, is the hyperbolic tangent function, Input to the function.

[0034] Furthermore, the loss function is expressed as: in, is the loss function, is the sample size, is the ideal silicon resonant frequency, is the real silicon resonant frequency output by the model.

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention obtains the theoretical frequency signal of the silicon resonator excitation power supply and the actual frequency signal of the excitation power supply, and performs fast Fourier transform to obtain the main frequency difference of the silicon resonator, and extracts the interference signal characteristics of the main frequency difference by establishing a main frequency analysis model, and respectively obtains the historical temperature, vibration, silicon resonant frequency data and interference signal characteristics of the silicon resonator, as well as the ideal silicon resonant frequency under a standard environment to form a training data set, and establishes a resonant frequency analysis model based on a neural network model, and trains the model through the training data set, and further improves the analysis accuracy by constructing an optimization model of the analysis model, collects real-time power supply interference characteristics, silicon resonator temperature values, and vibration values ​​as inputs of the trained model, and outputs a high-precision silicon resonant analysis frequency.

[0036] The present invention is based on; performing fast Fourier transform on the theoretical frequency signal and the actual frequency signal respectively, obtaining the main frequency difference of the silicon resonator, extracting the interference signal characteristics from the main frequency difference by establishing a main frequency analysis model, and directly displaying the difference in frequency by comparing the theoretical and actual frequencies. This difference indicates the deviation between the actual signal and the expected model, providing a basis for further analysis and calibration. By establishing a main frequency analysis model to extract the interference signal characteristics from the main frequency difference, more detailed frequency components can be decomposed, and the interference characteristics of the main frequency can be more accurately identified and analyzed. A resonant frequency analysis model based on a neural network model is established to output a high-precision silicon resonant analysis frequency. The neural network model can effectively capture the impact of these environmental variables on the signal over time, and comprehensively analyzes the impact of various factors on the analysis of the silicon resonant frequency. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a schematic diagram of the overall method flow of the present invention. DETAILED DESCRIPTION

[0038] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments.

[0039] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0040] Example

[0041] See also Figure 1 , the present invention provides a technical solution:

[0042] A high-precision analysis method for silicon resonant frequency, the specific steps comprising:

[0043] Step 1: Obtain the historical theoretical frequency signal of the silicon resonator excitation power supply and the actual frequency signal of the excitation power supply, perform fast Fourier transform on the theoretical frequency signal and the actual frequency signal respectively, obtain the main frequency difference of the silicon resonator, establish a main frequency analysis model, and extract interference signal characteristics from the main frequency difference through the model.

[0044] The theoretical frequency signal of the silicon resonator excitation power supply refers to the preset electrical signal frequency used to drive the silicon resonator. This frequency is calculated based on the design parameters of the silicon resonator, especially its mechanical structure and material properties. In theory, this frequency should match the natural resonant frequency of the silicon resonator to achieve the best vibration efficiency and output stability. The silicon resonant frequency is the actual vibration frequency generated by the silicon resonator when it is excited. If the frequency of the excitation power supply is not accurate enough, it will directly affect the resonant frequency of the silicon resonator, which will cause inaccurate frequency output. Therefore, the stability of the power supply is crucial to the frequency accuracy of the silicon resonator. Any instability of the power supply, such as voltage fluctuations, frequency jitter, etc., may cause fluctuations in the resonant frequency. In addition, electromagnetic interference or noise in the power supply line may also affect the performance of the silicon resonator, thereby affecting the stability and accuracy of the frequency. It is crucial to improve the resolution of the silicon resonant frequency by analyzing the interference signal in the excitation power supply.

[0045] The output of a silicon resonator is usually a time-domain signal that varies with time. To analyze the frequency characteristics of this signal, it first needs to be converted to a frequency domain representation. Fast Fourier transforms these time-domain signals into frequency-domain signals that represent the frequency components of the signal. This makes it clear which frequencies dominate the signal and which frequencies are barely present.

[0046] Fast Fourier is an optimized algorithm that is much faster than directly applying the Fourier transform. In applications such as silicon resonators that may require real-time or near-real-time analysis, Fast Fourier can quickly process large amounts of data and provide instant frequency analysis results, which is particularly important in silicon resonant frequency analysis.

[0047] In this embodiment, the specific steps of performing fast Fourier transform on the theoretical frequency signal and the actual frequency signal respectively to obtain the main frequency difference of the silicon resonator are:

[0048] Perform fast Fourier transform on the theoretical frequency signal and the actual frequency signal respectively, and convert the time domain signals of the theoretical frequency signal and the actual frequency signal into frequency domain signals. The specific calculation formula is:

[0049] in, is the frequency domain signal of the actual power supply frequency signal Quantity, is the frequency domain signal of the theoretical power frequency signal Quantity, is the time domain signal of the actual power frequency signal samples, The theoretical power frequency signal in the time domain is samples, is the total number of samples, Represents the frequency domain frequency components, .

[0050] By comparing the frequency domain signals between the real-time power supply and the theoretical power supply signal, the main frequency difference is obtained. The specific calculation formula is:

[0051] in, is the main frequency difference, is the frequency domain signal of the actual power supply frequency signal Quantity, is the frequency domain signal of the theoretical power frequency signal A quantity.

[0052] By comparing the theoretical and actual frequencies, the difference in frequency can be directly displayed. This difference indicates the deviation of the actual signal from the expected model and provides a basis for further analysis and calibration. Obtaining this frequency difference is a key step in determining the deviation of the actual behavior of the silicon resonator from the theoretical or expected behavior.

[0053] The specific calculation formula for establishing the main frequency analysis model and extracting the interference signal characteristics from the main frequency difference through the model is:

[0054] in, is the interference signal characteristic, is the amplitude coefficient, is the model order.

[0055] The main frequency analysis model is a Taylor Fourier multi-frequency model. By combining the polynomial characteristics of the Taylor series and the frequency domain characteristics of Fourier analysis, the model is allowed to adapt more accurately to local changes in the signal. This adaptability is particularly suitable for processing nonlinear or non-stationary signals. In the frequency domain, the Taylor Fourier multi-frequency model can decompose more detailed frequency components and more accurately identify and analyze the main frequency difference and its origin. In applications that require high-precision silicon resonant frequency analysis, even small frequency changes may affect the performance of the overall frequency analysis, because when analyzing the silicon resonant frequency, it may be affected by multiple interferences. The Taylor Fourier multi-frequency model can distinguish and quantify these different sources of interference and extract specific interference signal characteristics.

[0056] Step 2: Under the same excitation power supply, obtain the silicon resonance frequency data of the silicon resonator under different temperature and vibration environments, and obtain the ideal silicon resonance frequency of the silicon resonator under the same excitation power supply under a standard environment. The interference characteristics of the power supply, the temperature value, vibration value and ideal silicon resonance frequency of the silicon resonator obtained at the same time are timestamped to form a training data set.

[0057] Silicon is a solid material whose dimensions and physical structure will expand or contract thermally due to changes in temperature. As the temperature increases, the silicon crystal expands, which usually causes the material's vibration mode to change, thereby reducing the resonant frequency. Conversely, when the temperature decreases, the material contracts and the resonant frequency may increase. The vibration can induce mechanical stress in the silicon crystal structure. These stresses may cause the microstructure of the crystal to deform, affecting the vibration mode and thus changing the resonant frequency. Stress can also cause inelastic behavior of the silicon material, which also affects the resonant frequency. If the frequency of the external vibration is close to the resonant frequency of the silicon resonator, it may induce resonance. This resonance can significantly increase the amplitude and cause a shift in the resonant frequency. In addition, strong vibrations may cause nonlinear behavior of the system, further complicating the frequency response.

[0058] The standard working environment of silicon resonators mainly refers to those conditions that can ensure the normal operation of the equipment and are not affected by excessive environmental factors. The silicon resonant frequency in this environment is not affected by external interference, that is, the ideal resonant frequency. Under the same excitation power supply, the silicon resonant frequency data of the silicon resonator in different temperature and vibration environments is obtained. According to the difference in silicon resonant frequency under the same excitation power supply in different environments, the effects of temperature and vibration on the resonator can be effectively distinguished.

[0059] In this embodiment, the calculation formula of the training data set is:

[0060] in, is the training data set, for The temperature value at the moment, for The temperature value at the moment, for The interference signal characteristics at each moment, for The ideal silicon resonant frequency at the moment, is the data collection time, is the total number of samples, Is a positive integer.

[0061] Step 3: Establish a resonant frequency analysis model based on the neural network model, use the interference characteristics of the power supply, the temperature value and vibration value of the silicon resonator in the training data set as the input of the model, and the ideal silicon resonant frequency as the output of the model to train the model.

[0062] The neural network model based on the resonance frequency analysis model is a long short-term memory neural network, which is designed for processing and predicting time series data. As a time series data, the performance and expression of the silicon resonance frequency signal are affected by various environmental factors such as temperature and vibration. The long short-term memory neural network can effectively capture the impact of these environmental variables on the signal over time through its special network structure. By using the powerful modeling ability of the long short-term memory neural network for time series, the future changes in silicon resonance frequency can be predicted based on past data, and a high prediction accuracy can be maintained even when environmental conditions change.

[0063] In this embodiment, the resonance frequency analysis model based on the neural network model is a long short-term memory neural network, and the neural network model includes an input gate, a forget gate and an output gate;

[0064] The equation of the forget gate is:

[0065] in, is the current switch state of the forget gate, represents the sigmoid function, is the forget gate weight, is the forget gate bias parameter, is the hidden state at the previous moment, Input switch for current data;

[0066] Determine how much of the unit state at the previous moment needs to be retained to the current moment;

[0067] The equation for the input gate is:

[0068] in, is the current switch state of the input gate, represents the sigmoid function, is the input gate weight, is the input gate bias parameter, is the output hidden state of the previous moment, The interference characteristics of the power supply at the current moment, the temperature value and vibration value of the silicon resonator;

[0069] in, is the candidate cell state, To represent the hyperbolic tangent function, is the candidate cell weight, is the candidate cell state bias parameter, is the hidden state at the previous moment, Input switch for current data;

[0070] Determine how much of the network's input data needs to be saved to the unit state at the current moment;

[0071] The update equation is:

[0072] in, is the current cell state, is the cell state at the previous moment;

[0073] The output gate equation is:

[0074] in, is the current switch state of the output gate, represents the sigmoid function, is the output gate weight, is the output gate bias parameter, is the hidden state at the previous moment, Input switch for current data, is the ideal silicon resonant frequency at the current moment;

[0075] Controls how much of the current unit state needs to be output to the current output value;

[0076] Among them, the mathematical expressions of the sigmoid function and the hyperbolic tangent function are:

[0077] in, is the sigmoid function, Input for the sigmoid function, is the hyperbolic tangent function, Input to the function.

[0078] Step 4: By constructing an optimization model of the analytical model, comparing the deviation between the output frequency and the theoretical frequency, and setting the loss function of the neural network, the analytical accuracy can be further improved.

[0079] in, is the loss function, is the sample size, is the ideal silicon resonant frequency, is the real silicon resonant frequency output by the model.

[0080] The loss function is an indicator that measures the difference between the model's predicted value and the actual value. Choosing a suitable loss function can more accurately reflect the model's performance in analyzing the resonant frequency of the silicon resonator. During the training process, by continuously calculating the loss and updating the model parameters, the long short-term memory neural network can learn how to more accurately predict the resonant frequency. By gradually reducing the loss value, the model's prediction results will gradually approach the true value, thereby improving accuracy. By monitoring the performance of the loss function on the validation set, these parameters can be optimized to achieve better prediction results.

[0081] Step 5: Collect the real-time interference characteristics of the power supply, the temperature value and vibration value of the silicon resonator as the input of the trained model, and output the high-precision silicon resonance analysis frequency;

[0082] The above formulas are all dimensionless and numerical calculations. The formula is a formula for the most recent real situation obtained by collecting a large amount of data and performing software simulation. The preset parameters in the formula are set by technicians in this field according to actual conditions.

[0083] The above embodiments may be implemented in whole or in part by software, hardware, firmware or any other combination thereof. When implemented by software, the above embodiments may be implemented in whole or in part in the form of a computer program product. Those skilled in the art may appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein may be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed by hardware or software methods depends on the specific application and design constraints of the technical solution.

[0084] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, and may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0085] The above description is only a specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application.

Claims

1. A high-precision analysis method for silicon resonance frequency, characterized in that: The specific steps include: Step 1: Obtain the historical theoretical frequency signal of the silicon resonator excitation power supply and the actual frequency signal of the excitation power supply, perform fast Fourier transform on the theoretical frequency signal and the actual frequency signal respectively, obtain the main frequency difference of the silicon resonator, establish a main frequency analysis model, and extract interference signal characteristics from the main frequency difference through the model; Step 2: Under the same excitation power supply, obtain the silicon resonant frequency data of the silicon resonator under different temperature and vibration environments, and obtain the ideal silicon resonant frequency of the silicon resonator under the same excitation power supply in a standard environment, and stamp the interference characteristics of the power supply, the temperature value, vibration value and ideal silicon resonant frequency of the silicon resonator obtained at the same time with a timestamp to form a training data set; Step 3: Establish a resonant frequency analysis model based on a neural network model, use the interference characteristics of the power supply, the temperature value and vibration value of the silicon resonator in the training data set as the input of the model, and the ideal silicon resonant frequency as the output of the model to train the model; Step 4: By constructing an optimization model of the analytical model, by comparing the deviation between the output frequency and the theoretical frequency, the loss function of the neural network is set to further improve the analytical accuracy; Step 5: Collect the real-time interference characteristics of the power supply, the temperature value and vibration value of the silicon resonator as the input of the trained model, and output the high-precision silicon resonance analysis frequency; The resonance frequency analysis model based on the neural network model is a long short-term memory neural network, and the neural network model includes an input gate, a forget gate and an output gate; The equation of the forget gate is: in, is the current switch state of the forget gate, represents the sigmoid function, is the forget gate weight, is the forget gate bias parameter, is the hidden state at the previous moment, Input switch for current data; Determine how much of the unit state at the previous moment needs to be retained to the current moment; The equation for the input gate is: in, is the current switch state of the input gate, represents the sigmoid function, is the input gate weight, is the input gate bias parameter, is the output hidden state of the previous moment, The interference characteristics of the power supply at the current moment, the temperature value and vibration value of the silicon resonator; in, is the candidate cell state, To represent the hyperbolic tangent function, is the candidate cell weight, is the candidate cell state bias parameter, is the hidden state at the previous moment, Input switch for current data; Determine how much of the network's input data needs to be saved to the unit state at the current moment; The update equation is: in, is the current cell state, is the cell state at the previous moment; The output gate equation is: in, is the current switch state of the output gate, represents the sigmoid function, is the output gate weight, is the output gate bias parameter, is the hidden state at the previous moment, Input switch for current data, is the ideal silicon resonant frequency at the current moment; Controls how much of the current unit state needs to be output to the current output value; Among them, the mathematical expressions of the sigmoid function and the hyperbolic tangent function are: in, is the sigmoid function, Input for the sigmoid function, is the hyperbolic tangent function, Input to the function.

2. A high-precision analysis method for silicon resonance frequency according to claim 1, characterized in that: The specific steps of performing fast Fourier transform on the theoretical frequency signal and the actual frequency signal respectively to obtain the main frequency difference of the silicon resonator are: Perform fast Fourier transform on the theoretical frequency signal and the actual frequency signal respectively, and convert the time domain signals of the theoretical frequency signal and the actual frequency signal into frequency domain signals. The specific calculation formula is: in, is the frequency domain signal of the actual power supply frequency signal Quantity, is the frequency domain signal of the theoretical power frequency signal Quantity, is the time domain signal of the actual power frequency signal samples, The theoretical power frequency signal in the time domain is samples, is the total number of samples, Represents the frequency domain frequency components, ; By comparing the frequency domain signals between the real-time power supply and the theoretical power supply signal, the main frequency difference is obtained. The specific calculation formula is: in, is the main frequency difference, is the frequency domain signal of the actual power supply frequency signal Quantity, is the frequency domain signal of the theoretical power frequency signal Quantity; The specific calculation formula for establishing the main frequency analysis model and extracting the interference signal characteristics from the main frequency difference through the model is: in, is the interference signal characteristic, is the amplitude coefficient, is the model order.

3. The method for high-precision analysis of silicon resonance frequency according to claim 1, characterized in that: The calculation formula of the training data set is: in, is the training data set, for The temperature value at the moment, for The temperature value at the moment, for The interference signal characteristics at each moment, for The ideal silicon resonant frequency at the moment, is the data collection time, is the total number of samples, Is a positive integer.

4. The method for high-precision analysis of silicon resonance frequency according to claim 1, characterized in that: The expression formula of the loss function is: in, is the loss function, is the sample size, is the ideal silicon resonant frequency, is the real silicon resonant frequency output by the model.

Images