A cold start-up segment nonlinear temperature compensation method for a digital accelerometer

Abstract

This invention discloses a nonlinear temperature compensation method for the cold start segment of a digital accelerometer. By testing the cold start segment of the accelerometer, the nonlinear output characteristics of acceleration caused by cold start are isolated. Simultaneously, a time-dependent, near-normally distributed nonlinear temperature compensation model is established. Furthermore, an intelligent optimization algorithm is used to optimize the coefficients in the temperature compensation model, finally obtaining the model coefficients for temperature compensation in the cold start segment of the accelerometer, thereby achieving high-precision cold start of the accelerometer. This invention has been successfully applied to digital quartz flexural accelerometers and is suitable for temperature compensation of various accelerometers with strong nonlinear temperature characteristics in the cold start segment.

Description

Technical Field

[0001] This invention relates to the field of temperature compensation (or "temperature compensation") for digital accelerometers, and specifically to a nonlinear temperature compensation method for the cold start-up phase of a digital accelerometer. Background Technology

[0002] Quartz flexible accelerometers are widely used in important fields such as aerospace due to their advantages such as small size, fast response, high sensitivity and good repeatability.

[0003] As a core component of inertial navigation, the output accuracy of the accelerometer directly affects the attitude, velocity measurement, and positioning accuracy of the navigation system. Furthermore, due to the influence of quartz materials, temperature-induced errors are the main source of accuracy error in quartz flexible accelerometers. Existing technologies have proposed several methods for accelerometer temperature compensation. For example, patent specification CN109141479 A discloses a system-level accelerometer temperature compensation method, which establishes an accelerometer scaling factor error temperature compensation model and an accelerometer zero-point temperature compensation model, effectively solving the engineering application problem of accelerometer temperature compensation in inertial navigation systems and ensuring the temperature adaptability of the inertial navigation system. Patent specification CN 111679097 A discloses a high-precision accelerometer temperature compensation method, proposing a single-meter-level two-way variable temperature modeling method using a marble fixture, eliminating the influence of deformation of the strapdown inertial navigation system assembly and test fixture on accelerometer accuracy during previous temperature modeling processes.

[0004] With the rapid development of strapdown inertial navigation systems, in order to ensure the rapid start-up accuracy of the navigation system, it is inevitable to place higher demands on the performance indicators of the accelerometer, such as start-up time, start-up stability, and maximum drift error during the start-up phase.

[0005] In practical applications, it has been found that when a digital quartz flexural accelerometer restarts after sufficient heat dissipation in a non-working state, its startup output exhibits strong nonlinearity with temperature, making it impossible to use the traditional temperature compensation model based on thermal balance for temperature compensation. This significantly reduces the stability of the accelerometer's cold-start output.

[0006] Meanwhile, the good repeatability of quartz flexible accelerometers provides an important foundation for high-precision temperature error compensation via software. Therefore, to meet the high-precision requirements of high-precision navigation equipment for the cold start-up phase of accelerometers, proposing a nonlinear temperature compensation method for the cold start-up phase of accelerometers is of great significance. Summary of the Invention

[0007] To address the aforementioned technical problems and shortcomings in this field, this invention provides a nonlinear temperature compensation method for the cold-start segment of a digital accelerometer. This method employs a time-dependent, quasi-normally distributed temperature compensation model and utilizes an intelligent optimization algorithm to fit the strongly nonlinear temperature characteristics of the accelerometer's cold-start segment to obtain the optimal temperature compensation model coefficients. This invention has been successfully applied to digital quartz flexible accelerometers and is suitable for temperature compensation of various accelerometers with strongly nonlinear temperature characteristics in the cold-start segment.

[0008] From the perspective of practical engineering applications, this invention addresses the issue that the strong nonlinearity of the output during the cold start-up phase of an accelerometer significantly affects its output accuracy and is unsuitable for traditional temperature compensation models based on thermal balance. Therefore, this invention proposes a nonlinear temperature compensation method for the cold start-up phase of a digital accelerometer.

[0009] The specific technical solution is as follows:

[0010] A nonlinear temperature compensation method for the cold start segment of a digital accelerometer is proposed. By testing the cold start segment of the accelerometer, the nonlinear acceleration output characteristics caused by the cold start are isolated. At the same time, a time-related quasi-normal distribution nonlinear temperature compensation model is established. Furthermore, an intelligent optimization algorithm is used to optimize the coefficients in the temperature compensation model. Finally, the model coefficients used for temperature compensation of the cold start segment of the accelerometer are obtained, thereby achieving high-precision cold start of the accelerometer.

[0011] The nonlinear temperature compensation method for the cold start segment of the digital accelerometer specifically includes the following steps:

[0012] Step 1: Construct a temperature compensation model for the cold start-up output error of the accelerometer;

[0013] Step 2: Use a high-precision turntable and a controllable temperature chamber to perform a cold start test on the overall temperature-compensated accelerometer.

[0014] Step 3: Using intelligent optimization algorithms, with the sum of squared errors between the measured data and the fitted data as the fitness function, online intelligent optimization is performed on each temperature compensation coefficient in the temperature compensation model;

[0015] Step 4: Once the intelligent optimization algorithm meets the termination condition, the parameters corresponding to the optimal individual in the population are the optimal temperature compensation model coefficients of the cold start-up temperature compensation model. After obtaining the optimal coefficients of the temperature compensation model, substitute them into the cold start-up output error temperature compensation model established in Step 1 to complete the cold start-up temperature compensation of the accelerometer.

[0016] In step one, the temperature compensation model is a time-dependent nonlinear temperature compensation model, which includes a time-dependent correction coefficient and a quasi-normal distribution model, expressed by the following formula:

[0017]

[0018] In the formula, the first term on the right side of the equation is the time-related correction function, and the second term is the temperature-compensated model of a quasi-normal distribution.

[0019] Δa(t,T) represents the error value of the measured acceleration, that is, the true acceleration value should be the acceleration measurement value a plus Δa(t,T);

[0020] i represents the order of the model, i∈[0,N]; N represents the highest order of the model, the value of which depends on the nonlinearity of the data.

[0021] t is the time variable of the time-dependent correction function;

[0022] k i This is the adjustment factor for the time-dependent correction function;

[0023] t0 is the terminal time of the time-dependent correction function;

[0024] T is the temperature variable in a quasi-normal distribution temperature compensation model;

[0025] α is the amplitude adjustment coefficient for the quasi-normal distribution temperature-compensated model;

[0026] μ is the initial temperature adjustment coefficient for the quasi-normal distribution temperature compensation model;

[0027] σ is the dispersion adjustment coefficient for the quasi-normal distribution temperature compensation model.

[0028] In step one, the time-related correction function in the constructed cold-start output error temperature compensation model is used to correct the accelerometer output error within a specified time. The quasi-normal distribution temperature compensation model in the constructed cold-start output error temperature compensation model is used to fit and compensate the nonlinear output characteristics of the cold-start segment, where α is used to correct the amplitude of the nonlinear output characteristics, μ is used to correct the initial temperature of the nonlinear output characteristics, and σ is used to correct the dispersion of the nonlinear output characteristics.

[0029] Step two specifically includes: after the accelerometer is subjected to overall temperature compensation, cold start tests with different initial temperatures are performed at various positions within the circumference. Finally, the measured data are processed for zero-point error to obtain the nonlinear output characteristics of the accelerometer caused by cold start.

[0030] Preferably, the selection range of the different initial temperatures is -40℃ to 80℃, with an initial temperature set every 10℃.

[0031] In step three, the nonlinear characteristic data of the accelerometer cold start segment obtained from the test processing in step two is used as training data. The intelligent optimization algorithm is used to optimize each temperature compensation coefficient in the model, with the time-related nonlinear temperature compensation model established in step one as the model to be trained.

[0032] After obtaining the optimal model coefficients of the temperature compensation model for the output error of the accelerometer in the cold start phase, the temperature compensation model is written into the microprocessor, where k i , t0, α, μ, σ are coefficients obtained by the optimization algorithm and are fixed values; t is a time variable that needs to be timed by a microprocessor and is usually an integer multiple of the microprocessor's operating cycle; T is a temperature variable that needs to be obtained by a microprocessor from the real-time temperature parameters of the temperature sensor in the digital accelerometer.

[0033] In step three, k i , t0, α, μ, σ are the coefficients of the temperature compensation model to be optimized, and the fitness function is expressed as:

[0034]

[0035] u(k) represents the nonlinear characteristic data of the accelerometer cold start segment output obtained from the test processing in step two;

[0036] y(k) represents the data fitted by the temperature compensation model for the corresponding temperature compensation coefficient.

[0037] In step four, the intelligent optimization of parameters ends when the fitness function value in the intelligent optimization algorithm in step three meets the specified error precision or the number of population iterations reaches the specified value. At this time, the individual in the population corresponding to the minimum fitness function value is the optimal model coefficient of the temperature compensation model.

[0038] Preferably, the nonlinear temperature compensation method for the cold start segment of the digital accelerometer further includes step five, which combines the identified cold start segment temperature compensation model with the overall temperature compensation model of the accelerometer to achieve overall high-precision temperature compensation from the cold start segment to the thermal equilibrium state.

[0039] Compared with the prior art, the beneficial effects of this invention are as follows:

[0040] 1. This invention addresses the strong nonlinearity of the output during the cold start-up phase of a digital quartz flexible accelerometer by proposing a temperature compensation model based on time and a near-normal distribution. The time-related model is used to ensure the nonlinear temperature compensation during the cold start-up phase of the accelerometer, and the traditional temperature compensation can function normally under the thermal equilibrium state in the non-start-up phase.

[0041] 2. This invention addresses the strong nonlinearity of the output during the cold start-up phase of a digital quartz flexural accelerometer by proposing a temperature compensation model based on time and a near-normal distribution. The near-normal temperature compensation model has strong nonlinear fitting capabilities and can correct the amplitude and dispersion of the fitted data through appropriate parameters.

[0042] 3. The temperature compensation model established by the method of the present invention is a temperature compensation model for the output error of the cold start segment. It can be combined with the overall temperature compensation model and work simultaneously. Moreover, the model is independent of the input acceleration, which means it is applicable to the temperature compensation of the cold start segment at various positions of the accelerometer.

[0043] 4. Under the condition of fully testing the cold start-up data of the accelerometer and ensuring good repeatability, the method of the present invention uses an intelligent optimization algorithm to identify the parameters of the temperature compensation model. The identification process is carried out offline, and the application of the intelligent algorithm greatly improves the efficiency of model identification and temperature compensation during the start-up phase. Attached Figure Description

[0044] Figure 1 This is a flowchart illustrating a nonlinear temperature compensation method for the cold start-up phase of a digital accelerometer, as described in a specific embodiment of the present invention.

[0045] Figure 2 This is a flowchart illustrating the intelligent algorithm for identifying temperature-compensated model parameters in a specific embodiment of the present invention.

[0046] Figure 3 This is a time correlation curve of the accelerometer cold start-up test data in a specific embodiment of the present invention;

[0047] Figure 4 This is a temperature correlation curve of the accelerometer cold start-up test data in a specific embodiment of the present invention;

[0048] Figure 5 This is a comparison chart of the intelligent algorithm identification model curve and the original data curve in a specific embodiment of the present invention;

[0049] Figure 6 This is a test data diagram of the cold start-up phase after temperature compensation of the accelerometer in a specific embodiment of the present invention. Detailed Implementation

[0050] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0051] like Figure 1 As shown, this invention provides a nonlinear temperature compensation method for the cold start-up phase of a digital accelerometer, which specifically includes the following steps:

[0052] Step 1: Construct a temperature compensation model for the cold start-up output error of the accelerometer;

[0053] Step 2: Use a high-precision turntable and a controllable temperature chamber to perform a cold start test on the overall temperature-compensated accelerometer.

[0054] Step 3: Using intelligent optimization algorithms, with the sum of squared errors between the measured data and the fitted data as the fitness function, online intelligent optimization is performed on each temperature compensation coefficient in the temperature compensation model;

[0055] Step 4: Once the intelligent optimization algorithm meets the termination condition, the parameters corresponding to the best individual in the population are the optimal temperature compensation model coefficients of the cold start segment temperature compensation model. After obtaining the optimal coefficients of the temperature compensation model, substitute them into the cold start segment output error temperature compensation model established in Step 1 to complete the cold start segment temperature compensation of the accelerometer.

[0056] Step 5: Combine the identified cold start-up temperature compensation model with the traditional overall temperature compensation model to achieve overall temperature compensation for the accelerometer.

[0057] like Figure 1 As shown, in step one, the constructed cold-start section output error temperature compensation model includes a time-related correction coefficient and a quasi-normal distribution model, expressed by the formula:

[0058]

[0059] In the formula, the first term on the right side of the equation is the time-related correction function, and the second term is the temperature-compensated model of a quasi-normal distribution.

[0060] Δa(t,T) represents the error value of the measured acceleration, that is, the true acceleration value should be the acceleration measurement value a plus Δa(t,T);

[0061] i represents the order of the model, i∈[0,N]; N represents the highest order of the model, the value of which depends on the nonlinearity of the data, and in this embodiment N is 2;

[0062] t represents the time variable in the time-dependent model;

[0063] k i Adjust the coefficients for the time-dependent model;

[0064] t0 is the terminal time of the time-dependent model;

[0065] T is the temperature variable in a quasi-normal distribution temperature compensation model;

[0066] α is the amplitude adjustment coefficient for the quasi-normal distribution temperature compensation model;

[0067] μ is the initial temperature adjustment coefficient for the quasi-normal distribution temperature compensation model;

[0068] σ is the dispersion adjustment coefficient for the quasi-normal distribution temperature compensation model.

[0069] like Figure 1 As shown, in step one, the time-related correction function in the constructed cold-start segment output error temperature compensation model is used to correct the accelerometer output error within a specified time; the quasi-normal distribution temperature compensation model in the constructed cold-start segment output error temperature compensation model is used to fit and compensate the nonlinear output characteristics of the cold-start segment, where α is used to correct the amplitude of the nonlinear output characteristics, μ is used to correct the initial temperature of the nonlinear output characteristics, and σ is used to correct the dispersion of the nonlinear output characteristics.

[0070] like Figure 1 As shown, in step two, a high-precision turntable and a controllable temperature chamber are used to perform a cold start test on the accelerometer after overall temperature compensation. After the accelerometer undergoes overall temperature compensation, cold start tests are conducted at multiple positions within the circumference at different initial temperatures: -40℃, -30℃, -20℃, -10℃, 0℃, 10℃, 20℃, 30℃, 40℃, 50℃, 60℃, 70℃, and 80℃. Finally, the measured data for each group are processed for zero-point error, i.e., the output value of the acceleration stable section is subtracted, to obtain the time-related nonlinear output characteristics of the accelerometer caused by cold start, as shown below. Figure 3 As shown.

[0071] Error data obtained from multi-position cold start test of accelerometer are as follows: Figure 3 As shown, the error data was correlated with the temperature data of the starting section, and the resulting temperature correlation curve is shown below. Figure 4 As shown, the accelerometer data in the cold start phase exhibits a strong nonlinear relationship with temperature.

[0072] like Figure 1 As shown, in step three, the test results obtained in step two are used... Figure 3 , Figure 4 The time- and temperature-dependent nonlinear characteristic data of the accelerometer's cold-state start-up segment output is used as training data. An intelligent optimization algorithm is employed, using the cold-state start-up segment output error temperature compensation model established in step one as the training model, to optimize each temperature compensation coefficient within the model. The intelligent optimization algorithm can include genetic algorithms, immune algorithms, particle swarm optimization, ant colony optimization, simulated annealing, etc. This embodiment uses a symbiotic biological intelligent algorithm that incorporates multiple screening mechanisms and possesses strong global search and sentence completion convergence capabilities.

[0073] like Figure 2 As shown, in step three, the fitness function is the sum of squared errors between the measured data and the fitted data, and k is used as the fitness function. i , t0, α, μ, σ are the coefficients of the temperature compensation model to be optimized, and the fitness function can be expressed as:

[0074]

[0075] u(k) is the nonlinear characteristic data of the accelerometer cold start segment output obtained in step two;

[0076] y(k) represents the data fitted by the error temperature compensation model for the corresponding temperature compensation coefficient.

[0077] like Figure 1 As shown, in step four, the intelligent optimization of parameters ends when the fitness function value in the intelligent optimization algorithm in step three meets the specified error precision or the number of population iterations reaches the specified value (in this embodiment, the number of iterations is 200 as the termination condition). At this time, the population individual corresponding to the minimum fitness value is the optimal model coefficient of the error temperature compensation model.

[0078] like Figure 5 As shown, the undulating curve represents the test data of the accelerometer in the cold start phase, and the curve formed by the smooth circles represents the curve of the intelligent algorithm identification model. By substituting the model parameters obtained after the intelligent optimization algorithm model identification into the model and inputting the start phase temperature data, the temperature correlation curve of the identification model can be obtained. It can be seen that the identified model can efficiently fit the start phase error temperature correlation data, thus realizing high-precision temperature compensation of the accelerometer in the cold start phase.

[0079] After obtaining the optimal model coefficients for the accelerometer cold start-up output error temperature compensation model, the model needs to be written into the microprocessor, where k i t0, α, μ, and σ are coefficients obtained through the optimization algorithm and are fixed values, namely k1 = -0.00000000512, k2 = -0.00000000448, t0 = 30000, α = -0.0485605, μ = 37.65, and σ = 4.69872456, respectively; t is a time variable that needs to be timed by a microprocessor and is usually an integer multiple of the microprocessor's operating cycle; T is a temperature variable that needs to be obtained by a microprocessor from the real-time temperature parameter of the temperature sensor in the digital accelerometer.

[0080] like Figure 1 As shown, in step five, after obtaining the optimal coefficients of the temperature compensation model, substituting them into the cold-start segment output error temperature compensation model established in step one completes the cold-start segment temperature compensation of the accelerometer. Combining this with the overall temperature compensation model of the accelerometer achieves high-precision overall temperature compensation of the accelerometer from the cold-start segment to the thermal equilibrium state.

[0081] like Figure 6 As shown, after combining the startup temperature compensation model with the overall temperature compensation model and writing it into the accelerometer, the accelerometer startup data was retested under the same cold conditions. Figure 3It is evident that after the above-mentioned temperature compensation steps, the nonlinear characteristics of the accelerometer in the cold start phase can be effectively compensated by temperature, further proving the effectiveness of the proposed temperature compensation technology.

[0082] Furthermore, it should be understood that after reading the above description of the present invention, those skilled in the art can make various alterations or modifications to the present invention, and these equivalent forms also fall within the scope defined by the appended claims.

Claims

1. A method for non-linear temperature compensation of a cold start-up segment of a digital accelerometer, characterized in that, By testing the cold start segment of the accelerometer, the nonlinear acceleration output characteristics caused by the cold start are isolated. At the same time, a time-related quasi-normal distribution nonlinear temperature compensation model is established. Furthermore, intelligent optimization algorithms are used to optimize the coefficients in the temperature compensation model. Finally, the model coefficients for temperature compensation in the cold start segment of the accelerometer are obtained, thereby realizing high-precision cold start of the accelerometer. The nonlinear temperature compensation method for the cold start segment of the digital accelerometer specifically includes the following steps: Step 1: Construct a temperature compensation model for the cold start-up output error of the accelerometer; Step 2: Use a high-precision turntable and a controllable temperature chamber to perform a cold start test on the overall temperature-compensated accelerometer. Step 3: Using intelligent optimization algorithms, with the sum of squared errors between the measured data and the fitted data as the fitness function, online intelligent optimization is performed on each temperature compensation coefficient in the temperature compensation model; Step 4: Once the intelligent optimization algorithm meets the termination condition, the parameters corresponding to the best individual in the population are the optimal temperature compensation model coefficients of the cold start-up temperature compensation model. After obtaining the optimal temperature compensation model coefficients, substitute them into the cold start-up output error temperature compensation model established in Step 1 to complete the cold start-up temperature compensation of the accelerometer. In step one, the temperature compensation model is a time-dependent nonlinear temperature compensation model, which includes a time-dependent correction coefficient and a quasi-normal distribution model, expressed by the following formula: In the formula, the first term on the right side of the equation is the time-related correction function, and the second term is the temperature-compensated model of a quasi-normal distribution. represents the error value of the measured acceleration, i.e. the true acceleration value should be the acceleration measurement value a plus ; i represents the order of the model. N represents the highest order of the model, and its value depends on the nonlinearity of the data. t is the time variable of the time-dependent correction function; This is the adjustment factor for the time-dependent correction function; The terminal time of the time-dependent correction function; T is the temperature variable in a quasi-normal distribution temperature compensation model; For the amplitude adjustment coefficient of the temperature-compensated model similar to a normal distribution; This represents the initial temperature adjustment coefficient for a quasi-normal distribution temperature compensation model. This is the dispersion adjustment coefficient for a normal distribution temperature-compensated model.

2. The nonlinear temperature compensation method for the cold start-up phase of a digital accelerometer according to claim 1, characterized in that, Step two specifically includes: after the accelerometer is subjected to overall temperature compensation, cold start tests with different initial temperatures are performed at various positions within the circumference. Finally, the measured data are processed for zero-point error to obtain the nonlinear output characteristics of the accelerometer caused by cold start.

3. The nonlinear temperature compensation method for the cold start segment of a digital accelerometer according to claim 2, characterized in that, The selection range for the different initial temperatures is -40℃ to 80℃, with an initial temperature set every 10℃.

4. The nonlinear temperature compensation method for the cold start-up phase of a digital accelerometer according to claim 2 or 3, characterized in that, In step three, the nonlinear characteristic data of the accelerometer cold start segment obtained from the test processing in step two is used as training data. The intelligent optimization algorithm is used to optimize each temperature compensation coefficient in the model, with the time-related nonlinear temperature compensation model established in step one as the model to be trained.

5. The nonlinear temperature compensation method for the cold start segment of a digital accelerometer according to claim 4, characterized in that, In step three, with , , , , The fitness function for the temperature compensation model coefficients to be optimized is expressed as: u(k) represents the nonlinear characteristic data of the accelerometer cold start segment output obtained from the test processing in step two; y(k) represents the data fitted by the temperature compensation model for the corresponding temperature compensation coefficient.

6. The nonlinear temperature compensation method for the cold start-up phase of a digital accelerometer according to claim 1, characterized in that, In step four, the intelligent optimization of parameters ends when the fitness function value in the intelligent optimization algorithm in step three meets the specified error precision or the number of population iterations reaches the specified value. At this time, the individual in the population corresponding to the minimum fitness function value is the optimal model coefficient of the temperature compensation model.

7. The nonlinear temperature compensation method for the cold start-up phase of a digital accelerometer according to claim 1, characterized in that, The nonlinear temperature compensation method for the cold start segment of the digital accelerometer further includes step five, which combines the identified cold start segment temperature compensation model with the overall temperature compensation model of the accelerometer to achieve high-precision overall temperature compensation from the cold start segment to the thermal equilibrium state.

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