CN113392591B - MEMS accelerometer temperature drift error estimation method based on silicon microstructure analysis - Google Patents

MEMS accelerometer temperature drift error estimation method based on silicon microstructure analysis Download PDF

Info

Publication number
CN113392591B
CN113392591B CN202110785860.0A CN202110785860A CN113392591B CN 113392591 B CN113392591 B CN 113392591B CN 202110785860 A CN202110785860 A CN 202110785860A CN 113392591 B CN113392591 B CN 113392591B
Authority
CN
China
Prior art keywords
temperature
mems accelerometer
drift error
polar plate
neural network
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202110785860.0A
Other languages
Chinese (zh)
Other versions
CN113392591A (en
Inventor
齐兵
石帅帅
徐陆通
房磊
陈嘉宇
田帅帅
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Harbin Engineering University
Original Assignee
Harbin Engineering University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Harbin Engineering University filed Critical Harbin Engineering University
Priority to CN202110785860.0A priority Critical patent/CN113392591B/en
Publication of CN113392591A publication Critical patent/CN113392591A/en
Application granted granted Critical
Publication of CN113392591B publication Critical patent/CN113392591B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
    • G01P21/00—Testing or calibrating of apparatus or devices covered by the preceding groups
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/25—Design optimisation, verification or simulation using particle-based methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/004—Artificial life, i.e. computing arrangements simulating life
    • G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/045—Combinations of networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G06N3/084—Backpropagation, e.g. using gradient descent
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/08—Thermal analysis or thermal optimisation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Evolutionary Computation (AREA)
  • General Physics & Mathematics (AREA)
  • General Engineering & Computer Science (AREA)
  • Software Systems (AREA)
  • Artificial Intelligence (AREA)
  • General Health & Medical Sciences (AREA)
  • Mathematical Physics (AREA)
  • Computational Linguistics (AREA)
  • Molecular Biology (AREA)
  • Computing Systems (AREA)
  • Biophysics (AREA)
  • Biomedical Technology (AREA)
  • Data Mining & Analysis (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Health & Medical Sciences (AREA)
  • Computer Hardware Design (AREA)
  • Geometry (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Medical Informatics (AREA)
  • Micromachines (AREA)

Abstract

A MEMS accelerometer temperature drift error estimation method based on silicon microstructure analysis belongs to the field of novel micro-inertia devices. The method solves the problem that the temperature correlation quantity of the temperature drift error of the MEMS accelerometer is not completely explored in the traditional method, so that the non-accurate modeling of the temperature drift error is estimated, and further the estimation of the temperature drift error of the MEMS accelerometer is inaccurate. The invention starts from the microstructure effect, comprehensively analyzes the temperature dependence of the silicon-based material in detail, better decouples the temperature dependence, and can completely improve the environmental adaptability of the MEMS accelerometer by compensating the temperature drift error under the condition of complicated and changeable environmental temperature, and the MEMS accelerometer can accurately, stably and reliably output the acceleration information of the carrier in real time. The invention can be applied to the detection of the acceleration of the carrier.

Description

MEMS accelerometer temperature drift error estimation method based on silicon microstructure analysis
Technical Field
The invention belongs to the field of novel micro-inertial devices, and particularly relates to a MEMS accelerometer temperature drift error estimation method based on silicon microstructure analysis.
Background
With the development and progress of scientific technology, the desire of human beings to acquire renewable resources is increasingly strong. The deep space environment contains abundant mineral products and energy sources, and even a livable environment which can support the survival of earth life can exist. In order to effectively relieve the situation that the ratio of the natural resources occupied by all people on the earth is increasingly urgent, the exploration pace of human resources is gradually changed from the earth surface to deep space, and a large amount of manpower and material resources are invested to solve the current huge survival crisis of the earth, such as lunar soil exploitation, Mars exploration and the like. However, due to the serious threat of the extremely severe deep space environment, the current scientific technology is difficult to support free independent artificial exploration activities, so that the unmanned intelligent device is designed and widely applied, such as all-weather unmanned aerial vehicle monitoring system, relay satellite lunar vehicle, micro satellite, mars vehicle and other space detectors.
Human deep space exploration tasks are mainly focused on mars and the moon. Before the detection task is executed, the unmanned intelligent equipment is transmitted to a target planet to collect environmental information so as to prepare for subsequent successful landing of the human. Because the thrust of the carrier rocket is limited, the carried unmanned intelligent device has the characteristics of small volume, low power consumption, strong environmental adaptability and the like. Precision navigation equipment is a rigid requirement for unmanned intelligent devices for accurate completion of target tasks. Therefore, the micro inertial device is the primary choice of the navigation unit of the unmanned intelligent equipment and can be used for accurately measuring the motion state information and navigation positioning information of the unmanned intelligent device. Based on the above, the unmanned intelligent device can adjust the current operation instruction in real time according to the characteristics of the current operation environment and the operation condition of the unmanned intelligent device, so as to avoid possible risks, such as overturning and sinking of the unmanned detector and crash of the unmanned aerial vehicle. Acceleration information plays an important role in avoiding risks of the unmanned intelligent equipment and running safely and stably, and the fact also indicates that the MEMS accelerometer is a key component of the unmanned intelligent equipment.
MEMS accelerometers are made of silicon-based materials with temperature dependence, whose physical properties change with changes in ambient temperature. As the environment temperature in the space is about-180-130 ℃, the MEMS accelerometer is inevitably excited to output temperature drift errors due to large-range environment temperature change, and the output precision of the MEMS accelerometer is further reduced. The temperature drift error output by the MEMS accelerometer can excite the attitude error, the speed error and the course error of the micro-inertial navigation system to accumulate along with time, and potential hidden dangers are brought to the safety and the stability of the unmanned intelligent equipment. Therefore, the temperature drift error seriously restricts the universal application of the MEMS accelerometer under various complex conditions. Due to the limitation of the current material processing technology, the method can not be realized in a short time when the temperature dependence of the silicon-based material is completely eliminated in the aspect of process optimization, and the accurate and efficient estimation of the temperature drift error of the MEMS accelerometer based on the mathematical model is a main means for improving the output accuracy of the MEMS accelerometer. The traditional MEMS accelerometer temperature drift error model takes the environment temperature related quantity as input and the temperature drift error as output, and the temperature drift error is estimated by the environment temperature related quantity based on a mathematical model. Therefore, comprehensive and accurate environment temperature related quantity is the basis for accurately estimating the temperature drift error and is also the key for accurately describing the temperature drift error, but the temperature related quantity of the MEMS accelerometer temperature drift error is not completely explored in the traditional method, so that non-accurate modeling of the temperature drift error is caused, and the estimation of the MEMS accelerometer temperature drift error is inaccurate. Meanwhile, the mathematical model of the complex structure may reduce the real-time performance of estimation and may introduce a risk of reducing the compensation accuracy due to the lack of time for compensation. Therefore, how to estimate and compensate the temperature drift error in a quasi-fast manner becomes the most effective technical means for improving the environmental adaptability of the MEMS accelerometer.
Disclosure of Invention
The invention aims to solve the problem that the temperature-related quantity of the temperature drift error of an MEMS (micro-electromechanical system) accelerometer is not completely explored in the traditional method, so that the non-accurate modeling of the temperature drift error is estimated, and further the temperature drift error of the MEMS accelerometer is estimated incorrectly, and provides an MEMS accelerometer temperature drift error estimation method based on silicon microstructure analysis.
The technical scheme adopted by the invention for solving the technical problems is as follows: a MEMS accelerometer temperature drift error estimation method based on silicon microstructure analysis specifically comprises the following steps:
step one, acquiring temperature related quantity for estimating temperature drift error of MEMS accelerometer
The sensing circuit of the MEMS accelerometer is provided with a comb tooth structure, the sensing circuit of the MEMS accelerometer is abstracted into a flat capacitor consisting of a movable polar plate and a fixed polar plate, the comb tooth structure deforms when the environmental temperature changes, and the capacitance output deviation before and after the environmental temperature changes, namely before and after the comb tooth structure deforms, is deduced;
acquiring temperature related quantity for estimating temperature drift error of the MEMS accelerometer based on capacitance output deviation before and after comb tooth structure deformation;
step two, constructing a temperature drift error estimation model of the MEMS accelerometer based on the acquired temperature related quantity
And constructing an environment temperature related quantity by using the actually measured environment temperature as the input of a BP (back propagation) neural network, using the actually measured temperature drift error of the MEMS accelerometer as the output of the BP neural network, training the BP neural network, and estimating the temperature drift error of the MEMS accelerometer by using the trained BP neural network.
The invention has the beneficial effects that:
the invention provides an MEMS accelerometer temperature drift error estimation method based on silicon microstructure analysis, which starts from the microstructure effect, comprehensively analyzes the temperature dependence of a silicon-based material in detail, better decouples the temperature dependence, and can completely improve the environmental adaptability of the MEMS accelerometer by compensating the temperature drift error under the condition of complex and changeable environmental temperature, and the MEMS accelerometer can accurately, stably and reliably output the acceleration information of a carrier in real time. The method solves the problems that the temperature related quantity of the MEMS accelerometer temperature drift error is not completely explored, and a model for describing the relation between the environment temperature related quantity and the MEMS accelerometer temperature drift error is not accurate, so that the MEMS accelerometer temperature drift error is not accurately estimated.
Meanwhile, the model for describing the relation between the environmental temperature related quantity and the temperature drift error of the MEMS accelerometer, which is established by the invention, has a simple structure, can realize real-time estimation of the temperature drift error, and does not have the problem of reduction of compensation precision caused by untimely compensation.
Drawings
FIG. 1 is a graph of experimental temperature changes;
FIG. 2 is a graph of the change in the original acceleration values;
FIG. 3 is a diagram of a simulation result of a local optimum of a BP neural network;
FIG. 4 is a graph of the effect of PSO-optimized GA;
FIG. 5 is a comparison graph of the effects of the conventional model and the improved model I;
FIG. 6 is a comparison graph of the effects of the conventional model and the improved model II;
FIG. 7 is a comparison graph of the effects of the conventional model and the improved model III;
FIG. 8 is a comparison chart of genetic iterations of improved models II and III;
FIG. 9 is a schematic diagram of the structure of the MEMS accelerometer at rest in an ideal state;
FIG. 10 is a schematic diagram of the MEMS accelerometer in an ideal situation;
FIG. 11 is a schematic diagram of the MEMS accelerometer at rest in practice;
FIG. 12 is a schematic diagram of the MEMS accelerometer in operation;
FIG. 13 is a flow chart of an improved MEMS device error estimation model.
Detailed Description
In a first specific embodiment, a method for estimating a temperature drift error of a MEMS accelerometer based on silicon microstructure analysis in this embodiment specifically includes the following steps:
step one, acquiring temperature related quantity for estimating temperature drift error of MEMS accelerometer
Because the sensing circuit of the MEMS accelerometer is provided with the comb tooth structure, the sensing circuit of the MEMS accelerometer can be abstracted into a plate capacitor consisting of a movable polar plate and a fixed polar plate, and due to the temperature dependence of a silicon-based material, the comb tooth structure deforms when the environmental temperature changes, so that the internal structure of the MEMS accelerometer changes along with the structural deformation, and the calculation formula based on the plate capacitor is based on the three-dimensional space change
Figure GDA0003538667010000031
Deducing capacitance output deviation before and after the environmental temperature changes, namely before and after the comb tooth structure deforms;
acquiring temperature related quantity for estimating temperature drift error of the MEMS accelerometer based on capacitance output deviation before and after comb tooth structure deformation;
step two, constructing a temperature drift error estimation model of the MEMS accelerometer based on the acquired temperature related quantity
And constructing an environment temperature related quantity by using the actually measured environment temperature as the input of a BP (back propagation) neural network, using the actually measured temperature drift error of the MEMS accelerometer as the output of the BP neural network, training the BP neural network, and estimating the temperature drift error of the MEMS accelerometer by using the trained BP neural network.
The invention indirectly obtains the acceleration information of the carrier sensitive to the MEMS accelerometer through the capacitance value formed by the movable polar plate and the fixed polar plate. Because the silicon-based material has temperature dependence, the structural consistency of the silicon-based material changes along with the change of the environmental temperature, so that the comb tooth structure is deformed in three dimensions, and the output capacitance value and the acceleration of the carrier have deviation. The invention introduces the BP neural network with the advantages of precision and real-time property, and can accurately reproduce the complex nonlinear relation between the temperature related quantity and the temperature drift error of the MEMS accelerometer. The temperature drift error of the MEMS accelerometer is obtained in real time after the temperature drift error model of the MEMS accelerometer is calculated, the temperature drift error is compensated to the MEMS accelerometer in real time, and the MEMS accelerometer output after temperature compensation can be obtained, namely accurate carrier acceleration information is obtained, so that the safety and the stability of the unmanned intelligent equipment are guaranteed.
In a measured environmentTemperature T construction environment temperature related quantity delta T, delta T2、T、T2Constructing an Nx 4 dimensional input matrix by using the two input matrixes and constructing an Nx 1 dimensional target output matrix by using the actually measured temperature drift error of the MEMS accelerometer; and repeatedly training the BP neural network capable of describing the complex nonlinear relation by using the input matrix and the target output matrix until the deviation between the output of the BP neural network and the target output matrix meets the preset error requirement, precisely modeling the temperature drift error model of the BP neural network based on the GA-PSO composite optimization algorithm, and precisely identifying the parameters of the BP neural network.
The second embodiment is as follows: the difference between this embodiment and the first embodiment is that the specific process of the first step is as follows:
when the ambient temperature is T0When the length of the overlap between the movable polar plate and the fixed polar plate is b0The thickness of the comb teeth of the movable polar plate and the fixed polar plate is j0The distance between the comb teeth of the movable polar plate and the comb teeth of the fixed polar plate is u0After simplification, the capacitance Δ C is output0Comprises the following steps:
Figure GDA0003538667010000041
wherein epsilon0Is the dielectric constant;
when the ambient temperature changes to T, the acceleration of the carrier to be detected and the ambient temperature are assumed to be T0The acceleration of the carrier to be detected is the same, and the variation of the environment temperature is delta T-T0Since the silicon-based material has temperature dependence, the internal structure thereof expands or contracts in size. In the conventional model, u is then calculated in consideration of the linear thermal expansion property of the silicon-based material0、j0、h0And b0The value of (d) is changed as:
Figure GDA0003538667010000042
wherein u (T) is u0Corresponding changed value, j (T) is j0Corresponding changed value, h: (T) is h0Corresponding changed value, h0When the ambient temperature is T0When the width of the comb teeth of the polar plate is determined, b (T) is b0Corresponding changed value, alphaTIs a constant value;
therefore, the output deviation y of the theoretical capacitance value of the comb tooth structure of the sensing circuit influenced by the temperature can be calculated under the condition of considering the linear thermal expansion property of the silicon-based material1[α(T)]Comprises the following steps:
Figure GDA0003538667010000051
wherein k is an electrostatic force constant, Δ u is a distance variation between the movable plate comb teeth and the fixed plate comb teeth, and Δ u (t) -u0＝u0αTΔT；
Considering the non-linear thermal expansion property of silicon-based materials, i (T) ═ l0[1+α(T)]In the case of (b), wherein l0Alpha (T) is a nonlinear thermal expansion coefficient, alpha (T). times.10, for the initial length of the structure6＝-5.429+2.79×10-2T-3.226×10-5T2L (T) is the structure length after change only under the influence of the nonlinear thermal expansion of the silicon-based material;
theoretical capacitance value output deviation y of comb tooth structure of sensing circuit caused by nonlinear thermal expansion property of silicon-based material2[α(T)]Comprises the following steps:
Figure GDA0003538667010000052
wherein the content of the first and second substances,
Figure GDA0003538667010000053
i0when the ambient temperature is T0Length of comb teeth of time-actuated polar plate, n0When the ambient temperature is T0Width g of long beam of time-actuated polar plate0When the ambient temperature is T0The length of the comb teeth of the polar plate is timed,
Figure GDA0003538667010000054
m0when the ambient temperature is T0The width of the comb teeth of the movable polar plate,
Figure GDA0003538667010000055
e0when the ambient temperature is T0The distance from the comb teeth of the polar plate to the long beam of the movable polar plate is timed;
the capacitance output deviation before and after the environmental temperature change is:
y1[α(T)]+y2[α(T)]＝f(ΔT、ΔT2、T、T2)
will be Delta T, Delta T2T and T2As a temperature dependent quantity for estimating the MEMS accelerometer temperature drift error.
ΔC0Is the theoretical value of the change in capacitance, y, without taking into account the influence of thermal expansion1[α(T)]Is the output capacitance deviation y after only considering the linear thermal expansion coefficient2[α(T)]Only the output capacitance deviation after the nonlinear thermal expansion coefficient is considered, and then y is calculated1[α(T)]And y2[α(T)]And the sum is used as a temperature drift error, and the obtained temperature drift error is compensated to the output capacitor of the MEMS accelerometer, so that the acceleration information of the carrier is obtained.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the difference between the present embodiment and the first or second embodiment is that the BP neural network uses crtbp function to complete initialization of weight and bias parameters, uses GA (genetic) algorithm to select, intersect and mutate the initialized weight and bias parameters, then uses bs2rv function to decode the selected, intersected and mutated data, and uses the decoded data as the initialized particle parameters of PSO (particle swarm optimization) algorithm;
and after the output of the PSO algorithm is decoded, the decoding result is used as the initial weight and the bias of the BP neural network.
And solving the mean square error of the fit fitness function based on the measured data, the initial weight and the bias to serve as the particle fitness, and guiding the PSO algorithm to carry out speed and position updating operation.
Updating operator v with velocityk+1＝vk+c1r1(pk-xk)+c2r2(gk-xk) Completing the update of the particle velocity by using the position update operator xk+1＝xk+vk+1And finishing updating the particle position, and decoding the parameters obtained by continuous iteration to be used as the initial weight and the bias of the BP neural network. Wherein v iskRepresenting the current particle velocity, vk+1Represents the updated particle velocity, xkRepresenting the position of the current particle in the solution space.
A GA algorithm is introduced to optimize a BP neural network operation structure so as to eliminate the potential risk of local optimal values of the BP neural network, a PSO algorithm is introduced to solve the problem of probabilistic disorder of the GA algorithm, a BP neural network temperature drift error model based on the GA-PSO composite optimization algorithm is established based on the problem, and accurate identification of a MEMS accelerometer temperature drift error estimation model is guaranteed to have global optimality.
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between this embodiment and the first to third embodiments is that the GA algorithm uses a select selection function to complete the selection of data, uses a mut mutation function to complete the mutation of data, uses a recombin function to complete the recombination of data, and uses a reins function to obtain a new population.
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the difference between the first embodiment and the fourth embodiment is that the initialized weight and the bias parameter are processed by GA algorithm and PSO algorithm to obtain parameter x, and after decoding x, the decoding result is used as the initial weight and bias of the BP neural network;
Figure GDA0003538667010000071
where n denotes the number of iterations of the PSO algorithm, i ═ 1,2, … n, viRepresents the particle velocity, x, of the PSO algorithm after the ith iterationiRepresenting the position, x, of the particle after the ith iteration of the PSO algorithmjWhen j iteration of the BP algorithm is represented, the weight and the position of the bias of the BP neural network in a solution space are represented, eta is a learning rate, m is the iteration number of BP neural network training, j is the search number, j is 1,2, …, m and E (x)j) Is xjN denotes the number of iterations of the PSO algorithm, c1And c2Is a constant number r1And r2Is a random value between 0 and 1, piIs the historical optimum value, g, of the particle itself after the first i iterationsiIs the historical optimum value of the particle swarm after the previous i iterations.
A GA algorithm is introduced to optimize a BP neural network operation structure so as to eliminate the potential risk of local optimal values of the BP neural network, a PSO algorithm is introduced to solve the problem of probabilistic disorder of the GA algorithm, a BP neural network temperature drift error model based on the GA-PSO composite optimization algorithm is established based on the problem, and accurate identification of a MEMS accelerometer temperature drift error estimation model is guaranteed to have global optimality.
Based on the initial weight and the bias of the base temperature drift error model updated by the PSO algorithm in real time, the mean square error of the initial weight and the bias is obtained as the particle fitness by utilizing a fit fitness function based on the measured data, the initial weight and the bias, and the PSO algorithm is guided to carry out speed and position updating operation.
Other steps and parameters are the same as in one of the first to fourth embodiments.
The sixth specific implementation mode: the present embodiment differs from one of the first to fifth embodiments in that the decoding of the output of the PSO algorithm is performed by using the bs2rv function.
The seventh embodiment: the difference between this embodiment and one of the first to sixth embodiments is that the MEMS accelerometer takes heat conduction measures and the temperature sensor is tightly mounted on the surface of the MEMS accelerometer.
In this embodiment, the purpose of taking heat conduction measures by the MEMS accelerometer is to accurately obtain the ambient temperature related quantity, and ensure that the ambient temperature in the high-low temperature chamber is completely conducted to the MEMS accelerometer. In order to accurately obtain the temperature drift error of the MEMS accelerometer, a precise temperature measurement system is adopted, and a temperature sensor is tightly arranged on the surface of the MEMS accelerometer. The measurement precision of the precision temperature measurement system is more than 2 times higher than the environmental temperature change precision, the measurement frequency is higher than the output frequency of the MEMS accelerometer, and under the normal condition, the precision temperature measurement system with the temperature measurement precision of +/-0.01 ℃, the temperature control precision of +/-0.01 ℃ and the temperature measurement frequency of 1Hz is selected.
Other steps and parameters are the same as those in one of the first to sixth embodiments.
Examples
The invention provides a MEMS accelerometer temperature drift error precise modeling method based on microstructure thermal effect analysis, which specifically comprises MEMS accelerometer internal structure deformation analysis based on microstructure thermal effect, BP neural network temperature drift error model modeling based on GA-PSO composite optimization algorithm and parameter precise identification thereof.
(1) MEMS accelerometer internal structure deformation analysis based on microstructure thermal effect
The structure of a sensing circuit of the MEMS accelerometer changes along with the ambient temperature, and the capacitance measurement error of the sensing circuit is mainly considered as a key factor. Taking comb teeth of the sensing circuit as an example, due to the temperature dependence of the silicon-based material, the comb teeth can generate structural deformation in a three-dimensional space along with the change of the environmental temperature and the change of the structural consistency, which inevitably causes the change of the sensitive capacitance value of the sensing circuit. Starting from the analysis of the thermal effect of the microstructure, the simulation analysis is carried out on the three-dimensional deformation of the comb tooth structure of the sensing circuit at different environmental temperatures. The accuracy of the known MEMS accelerometer is mainly determined by a sensing circuit, the sensing circuit has a comb-shaped structure, the sensing circuit can be abstracted into a plate capacitor formed by a movable electrode plate and a fixed electrode plate, and the acceleration of a carrier can be indirectly measured by directly measuring the capacitance value of the plate capacitor. When the input acceleration is not changed, the output acceleration value a of the MEMS accelerometer0Is constant and has a capacitance variation Δ C with the MEMS accelerometer0Correlation, i.e. a0∝ΔC0. Since the ambient temperature affects the internal structure and thus excites the bias Δ a (T), the output a (T) of the MEMS accelerometer at the ambient temperature T can be expressed as：
a(T)＝a0+Δa(T) (1)
At this time, the MEMS accelerometer output can also be expressed as:
a(T)∝ΔC(T) (2)
the formula (1) is simplified to replace the formula (2) to obtain:
Δa(T)∝[ΔC0-ΔC(T)] (3)
and (3) analyzing the influence of the environment temperature change on the temperature drift error of the MEMS accelerometer by applying a nonlinear thermal expansion mathematical model based on the relation between the acceleration and the capacitance value.
Analysis of static base condition under internal structure non-expansion condition
The internal structure of the MEMS accelerometer in the static base condition is shown in fig. 9. Wherein, b is the length of the overlapping of the movable polar plate and the fixed polar plate, e is the distance between the comb teeth of the fixed polar plate and the long beam of the movable polar plate, h is the width of the comb teeth of the fixed polar plate, g is the length of the comb teeth of the fixed polar plate, u is the distance between the comb teeth of the movable polar plate and the fixed polar plate, m is the width of the comb teeth of the movable polar plate, n is the width of the long beam of the movable polar plate, j is the thickness of the movable polar plate and the fixed polar plate, and i is the length of the comb teeth of the movable polar plate. If the thermal expansion of the silicon-based material is not considered, the comb teeth are in middle balance, and at the moment, the capacitance value C of the accelerometer detected by the sensing circuit01Comprises the following steps:
C01＝C1+C2+C3 (4)
in the formula, C1Representing the capacitance between the short side of the comb teeth of the fixed polar plate and the long beam of the fixed polar plate; c2Representing the capacitance value between the upper long edge of the fixed polar plate comb teeth and the lower long edge of the movable polar plate comb teeth; c3The capacitance value between the long side below the fixed polar plate comb teeth and the long side above the movable polar plate comb teeth is represented, and the following expression holds at this time:
Figure GDA0003538667010000091
substituting equation (5) into equation (4) can yield:
Figure GDA0003538667010000092
analysis of moving base condition under internal structure non-expansion condition
When the MEMS accelerometer works on the moving base, the balance state of the comb structure is broken, the moving plate and the fixed plate are in the unbalanced state, and the comb of the moving plate deviates from the balance position, and fig. 10 shows an internal structure schematic diagram of the MEMS accelerometer under the moving base condition under an ideal condition. At this time, the capacitance value C detected by the sensing circuit1、C2、C3Can be expressed as:
Figure GDA0003538667010000093
formula (7) is replaced by formula (4), and capacitance value C of MEMS accelerometer02Can be expressed as:
Figure GDA0003538667010000094
the capacitance variation Δ C in an ideal state can be obtained by substituting the formula (6) and the formula (8) into the formula (2)0Comprises the following steps:
Figure GDA0003538667010000095
static base condition analysis under internal structure expansion conditions
Since semiconductor silicon has temperature dependence, the internal structure exhibits three-dimensional deformation with ambient temperature change, as shown in fig. 11. When the accelerometer is in a static base condition, the capacitance C of the accelerometer changes with ambient temperature03Can be expressed as:
C03(T)＝C1(T)+C2(T)+C3(T) (10)
at the moment, the size of the comb teeth is expanded or contracted, and the deformation condition of the internal structure is analyzed based on a silicon-based material thermal expansion model as follows:
Figure GDA0003538667010000101
in the formula (I), the compound is shown in the specification,
Figure GDA0003538667010000102
the formula (11) can be substituted for the formula (7):
Figure GDA0003538667010000103
the formula (12) is replaced by the formula (10), and the MEMS accelerometer outputs a capacitance value C after the ambient temperature changes03(T) can be expressed as:
Figure GDA0003538667010000104
the difference between formula (13) and formula (6) is used to obtain the carrier acceleration, which is:
Figure GDA0003538667010000105
formula simplification of equation (14) yields:
Figure GDA0003538667010000111
in the formula (I), the compound is shown in the specification,
Figure GDA0003538667010000112
similarly, the following expression holds:
Figure GDA0003538667010000113
from formulas (15) and (16):
Figure GDA0003538667010000114
from equation (17), the capacitance value varies with the ambient temperature, which is the temperature drift error of the MEMS accelerometer.
Dynamic base condition analysis under internal structure expansion condition
Under the condition of the movable base, the balance state of the comb tooth structure is broken, the movable polar plate and the fixed polar plate are in the non-balance state, and the comb teeth deviate from the balance position. Since semiconductor silicon has temperature dependency, its internal structure is deformed three-dimensionally with ambient temperature change, and fig. 12 shows the deformed internal structure. At this time, C1(T)、C2(T)、C3(T) can be expressed as:
Figure GDA0003538667010000115
the capacitance C can be obtained by substituting formula (18) for formula (10)04(T) is:
Figure GDA0003538667010000116
by subtracting the formula (19) from the formula (13), the capacitance value variation Δ c (t) under actual conditions is:
Figure GDA0003538667010000121
reduction of Δ C by the method represented by formula (17)0Δ c (t) available:
Figure GDA0003538667010000122
as can be seen from equation (21), when the accelerometer operates on a moving base, there is a deviation between the actual value and the expected value of the capacitance, which is related to α (T) and varies with the ambient temperature. Therefore, the following equation holds:
Δa(T)∝{ΔC0-y6[α(T)]}∝f[α(T)] (22)
based on equations (22) and (3), the following conclusions can be drawn that the temperature drift error of the output of the MEMS accelerometer is related to the temperature T and T2And (4) correlating. By combining the complete description of the traditional model on the environmental temperature related quantity and further optimizing the temperature drift error compensation model consideration of the MEMS accelerometer, the improved MEMS device error estimation model can be constructed based on the method and comprises the following steps:
ΔEMEMS＝f(ΔT、ΔT2、T、T2) (23)
(2) BP neural network temperature drift error model precise modeling and parameter precise identification based on GA + PSO optimization
On the premise of accurately measuring the temperature drift error of the MEMS accelerometer and the related quantity of the ambient temperature, how to accurately identify the complex nonlinear relation between the temperature drift error of the MEMS accelerometer and the related quantity of the ambient temperature is the key for accurately estimating and compensating the temperature drift error. Typically, the operating environment of a MEMS accelerometer is at a temperature of-20 ℃ to 50 ℃. In order to accurately test the temperature drift error of the MEMS accelerometer, the variation range of the environmental temperature is required to be-20-50 ℃, the environmental temperature is required to be kept stable for a period of time at the initial stage and the final stage of the test experiment, and the test value at the initial stage of the test experiment is used as the reference environmental temperature. Therefore, the accelerometer and the gravity acceleration are kept consistent in direction by using the static base experiment platform, and the MEMS accelerometer outputs a reference value as the gravity acceleration. Temperature-dependent quantities Δ T, Δ T shown by equation (23)2、T、T2And the temperature drift error of the MEMS accelerometer can have a complex nonlinear relation, so that the application of a multi-input multi-output nonlinear model with high precision and good real-time performance to fit the environment temperature related quantity and the complex nonlinearity of the temperature drift error of the MEMS accelerometer is necessary. The BP neural network is a multi-layer feedforward network (comprising an input layer, a hidden layer and an output layer) trained according to an error inverse propagation algorithm, takes a steepest descent method as a learning rule, and does not carry out back propagationAnd (4) adjusting the weight and the bias of the network to minimize the sum of squares of errors so as to approach the current model with any precision. The BP neural network can learn and store a large number of input-output mode mapping relations without a priori revealing mathematical equations describing the mapping relations; the method has the structural characteristics of multiple inputs and multiple outputs, and is generally suitable for various types of mathematical models. Therefore, the BP neural network is very suitable for accurately identifying the complex nonlinear relation between the MEMS accelerometer temperature drift error and the environment temperature related quantity.
And continuously training the BP neural network based on the input vector and the output vector, and finishing the training of the BP neural network when the mean square error between the actual output and the target output of the BP neural network is minimum. However, there is a potential risk of local minimum in the BP neural network, and fig. 3 shows a simulation result of local optimum of the BP neural network. Wherein, 2 parameters are selected from the weight parameters and are marked as weight parameter 1 and weight parameter 2. The X axis represents the value of the weight parameter 1, the Y axis represents the value of the weight parameter 2, the Z axis represents the corresponding pre-compensation and post-compensation mean square error when the weight parameters 1 and 2 take different values, and the concave area represents that the minimum value, namely the optimal value, exists in the area. As shown in fig. 3, there are a plurality of depressed areas, i.e., a plurality of local optimum values, in the simulation result. The local optimal value may cause the constructed BP neural network to be a non-optimal model, and further cause the estimation result to be a non-optimal result. Suppose X0Representing the positions of the weights ω and the bias b of the BP neural network in the cost function solution space, the objective function of the BP neural network can be represented as Y ═ f (X)0) When Y is not equal to the desired value
Figure GDA0003538667010000131
Then, search for X0The cost function of (a) can be expressed as:
Figure GDA0003538667010000132
x can be obtained by the position update operator0The position x in the solution space is:
Figure GDA0003538667010000133
in the formula, k is the number of searching times (k < m); eta is the learning rate; x is the number of0Is X0The initial position of (a). When x is shown in FIG. 30When located in the region d, a locally optimal solution X of X can be obtained based on the formula (25)d(ii) a When x is0When the solution is positioned in the area a, the local optimal solution X of X can be obtaineda. Therefore, the BP neural network adopts the gradient algorithm to iteratively solve x, and the local optimal problem can occur due to the defects of the iterative algorithm in the iterative process, wherein x0Is a potential factor causing the BP neural network to be locally optimal. Assuming that an aggregate of x is used as a population, the weight omega and the bias b of the neural network are used as chromosome genes of individual organisms, simulating the natural evolution process of the population by using a GA genetic algorithm, carrying out operations such as crossing and mutation on the chromosome genes of the individual organisms in the population, and converting the global optimal solution problem for solving the BP neural network into the search for genes with optimal fitness.
The genetic algorithm adopts a binary coding mode, each binary bit represents a gene value, and binary decoding values of the weight omega and the bias b are substituted into an initial position x0In (1) obtaining
Figure GDA0003538667010000143
In the formula, N1Representing the binary digit number of binary coding by the weight omega and the bias b. Obtaining offspring x by using crossover operator of genetic algorithmcUsing mutation operators to randomly select xciAnd mutating the gene value of one or more loci to obtain x'ci. Then, decode x'ciObtaining a correction weight omega 'and a correction bias b' of the BP neural network, substituting the correction weight omega 'and the correction bias b' into the BP neural network, and calculating an individual x 'by a fitness function of the following formula'ciFitness in the population:
Figure GDA0003538667010000141
iteration is carried out through continuous cross variation, and an individual x with high fitness is selectedoldObtaining the expected initial solution position x of the BP neural network by the following formulanew：
xnew＝xold+xc (28)
The core of the GA algorithm lies in the cross variation of genes. As shown in fig. 3, when x is being processednewAfter the value range of (a) is reduced to a, b and c areas, the value range of (b) is defined by xnewTo the global optimal solution xaThe approximation process is dominated by a mutation operator, while the mutation process of the GA algorithm is a probabilistic unordered process, which results in more iterations required to obtain a global optimum value, i.e., the local optimization capability of the GA algorithm is poor. In order to solve the local optimization problem of the GA algorithm, the calculation process of optimizing the GA algorithm by the PSO algorithm is introduced, a brand-new GA + PSO algorithm is constructed, the movement of the whole population generates the disordered-to-ordered evolution from the GA algorithm in a solution space by sharing information by individuals in the population, and the evolution from x to x is calculatednewAnd converting the process of solving the global optimal value into a bird group foraging process. PSO algorithm selects x after GA algorithm cross mutationnewInputting x as the initial position of the particle swarm0. Initial particle position x obtained by velocity update operator and position operator0Comprises the following steps:
Figure GDA0003538667010000142
in the formula, c1And c2Is a constant number r1And r2Is a random value between 0 and 1, pkIs the historical optimum of the particle itself, gkIs a historical optimum value of the particle swarm, and n represents the iteration number of the PSO algorithm. At this time, formula (29) is substituted into formula (25) to obtain the cost function solution x of the BP neural network model as follows:
Figure GDA0003538667010000151
to verify the optimization effect of the PSO algorithm on the GA algorithm, the following minimum value of the following formula is calculated by using the GA algorithm and the GA + PSO algorithm, respectively:
z＝-ysin(2πx)-xcos(2πy) (31)
wherein, the limiting parameter value range is as follows: x ∈ [ -2,2], y ∈ [ -2,2 ]. FIG. 4 shows a PSO-optimized GA effect graph. The BP neural network optimized based on the GA algorithm and the PSO algorithm has the following two advantages:
(1) the BP neural network can avoid local minima. Since the core expression of the GA algorithm is selection, mutation, and selection, even when there are a plurality of local optimal values, the result is globally optimal.
(2) The GA algorithm has faster iteration effect. After the PSO algorithm is introduced, the movement of the whole population is subjected to the evolution from the disorder to the order of the GA algorithm in a solution space by utilizing the sharing of the information by the individuals in the population, so that the iteration efficiency of the GA algorithm is greatly improved.
In summary, the precise modeling process of the BP neural network temperature drift error model based on GA + PSO optimization is shown in fig. 13, and the construction process specifically includes:
step 1: the particle position and velocity are initialized. Generate 100 particles xi(i ═ 1,2 … 100), as initial weights and biases for the BP neural network, and as the position (x) of the particle in the PSO algorithm blocki)2＝…(ωi)2…(bi)2… are provided. At the same time, for particle xiIn the range of [ -0.5, 0.5 [)]Generating 30 random arrays as initial speed v0。
Step 2: and updating individual extremum and group extremum. According to the particle position (x) in step 1i)2And velocity v0The velocity and position of the particles are updated. And updating the individual fitness extreme value gbest and the group fitness extreme value zbest according to the fitness value xfit of the particle. If xfit t>gbest, then xfit is given to gbest. If gbest<zbest, then gbest is assigned to zbest.
Step 3: it is decided whether a termination condition is satisfied. Generating new clusters according to the result of step 2x′i(i is 1,2 … 100), decoding based on equation (27) to obtain a weight ω 'and an offset b' of the BP neural network, and taking ω 'and b' as the weight ω of the BP neural network0And bias b0The hidden layer transfer function ρ is the tansig function:
Figure GDA0003538667010000152
based on this, the excitation of each hidden cell ojSatisfies the following conditions:
Figure GDA0003538667010000161
the weight adjustment amount Δ ω satisfies the following equation:
Δω＝η·δ·ν (34)
wherein η is learning rate, η is made to be 0.01, δ is local gradient, and ν is upper layer output signal. Neural network output yiSatisfies the following conditions:
Figure GDA0003538667010000162
according to yiValue calculating the iterative effect MSE of GA + BP this time, if the MSE value is iterated continuously for three times and has not changed, then meet the termination condition, obtain weight omega 'and bias b' optimum value of BP neural network; if not, the next step is carried out.
Step 4: crossover and mutation. And (3) calculating the fitness of the weight and the bias according to the test error in the step (3), selecting a chromosome with high fitness, carrying out intersection and variation, taking a group obtained by the intersection variation as an initial position of the particles in the particle swarm, and continuing to execute the step (1).
And (4) after the steps 1-4 are executed, finishing the construction of the BP neural network temperature drift error model based on GA + PSO optimization. Based on this, the parameter identification process of the improved MEMS accelerometer temperature drift error estimation model is specifically as follows:
1. and respectively implementing two groups of temperature rise and fall experiments, wherein one group of temperature experiment data is taken as a training sample set, and the other group of temperature experiment data is taken as a verification sample set. The specific experimental steps are as follows:
step 1: the MEMS accelerometer is attached to and fixed on a precision turntable in a high-low temperature box through silicone grease, and a temperature sensor in a precision temperature measurement system is tightly attached to the MEMS accelerometer to enable the measured temperature to be TaAnd the MEMS accelerometer output is DaAnd starting the wireless transmission module and the USB redundancy backup storage module, and simultaneously preparing a PC (personal computer) to receive the recorded data in real time.
Step 2: reducing the ambient temperature of the high-low temperature box to-20 ℃, and starting to store T after the test data of the MEMS accelerometer and the precision temperature measurement system are stabilized for 1haAnd Da。
Step 3: the temperature of the high-low temperature box rises from-20 ℃ to 50 ℃ at the speed of 18 ℃/h when the temperature T is higher than the temperature of the low-temperature boxaAfter the temperature reaches 50 ℃, the experiment is stopped after the environmental temperature is kept stable for 1h, and simultaneously all test data T in the temperature rise process are recordedaAnd Da。
Step 4: repeating the steps (3) to (4) for three times, and simultaneously recording all the test data TaAnd Da。
2. And subtracting the reference output from the actual output of the MEMS accelerometer in the training sample set to obtain the MEMS accelerometer temperature drift error sample set. Subtracting the actual environment temperature of the MEMS accelerometer from the reference temperature of the MEMS accelerometer in the training sample set to obtain an environment temperature variation sample set delta T of the MEMS accelerometer, and multiplying the environment temperature sample set delta T of the MEMS accelerometer by itself to obtain a variation square term sample set delta T2Multiplying the ambient temperature sample set T by itself to obtain T2。
3. By Δ T, Δ T2、T、T2And (3) inputting the BP neural network, taking the temperature drift error of the MEMS accelerometer as the BP neural network output, taking the parameters processed by the GA-PSO optimization algorithm as the initial parameter values of the BP neural network, and training the BP neural network until the difference between the output of the BP neural network and the temperature drift error of the corresponding MEMS accelerometer meets the design requirement.
And 4, subtracting the output of the BP neural network from the corresponding output of the MEMS accelerometer, thereby obtaining a result after the temperature drift error of the MEMS accelerometer is compensated.
Based on all the steps, the measured data shown in the figures 1 and 2 are used for training a temperature drift error model, and the BP neural network structure and the parameters thereof are accurately identified.
Then, the measured values are calculated as Δ T and Δ T2、T、T2And (2) inputting the BP neural network, taking the temperature drift error of the MEMS accelerometer as the BP neural network output, and constructing an improved MEMS accelerometer temperature drift error estimation model (the first improved model is only based on the temperature related quantity obtained by the invention and the BP neural network, and is not optimized by adopting GA and PSO algorithms) as a performance reference for verifying the GA-PSO optimization algorithm. And (3) checking the first improved model by adopting a verification sample set, and simultaneously introducing an MSE (mean square error) value performance compensation evaluation formula to evaluate the improvement optimization degree of the model:
Figure GDA0003538667010000171
wherein, MSDoldRepresenting a traditional model for compensating temperature drift errors of MEMS accelerometers based on ambient temperature T and BP neural networks, MSDnewRepresents an improved MEMS accelerometer temperature drift error compensation model based on silicon microstructure analysis, and Q represents the optimization degree of compensation performance.
MSD＝MSE(x-x′) (37)
Wherein x represents a sample to be evaluated, x 'represents a reference value of the sample to be evaluated, MSE is a mean square error algorithm, and MSD is a mean square error between x and x'. The mean square error visually reflects the dispersion degree between the sample to be evaluated and the reference value thereof, and the smaller the mean square error is, the smaller the dispersion degree between the sample to be evaluated and the reference value thereof is.
Based on the above, the performance of the improved model is evaluated by a compensation performance evaluation formula by taking a traditional model based on the BP neural network (only adopting the temperature T and the BP neural network) as a reference and comparing MSE values before and after the improvement of the analysis model. Table 1 shows the compensation performance and the evaluation result Q of the conventional model and the improved model I1FIG. 5 showsA comparison graph of the traditional model and the improved model is shown.
TABLE 1 comparison of Compensation Performance between conventional model and improved model one
Figure GDA0003538667010000181
As shown in Table 1, compared with the conventional model, the temperature drift error compensation accuracy of the first improved model is improved, and the accuracy is improved by 5.72% at most. This indicates a completely new ambient temperature related quantity TR(ΔT、ΔT2、T、T2) The temperature dependence of the silicon-based material is well decoupled, and the environmental adaptability of the MEMS accelerometer is remarkably improved.
In order to explain the performance improvement degree of the GA algorithm and the GA-PSO algorithm on the BP neural network, training of an improved MEMS accelerometer temperature drift error estimation model (an improved model II, an improved MEMS accelerometer temperature drift error estimation model (an improved model III) based on the temperature related quantity and the BP neural network obtained by the invention and optimized by the GA algorithm) and an improved MEMS accelerometer temperature drift error estimation model (an improved model III, an improved model II and an improved model III) based on the GA-PSO algorithm is respectively carried out on three groups of experimental data, and the evaluation results Q of the traditional model, the improved model II and the improved model III are respectively2、Q3The comparison results are shown in table 2, the two-comparison graph of the conventional model and the improved model is shown in fig. 6, and the three-comparison graph of the conventional model and the improved model is shown in fig. 7.
TABLE 2 comparison of Compensation Performance between conventional model and improved model two and improved model three
Figure GDA0003538667010000182
As shown in table 2, it can be calculated according to the optimization degree calculation formula that the compensation performance of the second improved model is improved by 15.06% compared with the conventional model, and the compensation performance of the third improved model is improved by 16.01% compared with the conventional model. As shown in FIGS. 6 and 7, the temperature error estimation accuracy of the MEMS accelerometer is higher after the GA algorithm and the GA-PSO algorithm are introduced into the improved model. In addition, compared with the iteration process of the improved model II, the improved model III after the GA-PSO algorithm is introduced obtains a better iteration effect with fewer iteration times. FIG. 8 shows a comparison of genetic iterations for improved model two and improved model three.
As shown in fig. 8, the left ordinate represents the MSE value of each generation of the second improved model and the third improved model on the premise that the iteration number increases, the right ordinate represents the optimization degree of the PSO algorithm to the iteration process, and the optimization degree calculation formula of the iteration effect is as follows:
Figure GDA0003538667010000191
it can be known from the corresponding curve of the coordinates on the right side of fig. 8 that after the GA algorithm is iterated to 50 times, the error of the second improved model gradually approaches the minimum value, and after the GA-PSO compounding is introduced, the error of the third improved model approaches the minimum value when the iteration is iterated to 30 generations, the third improved model optimizes the iteration process of the second improved model by 40%, and the real-time performance and the effectiveness of temperature drift error estimation are effectively improved.
In summary, the new environmental temperature correlation TR(ΔT、ΔT2、T、T2) The temperature dependence of the silicon-based material is well decoupled, and the environmental adaptability of the MEMS accelerometer is remarkably improved by the GA-PSO optimized BP neural network temperature drift compensation model.
Therefore, the improved MEMS accelerometer temperature drift error estimation model based on silicon microstructure analysis ensures stable and accurate operation of the MEMS accelerometer, effectively decouples the temperature dependence of silicon-based materials, and remarkably improves the environmental adaptability of the MEMS accelerometer.
The above-described calculation examples of the present invention are merely to explain the calculation model and the calculation flow of the present invention in detail, and are not intended to limit the embodiments of the present invention. It will be apparent to those skilled in the art that other variations and modifications of the present invention can be made based on the above description, and it is not intended to be exhaustive or to limit the invention to the precise form disclosed, and all such modifications and variations are possible and contemplated as falling within the scope of the invention.

Claims (5)

1. A MEMS accelerometer temperature drift error estimation method based on silicon microstructure analysis is characterized by specifically comprising the following steps:
step one, acquiring temperature related quantity for estimating temperature drift error of MEMS accelerometer
The sensing circuit of the MEMS accelerometer is provided with a comb tooth structure, the sensing circuit of the MEMS accelerometer is abstracted into a flat capacitor consisting of a movable polar plate and a fixed polar plate, the comb tooth structure deforms when the environmental temperature changes, and the capacitance output deviation before and after the environmental temperature changes, namely before and after the comb tooth structure deforms, is deduced;
acquiring temperature related quantity for estimating temperature drift error of the MEMS accelerometer based on capacitance output deviation before and after comb tooth structure deformation;
the specific process of the step one is as follows:
when the ambient temperature is T0When the length of the overlap between the movable polar plate and the fixed polar plate is b0The thickness of the comb teeth of the movable polar plate and the fixed polar plate is j0The distance between the comb teeth of the movable polar plate and the comb teeth of the fixed polar plate is u0The capacitance Δ C outputted at this time0Comprises the following steps:
Figure FDA0003538666000000011
wherein epsilon0Is the dielectric constant;
when the ambient temperature changes to T, the acceleration of the carrier to be detected and the ambient temperature are assumed to be T0The acceleration of the carrier to be detected is the same, and the variation of the environment temperature is delta T-T0Then u in consideration of the linear thermal expansion property of the silicon-based material0、j0、h0And b0The value of (d) is changed as:
Figure FDA0003538666000000012
wherein u (T) is u0Corresponding changed value, j (T) is j0Corresponding changed values of h (T) h0Corresponding changed value, h0When the ambient temperature is T0When the width of the comb teeth of the polar plate is determined, b (T) is b0Corresponding changed value, alphaTIs a constant value;
under the condition of considering the linear thermal expansion property of the silicon-based material, the output deviation y of the theoretical capacitance value of the comb tooth structure of the sensing circuit under the influence of temperature1[α(T)]Comprises the following steps:
Figure FDA0003538666000000021
wherein k is an electrostatic force constant, Δ u is a distance variation between the movable plate comb teeth and the fixed plate comb teeth, and Δ u (t) -u0＝u0αTΔT；
Considering the non-linear thermal expansion property of silicon-based materials, i (T) ═ l0[1+α(T)]In the case of (b), wherein l0Alpha (T) is a nonlinear thermal expansion coefficient, alpha (T). times.10, for the initial length of the structure6＝-5.429+2.79×10-2T-3.226×10-5T2L (T) is the structure length after change only under the influence of the nonlinear thermal expansion of the silicon-based material;
theoretical capacitance value output deviation y of comb tooth structure of sensing circuit caused by nonlinear thermal expansion property of silicon-based material2[α(T)]Comprises the following steps:
Figure FDA0003538666000000022
wherein the content of the first and second substances,
Figure FDA0003538666000000023
i0when the ambient temperature is T0Length of comb teeth of time-actuated polar plate, n0Is when the environment isTemperature of T0Width g of long beam of time-actuated polar plate0When the ambient temperature is T0The length of the comb teeth of the polar plate is timed,
Figure FDA0003538666000000024
m0when the ambient temperature is T0The width of the comb teeth of the movable polar plate,
Figure FDA0003538666000000025
e0when the ambient temperature is T0The distance from the comb teeth of the polar plate to the long beam of the movable polar plate is timed;
the capacitance output deviation before and after the environmental temperature change is:
y1[α(T)]+y2[α(T)]＝f(ΔT、ΔT2、T、T2)
will be Delta T, Delta T2T and T2As a temperature related quantity for estimating the temperature drift error of the MEMS accelerometer;
step two, constructing a temperature drift error estimation model of the MEMS accelerometer based on the acquired temperature related quantity
Constructing an environment temperature related quantity by using the actually measured environment temperature as an input of a BP (back propagation) neural network, using the actually measured temperature drift error of the MEMS accelerometer as an output of the BP neural network, and estimating the temperature drift error of the MEMS accelerometer by using the trained BP neural network after the BP neural network is trained;
the BP neural network completes initialization of weight and bias parameters by using a crtbp function, selects, crosses and mutates the initialized weight and bias parameters by using a GA algorithm, decodes the selected, crossed and mutated data by using a bs2rv function, and takes the decoded data as the initialized particle parameters of the PSO algorithm;
and after the output of the PSO algorithm is decoded, the decoding result is used as the initial weight and the bias of the BP neural network.
2. The method of claim 1, wherein the GA algorithm uses a select selection function to complete data selection, a mut variation function to complete data variation, a recombin function to complete data recombination, and a reins function to obtain a new population.
3. The MEMS accelerometer temperature drift error estimation method based on silicon microstructure analysis according to claim 2, wherein the initialized weight and bias parameters are processed by GA algorithm and PSO algorithm to obtain parameter x, and after decoding x, the decoding result is used as the initial weight and bias of BP neural network;
Figure FDA0003538666000000031
where n denotes the number of iterations of the PSO algorithm, i ═ 1,2, … n, viRepresents the particle velocity, x, of the PSO algorithm after the ith iterationiRepresenting the position, x, of the particle after the ith iteration of the PSO algorithmjWhen j iteration of the BP algorithm is represented, the weight and the position of the bias of the BP neural network in a solution space are represented, eta is a learning rate, m is the iteration number of BP neural network training, j is the search number, j is 1,2, …, m and E (x)j) Is xjN denotes the number of iterations of the PSO algorithm, c1And c2Is a constant number r1And r2Is a random value between 0 and 1, piIs the historical optimum value, g, of the particle itself after the first i iterationsiIs the historical optimum value of the particle swarm after the previous i iterations.
4. The method of claim 3, wherein the decoding of the PSO algorithm output is performed using the bs2rv function.
5. The method as claimed in claim 4, wherein the MEMS accelerometer adopts heat conduction measures, and the temperature sensor is tightly mounted on the surface of the MEMS accelerometer.
CN202110785860.0A 2021-07-12 2021-07-12 MEMS accelerometer temperature drift error estimation method based on silicon microstructure analysis Active CN113392591B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110785860.0A CN113392591B (en) 2021-07-12 2021-07-12 MEMS accelerometer temperature drift error estimation method based on silicon microstructure analysis

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110785860.0A CN113392591B (en) 2021-07-12 2021-07-12 MEMS accelerometer temperature drift error estimation method based on silicon microstructure analysis

Publications (2)

Publication Number Publication Date
CN113392591A CN113392591A (en) 2021-09-14
CN113392591B true CN113392591B (en) 2022-04-19

Family

ID=77625874

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110785860.0A Active CN113392591B (en) 2021-07-12 2021-07-12 MEMS accelerometer temperature drift error estimation method based on silicon microstructure analysis

Country Status (1)

Country Link
CN (1) CN113392591B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114021454B (en) * 2021-11-03 2022-10-21 国网山东省电力公司营销服务中心(计量中心) Electric energy meter comprehensive verification test error decoupling method and system

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106338283A (en) * 2016-09-27 2017-01-18 哈尔滨工程大学 High-precision interference type optical fiber gyroscope temperature drift error model optimizing method

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8643444B2 (en) * 2012-06-04 2014-02-04 Broadcom Corporation Common reference crystal systems
US11636322B2 (en) * 2020-01-03 2023-04-25 Silicon Storage Technology, Inc. Precise data tuning method and apparatus for analog neural memory in an artificial neural network

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106338283A (en) * 2016-09-27 2017-01-18 哈尔滨工程大学 High-precision interference type optical fiber gyroscope temperature drift error model optimizing method

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
"AnoveltemperaturedrifterrormodelforMEMScapacitiveaccelerometer";BingQi等;《2017IEEE2ndAdvancedInformationTechnology,ElectronicandAutomationControlConference(IAEAC)》;20171002;第182-186页摘要、第I-III节 *
"圆片级封装全硅梳齿电容式MEMS加速度计设计";牛昊彬等;《中国惯性技术学报》;20201015;第28卷(第5期);第672-676页第1-3节 *
基于PSO优化SVM的MEMS加速度计温度补偿方法研究;刘滔等;《现代电子技术》;20180514(第10期);第1-3节 *
基于神经网络的石英加速度计的二维时、温漂移补偿;任春华等;《中国惯性技术学报》;20070615(第03期);第1-3节 *
电容式微加速度计的刻度温漂的半解析模型;何江波等;《传感技术学报》;20160115(第01期);第1-3节 *

Also Published As

Publication number Publication date
CN113392591A (en) 2021-09-14

Similar Documents

Publication Publication Date Title
Kammer Sensor placement for on-orbit modal identification and correlation of large space structures
Marwala Finite element model updating using computational intelligence techniques: applications to structural dynamics
Farhat et al. Updating finite element dynamic models using an element-by-element sensitivity methodology
Berman et al. Improvement of a large analytical model using test data
CN109885916B (en) Mixed test online model updating method based on LSSVM
CN109614580A (en) Antidetonation bulk testing model update method based on online Xgboost algorithm
CN113392591B (en) MEMS accelerometer temperature drift error estimation method based on silicon microstructure analysis
CN110631792A (en) Seismic hybrid test model updating method based on convolutional neural network
CN115270239A (en) Bridge reliability prediction method based on dynamic characteristics and intelligent algorithm response surface method
Chukwu et al. Analysis of some meteorological parameters using artificial neural network method for Makurdi, Nigeria
Moayedi et al. Applicability and comparison of four nature-inspired hybrid techniques in predicting driven piles’ friction capacity
El Maani et al. Multiobjective backtracking search algorithm: application to FSI
CN103559340A (en) Irrelevant multisource frequency domain load identification method based on COMI-PSO (comprehensive improved particle swarm optimization) algorithm
YiFei et al. Metamodel-assisted hybrid optimization strategy for model updating using vibration response data
Peng et al. Data-driven model order reduction with proper symplectic decomposition for flexible multibody system
Wang et al. Determination of elastoplastic properties of 2024 aluminum alloy using deep learning and instrumented nanoindentation experiment
CN112231821B (en) Reliability analysis-based basic seismic isolation structure system optimization method
Ding et al. Regional seismic waveform inversion using swarm intelligence algorithms
Menon Structural optimization using ANSYS and regulated multiquadric response surface model
Ni et al. Recursive identification of inertia tensor parameters of space solar power satellite based on distributed placement of attitude sensors
CN110502849A (en) A kind of perturbation mode construction method applied to four-dimensional Variational Data Assimilation System
CN114004117A (en) Slope earthquake slip probability analysis method considering soil body parameter space variability
Jia Monolithic and partitioned Rosenbrock-based time integration methods for dynamic substructure tests
CN112241122A (en) Self-adaptive drag-free control method based on set value identification algorithm
Martins et al. In-Situ Health Monitoring of Aerospace Structures via Dynamic Strain Measurements

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant