A precision identification method for model parameters of MEMS device temperature drift error estimation

Abstract

A MEMS device temperature drift error estimation model parameter precision identification method is provided to solve the problem of low precision of MEMS device output caused by low precision of temperature drift error estimation model output. The MEMS device temperature drift error estimation model based on RBFNN is initialized; the excitation function configuration set of RBFNN is constructed; the model is trained according to the training sample and the configuration set, and the MEMS device output and the corresponding temperature drift error are compensated by using the temperature drift error; the mean square error of the compensated MEMS device output is taken as the precision index, the actual calculation time of the compensated temperature drift error estimation is taken as the real-time index, and the two are taken as the input, the configuration set is taken as the output expert knowledge base; the knowledge base is decomposed by using the fuzzy theory, the best excitation function configuration scheme is obtained according to the precision index target value and the real-time index target value, the trained model is updated, and a new model is obtained; the environmental temperature is used to output the temperature drift error by using the new model, and the MEMS device output is compensated.

Description

Technical Field

[0001] This invention relates to a precise parameter identification method, specifically a precise parameter identification method for a MEMS device temperature drift error estimation model, belonging to the field of micro inertial sensors. Background Technology

[0002] Outer space contains abundant natural resources, such as helium-3, titanium, iron, and rare earth elements, leading to a gradual shift in resource extraction from Earth to deep space. However, the harsh environment of deep space, including low temperatures, vacuum, and high-intensity radiation, severely limits direct human involvement. Unmanned intelligent devices (UAVs) play a crucial role in this process. These UAVs are launched beforehand to the vicinity of the target planet to explore the local environment and transmit relevant data back to the mission center in a timely manner to formulate mission plans; examples include Mars rovers and relay satellites. Due to the complex and ever-changing deep space environment, terrain features can change rapidly due to strong winds, rain, snow, and other severe convective weather, potentially causing UAVs to overturn, collide, or shut down due to low temperatures. Therefore, the ability of UAVs to cope with extreme and harsh environments is a vital guarantee for the successful execution of missions. As is well known, the effective payload of launch vehicles is limited, making smaller and lighter MEMS devices the preferred choice for UAVs. MEMS devices are made of temperature-dependent silicon-based materials. Since the temperature in deep space ranges from -180℃ to 130℃, changes in ambient temperature alter their physical properties and induce temperature drift errors, thus reducing the accuracy of MEMS device outputs. Due to current material technology limitations, eliminating the temperature dependence of silicon-based materials through optimized manufacturing processes is extremely difficult. Therefore, MEMS device temperature drift error compensation methods mainly include temperature control and algorithm estimation. Temperature control uses a temperature control system to maintain the ambient temperature at a certain value, but high power consumption, large size, and complex control make this method difficult to apply on a large scale. Algorithm estimation uses mathematical models to accurately estimate temperature drift errors and compensate for device outputs in real time, offering advantages such as high accuracy, ease of implementation, and low cost. The accuracy of algorithm estimation depends on precise temperature drift error tracing technology and accurate identification of temperature drift error estimation model parameters. Precise temperature drift error tracing technology uses theoretical derivation to accurately locate the key factors affecting the temperature drift error of MEMS devices, namely, ambient temperature-related quantities. After accurately acquiring the relevant quantities of ambient temperature, accurately describing the relationship between the relevant quantities of ambient temperature and temperature drift error directly determines the accuracy of temperature drift error estimation, which is to accurately identify the parameters of the temperature drift error estimation model.

[0003] Radial Basis Function Neural Networks (RBFNNs) are typical three-layer neural networks, consisting of one input layer, one hidden layer, and one output layer. During network training, they effectively avoid local optima and maintain a globally optimal approximation of the objective function, thus being widely used for accurately identifying parameters of complex nonlinear models. However, since the accuracy and real-time performance of neural networks depend on the activation function and internal structure, traditional neural network-based MEMS device temperature drift error estimation model parameter identification often relies excessively on human experience. Repeated testing and numerous test results are required to ensure optimal model parameter identification, which increases the complexity of parameter identification and introduces a degree of uncertainty and unpredictability. Furthermore, it may, to some extent, overemphasize accuracy at the expense of real-time performance to slow down temperature drift error estimation calculations, or vice versa, leading to low output accuracy in MEMS devices. Summary of the Invention

[0004] To address the problem that traditional RBFNN-based MEMS device temperature drift error estimation models rely on human experience to identify model parameters, resulting in a degree of blindness and uncertainty in the identification results, leading to low accuracy of the output temperature drift error and consequently low accuracy of the MEMS device output, this invention proposes a precise identification method for MEMS device temperature drift error estimation model parameters.

[0005] It includes the following steps:

[0006] S1. Initialize the structural parameters of the RBFNN neural network to obtain the initialized MEMS device temperature drift error estimation model based on RBFNN;

[0007] S2. Construct the hidden layer activation function set and the output layer activation function set of the RBFNN neural network based on the structural parameters of the RBFNN neural network. Cross-merge the hidden layer activation function set and the output layer activation function set to obtain the activation function configuration set.

[0008] S3. Obtain the measured ambient temperature and corresponding temperature drift error of the MEMS device as training samples. Based on the activation function configuration set and training samples, train the initialized RBFNN-based MEMS device temperature drift error estimation model. Input the ambient temperature and output the temperature drift error. Stop training when the difference between the mean square error of the output temperature drift error and the mean square error of the corresponding actual temperature drift error is 0.0000001. The trained RBFNN-based MEMS device temperature drift error estimation model is obtained.

[0009] The ambient temperature of the MEMS device is input into the trained RBFNN-based MEMS device temperature drift error estimation model, and the corresponding temperature drift error is output. The output of the MEMS device and the temperature drift error corresponding to the output of the MEMS device are obtained. The difference between the output of the MEMS device and the output temperature drift error is obtained to obtain the compensated output of the MEMS device. The output temperature drift error is replaced with the temperature drift error corresponding to the output of the MEMS device to obtain the compensated temperature drift error.

[0010] S4. Using the mean square error of the compensated MEMS device output as the accuracy index and the actual calculation time of the compensated temperature drift error estimate as the real-time index, the accuracy index and the real-time index are used as inputs and the set of excitation function configurations are used as outputs to construct an Expert-Fuzzy auxiliary decision-making expert knowledge base.

[0011] S5. Using fuzzy theory, the accuracy index, real-time index, and activation function configuration set in the Expert-Fuzzy Assisted Decision-Making Expert Knowledge Base are decomposed. The mean square error of the accuracy index and the calculation time of the real-time index are taken as the input fuzzy set, and the corresponding activation function configuration set is taken as the output fuzzy set. The optimal activation function configuration scheme is obtained based on the target values ​​of the accuracy index and the target values ​​of the real-time index output by a certain compensated MEMS device.

[0012] S6. Update the structural parameters of the RBFNN neural network according to the optimal activation function configuration scheme, and update the trained RBFNN-based MEMS device temperature drift error estimation model in S3 according to the updated RBFNN neural network structural parameters, so as to obtain the RBFNN-based MEMS device temperature drift error estimation model that satisfies the MEMS device output accuracy index and the MEMS device output real-time index.

[0013] S7. Obtain the ambient temperature of the MEMS device. Use the RBFNN-based MEMS device temperature drift error estimation model in S6 to output the temperature drift error. Subtract the temperature drift error from the MEMS device output to obtain the compensated MEMS device output, which is the MEMS device.

[0014] Furthermore, the structural parameters of the RBFNN neural network in S1 are:

[0015] ①The RBFNN neural network consists of an input layer, a hidden layer, and an output layer.

[0016] ②The number of hidden layer neurons is the same as the number of input training samples;

[0017] ③ The input layer has a single input, and the input layer neurons are in the same dimension as the ambient temperature, that is, the input is the ambient temperature;

[0018] ④ The output layer is a single output, and the output layer neurons are in the same dimension as the temperature drift error, that is, the output is the temperature drift error;

[0019] ⑤ The hidden layer activation function is a radial basis function, and the output layer activation function is a linear function.

[0020] Furthermore, the RBFNN-based MEMS device temperature drift error estimation model initialized in S1:

[0021] ΔE=f″ pureline [f′ Radialbasis (x)] (1)

[0022] Where ΔE represents the estimated temperature drift error, x represents the input quantity, and f′ Radialbasis This indicates that the hidden layer activation function is a radial basis function, f″ pureline This indicates that the output layer activation function is a linear function.

[0023] Furthermore, the specific process of S2 is as follows:

[0024] Hidden layer activation function set:

[0025] f′={tansig,logsig,purelin,satlins,radbas} (2)

[0026] Where tansig is a symmetric sigmoid function, logsig represents a logarithmic sigmoid function, purelin represents a linear function, satlins represents a symmetric linear saturated function, and radbas represents a radial basis function.

[0027] Output layer activation function set:

[0028] f″={purelin,satlins} (3)

[0029] The hidden layer activation function set includes m activation functions, and the output layer activation function set includes n activation functions. The hidden layer activation function set and the output layer activation function set are cross-merged to obtain the activation function configuration set D. m×n .

[0030] Furthermore, the specific process of S3 is as follows:

[0031] Based on the measured ambient temperature and corresponding temperature drift error of MEMS devices, a specific excitation function configuration from the set of excitation function configurations is selected sequentially to train the initialized RBFNN-based MEMS device temperature drift error estimation model. The ambient temperature is input, and the temperature drift error is output. Training stops when the difference between the mean square error of the output temperature drift error and the mean square error of the corresponding actual temperature drift error is 0.0000001. This yields the trained RBFNN-based MEMS device temperature drift error estimation model.

[0032] ΔE=f″[f′(T)] (4)

[0033] Where T represents the ambient temperature;

[0034] The ambient temperature of the MEMS device is input into the trained RBFNN-based MEMS device temperature drift error estimation model, and the corresponding temperature drift error is output. The MEMS device output and the corresponding temperature drift error are obtained at this time. The difference between the MEMS device output and the output temperature drift error is obtained to obtain the compensated MEMS device output. The output temperature drift error is replaced with the temperature drift error corresponding to the MEMS device output to obtain the compensated temperature drift error. Thus, the compensated MEMS device output and the compensated temperature drift error under all excitation function configurations are obtained.

[0035] Furthermore, in S4, the mean square error of the compensated MEMS device output is used as the accuracy indicator, and the actual calculation time of the compensated temperature drift error estimate is used as the real-time indicator. The expression is as follows:

[0036]

[0037] Among them, D o This represents the output of the MEMS device, where A represents the MSE value of the MEMS device output after compensation, and T represents the output of the MEMS device. start T represents the start time of the temperature drift error estimation calculation. stop δT represents the termination time of the temperature drift error estimation calculation, and δT represents the calculation time required for the temperature drift error estimation.

[0038] Furthermore, the Expert-Fuzzy Assisted Decision-Making Expert Knowledge Base in S4 is as follows:

[0039] (A,δT)∝f″[f′(T)] (6).

[0040] Furthermore, the specific process of S5 is as follows:

[0041] S51. Using fuzzy theory, the accuracy indicators, real-time indicators, and activation function configuration sets in the Expert-Fuzzy Assisted Decision-Making Expert Knowledge Base are decomposed into fuzzy sets. The principle of fuzzy set partitioning is mainly based on clustering and classification. That is, the accuracy indicators and real-time indicators are classified into fuzzy sets according to their amplitude. After classification, fuzzy sets named as negative large NB, negative medium NM, negative small NS, positive small PS, positive medium PM, and positive large PB are obtained. The mean square error of the accuracy indicators and the calculation time of the real-time indicators are both input fuzzy sets, and the corresponding activation function configuration sets are output fuzzy sets.

[0042] S52. Both the input fuzzy set and the output fuzzy set are described using the membership function trimf. The input fuzzy set is fuzzified and its values ​​are obtained according to performance classification, and the output fuzzy set is fuzzified and its values ​​are obtained sequentially according to the excitation function configuration set index. This process yields the target values ​​for accuracy, real-time performance, and excitation function configuration of a certain compensated MEMS device output. The specific process is as follows:

[0043] For the output of a certain compensated MEMS device, based on the classified fuzzy set, the accuracy index fuzzy set is described by the membership function trimf and used as input 1, with input 1 fuzzy set I1[NB, NM, NS, PS, PM, PB] and the target value of the accuracy index is (0, 1, 2, 3, 4, 5); the real-time index fuzzy set is described by the membership function trimf and used as input 2, with input 2 fuzzy set I2[NB, PS, PB] and the target value of the real-time index is (0, 1, 2); the excitation function configuration set is described by the membership function trimf and used as the output, with the output fuzzy set being O and taking values ​​of (0, 10, 20, 30, 40, 50, 60, 70, 80, 90).

[0044] S53. Using fuzzy operation rules, construct fuzzy operations with the fuzzy set I1 of input 1, the fuzzy set I2 of input 2, and the fuzzy set O of output to obtain the corresponding fuzzy results. Based on the fuzzy results, obtain the optimal excitation function configuration scheme from the excitation function configuration set.

[0045] Furthermore, the formula for determining the value in S52 is:

[0046]

[0047] Furthermore, the fuzzy operation rules in S53 are as follows:

[0048]

[0049] Beneficial effects:

[0050] This invention, based on the Radial Basis Function Neural Network (RBFNN) capable of describing complex nonlinear relationships, utilizes fuzzy theory and expert experience to construct a parameter identification method for the temperature drift error estimation model of MEMS devices based on RBFNN under Expert-Fuzzy assisted decision-making. The mean square error of the MEMS device output is used as the accuracy indicator, and the actual computation time for temperature drift error estimation is used as the real-time indicator. Accuracy and real-time indicators are used as inputs, and the set of activation function configurations is used as the output to construct an Expert-Fuzzy assisted decision-making expert knowledge base. Based on the target performance indicators, the activation function configuration parameters of the temperature drift error estimation model of MEMS devices based on RBFNN are easily and accurately identified. This solves the problem of traditional temperature drift error compensation methods for capacitive MEMS devices, which rely too heavily on human experience in constructing the temperature drift error estimation model. It improves the output result of the temperature drift error estimation model, i.e., the temperature drift error, thus leading to more accurate MEMS devices. Furthermore, it purposefully simplifies the testing process based on traditional methods, ultimately achieving accurate and stable testing, rapid and convenient operation, and reliable test results. It effectively decouples the temperature dependence of silicon-based materials and improves the environmental adaptability of MEMS devices. Attached Figure Description

[0051] Figure 1 This is a graph showing the measured results of the MEMS device IIS328DQ;

[0052] Figure 2 This is a comparison chart of the performance improvement of the IIS328DQ before and after temperature drift error compensation using the traditional model and the improved model;

[0053] Figure 3 This is a schematic diagram of the RBFNN structure;

[0054] Figure 4 It is a Surface plot of the method for accurately identifying parameters of the temperature drift error estimation model;

[0055] Figure 5 This is a flowchart of the precise identification method for temperature drift error estimation model parameters; Detailed Implementation

[0056] Specific implementation method one: Combining Figures 1-5 This embodiment describes a method for precise identification of parameters in a MEMS device temperature drift error estimation model. This method aims to provide a set of RBFNN configuration parameters based on the measured data of the MEMS device after compensation using the RBFNN-based temperature drift error estimation model and its target performance. It includes the following steps:

[0057] S1. Based on the experience of optimal RBFNN performance under various structural parameters determined by extensive expert testing, the structural parameters of the RBFNN neural network are initialized to obtain the initialized RBFNN-based MEMS device temperature drift error estimation model:

[0058] ①The RBFNN neural network consists of an input layer, a hidden layer, and an output layer.

[0059] ②The number of hidden layer neurons is the same as the number of input training samples.

[0060] ③ The input layer is a single input, and the input layer neurons are in the same dimension as the ambient temperature, that is, the input is the ambient temperature.

[0061] ④ The output layer is a single output, and the output layer neurons are in the same dimension as the temperature drift error, that is, the output is the temperature drift error.

[0062] ⑤ The hidden layer activation function is a radial basis function, and the output layer activation function is a linear function.

[0063] Initialized MEMS device temperature drift error estimation model based on RBFNN:

[0064] ΔE=f″ pureline [f′ Radialbasis (x)] (1)

[0065] Where ΔE is the estimated temperature drift error, x represents the input (ambient temperature), and f′ Radialbasis The hidden layer activation function is represented by radial basis functions, f″ pureline This indicates that the output layer activation function is a linear function.

[0066] S2. Performance testing of the RBFNN-based MEMS device temperature drift error estimation model under different structural parameter configurations mainly focuses on the activation function configuration. Based on expert experience, the hidden layer activation function set and output layer activation function set of the RBFNN neural network are constructed according to commonly used activation functions. The hidden layer activation function set includes m activation functions, and the output layer activation function set includes n activation functions. The hidden layer activation function set and the output layer activation function set are then cross-merged to construct the activation function configuration set D. m×n .

[0067] Hidden layer activation function set:

[0068] f′={tansig,logsig,purelin,satlins,radbas} (2)

[0069] Output layer activation function set:

[0070] f″={purelin,satlins} (3)

[0071] Where tansig is a symmetric sigma function, logsig represents a logarithmic sigma function, purelin represents a linear function, satlins represents a symmetric linear saturated function, and radbas represents a radial basis function.

[0072] S3. Obtain the measured ambient temperature and corresponding temperature drift error of the MEMS devices in the unmanned intelligent device as training samples, and configure the set D according to the excitation function. m×n The initial RBFNN-based MEMS device temperature drift error estimation model is trained with training samples. The ambient temperature is input and the temperature drift error is output. Training stops when the difference between the mean square error (MSE) of the output temperature drift error and the mean square error of the corresponding actual temperature drift error is 0.0000001. The trained RBFNN-based MEMS device temperature drift error estimation model is obtained.

[0073] The ambient temperature of the MEMS devices in the unmanned intelligent device is input into a pre-trained MEMS device temperature drift error estimation model based on RBFNN, and the corresponding temperature drift error is output. Based on the carrier's attitude information such as acceleration, angular velocity, atmospheric pressure, and heading angle, the MEMS device output (acceleration, angular velocity, air pressure, heading angle, etc.) and the corresponding temperature drift error are obtained. The difference between the MEMS device output and the corresponding temperature drift error is calculated to obtain the compensated MEMS device output. This compensated temperature drift error is then used to replace the corresponding temperature drift error in the MEMS device output. The specific process is as follows:

[0074] Based on the measured ambient temperature and corresponding temperature drift error of MEMS devices in unmanned intelligent equipment, the excitation function configuration set D is selected sequentially. m×n A specific activation function configuration is used to train the initialized RBFNN-based MEMS device temperature drift error estimation model, resulting in a trained RBFNN-based MEMS device temperature drift error estimation model:

[0075] ΔE=f″[f′(T)] (4)

[0076] Where T represents ambient temperature.

[0077] Based on equation (4), the estimated value of temperature drift error and the MEMS device output before compensation are obtained. The MEMS device output at this time is the MEMS device output before compensation, which is a known quantity. According to the MEMS device output at this time, its corresponding existing temperature drift error can be obtained. After compensating the MEMS device output, the temperature drift error of the above output replaces the existing temperature drift error, that is, the MEMS device output compensation and temperature drift error compensation are completed. Thus, the MEMS device output and the compensated temperature drift error after compensation by the MEMS device temperature drift error estimation model based on RBFNN under the configuration of m×n excitation functions can be obtained.

[0078] S4. The mean square error of the compensated MEMS device output is used as the accuracy indicator (measured value), and the actual calculation time of the compensated temperature drift error estimate is used as the real-time indicator (measured value), as specifically expressed below:

[0079]

[0080] Among them, D o This represents the output of the MEMS device, where A represents the MSE value of the MEMS device output after compensation, and T represents the output of the MEMS device. start T represents the start time of the temperature drift error estimation calculation. stop δT represents the termination time of the temperature drift error estimation calculation, and δT represents the calculation time required for the temperature drift error estimation.

[0081] Using accuracy and real-time metrics as inputs, the activation function configuration set D m×n As the output, an Expert-Fuzzy Assisted Decision-Making Knowledge Base with "2 inputs and 1 output" is constructed, specifically represented as follows:

[0082] (A,δT)∝f″[f′(T)] (6)

[0083] Thus, the performance test of the temperature drift error estimation model for MEMS devices based on RBFNN was completed.

[0084] S5. Using fuzzy theory, analyze the accuracy index A, real-time index δT, and activation function configuration set D in the Expert-Fuzzy Assisted Decision Knowledge Base. m×n The process involves decomposing the mean square error of the accuracy metric and the calculation time of the real-time metric into input fuzzy sets, and the corresponding set of excitation function configurations into output fuzzy sets. The optimal excitation function configuration scheme is then obtained based on the target values ​​of the accuracy and real-time metrics output by a compensated MEMS device. The specific process is as follows:

[0085] Based on expert experience, fuzzy theory is used to integrate the accuracy index A, real-time index δT, and activation function configuration set D from the Expert-Fuzzy Assisted Decision-Making Expert Knowledge Base.m×n The data is decomposed into fuzzy sets. The fuzzy set partitioning principle is mainly based on clustering and classification. That is, the accuracy index A and the real-time index δT are classified according to their amplitudes, roughly defining the fuzzy sets, and naming them as follows based on the specific fuzzy classification: negative large NB, negative medium NM, negative small NS, positive small PS, positive medium PM, and positive large PB. The mean square error of the accuracy index and the calculation time of the real-time index are used as the input fuzzy sets, and their corresponding activation function configuration sets D are... m×n To output a fuzzy set.

[0086] Both the input and output fuzzy sets are described using the membership function trimf. The input fuzzy set is fuzzified and its values ​​are assigned based on performance classification, while the output fuzzy set is configured according to the activation function. m×n The serial numbers are sequentially fuzzed to obtain values, and the specific process is as follows:

[0087] Based on the specific classification configuration of the fuzzy classification set, the accuracy index fuzzy set is described by the membership function trimf and used as input 1. Input 1 fuzzy set I1[NB, NM, NS, PS, PM, PB] takes values ​​of (0, 1, 2, 3, 4, 5); the real-time index fuzzy set is described by the membership function trimf and used as input 2. Input 2 fuzzy set I2[NB, PS, PB] takes values ​​of (0, 1, 2); the activation function configuration set D... m×n The membership function `trimf` is used to describe and output the fuzzy set O, with values ​​ranging from (0, 10, 20, 30, 40, 50, 60, 70, 80, 90). The specific values ​​are described below:

[0088]

[0089] The following fuzzy operation rules are used to construct fuzzy operations on the input fuzzy set I1, the input fuzzy set I2, and the output fuzzy set O to obtain the corresponding fuzzy results. This realizes the fuzzy operation relationship mapping the input fuzzy set to the output fuzzy set, as shown below:

[0090]

[0091] Based on the fuzzy computation results, the set D of the activation function can be configured. m×n The optimal activation function configuration scheme and RBFNN neural network parameter configuration are obtained. After updating the RBFNN neural network, a MEMS device temperature drift error estimation model based on RBFNN that meets the requirements of target accuracy and real-time performance can be obtained. The parameter generation method of the temperature drift error estimation model based on RBFNN under Expert-Fuzzy assisted decision-making is completed, as shown in the following figure:

[0092] ΔE=f″ T[f′ T (x)] (9)

[0093] Where, f′ T f″ is the excitation function selected from equation (2) after fuzzy computation by equation (8). T The excitation function is selected from equation (3) after fuzzy operation by equation (8).

[0094] S6. Obtain the ambient temperature of MEMS devices in the unmanned intelligent equipment. Based on the carrier attitude information such as carrier acceleration, carrier angular velocity, current atmospheric pressure of the carrier environment, and current heading angle of the carrier, use the MEMS device temperature drift error estimation model based on RBFNN in S6 to output the corresponding temperature drift error. Subtract the known MEMS device output (acceleration, angular velocity, air pressure, heading angle, etc.) from the corresponding temperature drift error to obtain the compensated MEMS device output, that is, to obtain a more accurate MEMS device.

[0095] Example

[0096] This method aims to provide a set of RBFNN structural parameter schemes based on the actual data results and target results of the RBFNN-based MEMS device temperature drift error estimation model. The specific implementation schemes include the actual performance test scheme of the RBFNN-based MEMS device temperature drift error estimation model and the model parameter generation model of the RBFNN-based temperature drift error estimation model under Expert-Fuzzy assisted decision.

[0097] Constructing an improved temperature drift error estimation model for capacitive MEMS devices is a priori process. This involves training a known RBFNN-based temperature drift error estimation model for MEMS devices using environmental temperature-related quantities and the temperature drift error itself. Then, the corresponding temperature drift error can be accurately estimated based on the environmental temperature-related quantities. Considering the potentially complex nonlinear relationship between environmental temperature-related quantities and the temperature drift error, a mathematical method capable of accurately describing this complex nonlinear relationship is required to precisely identify the parameters of the improved temperature drift error estimation model for capacitive MEMS devices.

[0098] Figure 3 This is a schematic diagram of the RBFNN neural network structure. Wherein, I... i (i = 1…N) represents the i-th neuron in the input layer of the RBFNN, O i (i = 1…M) represents the i-th neuron in the output layer, H i (i = 1…K) represents the i-th neuron in the hidden layer, X i (i = 1…N) represents the i-th input, Y i(i = 1…M) represents the i-th output. In precise training of RBFNN, the number of neurons in its hidden layer depends on the number of input samples. Therefore, adjusting the hidden layer activation function is the most important way to improve the accuracy of RBFNN. Although nonlinear activation functions can improve accuracy, their computational real-time performance will also decrease significantly. More importantly, adjusting the hidden layer activation function is somewhat arbitrary and requires continuous adjustment based on the measured performance of the RBFNN. Therefore, how to select a more suitable activation function is a key problem that needs to be solved in the parameter identification of the improved capacitive MEMS device temperature drift error estimation model. Table 1 shows the commonly used activation functions of RBFNN.

[0099] Table 1 Commonly Used Activation Functions for RBFNN

[0100]

[0101] based on Figure 1 The measured data of the MEMS accelerometer are given. The performance indicators are the output MSE ratio and calculation time of the MEMS accelerometer before and after temperature drift error compensation. The performance indicators of RBFNN under different combinations of hidden layer and output layer excitation functions are shown in Table 2.

[0102] Table 2 Performance improvement of RBFNN under different activation function combinations

[0103]

[0104]

[0105] As shown in Table 2, different combinations of activation functions can achieve varying degrees of accuracy improvement, and the computation time also increases with the complexity of the activation functions. However, the degree of performance improvement and the computation time cannot be described precisely in mathematical terms, which is the fundamental reason why the determination of activation functions relies on human experience.

[0106] Fuzzy theory, based on fuzzy sets, studies and quantifies concepts that are vague and uncertain, translating them into computer language. It directly expresses human thought processes in a relatively simple mathematical form, employing a less complex mathematical analysis process to perform practical mathematical analysis of complex systems in a way that aligns with human thinking. Therefore, based on expert experience, a fuzzy set classification is constructed to describe the degree of performance improvement and computation time. Fuzzy theory is then used to describe the logical relationships of fuzzy sets and calculate the optimal fuzzy result. Based on this, fuzzy theory is used to fuzzify the data shown in Table 1, resulting in:

[0107] Table 3. Performance Fuzzy Set Representation of RBFNN

[0108]

[0109]

[0110] Where NB represents negative large, NM represents negative medium, NS represents negative small, PS represents positive small, PM represents positive medium, and PB represents positive large. Based on expert experience, the following fuzzy rule table is constructed from Tables 2 and 3:

[0111] Table 4 Fuzzy Rule Table

[0112]

[0113] As shown in Table 4, the fuzzy inputs are the boost factor and computation time, and the fuzzy output is the combination of excitation functions. The fuzzy sets of input 1, input 2, and output are described using the membership function `trimf`. The fuzzy set of input 1 is [NB, NM, NS, PS, PM, PB] = (0, 1, 2, 3, 4, 5), the fuzzy set of input 2 is [NB, PS, PB] = (0, 1, 2), and the output fuzzy set takes values ​​of (0, 10, 20, 30, 40, 50, 60, 70, 80, 90) and is the combination of excitation functions shown in Table 4. A method for accurate parameter identification of the temperature drift error estimation model under Expert-Fuzzy assisted decision-making is constructed based on the MATLAB Fuzzy module. Figure 4 Its Surface diagram is provided.

[0114] To verify the accuracy and versatility of the improved temperature drift error estimation model, a heating experiment was designed using thermal conductivity analysis. A MEMS accelerometer, IIS328DQ, was randomly selected as the test object to measure its temperature drift error. The sensitivity ΔE of the IIS328DQ is known. S It is 0.98 mg / bit, zero-rate temperature change coefficient. The sensitivity is ±0.8 mg / ℃, and the operating temperature range is -40℃ to 85℃. After dimensional changes, the sensitivity temperature coefficient is... It can be represented as:

[0115]

[0116] The temperature control interval ΔT is shown below:

[0117]

[0118] To simplify the testing procedure, let ΔT = 0.4℃. Then, the temperature drift error of the IIS328DQ under static base conditions was tested using a high and low temperature chamber SET-Z-021. The internal length of the high and low temperature chamber L = 0.6m, and its internal air density ρ = 1.293kg / m³. 3 Given a thermal conductivity λ = 0.0267 W / m℃ and a specific heat capacity C = 1.005 kJ / (kg×K), the temperature control time t is... s :

[0119]

[0120] In the formula, b2 = L / 2, b1 = b2 - L′, and L′ is the length of half of the IIS328DQ. Therefore, the high and low temperature chamber needs to control the internal temperature to change slowly with a temperature control time of 29.232 s and a temperature control interval of 0.4 ℃. To further simplify the test procedure, the temperature control time is set to 35 s. In addition, a precision temperature measurement system with a temperature measurement accuracy of ±0.03 ℃ and a temperature measurement frequency of 10 Hz is used to accurately measure the temperature of the MEMS device. Therefore, the specific design of the heating experiment is as follows:

[0121] 1. The IIS328DQ is installed on a base inside the high and low temperature chamber, with the axis to be measured pointing vertically downwards. The reference value is 1g. An external PT1000 temperature sensor is installed on the IIS328DQ. The temperature drift error precision estimation system sends the measured target temperature value and the raw output to the PC via a serial port.

[0122] 2. Lower the ambient temperature of the high and low temperature chamber to -20℃, and after the ambient temperature stabilizes, continuously record the target temperature value and the original output for at least 0.5 hours.

[0123] 3. Heat to 50℃ at a rate of 41℃ / h, i.e., 0.4℃ / 35s. When the measured temperature reaches 50℃, stop heating and maintain a stable temperature for at least 0.5 hours.

[0124] 4. Repeat steps 2 and 3 three times, and randomly select one set of data as the test result.

[0125] Depend on Figure 1 It can be seen that the MSE of the measured data of the MEMS accelerometer IIS328DQ is 1.19 × 10⁻⁶. -2 Furthermore, the calculation time for a single estimation of temperature drift error is 4.02 × 10⁻⁶. -4 S. Assume that after temperature drift error compensation, the root mean square error of the measured data is to be improved by at least three orders of magnitude, i.e., the MSE is 10. -6 The calculation time for a single estimation of temperature drift error is set to 4 × 10. -4 S. After calculation using the Expert-Fuzzy Assisted Decision-Making Accurate Estimation Model, RBFNN adopts "radial basis function / linear function" as the activation function. To accurately evaluate the accuracy of the improved temperature drift error precise estimation model, traditional and improved temperature drift error estimation models are constructed for comparative analysis. The specific construction process is as follows:

[0126] Step 1: Select -20℃ as the reference temperature value, and take the measured data of IIS328DQ at this time as the output reference value of MEMS device;

[0127] Step 2: Calculate the temperature drift error based on the measured data and reference values ​​of IIS328DQ;

[0128] Step 3: Based on ambient temperature and temperature drift error, construct traditional and improved temperature drift error estimation models by training RBFNN.

[0129] Figure 2 Three sets of performance improvement charts for measured data of the IIS328DQ before and after temperature drift error compensation using the traditional and improved models are presented. Based on this, the temperature drift error of the IIS328DQ is effectively eliminated after precise compensation using both the traditional and improved models. However, the measured data after compensation using the improved model shows a more significant convergence trend and less volatility. To more accurately illustrate the performance improvement in temperature drift error estimation, a precision improvement evaluation formula is introduced to numerically analyze the performance improvement:

[0130]

[0131] In the formula, Q is the performance improvement parameter for temperature drift error estimation, and MSE is... C The root mean square error (RMSE) of the output after compensation by the traditional model is given. N The root mean square error (RMSE) of the output results after compensation by the improved model is shown in Table 4. Table 4 presents the RMSE of the MEMS accelerometer output before and after compensation by the traditional model and the improved model, as well as their improvement, and the actual calculation time for estimating the temperature drift error by the improved model.

[0132] Table 5 shows the root mean square error of the test data before and after compensation.

[0133]

[0134] As shown in Table 5, after precise compensation for temperature drift error in the improved model, the average root mean square error of the measured data of IIS328DQ was improved by 6.11 × 10⁻⁶. -6 Its average computation time is 3.44 × 10⁻⁶. -4 All parameters S meet the design specifications, demonstrating that the expert-fuzzy assisted decision-making method for accurately constructing the temperature drift error estimation model can provide an effective reference for optimizing and improving the temperature drift error compensation model, and efficiently, easily, and accurately identify the parameters of the improved model. Furthermore, compared to the traditional temperature drift error estimation model, the improved temperature drift error estimation model improved the root mean square error by 15.92%, 10.06%, and 9.81%, respectively. This indicates that the improved model has higher accuracy and consistency in temperature drift error estimation, and also demonstrates that the improved temperature drift error estimation model has better accuracy in tracing the source of temperature drift errors, effectively decoupling the temperature dependence of MEMS devices and improving their environmental adaptability.

Claims

1. A method for precise identification of parameters in a MEMS device temperature drift error estimation model, characterized in that: It includes the following steps: S1. Initialize the structural parameters of the RBFNN neural network to obtain the initialized MEMS device temperature drift error estimation model based on RBFNN; S2. Construct the hidden layer activation function set and the output layer activation function set of the RBFNN neural network based on the structural parameters of the RBFNN neural network. Cross-merge the hidden layer activation function set and the output layer activation function set to obtain the activation function configuration set. S3. Obtain the measured ambient temperature and corresponding temperature drift error of the MEMS device as training samples. Based on the activation function configuration set and training samples, train the initialized RBFNN-based MEMS device temperature drift error estimation model. Input the ambient temperature and output the temperature drift error. Stop training when the difference between the mean square error of the output temperature drift error and the mean square error of the corresponding actual temperature drift error is 0.0000001. The trained RBFNN-based MEMS device temperature drift error estimation model is obtained. The ambient temperature of the MEMS device is input into the trained RBFNN-based MEMS device temperature drift error estimation model, and the corresponding temperature drift error is output. The output of the MEMS device and the temperature drift error corresponding to the output of the MEMS device are obtained. The difference between the output of the MEMS device and the output temperature drift error is obtained to obtain the compensated output of the MEMS device. The output temperature drift error is replaced with the temperature drift error corresponding to the output of the MEMS device to obtain the compensated temperature drift error. S4. Using the mean square error of the compensated MEMS device output as the accuracy index and the actual calculation time of the compensated temperature drift error estimate as the real-time index, the accuracy index and the real-time index are used as inputs and the set of excitation function configurations are used as outputs to construct an Expert-Fuzzy auxiliary decision-making expert knowledge base. S5. Using fuzzy theory, the accuracy index, real-time index, and activation function configuration set in the Expert-Fuzzy Assisted Decision-Making Expert Knowledge Base are decomposed. The mean square error of the accuracy index and the calculation time of the real-time index are taken as the input fuzzy set, and the corresponding activation function configuration set is taken as the output fuzzy set. The optimal activation function configuration scheme is obtained based on the target values ​​of the accuracy index and the target values ​​of the real-time index output by the compensated MEMS device. S6. Update the structural parameters of the RBFNN neural network according to the optimal activation function configuration scheme, and update the trained RBFNN-based MEMS device temperature drift error estimation model in S3 according to the updated RBFNN neural network structural parameters, so as to obtain the RBFNN-based MEMS device temperature drift error estimation model that satisfies the MEMS device output accuracy index and the MEMS device output real-time index. S7. Obtain the ambient temperature of the MEMS device. Use the RBFNN-based MEMS device temperature drift error estimation model in S6 to output the temperature drift error. Subtract the temperature drift error from the MEMS device output to obtain the compensated MEMS device output, which is the MEMS device.

2. The method for precise identification of parameters of a MEMS device temperature drift error estimation model according to claim 1, characterized in that: The structural parameters of the RBFNN neural network in S1 are: The RBFNN neural network consists of an input layer, a hidden layer, and an output layer. The number of hidden layer neurons is the same as the number of input training samples; The input layer has a single input, and the input layer neurons are in the same dimension as the ambient temperature, meaning the input is the ambient temperature. The output layer has a single output, and the output layer neurons are in the same dimension as the temperature drift error, meaning the output is the temperature drift error. The hidden layer activation function is a radial basis function, and the output layer activation function is a linear function.

3. The method for precise identification of parameters of a MEMS device temperature drift error estimation model according to claim 2, characterized in that: The RBFNN-based MEMS device temperature drift error estimation model initialized in S1: （1） in, This indicates the estimated temperature drift error. Indicates the input quantity. This indicates that the hidden layer activation function is a radial basis function. This indicates that the output layer activation function is a linear function.

4. The method for precise identification of parameters of a MEMS device temperature drift error estimation model according to claim 3, characterized in that: The specific process of S2 is as follows: Hidden layer activation function set: （2） Where tansig is a symmetric sigmoid function, logsig represents a logarithmic sigmoid function, purelin represents a linear function, satlins represents a symmetric linear saturated function, and radbas represents a radial basis function. Output layer activation function set: （3） The set of hidden layer activation functions includes The output layer activation function set includes [number] activation functions. The set of activation functions is obtained by cross-merging the set of activation functions in the hidden layer and the set of activation functions in the output layer. .

5. The method for precise identification of parameters of a MEMS device temperature drift error estimation model according to claim 4, characterized in that: The specific process of S3 is as follows: Based on the measured ambient temperature and corresponding temperature drift error of MEMS devices, a specific excitation function configuration from the set of excitation function configurations is selected sequentially to train the initialized RBFNN-based MEMS device temperature drift error estimation model. The ambient temperature is input, and the temperature drift error is output. Training stops when the difference between the mean square error of the output temperature drift error and the mean square error of the corresponding actual temperature drift error is 0.0000001. This yields the trained RBFNN-based MEMS device temperature drift error estimation model. （4） in, Represents ambient temperature; The ambient temperature of the MEMS device is input into the trained RBFNN-based MEMS device temperature drift error estimation model, and the corresponding temperature drift error is output. The MEMS device output and the corresponding temperature drift error are obtained at this time. The difference between the MEMS device output and the output temperature drift error is obtained to obtain the compensated MEMS device output. The output temperature drift error is replaced with the temperature drift error corresponding to the MEMS device output to obtain the compensated temperature drift error. Thus, the compensated MEMS device output and the compensated temperature drift error under all excitation function configurations are obtained.

6. The method for precise identification of parameters of a MEMS device temperature drift error estimation model according to claim 5, characterized in that: In S4, the mean square error of the compensated MEMS device output is used as the accuracy indicator, and the actual calculation time of the compensated temperature drift error estimate is used as the real-time indicator. The expression is: （5） in, Indicates the output of MEMS devices. This represents the MSE value output by the MEMS device after compensation. This indicates the start time of the temperature drift error estimation calculation. This indicates the termination time of the temperature drift error estimation calculation. This indicates the calculation time required to estimate the temperature drift error.

7. The method for precise identification of parameters of a MEMS device temperature drift error estimation model according to claim 6, characterized in that: The Expert-Fuzzy Decision Support Expert Knowledge Base in S4 is as follows: （6）。 8. The method for precise identification of parameters of a MEMS device temperature drift error estimation model according to claim 7, characterized in that: The specific process of S5 is as follows: S51. Using fuzzy theory, the accuracy indicators, real-time indicators, and activation function configuration sets in the Expert-Fuzzy Assisted Decision-Making Expert Knowledge Base are decomposed into fuzzy sets. The principle of fuzzy set partitioning is mainly based on clustering and classification. That is, the accuracy indicators and real-time indicators are classified into fuzzy sets according to their amplitude. After classification, fuzzy sets named as negative large NB, negative medium NM, negative small NS, positive small PS, positive medium PM, and positive large PB are obtained. The mean square error of the accuracy indicators and the calculation time of the real-time indicators are both input fuzzy sets, and the corresponding activation function configuration sets are output fuzzy sets. S52. Both the input fuzzy set and the output fuzzy set are described using the membership function trimf. The input fuzzy set is fuzzified and its values ​​are obtained according to performance classification, and the output fuzzy set is fuzzified and its values ​​are obtained sequentially according to the excitation function configuration set index. This process yields the target values ​​for accuracy, real-time performance, and excitation function configuration of a certain compensated MEMS device output. The specific process is as follows: For the output of a certain compensated MEMS device, based on the classified fuzzy set, the accuracy index fuzzy set is described by the membership function trimf and used as input 1, where input 1 is the fuzzy set. [NB, NM, NS, PS, PM, PB], the accuracy index target value is (0, 1, 2, 3, 4, 5); the real-time index fuzzy set is described by the membership function trimf and used as input 2, input 2 fuzzy set [NB, PS, PB], the target value of the real-time performance index is (0, 1, 2); the activation function configuration set is described by the membership function trimf and used as the output, the output fuzzy set is... The value can be (0, 10, 20, 30, 40, 50, 60, 70, 80, 90). S53, Input 1 fuzzy set Input 2 fuzzy sets Output fuzzy sets Fuzzy computation is constructed using fuzzy computation rules to obtain corresponding fuzzy results. Based on the fuzzy results, the optimal excitation function configuration scheme is obtained from the excitation function configuration set.

9. The method for precise identification of parameters of a MEMS device temperature drift error estimation model according to claim 8, characterized in that: The formula for determining the value in S52 is: （7）。 10. The method for precise identification of parameters of a MEMS device temperature drift error estimation model according to claim 9, characterized in that: The fuzzy operation rules in S53 are as follows: （8）。

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