CN114324979A - Accelerometer vibration detuning error evaluation method and device, storage medium and equipment - Google Patents
Accelerometer vibration detuning error evaluation method and device, storage medium and equipment Download PDFInfo
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Abstract
The invention discloses an accelerometer vibration maladjustment error evaluation method, an accelerometer vibration maladjustment error evaluation device, a storage medium and equipment, wherein the evaluation method comprises the following steps: (1) establishing accelerometer input excitation based on a random vibration principle; (2) establishing an accelerometer vibration output model, and modeling accelerometer output into a truncated normal distribution; (3) and (3) deducing the expectation of the truncated normal distribution according to the steps (1) and (2) and calculating the vibration imbalance error of the accelerometer. The evaluation device includes: an input excitation establishing module is used for establishing accelerometer input excitation based on a random vibration principle; the output model establishing module is used for establishing an accelerometer vibration output model and establishing an accelerometer output model as a truncation type normal distribution; and the calculation module is used for calculating the vibration imbalance error of the accelerometer according to the expectation of the derivation truncation type normal distribution. The evaluation method can effectively reduce the design risk of the inertial navigation system, shorten the development time and improve the reliability of the inertial navigation system.
Description
Technical Field
The invention relates to the technical field of accelerometers, in particular to an accelerometer vibration imbalance error evaluation method, device, storage medium and equipment.
Background
The aircraft is influenced by atmospheric fluctuation, self engine vibration and the like in the flying process, the attitude stability of the aircraft is ensured, and the inertial navigation system is ensured not to be interfered by the vibration signals and to output effective attitude information. The accelerometer is used as a main device for measuring the inertial navigation of the aircraft, is sensitive to vibration information, and the output precision of the accelerometer directly influences the precision of an inertial navigation system.
The conventional technical scheme is that after the design of an inertial navigation system is finished, the flying application working condition of an aircraft is simulated through a vibrating table to verify the performance index of the inertial navigation system.
Disclosure of Invention
In order to solve the defects of the prior art, the invention provides an accelerometer vibration imbalance error evaluation method, an accelerometer vibration imbalance error evaluation device, a storage medium and an accelerometer vibration model.
In order to realize the purpose of the invention, the following scheme is adopted:
an accelerometer vibration detuning error assessment method comprises the following steps:
(1) establishing accelerometer input excitation based on a random vibration principle;
(2) establishing an accelerometer vibration output model, and modeling accelerometer output into a truncated normal distribution;
(3) and (3) deducing the expectation of the truncated normal distribution according to the steps (1) and (2) and calculating the vibration imbalance error of the accelerometer.
Further, in the step (1), the random vibration signals generated in the external vibration process generally follow a Gaussian distribution X-N (mu, delta)2) The accelerometer tests were all performed under a 1g gravity field.
Further, in the step (2), the output of the accelerometer follows normal distribution X-N (mu, delta)2) The probability density function is expressed as:
taking a truncation interval (a, b), wherein a is the minimum value of the output range of the accelerometer, b is the maximum value of the output range of the accelerometer, and expressing the probability density function of X by a standard normal distribution probability density function and a cumulative distribution function through a standardized variable:
where Φ (t) is the standard normal distribution cumulative distribution function:
phi (t) is a standard normal distribution probability density function:
further, in step (3), the expectation of the truncated normal distribution is derived from steps (1) and (2):
substituting equation (1) into equation (2):
further, under random vibration, the mean value μ' of the vibration detuning error of the accelerometer is:
wherein mu is 1g under a gravity field, delta is a random vibration signal input root mean square, and a and b are accelerometer measuring ranges.
An accelerometer vibration misalignment error assessment apparatus comprising:
establishing an input excitation module for establishing accelerometer input excitation based on a random vibration principle, wherein accelerometer tests are carried out in a 1g gravity field;
the output model establishing module is used for establishing an accelerometer vibration output model and establishing an accelerometer output model as a truncation type normal distribution;
and the calculation module is used for calculating the vibration imbalance error of the accelerometer according to the expectation of the derivation truncation type normal distribution.
Furthermore, when the output model building module builds the output model, the output of the accelerometer follows normal distribution X-N (mu, delta)2) The probability density function is expressed as:
taking a truncation interval (a, b), wherein a is the minimum value of the output range of the accelerometer, b is the maximum value of the output range of the accelerometer, and expressing the probability density function of X by a standard normal distribution probability density function and a cumulative distribution function through a standardized variable:
where Φ (t) is the standard normal distribution cumulative distribution function:
phi (t) is a standard normal distribution probability density function:
further, the calculation module derives an expectation of a truncated normal distribution:
substituting equation (1) into equation (2):
further, under random vibration, when the calculation module calculates the accelerometer vibration imbalance error, the accelerometer vibration imbalance error mean value μ' is:
wherein mu is 1g under a gravity field, delta is a random vibration signal input root mean square, and a and b are accelerometer measuring ranges.
A computer-readable storage medium having stored thereon a computer program which, when executed by a processor, controls a storage medium device to perform the accelerometer vibration misalignment error assessment method described above.
An electronic device, comprising: at least one processor and memory; the memory stores computer-executable instructions, and the at least one processor executes the computer-executable instructions stored in the memory, so that the at least one processor executes the accelerometer vibration imbalance error assessment method.
The invention has the beneficial effects that: aiming at an alternating current signal generated by external vibration in the application of an inertial navigation system, an evaluation method is provided for the imbalance error of an accelerometer in a vibration environment, and the evaluation method can effectively reduce the design risk of the inertial navigation system, shorten the development time and improve the reliability of the inertial navigation system; the evaluation method is small in required calculation amount, simple and easy to implement, low in implementation cost, beneficial to improvement of offset error evaluation under accelerometer vibration, beneficial to improvement of direct current offset performance of accelerometer products in high-precision measurement, and good in practical value.
Drawings
FIG. 1 shows the random vibration acceptance test requirements of a certain integrated navigation product in an embodiment;
FIG. 2 is a random vibration sampling level test requirement of a certain integrated navigation product in an embodiment;
FIG. 3 is an error curve of accelerometer vibration imbalance under the condition of FIG. 1 for a certain integrated navigation product in an embodiment;
FIG. 4 is a graph of the accelerometer vibration detuning error under the condition of FIG. 2 for a certain integrated navigation product in an embodiment;
FIG. 5 is a vibration detuning error curve of an accelerometer of an integrated navigation product according to an embodiment after the accelerometer has modified range under the condition of FIG. 2;
FIG. 6 is a flowchart of an evaluation method in an embodiment.
Detailed Description
Example 1
As shown in fig. 6, the present embodiment provides an accelerometer vibration detuning error evaluation method, including the following steps:
(1) establishing accelerometer input excitation based on a random vibration principle;
the random vibration signal is a non-deterministic signal that cannot be described by a deterministic mathematical relationship, but only by statistical methods. Accurate values cannot be predicted at any instant in the future, and any observed value only represents a result which can be generated in the variation range of the observed value, but the variation of the observed value is subject to a statistical rule. A given random spectrogram contains all information of the random signal, including the frequency range of the random vibration, the energy value of each frequency of the random vibration and the root mean square of the random vibration acceleration. The performance of the accelerometer in most application scenarios can be measured by random vibration.
The random vibration signal generally follows Gaussian distribution X-N (mu, delta)2) Wherein, mu, delta2For normal distribution random variable mathematical expectation and variance, accelerometer tests are all performed under a 1g gravity field, X-N (mu, delta)2) Obeying a gaussian distribution, the random variable Y ═ X +1 similarly obeys a gaussian distribution, Y to N (μ +1, δ)2)。
(2) Establishing an accelerometer vibration output model, and modeling accelerometer output into a truncated normal distribution;
in the step (2), the accelerometer senses an input signal, the output of the accelerometer is consistent with the input and also obeys Gaussian distribution, but the output of the accelerometer is modeled into a cut-off normal distribution because the accelerometer has a measuring range, and the output of the accelerometer obeys normal distribution X-N (mu, delta)2) The probability density function is expressed as:
taking a truncation interval (a, b), wherein a is the minimum value of the output range of the accelerometer, b is the maximum value of the output range of the accelerometer, and expressing the probability density function of X by a standard normal distribution probability density function and a cumulative distribution function through a standardized variable:
where Φ (t) is the standard normal distribution cumulative distribution function:
phi (t) is a standard normal distribution probability density function:
(3) deducing expectation of the truncated normal distribution according to the steps (1) and (2), and calculating the vibration imbalance error of the accelerometer;
in step (3), the expectation of the truncated normal distribution is deduced from steps (1) and (2):
substituting equation (1) into equation (2):
under random vibration, the mean value μ' of the vibration detuning error of the accelerometer is:
wherein mu is 1g under a gravity field, delta is a random vibration signal input root mean square, and a and b are accelerometer measuring ranges.
Specific examples of the present invention are described in further detail below.
For example, in a combined navigation product, the random vibration power spectral density of the combined navigation product is as shown in fig. 1 and 2, the accelerometer has a range of ± 30g, and under the vibration condition of fig. 1 and 2, the accelerometer parallel to the gravity field works for 50s, and the error offset is less than 20 m.
The method comprises the following specific steps:
(1) establishing accelerometer input excitation based on a random vibration principle, wherein the root mean square of random vibration is calculated to be mu-1 and delta-7.67 as shown in fig. 1;
(2) establishing an accelerometer vibration output model, wherein the accelerometer output follows normal distribution X-N (mu, delta)2) The truncation interval (-30,30) is the accelerometer with the measuring range of +/-30 g;
(3) calculating the vibration maladjustment error of the accelerometer, and substituting the data in the steps (1) and (2)
The accelerometer vibration detuning error mu' is related to the random vibration input root mean square curve as shown in FIG. 3. As can be seen from FIG. 3, under the condition of FIG. 1, the vibration detuning error of the accelerometer is 0.001539g, and the displacement deviation thereof is less than 2m, so as to meet the task requirement. Repeating steps (1), (2) and (3) under the conditions of fig. 2, wherein the root mean square of the random oscillations in step (1) is calculated as μ ═ 1, δ ═ 18.34; the accelerometer vibration detuning error mu' is related to the random vibration input root mean square curve as shown in FIG. 4. As can be seen from FIG. 4, under the condition of FIG. 2, the vibration detuning error of the accelerometer is 0.3813g, the displacement deviation thereof is much larger than 20m, and the task requirement cannot be met, and the random vibration test is performed on the actual product under the condition, and the calculation result of FIG. 4 is verified.
Repeating steps (1), (2) and (3) under the conditions of fig. 2, wherein the root mean square of the random oscillations in step (1) is calculated as μ ═ 1, δ ═ 18.34; step (2) accelerometer vibration output model establishment, wherein accelerometer output obeys normal distribution X-N (1, 18.34)2) The truncation interval (-60,60) is the accelerometer with the measuring range of +/-60 g; the accelerometer vibration detuning error mu' is plotted against the random vibration input root mean square curve in FIG. 5. As can be seen from FIG. 5, under the condition of FIG. 2, the vibration offset error of the accelerometer is 0.01245g, and the displacement deviation is less than 20m, so that the task requirement can be met, and the calculation result of FIG. 5 is verified by performing a random vibration test on an actual product under the condition.
As can be seen from fig. 3, 4 and 5, under the same input vibration condition, the larger the accelerometer range is, the smaller the vibration detuning error μ' is; the larger the root mean square value of the certain input vibration condition of the accelerometer range is, the larger the vibration detuning error mu' of the accelerometer is.
The error evaluation method of the embodiment is small in required calculated amount, simple and easy to implement, low in implementation cost, not only beneficial to improvement of imbalance error evaluation under accelerometer vibration, but also beneficial to improvement of direct current offset performance of accelerometer products in high-precision measurement, and good in practical value.
Example 2
The embodiment provides another accelerometer vibration detuning error evaluation device, which comprises:
establishing an input excitation module for establishing accelerometer input excitation based on a random vibration principle, wherein accelerometer tests are carried out in a 1g gravity field;
the output model establishing module is used for establishing an accelerometer vibration output model and establishing an accelerometer output model as a truncation type normal distribution;
the output of the accelerometer follows normal distribution X-N (mu, delta)2) The probability density function is expressed as:
taking a truncation interval (a, b), wherein a is the minimum value of the output range of the accelerometer, b is the maximum value of the output range of the accelerometer, and expressing the probability density function of X by a standard normal distribution probability density function and a cumulative distribution function through a standardized variable:
where Φ (t) is the standard normal distribution cumulative distribution function:
phi (t) is a standard normal distribution probability density function:
the calculation module is used for calculating the vibration detuning error of the accelerometer according to the expectation of the derivation truncation type normal distribution;
when deriving the expectation of a truncated normal distribution:
substituting equation (1) into equation (2):
under random vibration, when the calculation module calculates the accelerometer vibration maladjustment error, the accelerometer vibration maladjustment error mean value mu' is:
wherein mu is 1g under a gravity field, delta is a random vibration signal input root mean square, and a and b are accelerometer measuring ranges.
Example 3
The present embodiment provides a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, controls a storage medium device to execute the accelerometer vibration imbalance error assessment method of embodiment 1.
Example 4
The embodiment provides an electronic device, including: at least one processor and memory; wherein the memory stores computer-executable instructions, and the computer-executable instructions stored in the memory are executed on the at least one processor to cause the at least one processor to perform the accelerometer vibration imbalance error assessment method of embodiment 1.
The above embodiments are only for illustrating the technical ideas and features of the present invention, and are not meant to be exclusive or limiting of the present invention. It will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the scope of the invention.
Claims (10)
1. An accelerometer vibration imbalance error assessment method is characterized by comprising the following steps:
(1) establishing accelerometer input excitation based on a random vibration principle;
(2) establishing an accelerometer vibration output model, and modeling accelerometer output into a truncated normal distribution;
(3) and (3) deducing the expectation of the truncated normal distribution according to the steps (1) and (2) and calculating the vibration imbalance error of the accelerometer.
2. The method for evaluating the vibration detuning error of the accelerometer according to claim 1, wherein in the step (1), the random vibration signals generated in the external vibration process generally follow a Gaussian distribution X-N (mu, delta)2) The accelerometer tests were all performed under a 1g gravity field.
3. The method of claim 2, wherein in step (2), the accelerometer output follows a normal distribution X-N (μ, δ)2) The probability density function is expressed as:
taking a truncation interval (a, b), wherein a is the minimum value of the output range of the accelerometer, b is the maximum value of the output range of the accelerometer, and expressing the probability density function of X by a standard normal distribution probability density function and a cumulative distribution function through a standardized variable:
where Φ (t) is the standard normal distribution cumulative distribution function:
phi (t) is a standard normal distribution probability density function:
4. the method according to claim 3, wherein in step (3), the expectation of the truncated normal distribution is derived from steps (1) and (2):
substituting equation (1) into equation (2):
5. the method of claim 4, wherein the mean value μ' of the vibration imbalance errors of the accelerometer under random vibration is:
wherein mu is 1g under a gravity field, delta is a random vibration signal input root mean square, and a and b are accelerometer measuring ranges.
6. An accelerometer vibration imbalance error assessment apparatus, comprising:
establishing an input excitation module for establishing accelerometer input excitation based on a random vibration principle, wherein accelerometer tests are carried out in a 1g gravity field;
the output model establishing module is used for establishing an accelerometer vibration output model and establishing an accelerometer output model as a truncation type normal distribution;
and the calculation module is used for calculating the vibration imbalance error of the accelerometer according to the expectation of the derivation truncation type normal distribution.
7. The apparatus of claim 6, wherein the output model building module builds the output model such that the accelerometer output follows a normal distribution X-N (μ, δ) when the accelerometer output is modeled2) The probability density function is expressed as:
taking a truncation interval (a, b), wherein a is the minimum value of the output range of the accelerometer, b is the maximum value of the output range of the accelerometer, and expressing the probability density function of X by a standard normal distribution probability density function and a cumulative distribution function through a standardized variable:
where Φ (t) is the standard normal distribution cumulative distribution function:
phi (t) is a standard normal distribution probability density function:
8. the accelerometer vibration imbalance error assessment device of claim 8, wherein the calculation module derives the expected time of the truncated normal distribution:
substituting equation (1) into equation (2):
9. a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, controls a storage medium device to perform the accelerometer vibration misalignment error assessment method of any of claims 1-5.
10. An electronic device, comprising: at least one processor and memory; wherein the memory stores computer-executable instructions, wherein execution of the computer-executable instructions stored in the memory on the at least one processor causes the at least one processor to perform the accelerometer vibration imbalance error assessment method of any one of claims 1 to 5.
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