A method for testing temperature drift error of MEMS device based on spatial heat flow dynamic analysis

Abstract

The application discloses a kind of MEMS device temperature drift error test methods based on space heat flow dynamic analysis, it belongs to the field of novel sensor device.The application solves the problem of low precision and poor real-time of existing test methods.The method of the application is as follows: first, install the MEMS device in a sealed high-low temperature chamber, then install a temperature sensor on the surface of the MEMS device;then, adjust the environmental temperature in the high-low temperature chamber from the lowest working temperature of the MEMS device to the highest working temperature according to the designed temperature control interval and temperature control time, and record the environmental temperature of the MEMS device and the output data of the MEMS device in real time during the rising process of the environmental temperature in the high-low temperature chamber;subtract the recorded output data of the MEMS device from the reference value of the output data of the MEMS device to obtain the temperature drift error data of the MEMS device.The method of the application can be applied to the test of temperature drift error of MEMS device.

Description

Technical Field

[0001] This invention belongs to the field of novel sensor devices, specifically relating to a method for testing the temperature drift error of MEMS devices. Background Technology

[0002] Entering the 21st century, in order to achieve comprehensive breakthroughs in science and technology, humanity's demand for natural resources has been continuously increasing, such as energy minerals, rare earth elements, non-ferrous metals, and forests. However, humanity is facing a new situation of technological development bottlenecks caused by over-exploitation of resources, which further restricts the current development of human science and technology. How to effectively reverse the adverse situation caused by the scarcity of natural resources is a key issue that urgently needs to be addressed. Therefore, humanity's desire to explore the natural resources of unexplored and unfamiliar regions has become increasingly strong, and in recent years, human exploration has shifted from the Earth's surface and underground to the vast universe. The universe contains numerous planets, which must contain abundant and sustainably usable natural resources, and may even contain ideal environments that can support life on Earth. Due to the extremely harsh environment of deep space, with extreme temperatures, lack of oxygen, and radiation all threatening life, unmanned systems have become the main force and driving force for humanity's deep space missions. Examples include all-weather unmanned aerial vehicle monitoring systems, microsatellites, relay satellites, lunar rovers, and Mars rovers.

[0003] Unmanned rovers are pioneers in space exploration missions, providing essential data for successful landings. Due to the thrust limitations of current launch vehicles, the onboard detection equipment must possess advantages such as small size, low power consumption, and stable reliability. Therefore, unmanned rovers need to carry miniaturized detection equipment, making MEMS devices the optimal choice, such as MEMS accelerometers, MEMS gyroscopes, MEMS magnetometers, MEMS barometers, and MEMS thermometers. MEMS devices are fabricated from temperature-dependent silicon-based materials. Considering that the ambient temperature in space is approximately -180℃ to 130℃, rapid temperature changes can alter the physical properties of silicon-based materials, thereby inducing temperature drift errors in MEMS devices and reducing their output accuracy. For example, taking a certain type of MEMS gyroscope with an output sensitivity of ±0.00875° / s as an example, a 10℃ change in ambient temperature will result in an output temperature drift error of approximately 0.7° / s. This temperature drift error will induce navigation system output errors that accumulate over time, posing a potential threat to the safe and stable operation of the vehicle. Therefore, temperature drift error severely restricts the application and promotion of MEMS devices in all fields, all weather conditions, and all climates. Effectively compensating for the temperature drift error of MEMS devices is the key to decoupling the dependence of MEMS devices on ambient temperature and improving the environmental adaptability and accuracy of MEMS devices.

[0004] Based on this, accurate compensation for temperature drift error in MEMS devices depends on three factors: first, accurately tracing the environmental temperature-related quantities that stimulate the temperature drift error, thereby constructing an accurate temperature drift error model for MEMS devices; second, accurately reproducing the complex relationship between environmental temperature-related quantities and temperature drift error, avoiding globally imprecise or locally optimal descriptions of the temperature drift error; and third, accurately assessing the temperature drift error, providing a good data foundation for accurately identifying the parameters of the MEMS device temperature drift error model. Therefore, accurately assessing the temperature drift error is fundamental to accurate compensation for MEMS device temperature drift error. Only when the temperature drift error test of MEMS devices is accurate can the accuracy of the construction and identification of the MEMS device temperature drift error model be effectively guaranteed. However, traditional precise testing methods for MEMS device temperature drift error do not deeply analyze the MEMS device temperature drift error testing process, resulting in incomplete parameter design in these methods. In particular, the design of temperature control time and temperature control interval relies too heavily on human experience, leading to problems such as low accuracy in error testing and poor real-time performance in test control. Therefore, accurate measurement of temperature drift error in MEMS devices is fundamental to effectively decoupling the temperature dependence of silicon-based materials and improving the environmental adaptability of MEMS devices. It is essential to propose a new method for testing temperature drift error in MEMS devices to address the problems of low accuracy and poor real-time performance of existing testing methods. Summary of the Invention

[0005] The purpose of this invention is to solve the problems of low accuracy and poor real-time performance of existing testing methods. It proposes a MEMS device temperature drift error testing method based on spatial heat flow dynamic analysis to accurately and efficiently test the temperature drift error of MEMS devices.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0007] A method for testing the temperature drift error of MEMS devices based on dynamic analysis of spatial heat flow, the method specifically includes the following steps:

[0008] Step 1: Install the MEMS device inside a sealed high and low temperature chamber, and then install the temperature sensor on the surface of the MEMS device.

[0009] Step 2: Lower the ambient temperature inside the high and low temperature chamber to the minimum operating temperature T of the MEMS device. L and maintain the ambient temperature at temperature T L Until the test PC receives the MEMS device output data D test When both the temperature data measured by the temperature sensor and the ambient temperature T of the MEMS device are stable, record the ambient temperature T. test and the data output by MEMS devices D test ;

[0010] Step 3: Set the temperature control interval to ΔT and the temperature control time to t. p ;

[0011] The MEMS device output data D at the lowest operating temperature test The moment when both the temperature data measured by the temperature sensor and the actual temperature stabilize is recorded as t0. Starting from time t0, the data is expressed as ΔT / t. p The ambient temperature inside the high and low temperature chamber is increased at a constant rate until it reaches the maximum operating temperature T of the MEMS device. H Then, maintain the output data of the MEMS device and the measurement data of the temperature sensor stable for t′ hours;

[0012] During the temperature rise inside the high and low temperature chamber, the ambient temperature T of the MEMS device is recorded in real time. test and MEMS device output data D test ;

[0013] Step 4: Repeat steps 2 and 3 until the maximum number of iterations is reached;

[0014] The temperature drift error of the MEMS device is obtained by subtracting the recorded MEMS device output data from the MEMS device output reference value.

[0015] The beneficial effects of this invention are:

[0016] This invention analyzes the temperature drift error testing process of MEMS devices from the perspective of dynamic heat flow based on spatial heat flow dynamics analysis, and constructs a precise testing method for temperature drift error of MEMS devices based on this. It overcomes the problem that the parameter design of traditional precise testing methods for temperature drift error of MEMS devices relies too much on human experience and is not comprehensive and accurate enough. It improves the accuracy of temperature drift error testing of MEMS devices and the real-time performance of test control, and can test the temperature drift error of MEMS devices more accurately and in real time. Attached Figure Description

[0017] Figure 1 This is a flowchart of the method of the present invention;

[0018] Figure 2a Front view of MEMS devices installed inside a high and low temperature chamber;

[0019] Figure 2b A side view of a MEMS device installed inside a high and low temperature chamber;

[0020] Figure 2c A top view of MEMS devices installed inside a high and low temperature chamber;

[0021] Figure 3 This is a graph showing the temperature change over time during the test.

[0022] Figure 4 A graph showing the measured data of L3GD20H under static foundation conditions;

[0023] Figure 5a A comparison chart of MEMS gyroscope outputs before and after temperature drift error compensation, obtained from the first test;

[0024] Figure 5b The image shows a comparison of the MEMS gyroscope output before and after temperature drift error compensation, obtained from the second test.

[0025] Figure 5c The image shows a comparison of the MEMS gyroscope output before and after temperature drift error compensation, obtained from the third test.

[0026] Figure 5d This is a comparison chart of the MEMS gyroscope output before and after temperature drift error compensation, obtained from the fourth test.

[0027] Figure 5e This is a comparison chart of the MEMS gyroscope output before and after temperature drift error compensation, obtained from the 5th test. Detailed Implementation

[0028] Specific Implementation Method 1: Combination Figure 1 This embodiment describes a method for testing the temperature drift error of MEMS devices based on dynamic analysis of spatial heat flow. The method specifically includes the following steps:

[0029] Step 1: Install the MEMS device inside a sealed high and low temperature chamber, and then install the temperature sensor on the surface of the MEMS device.

[0030] Step 2: Lower the ambient temperature inside the high and low temperature chamber to the minimum operating temperature T of the MEMS device. L and maintain the ambient temperature at temperature T L Until the test PC receives the MEMS device output data D test When both the temperature data measured by the temperature sensor and the ambient temperature T of the MEMS device are stable, record the ambient temperature T. test and the data output by MEMS devices D test ;

[0031] Step 3: Set the temperature control interval to ΔT and the temperature control time to t. p ;

[0032] The MEMS device output data D at the lowest operating temperature test The moment when both the temperature data measured by the temperature sensor and the actual temperature stabilize is recorded as t0. Starting from time t0, the data is expressed as ΔT / t.p The ambient temperature inside the high and low temperature chamber is increased at a constant rate until it reaches the maximum operating temperature T of the MEMS device. H Then, maintain the output data of the MEMS device and the measurement data of the temperature sensor stable for t′ hours;

[0033] During the temperature rise inside the high and low temperature chamber, the ambient temperature T of the MEMS device is recorded in real time. test and MEMS device output data D test (i.e., record multiple sets of T) test and D test Data, and T within the same group test and D test The data comes from the same point in time.

[0034] Step 4: Repeat steps 2 and 3 until the maximum number of iterations is reached;

[0035] The temperature drift error of the MEMS device is obtained by subtracting the recorded MEMS device output data from the MEMS device output reference value.

[0036] For any set of recorded ambient temperature and MEMS device output data, the temperature drift error is obtained by subtracting the MEMS device output data from the MEMS device output reference value, and the temperature difference ΔT and ΔT' are obtained by subtracting the ambient temperature from the reference temperature. 2 The obtained temperature drift error is compared with ΔT and ΔT 2 A set of training data is formed, and each set of recorded data is processed separately. The obtained training data is then used to train the model. Experiments have shown that the model trained using the temperature drift error measured by the method of this invention can obtain better temperature drift error compensation results.

[0037] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the specific process of step one is as follows:

[0038] The MEMS device is mounted onto the metal casing using thermal grease to obtain the assembled MEMS device module; then the MEMS device module is mounted onto the mounting base inside the high and low temperature chamber.

[0039] The temperature sensor of the temperature measurement system is mounted on the surface of the MEMS device, and the temperature sensor is used to measure the ambient temperature T. test Perform real-time measurements.

[0040] The other steps and parameters are the same as in Specific Implementation Method 1.

[0041] Specific Implementation Method 3: This implementation method differs from Specific Implementation Method 1 or 2 in that the measurement accuracy of the temperature sensor is greater than twice the accuracy of the ambient temperature change, and the measurement frequency of the temperature sensor is higher than the output frequency of the MEMS device.

[0042] The temperature sensor has a temperature measurement accuracy of ±0.01℃, a temperature control accuracy of ±0.03℃, and a temperature measurement frequency of 1Hz.

[0043] Other steps and parameters are the same as in specific implementation method one or two.

[0044] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the calculation method for the temperature control interval ΔT is as follows:

[0045] The temperature drift error ΔE of MEMS devices consists of zero bias error, trend term error, and random error:

[0046] ΔE=E B +E T +E R (1)

[0047] In the formula, E B For zero bias error, E T E represents the trend term error. R This is random error;

[0048] Based on the zero-rate temperature change coefficient and sensitivity temperature change coefficient of MEMS devices, the MEMS device temperature drift error estimation equation of equation (2) is constructed:

[0049] ΔE=αΔT+βΔT (2)

[0050] In the formula, ΔT=TT L T is the current ambient temperature. L The initial ambient temperature is α, the zero-rate temperature change coefficient is β, and the sensitivity temperature change coefficient is β.

[0051] Since ΔE≤ΔE S Then the temperature control interval ΔT for exciting the temperature drift error of the MEMS device is:

[0052]

[0053] Where, ΔE S The sensitivity of MEMS device to target information is represented by |·|, where |·| represents the absolute value.

[0054] The temperature control interval design based on spatial heat flow dynamic analysis of this invention aims to plan the temperature control interval of a precise testing method for temperature drift error of MEMS devices, ensuring the accuracy and reliability of the minimum temperature drift error of the excited MEMS device. Based on the temperature drift error characteristic parameters of the MEMS device (zero-rate temperature change coefficient and sensitivity temperature change coefficient), a temperature drift error estimation equation for the MEMS device is constructed, and from this equation, the temperature control interval corresponding to the maximum temperature drift error of the MEMS device is accurately derived without affecting the sensitivity of the MEMS device.

[0055] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0056] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the temperature control time t... p The calculation method is as follows:

[0057] According to the law of conservation of energy and Newton's law of cooling, the equation for the heat flux density in space can be expressed as:

[0058]

[0059] Where u is the ambient temperature of any point A in the high and low temperature chamber at time t, q is the spatial heat flux density at point A, and k h The thermal conductivity of the air in the high and low temperature chamber. Let A be the rate of change of the ambient temperature at point A along the x-axis. Let A be the rate of change of the ambient temperature at point A along the y-axis. Let A be the rate of change of the ambient temperature at point A along the z-axis. Let A be the unit vector of point A on the x-axis. Let A be the unit vector of point A on the y-axis. Let A be the unit vector of point A on the z-axis;

[0060] The heat transfer equation for heat conduction from the x-axis to the MEMS device is:

[0061]

[0062] Among them, Q x Let q be the heat at point A on the x-axis. x ) A Let be the heat flux density at point A on the x-axis, (q x ) A+Δx Let Δx be the heat flux density at point A+Δx on the x-axis, Δy be the width of the heat conduction plane at point A on the x-axis, Δz be the height of the heat conduction plane at point A on the x-axis, and Δt be the heat conduction time.

[0063] Considering that MEMS devices are heated along the x-axis, y-axis, and z-axis respectively, similarly, the heat transfer equations along the y-axis and z-axis are constructed based on equation (5):

[0064]

[0065] Among them, Q y Let Q be the heat at point A on the y-axis. z The heat at point A on the z-axis;

[0066] The dynamic analysis equation for the spatial heat flux density at point A in three-dimensional space is:

[0067]

[0068] Where Q represents the heat at point A in three-dimensional space, and F(x,y,z,t) is the heat flux density of the potential heat source at point A in three-dimensional space. It is a unit vector matrix in three-dimensional space, and The superscript T indicates transpose;

[0069] Let the operating time of the high and low temperature chamber be t. s Based on the specific heat capacity formula, the heat conservation equation inside the high and low temperature chamber is constructed as follows:

[0070]

[0071] Where C is the specific heat capacity of the air inside the high and low temperature chamber under closed conditions, m is the mass of the air inside the high and low temperature chamber under closed conditions, and ΔT′ is the change in ambient temperature inside the high and low temperature chamber under closed conditions, and ΔT′=|T H -T L |;

[0072] Equation (9) is obtained from equation (8):

[0073]

[0074] Where ρ is the density of the air inside the high and low temperature chamber under closed conditions;

[0075] Equation (9) can be simplified to:

[0076]

[0077] Integrating equation (10) on the x-axis, y-axis, and z-axis respectively, we get:

[0078]

[0079] Where L1 is the length of the high and low temperature chamber, L2 is the width of the high and low temperature chamber, and L3 is the height of the high and low temperature chamber;

[0080] Equation (11) is transformed to obtain:

[0081]

[0082] In the formula, T x T represents the target control value of the temperature control unit of the high and low temperature chamber on the x-axis. y T represents the target control value of the temperature control unit of the high and low temperature chamber on the y-axis. z The target control value of the temperature control unit of the high and low temperature chamber on the z-axis;

[0083] When the heat inside the high and low temperature chamber is conserved, the operating time t of the high and low temperature chamber is... s As shown below:

[0084]

[0085] Then the temperature control time t p for:

[0086] t s ≤t p (14)

[0087] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0088] The temperature control time design based on spatial heat flow dynamic analysis of this invention aims to plan the temperature control time of a precise testing method for temperature drift error of MEMS devices, ensuring the real-time performance and redundancy of minimizing the temperature drift error of MEMS devices. Based on the law of conservation of energy and Newton's law of cooling, combined with the physical parameters of the measured environment of MEMS devices, a dynamic analysis equation for spatial heat flux density is constructed, and the temperature control time is accurately calculated from this equation, thereby accurately, completely, and reliably exciting the temperature drift error of MEMS devices.

[0089] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that the value of t′ is 1.

[0090] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0091] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One to Six in that the maximum number of iterations is 5.

[0092] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0093] Example

[0094] This invention provides a precise testing method for temperature drift error of MEMS devices based on dynamic analysis of spatial heat flow. The main purpose of this invention is to accurately test the temperature drift error of MEMS based on heating experiments and lay the foundation for accurate compensation. Specifically, it includes a MEMS device installation and testing scheme, a temperature control interval design method based on dynamic analysis of spatial heat flow, and a temperature control time design method based on dynamic analysis of spatial heat flow.

[0095] (I) MEMS Device Mounting and Testing Scheme

[0096] The assessment of temperature drift error in MEMS devices requires changes in ambient temperature, as different ambient temperatures excite different temperature drift errors in MEMS devices. Furthermore, ambient heat needs to be fully conducted to effectively excite the MEMS device to produce the corresponding temperature drift error. Considering the hysteresis of heat conduction, the temperature drift error of the MEMS device will inevitably be over-excited or under-excited, thus reducing the accuracy of its temperature drift error test. Therefore, designing appropriate heating experiments is crucial for accurate testing of temperature drift error in MEMS devices.

[0097] Therefore, the heating experiment needs to meet the following conditions:

[0098] (1) A high-low temperature chamber with a sealed insulation design was used as the experimental carrier.

[0099] High and low temperature chambers effectively create temperature variation environments, providing the necessary excitation conditions for temperature drift errors in MEMS devices. A high and low temperature chamber with a sealed, insulated design ensures high testing efficiency and minimizes external interference to guarantee the reliability of test results. MEMS devices need to be installed inside the high and low temperature chamber with an integrated mounting base to complete temperature drift error assessment tests. Currently, mainstream high and low temperature chambers adopt a front-door design with temperature control units on the left and right sides, a precision turntable in the center, and a fully sealed, insulated design. Figure 2a , Figure 2b and Figure 2c A schematic diagram of MEMS devices installed inside a high and low temperature chamber is provided.

[0100] MEMS devices are tightly attached to a metal casing using thermally conductive silicone grease to increase the heat exchange area and improve real-time heat conduction. The assembled MEMS device module is then tightly mounted on a mounting base inside a high and low temperature chamber to complete temperature drift error testing. Simultaneously, the temperature sensor of a precision temperature measurement system is attached to the surface of the metal casing of the MEMS device module.

[0101] (2) The mounting of MEMS devices should have good thermal conductivity.

[0102] To effectively control the temperature gradient effect and improve the real-time performance of the test (i.e., the real-time performance of heat conduction), the MEMS device is tightly attached to the metal shell with thermal grease. At the same time, the temperature sensor of the precision temperature measurement system is also attached to the MEMS device module with thermal grease, thereby increasing the module's thermal conductivity. This ensures that the ambient temperature inside the temperature control chamber is basically consistent with the temperature of its internal structure, minimizing the heat conduction delay effect.

[0103] (3) Precision temperature measurement system.

[0104] To obtain more accurate ambient temperature-related quantities, a precision temperature measuring device is used to measure the surface temperature of the MEMS device. The temperature measurement accuracy of the precision temperature measuring device should be more than twice the interval of ambient temperature change, and the temperature measurement frequency should be higher than the output frequency of the MEMS device. A margin for temperature drift error assessment is reserved to ensure the accuracy of the test results.

[0105] (II) Temperature Control Interval Design Method Based on Space Heat Flow Dynamic Analysis

[0106] The MEMS device temperature drift error compensation model is a priori process. Based on extensive measured MEMS device outputs, a well-structured and parameterized mathematical model is gradually constructed through large-scale data training and continuous experience accumulation. The MEMS device temperature drift error compensation model uses ambient temperature-related quantities as input and MEMS device temperature drift error as output. Its accuracy primarily depends on the accuracy of the ambient temperature-related quantities and the MEMS device temperature drift error, and secondly on whether the model output can be accurately described through the model input to meet accuracy requirements. Therefore, accurately assessing the temperature drift error becomes a prerequisite for accuracy.

[0107] The temperature drift error ΔE of MEMS devices consists of zero bias error, trend term error, and random error, and can be specifically expressed as:

[0108] ΔE=E B +E T +E R (15)

[0109] In the formula, E B For zero bias error (i.e., the fixed deviation between the actual output value of a MEMS device and its theoretical value), E T E represents the trend term error (i.e., the deviation that varies with ambient temperature). R This represents random error (i.e., deviations that fluctuate randomly and offset each other). For E... R In other words, E B and E T This accounts for the vast majority of temperature drift error, and the temperature drift error compensation model aims to eliminate E. B and E TThe most important method, and the main way to suppress temperature drift error. Based on the technical manual for MEMS devices, E B and E T It can be obtained from the following expression:

[0110] ΔE=αΔT+βΔT (16)

[0111] In the formula, ΔT=TT L α is the zero-rate level change coefficient (Zero-rate level change vs. temperature), β is the sensitivity change coefficient (Sensitivity change vs. temperature), and the minimum sensitivity of the MEMS device is set to ΔE. S If the temperature drift error ΔE overwhelms the sensitivity ΔE of the MEMS gyroscope S Otherwise, the target information of the MEMS device cannot be accurately measured. Therefore, the temperature drift error ΔE of the MEMS device should be less than or equal to the sensitivity ΔE of the MEMS device. S This ensures that the target information and temperature drift error of MEMS devices are accurately measured, i.e., ΔE ≤ ΔE S Based on this, the following expression holds true:

[0112]

[0113] When the temperature control interval of the heating experiment meets the requirements of equation (17), the temperature drift error of the MEMS device can be accurately measured. Therefore, the temperature control interval of the heating experiment must be designed according to equation (17) in order to ensure the accuracy of the temperature drift error ΔE test of the MEMS device.

[0114] (III) Temperature Control Time Design Method Based on Space Heat Flow Dynamic Analysis

[0115] Based on the theory of heat conduction, it is known that heat takes time to travel from point A to point B. Let's assume the temperature sequence at point A is T. A = [T′, T″], after the time series t = [t1, t2], the temperature value of point B is T. B =[T′,T″]. When t1<t<t2, T′<T B <T″. If T <T″ at this time A =T″, then the final strain of the ambient temperature at point B will be T″, however, T B The =T″ process has not been stably established. If the above process is applied to the temperature drift error assessment test, the temperature drift error will not be accurately assessed. Therefore, properly arranging the temperature control sequence to ensure complete heat conduction and stable, balanced operation is an important guarantee for accurate assessment of temperature drift error.

[0116] MEMS gyroscopes need to be installed inside a high-low temperature chamber with an integrated precision turntable to complete temperature drift error testing. Currently, most mainstream high-low temperature chambers adopt a front-opening design with temperature control units arranged on the left and right sides. The precision turntable is located in the center of the high-low temperature chamber, and the entire chamber adopts a sealed and insulated design.

[0117] According to the law of conservation of energy and Newton's law of cooling, the equation for the heat flux density in space is as follows:

[0118]

[0119] Where u is the ambient temperature at any point in the high and low temperature chamber at time t, q is the spatial heat flux density at that point, and k h The thermal conductivity of the air in this incubator, This represents the rate of spatial change of the ambient temperature at that point along the x-axis. This represents the rate of spatial change of the ambient temperature at that point along the y-axis. This represents the rate of spatial change of the ambient temperature at that point along the z-axis. It is a unit vector on the x-axis. Let be a unit vector on the y-axis. Let be a unit vector on the z-axis. Considering that heat from the x-axis is conducted solely to the MEMS device, the heat transfer equation based on equation (18) is as follows:

[0120]

[0121] Among them, Q x Let q be the heat at point A on the x-axis. x ) A Let be the heat flux density at point A on the x-axis, (q x ) A+ΔA Let Δy be the heat flux density at point A+ΔA near point A on the x-axis, Δy be the width of the heat conduction plane at point A on the x-axis, Δz be the height of the heat conduction plane at point A on the x-axis, and Δt be the heat conduction time. Δy and Δz constitute the heat conduction plane, from which heat is conducted to point A+ΔA near point A on the x-axis, where ΔA can also be represented as Δx. Considering that the MEMS device is heated on the x-axis, y-axis, and z-axis respectively, the heat transfer equations on the y-axis and z-axis can be constructed based on equation (19) as follows:

[0122]

[0123] Among them, Q y Let Q be the heat at point A on the y-axis. z Let be the heat at point A on the z-axis. Based on equations (19) and (20), the heat at point A in three-dimensional space can be expressed as follows:

[0124]

[0125] Here, F(x,y,z,t) is the heat flux density of the potential heat source at point A in three-dimensional space, which is related to the position (x,y,z) of point A and the time t. It is a unit vector matrix in three-dimensional space and Let the operating time of the high and low temperature chamber be t. s Based on the specific heat capacity formula, the heat conservation equation for the high and low temperature chamber can be constructed as follows:

[0126]

[0127] Where C is the specific heat capacity of the air inside the high and low temperature chamber under closed conditions, m is the mass of the air inside the high and low temperature chamber under closed conditions, and ΔT′ is the change in ambient temperature inside the high and low temperature chamber under closed conditions, and ΔT′=|T H -T L Based on this, equation (22) can be further derived and obtained as follows:

[0128]

[0129] Where ρ is the density of the air inside the high and low temperature chamber under sealed conditions. Considering that the heat flow density is different at different locations in the heat conduction path during the heat conduction process, the further the heat conduction path, the smaller the heat flow density and the lower the heat conduction efficiency. Since the MEMS device is a sensor, the heat it emits is relatively negligible compared to the ambient temperature of the high and low temperature chamber. Therefore, the actual effect of F(x,y,z,t) on the heat inside the high and low temperature chamber is negligible on the order of magnitude. Therefore, equation (23) can be further derived as follows:

[0130]

[0131] To calculate the total heat along the heat conduction path, integrate equation (24) on the x-axis, y-axis, and z-axis respectively, and then obtain the following expression:

[0132]

[0133] After integration, equation (25) is transformed to obtain:

[0134]

[0135] In the formula, T x T represents the target control value of the temperature control unit of the high and low temperature chamber on the x-axis. y T represents the target control value of the temperature control unit of the high and low temperature chamber on the y-axis. zThis represents the target control value of the temperature control unit of the high and low temperature chamber on the z-axis. Based on this, when the heat inside the high and low temperature chamber is conserved, the operating time t of the high and low temperature chamber is... s The following can be derived:

[0136]

[0137] Typically, high and low temperature chambers are designed as cubes with dimensions of L×L×L, and the target values ​​for the temperature control unit on the x, y, and z axes are the final ambient temperature T. b Therefore, equation (27) can be further simplified to:

[0138]

[0139] As shown in equation (28), when the parameters of the high and low temperature chamber and the ambient temperature control parameters are known, the temperature control time that ensures the minimum temperature drift error of the excited MEMS device can be directly calculated using equation (28). Based on this, the temperature control time t of the precision testing method for temperature drift error of MEMS devices is... p As shown below:

[0140] t s ≤t p (29)

[0141] To illustrate the precision of the method for testing the temperature drift error of MEMS devices in this invention, STMicroelectronics' L3GD20H MEMS gyroscope was used as an example. The temperature drift error of the MEMS gyroscope was tested using both the traditional method and the improved method based on spatial thermal flow dynamic analysis. A temperature drift error compensation model was constructed based on temperature-related quantities and the temperature drift error. The accuracy of the traditional and improved methods in testing the temperature drift error of MEMS devices was indirectly demonstrated by directly analyzing the temperature drift error compensation effect. The proposed temperature drift error compensation model is shown below:

[0142] ΔE=ANN RBF (ΔT,ΔT 2 (30)

[0143] Among them, ANN RBF It is a single-input, two-output RBF neural network.

[0144] According to the L3GD20H manual, ΔE S = 8.75 mdps / digit, α = ±0.04 dps / ℃, operating temperature range is -40℃~85℃, and the β parameter after dimensional conversion is:

[0145]

[0146] Based on equation (17), we can obtain:

[0147]

[0148] To ensure accurate assessment of temperature drift error while simplifying experimental procedures, ΔT = 0.5℃ was set. The L3GD20H was tested using a SET-Z-021UF high and low temperature chamber, with C = 1.005 kJ / (kg×K). h =0.0267W / m℃, L=0.6m, ρ=1.293kg / m 3 At this point, equation (28) can be expressed as:

[0149] t s =25.766s (33)

[0150] Therefore, it can be seen that after 25.766 seconds, the temperature control interval change of 0.5℃ is uniformly and stably transmitted to the center region of the precision turntable. Based on the consideration of simplifying the control process, let t... p =30s. Therefore, select any L3GD20H to conduct 5 sets of temperature drift error assessment experiments, using a precision temperature measurement system with a temperature measurement accuracy of ±0.03℃ and a temperature measurement frequency of 10Hz to monitor the ambient temperature in real time. The specific steps of the temperature drift error assessment test are as follows:

[0151] (1) The MEMS gyroscope is tightly attached to the metal casing using thermal grease. The module is then mounted on a turntable, and the temperature sensor of the precision temperature measurement system is placed in close contact with the surface of the metal casing for measurement. Test PC real-time reception Ensure the work is ready.

[0152] (2) Start the turntable and make it rotate at the target speed ω. s Record MEMS gyroscope data output

[0153] (3) When the ambient temperature drops to -40℃ and the measured data of the MEMS gyroscope and temperature measurement system are stable, start recording the surface temperature of the MEMS gyroscope. and MEMS gyroscope data output

[0154] (4) Increase the ambient temperature to 85℃ at a heating rate of 60℃ / h, i.e. 0.5℃ / 30s, and maintain the measured data of MEMS gyroscope and temperature measurement system stable for 1h, while recording the measured data during the heating process.

[0155] (5) Repeat steps (2) to (4) 5 times and record the temperature drift error assessment test data.

[0156] Figure 3A flowchart for the temperature drift error assessment test is provided. To facilitate the testing of the MEMS gyroscope, it is designed to operate in a static base state, i.e., ω s =0. Figure 4 The measured data for L3GD20H at this time are given.

[0157] As shown in Equation (30), a temperature drift error compensation model is constructed based on temperature-related quantities and temperature drift error. The accuracy of the precision testing method for temperature drift error of MEMS devices based on spatial heat flow dynamic analysis is demonstrated by analyzing the temperature drift error compensation effect. The parameter identification process of the temperature drift error estimation model is as follows:

[0158] (1) Two sets of temperature increase experiments were carried out respectively. One set of temperature experiment data was randomly selected as the training sample set, and the other set of temperature experiment data was selected as the verification sample set.

[0159] (2) Subtract the reference output from the actual output of the MEMS devices in the training sample set to obtain the MEMS device temperature drift error sample set. Subtract the reference temperature of the MEMS devices from the reference temperature of the MEMS devices in the training sample set to obtain the ambient temperature change sample set ΔT of the MEMS devices. Multiply the ambient temperature sample set ΔT of the MEMS devices by itself to obtain the square term sample set ΔT of the change. 2 .

[0160] (3) Using ΔT and ΔT 2 The RBF neural network is used as the input and the MEMS device temperature drift error as the output. The RBF neural network is trained until the difference between the output of the RBF neural network and the corresponding MEMS device temperature drift error meets the design requirements.

[0161] (4) Subtract the output of the RBF neural network from the corresponding output of the MEMS device to obtain the result after temperature drift error compensation of the MEMS device.

[0162] Based on all the above steps, using Figure 4 The experimental data shown were used to train the RBF neural network shown in equation (30), and its structure and parameters were accurately identified. Then, the temperature drift error compensation model based on the original MEMS gyroscope data tested by the traditional method and the improved method was re-examined using the validation sample set. Figure 5a , Figure 5b , Figure 5c , Figure 5d , Figure 5e The output of the MEMS gyroscope after compensation by a temperature drift error compensation model based on the raw data of the MEMS gyroscope tested using traditional and improved methods is presented.

[0163] Depend on Figure 5a , Figure 5b , Figure 5c , Figure 5d , Figure 5e As shown, the MEMS gyroscope output is more stable after compensation by the temperature drift error compensation model of the original data tested with the improved method. This indicates that it can more accurately estimate the temperature drift error, ensuring the stable and reliable operation of the MEMS gyroscope. Furthermore, the accuracy is evaluated using the mean square error formula, and the results are as follows:

[0164]

[0165] Where x1 is the MEMS gyroscope output after compensation using a temperature drift error compensation model based on the original MEMS gyroscope data tested using a traditional method, x2 is the MEMS gyroscope output after compensation using a temperature drift error compensation model based on the original MEMS gyroscope data tested using an improved method, x′ is the reference value of the MEMS gyroscope output, MSE is the mean square error algorithm, MSD1 is the mean square error of x1 and x′, MSD2 is the mean square error of x2 and x′, and Q′ is the improvement of MSD2 relative to MSD1. The mean square error is an intuitive indicator that reflects the dispersion between the evaluation sample and its reference value. The smaller the mean square error, the smaller the dispersion between the evaluation sample and its reference value. Therefore, the mean square errors of the compensated MEMS gyroscope outputs are shown in Table 2.

[0166] Table 1. Root mean square error before and after compensation

[0167]

[0168] As shown in Table 1, the output accuracy of the MEMS gyroscope after compensation using the temperature drift error compensation model based on the original MEMS gyroscope data tested using the improved method is effectively improved, increasing by 8% compared to the MEMS gyroscope output accuracy after compensation using the temperature drift error compensation model based on the original MEMS gyroscope data tested using the traditional method. Therefore, the improved method can more accurately test the temperature drift error of MEMS devices, providing an important guarantee for the stable and accurate operation of MEMS devices, and also providing important support for improving their environmental adaptability.

[0169] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for testing the temperature drift error of MEMS devices based on dynamic analysis of spatial heat flow, characterized in that, The method specifically includes the following steps: Step 1: Install the MEMS device inside a sealed high and low temperature chamber, and then install the temperature sensor on the surface of the MEMS device. Step 2: Lower the ambient temperature inside the high and low temperature chamber to the minimum operating temperature of the MEMS device. and maintain the ambient temperature at a temperature Until the test PC receives the MEMS device output data When both the temperature data measured by the temperature sensor and the actual temperature are stable, record the ambient temperature of the MEMS device. and data output by MEMS devices ; Step 3: Set the temperature control interval to Temperature control time is ; MEMS device output data at the lowest operating temperature The moment when both the temperature data measured by the temperature sensor and the temperature data stabilize are recorded as From time Beginning, with / The ambient temperature inside the high and low temperature chamber is increased at a constant rate until it reaches the maximum operating temperature of the MEMS device. Then, maintain the stability of the MEMS device output data and temperature sensor measurement data. Hour; During the temperature rise inside the high and low temperature chamber, the ambient temperature of the MEMS device is recorded in real time. and MEMS device output data ; The temperature control time The calculation method is as follows: According to the law of conservation of energy and Newton's law of cooling, the equation for the heat flux density in space can be expressed as: （4） in, Let point A in the high and low temperature chamber be... The ambient temperature at any given time Let A be the spatial heat flux density. The thermal conductivity of the air in the high and low temperature chamber. Let A be the rate of change of the ambient temperature at point A along the x-axis. Let A be the rate of change of the ambient temperature at point A along the y-axis. Let A be the rate of change of the ambient temperature at point A along the z-axis. Let A be the unit vector of point A on the x-axis. Let A be the unit vector of point A on the y-axis. Let A be the unit vector of point A on the z-axis; The heat transfer equation for heat conduction from the x-axis to the MEMS device is: （5） in, Let A be the heat at point A on the x-axis. Let A be the heat flux density at point A on the x-axis. Let A+ be a point on the x-axis. Heat flux density at that point Let A be the width of the heat conduction plane at point A on the x-axis. Let A be the height of the heat conduction plane at point A on the x-axis. This refers to the heat conduction time. Considering that MEMS devices are heated along the x-axis, y-axis, and z-axis respectively, similarly, the heat transfer equations along the y-axis and z-axis are constructed based on equation (5): （6） in, Let A be the heat at point A on the y-axis. The heat at point A on the z-axis; The dynamic analysis equation for the spatial heat flux density at point A in three-dimensional space is: （7） in, Let A be the heat at point A in three-dimensional space. It is the heat flux density of the potential heat source at point A in three-dimensional space. It is a unit vector matrix in three-dimensional space, and The superscript T indicates transpose; Let the working time of the high and low temperature chamber be Based on the specific heat capacity formula, the heat conservation equation inside the high and low temperature chamber is constructed as follows: （8） in, This refers to the specific heat capacity of the air inside a high and low temperature chamber under sealed conditions. The mass of air inside a high and low temperature chamber under closed conditions. For the temperature changes inside the high and low temperature chamber under closed conditions and ; Equation (9) is obtained from equation (8): （9） in, This refers to the density of the air inside a high and low temperature chamber under sealed conditions. Equation (9) can be simplified to: （10） Integrating equation (10) on the x-axis, y-axis, and z-axis respectively, we get: （11） in, It is the length of the high and low temperature chamber. It is the width of the high and low temperature chamber. It is the height of the high and low temperature chamber; Equation (11) is obtained after formula transformation: （12） In the formula, This represents the target control value of the temperature control unit of the high and low temperature chamber on the x-axis. This represents the target control value of the temperature control unit of the high and low temperature chamber on the y-axis. The target control value of the temperature control unit of the high and low temperature chamber on the z-axis; When the heat inside the high and low temperature chamber is conserved, the operating time of the high and low temperature chamber... As shown below: （13） Temperature control time for: （14） Step 4: Repeat steps 2 and 3 until the maximum number of iterations is reached; The temperature drift error of the MEMS device is obtained by subtracting the recorded MEMS device output data from the MEMS device output reference value.

2. The method for testing the temperature drift error of MEMS devices based on dynamic analysis of spatial heat flow according to claim 1, characterized in that, The specific process of step one is as follows: The MEMS device is mounted onto the metal casing using thermal grease to obtain the assembled MEMS device module; then the MEMS device module is mounted onto the mounting base inside the high and low temperature chamber. The temperature sensor of the temperature measurement system is mounted on the surface of the MEMS device, and the temperature sensor is used to measure the ambient temperature. Perform real-time measurements.

3. The method for testing the temperature drift error of MEMS devices based on dynamic analysis of spatial heat flow according to claim 2, characterized in that, The temperature sensor has a measurement accuracy greater than twice that of the ambient temperature change, and its measurement frequency is higher than the output frequency of the MEMS device.

4. The method for testing the temperature drift error of MEMS devices based on dynamic analysis of spatial heat flow according to claim 1, characterized in that, The temperature control interval The calculation method is as follows: MEMS device temperature drift error It consists of zero bias error, trend term error, and random error: （1） In the formula, Zero bias error For trend term error, This is random error; Based on the zero-rate temperature change coefficient and sensitivity temperature change coefficient of MEMS devices, the MEMS device temperature drift error estimation equation of equation (2) is constructed: （2） In the formula, , The current ambient temperature. The initial ambient temperature, The zero-rate temperature change coefficient, This is the sensitivity temperature change coefficient; because The temperature control interval for exciting the temperature drift error of MEMS devices. for: （3） in, Sensitivity to target information in MEMS devices Represents absolute value.

5. The method for testing the temperature drift error of MEMS devices based on dynamic analysis of spatial heat flow according to claim 1, characterized in that, The The value of is 1.

6. The method for testing the temperature drift error of MEMS devices based on dynamic analysis of spatial heat flow according to claim 1, characterized in that, The maximum number of iterations is set to 5.

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