CN109579878B - Inertial element error model rapid identification method based on frequency scanning excitation signal - Google Patents
Inertial element error model rapid identification method based on frequency scanning excitation signal Download PDFInfo
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Abstract
The invention provides a method for quickly identifying an inertial element error model based on a frequency scanning excitation signal, and belongs to the field of inertial test. The application starts from the application of an inertial element in aerospace tasks or weaponry and other aspects, and provides an excitation signal capable of fitting the working state of the inertial element by analyzing the working environment, wherein the excitation signal excites high-order terms which are often ignored in a parameter model compared with the existing signal, so that the aim of more accurately and truly obtaining the high-order term coefficient in an error model is fulfilled, and a cushion is laid for the subsequent compensation work; the time cost of the existing testing method is greatly reduced for the design of the whole testing method and the design of the error model parameter identification method, and the identification precision and the identification comprehensiveness of each order of parameters of the error model are greatly improved compared with the existing quick calibration method.
Description
Technical Field
The invention relates to a method for quickly identifying an inertial element error model based on a frequency scanning excitation signal, and belongs to the field of inertial test.
Background
The inertia element test means that output data of the inertia element is obtained on given input special test equipment, and experimental data is filtered, fitted and the like to obtain performance parameters of the inertia element or parameter items of different orders are separated, so that an error model of the inertia element is perfected, and theoretical support is provided for subsequent compensation. Currently, the error model of the inertial element includes a static error model, a dynamic error model, and a random error model. The static error model reflects the relation between the error and the specific force, the dynamic error model reflects the relation between the error and the angular motion, the static error model and the dynamic error model can compensate the error and the angular motion to a large extent through mathematical processing, and the part which cannot be compensated belongs to the random error model along with experimental environment factors, excitation coupling and the like. Therefore, the random error is an important index representing the performance of the inertial element.
At present, the test items for the gyroscope mainly include a drift test, a static test and a dynamic test. The static test mainly comprises a force feedback method, polar axis rolling and the like, and the dynamic test mainly completes error model identification by processing response data of an inertial element to a multi-axis turntable excited single-frequency dynamic excitation test signal. The test of the accelerometer mainly comprises a gravity field rolling experiment, a centrifuge test, a vibration table test and the like. In many test methods, static test development is mature, and currently, the random error model is determined by using a model in a static state as a result, but the adaptability verification in dynamic test is difficult to complete. The dynamic test excitation signal is generally a uniform angular velocity or a coupling angular velocity that makes the uniform angular velocity in a specific direction, and only represents the response of the inertial element at a certain frequency in a frequency domain. In order to obtain error model parameters, a series of static and dynamic combined experiments need to be carried out in batches, and under the condition that the inertial elements need to be produced, tested and calibrated in a large scale, the consumption of manpower, financial resources, material resources and time cost is large; meanwhile, static tests or single-frequency dynamic tests performed on the inertia element cannot completely simulate the dynamic excitation borne by the inertia element in actual operation.
The fast self-calibration method for the error coefficient of the high-precision inertial gyroscope is provided by the Yan-hai swallow in research on the self-calibration method for the error coefficient of the high-precision inertial gyroscope, the calibration method is carried out by means of a platform provided with the gyroscope, external auxiliary equipment is not needed, the attitude of the platform is continuously changed relative to the earth under the action of excitation torque, the inertial navigation platform generates an attitude angle error of the platform under the driving of gyroscope drift, and therefore error information of the gyroscope can be separated. The specific test method is that the static gravity component excitation is applied by changing the position of the gyroscope (namely, the position of the gyroscope is turned over), so that the feedback output (the output of the platform attitude angle sensor) of the gyroscope at different positions is measured, and a simultaneous equation set is established, thereby solving each drift coefficient of the inertial instrument.
Wangjia proposes a rapid calibration method for an inertial measurement unit in an IMU440 inertial measurement unit rapid calibration method and experiment based on a biaxial rate turntable, and establishes a deterministic error model of a gyroscope and an accelerometer. The inertial measurement unit is integrated with three accelerometers and three gyroscopes, wherein the rate excitation applied to the gyroscopes is positive and negative bidirectional and the excitation applied to the accelerometers is static position excitation.
The general error model of the gyroscope is as follows: omegagRepresenting the steady state output of the gyroscope; kIRepresenting a gyroscope scale factor; omegaeIThe method is characterized in that the rotation angular velocity component of the earth on an input shaft is represented, and the input of the component in the direction of a sensitive shaft of a gyroscope can be 0 under the laboratory condition according to the change of the direction of a shaft system; dERepresenting zero offset of important index parameters of the gyroscope; dS、DI、DORespectively representing the sensitivity coefficients of the gyroscope rotating shaft, the input shaft and the output shaft; dIO、DOS、DSIRespectively representing the cross coupling coefficients of all the shafts under the coupling action of specific force components under the gravity field; dSS、DIIRespectively representing second-order sensitivity coefficients of the gyroscope in the directions of the rotation axis and the input axis; gI、gO、gSRespectively representing the components of specific force in the input shaft, the output shaft and the rotation shaft under the gravity field; epsilongRepresenting random errors in the test procedure.
ωg-K1ωeI＝DF+DIgI+DOgO+DSgS+DIOgIgS+DOSgOgS
+DSIgSgI+DIIgi 2+DSSgs 2+εg
The existing error model parameter obtaining method needs to carry out a series of tests continuously, wherein the tests comprise a static gravity excitation method, a multi-position rolling method and a speed calibration method, each method can obtain partial parameters in a parameter model through corresponding calculation according to different side emphasis points and excitation mechanisms, the time for carrying out a gyroscope error model calibration test for one time is as long as dozens of hours, and a zero searching process is needed in each test. As described above, for the method widely used in static test, static test development is mature for testing inertial components, and currently, the random error model is determined by using the model in a static state as a result, but the adaptive verification of the static error model in dynamic test is difficult to perform. At present, the dynamic test excitation signal is generally a uniform angular velocity or a coupling angular velocity of the uniform angular velocity in a specific direction, and the excitation signal in the frequency domain mostly represents a peak value at a single frequency, so that the frequency domain response only represents the response of the inertia element at a certain frequency. In order to obtain error model parameters, a series of static and dynamic combined experiments need to be carried out in batches, and under the condition that the inertial elements need to be produced, tested and calibrated in a large scale, the consumption of manpower, financial resources, material resources and time cost is large; meanwhile, because the working environment of the inertia test element is a high-G environment or an environment with high overload and severe dynamic process, the static test or single-frequency dynamic test of the inertia element cannot truly restore the dynamic excitation borne by the inertia element in the actual work, and therefore, the judgment on the reliability of the obtained parameter model has deviation.
Disclosure of Invention
The invention aims to solve the problems in the prior art, and further provides a method for quickly identifying an inertial element error model based on a frequency scanning excitation signal.
The purpose of the invention is realized by the following technical scheme:
a method for quickly identifying an inertial element error model based on a frequency scanning excitation signal comprises the following specific steps: the method comprises the following steps: the excitation signal is designed to be expressed as
a＝2π(fc-f0)/(n+1)Tn
b＝2πf0
In the formula (f)cRepresenting a frequency of interest; f. of0Representing an initial frequency; t represents the excitation signal duration; n is0Represents the attenuation coefficient; g represents amplitude gain, t represents a time variable, and n is the order of the time variable;
step two: and (3) solving a first derivative and a second derivative of the excitation signal to obtain the velocity and the acceleration of the excitation signal:
real-time velocity information of the excitation signal:
acceleration information of real-time signals:
step three: by the formula
The method comprises the steps that an input signal obtains time of any frequency and obtains frequency of any time;
step four: and identifying parameters by adopting a harmonic analysis method and an entropy analysis method.
The invention relates to a method for quickly identifying an inertial element error model based on a frequency scanning excitation signal, wherein n is0、n、f0、fcAll can carry out the parameter value setting according to actual need equipment bearing range and components and parts operational environment promptly.
The invention relates to a method for quickly identifying an inertial element error model based on a frequency scanning excitation signal, which comprises the following steps of: and respectively obtaining the output of the inertia test element under each attitude condition by adopting a test mode of combining multiple attitudes, carrying out Fourier transform analysis on the output, obtaining a constant term coefficient, a first harmonic term coefficient and a second harmonic term coefficient by comparison, and identifying the error parameter model.
The invention relates to a method for quickly identifying an inertial element error model based on a frequency scanning excitation signal, which takes the application of an inertial element in the aspects of space missions or weaponry and the like as a starting point, provides an excitation signal capable of fitting the working state of the inertial element practically through the analysis of the working environment, and compared with the existing signal, the excitation signal excites the high-order terms which are often ignored in a parameter model, so that the purpose is to more accurately and truly obtain the high-order term coefficients in the error model and lay a cushion for the subsequent compensation work; the time cost of the existing testing method is greatly reduced for the design of the whole testing method and the design of the error model parameter identification method, and the identification precision and the identification comprehensiveness of each order of parameters of the error model are greatly improved compared with the existing quick calibration method.
Drawings
FIG. 1 is a waveform diagram of an excitation signal of the fast inertial element error model identification method based on a frequency-swept excitation signal according to the present invention.
FIG. 2 is a second order position signal plot of the excitation signal of the present invention.
FIG. 3 is a second order rate signal plot of the excitation signal of the present invention.
FIG. 4 is a second order acceleration signal curve of the excitation signal of the present invention.
Detailed Description
The invention will be described in further detail below with reference to the accompanying drawings: the present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation is given, but the scope of the present invention is not limited to the following embodiments.
The first embodiment is as follows: as shown in fig. 1 to 4, the method for quickly identifying an error model of an inertial component based on a frequency-scan excitation signal according to the present embodiment includes the following specific steps: the method comprises the following steps: the excitation signal is designed to be expressed as
a＝2π(fc-f0)/(n+1)Tn
b＝2πf0
In the formula (f)cRepresenting a frequency of interest; f. of0Representing an initial frequency; t represents the excitation signal duration; n is0Represents the attenuation coefficient; g represents amplitude gain, t represents a time variable, and n is the order of the time variable;
step two: and (3) solving a first derivative and a second derivative of the excitation signal to obtain the velocity and the acceleration of the excitation signal:
real-time velocity information of the excitation signal:
acceleration information of real-time signals:
step three: by passing
The method comprises the steps that an input signal obtains time of any frequency and obtains frequency of any time;
step four: and identifying parameters by adopting a harmonic analysis method and an entropy analysis method.
The invention relates to a method for quickly identifying an inertial element error model based on a frequency scanning excitation signal, n0、n、f0、fcAll can carry out the parameter value setting according to actual need equipment bearing range and components and parts operational environment promptly.
The input excitation adopted by the existing inertia test element test method is a gravity component, constant speed, multidirectional constant speed coupling or single frequency sinusoidal signal. The signals have different expression forms in the time domain, but are uniformly expressed as single spectrum content in the frequency domain, so that the full-coverage dynamic excitation of the inertia test element in the working environment frequency band of the actual task execution equipment cannot be met. To improve the existing testing methods, the present application is in exciting the signalThe design of the number firstly ensures that the signal has enough abundant frequency spectrum content; secondly, based on the analysis simulation of the working environment of the inertia test element, the amplitude and the frequency of the excitation signal are adjusted to enable the amplitude and the frequency to be within an allowable range so as to excite the inertia test element to the maximum extent. Considering the above conditions comprehensively, the excitation signal expression is designed as follows:
a＝2π(fc-f0)/(n+1)Tn
b＝2πf0
in the formula (f)cRepresenting a frequency of interest; f. of0Representing an initial frequency; t represents the excitation signal duration; n is0Represents the attenuation coefficient; g represents amplitude gain, t represents time variable, and n is the order of the time variable. n is0、n、f0、fcParameter value setting can be carried out according to actual needs (equipment bearing range and component working environment). Fig. 1 is a frequency domain characteristic of an excitation signal, and the amplitude of the excitation signal is continuous in a frequency domain of interest in a frequency domain characteristic diagram, which can satisfy excitation in a wide frequency domain.
Considering the performance upper limit of the inertia instrument test equipment in design, such as the limit of factors of bearable maximum overload, load and the like, the excitation waveform is introduced with n0And G to limit the magnitude margins of acceleration and velocity, respectively. The adjusting parameters enable the inertial instrument and the inertial instrument testing equipment not to be damaged when the input speed and the acceleration value are large by adjusting the waveform, and can effectively limit the acceleration and the speed position instruction within the testing capacity range of hardware. What the excitation signal represents is position information for which the first and second derivatives can be taken for its speed and acceleration, respectively:
y 'represents the real-time velocity information of the excitation signal, Y' represents the acceleration information of the real-time signal, and n is 2 in consideration of the performance of the inertial meter test equipment, and the waveform curves of the position, velocity and acceleration of the excitation signal are shown in fig. 2-4. The waveform transformation rate can analyze that the dynamic process starts more slowly with the increase of the value of the representation time order, but the dynamic process is accelerated quickly, so the time order can be determined according to the requirement. The frequency spectrum of the time domain continuous signal in the frequency domain is represented as a covering f0To fcA rectangular region of (a); the frequency band threshold value can be freely set according to the actual working characteristics of the inertial instrument. For a more complete test, the following expression was introduced:
the above formula enables acquisition of time of any frequency and acquisition of frequency of any time for an input signal, and provides convenience for actual test operation and data analysis. The practical significance of the individual parameters in the signal is explained below for a complete experimental design. In the testing process of the inertial instrument, the working frequency range of the inertial instrument can be obtained by knowing the working mode and the working performance of the inertial instrument, if the performance near a certain frequency is mined, the working frequency range can be solved according to the formula, the initial frequency can be randomly set in the effective working range, wherein the initial frequency is fc＜f0And fc＞f0Two cases. When f isc＞f0In the test with the duration of T, the time for reaching any set frequency is TiThe working frequency of the inertia instrument at the T moment after the test is finished is the cut-off frequency fc. When f isc＜f0In the case of tests of duration T, due to the presence of the attenuation factorThe second derivative will reach the peak value, i.e. the frequency is 0, and the time to reach the frequency 0 is tzIn this case, it is taken from 0 to tzAnd analyzing the test data at any moment.
Example two: as shown in fig. 1, in the present embodiment, a method for quickly identifying an error model of an inertial element based on a frequency-scan excitation signal includes: and respectively obtaining the output of the inertia test element under each attitude condition by adopting a test mode of combining multiple attitudes, carrying out Fourier transform analysis on the output, obtaining a constant term coefficient, a first harmonic term coefficient and a second harmonic term coefficient by comparison, and identifying the error parameter model.
The identification of the parameters of the error model of the inertial instrument refers to separating interested harmonic terms from output data of the inertial instrument by processing such as harmonic analysis, filtering and the like. The current main research method is to determine the system state variable by combining the characteristics of an inertial navigation test equipment error model and an inertial instrument error parameter model, and establish a specific expression of a system state equation according to the input compensated for an error source. The parameter identification mainly considers a harmonic analysis method and an entropy analysis method.
Harmonic analysis method:
the dynamic error model of a classical rotor gyroscope is shown as follows:
the accelerometer error model is shown as follows:
U＝KF+KIaI+KIIaI 2+Koq|aI|aI+KIIIaI 3+KPaP+KPPaP 2+KPPPap 3+KOaO+KOOaO 2
+KOOOaO 3+KIPaIaP+KIOaIaO+KPOaPaO+KIPPaIaP 2+KIOOaIaO 2+KOPPaOaP 2
+KOIIaOaI 2+KPIIaPaI 2+KPOOaPaO 2+KIPOaIaPaO+ε
the amplitude and the influence degree of the constant term and the primary term in the error model are larger than those of the high-order term, so that the influence of the second-order term and the high-order term in the traditional ship-based inertia test element can be ignored, but high overload is common in mission environments such as aerospace, strategic missiles and the like, so that the excitation degree of the high-order term is higher, and the identification of the second-order term is also of great significance in the identification of the system error model. In the experimental process, the output of the inertia test element under each attitude condition is respectively obtained by adopting a test mode of combining multiple attitudes, Fourier transform analysis is carried out on the output, a constant term coefficient, a first harmonic term coefficient and a second harmonic term coefficient can be obtained by comparison, and the identification of an error parameter model is realized.
Entropy analysis method:
entropy analysis methods and methods of estimation or model fitting based on isentropic optimization criteria such as maximum entropy and minimum mutual entropy have been widely used in various mathematical statistical analyses, information and signal processing, system analysis and identification, error analysis and data processing. The estimation principle of the maximum entropy method is a method which does not make any subjective assumption except the actual measurement data obtained, namely, the estimation is carried out according to the principle of the least certainty; the minimum mutual entropy method is to apply the existing data and also require the data to be in accordance with the constraint of the prior condition, and is closest to the prior information. In the application, the entropy analysis method is considered preferentially for data processing and error model coefficient separation, and more information related to model parameters is obtained from the output data of the inertial instrument from the information aspect.
Example three: as shown in fig. 1-4, the present embodiment relates to a method for fast identifying an error model of an inertial element based on a frequency-scan excitation signal, and the method has the following advantages:
compared with the prior art, the excitation principle designed by the application is greatly innovative in excitation mode, is not limited to excitation under static conditions (for example, gravity components under different postures are used as input or uniform motion is used as input), and is greatly innovative in input signal form and content when the user looks at dynamic excitation under high overload.
Compared with the prior art, the excitation signal designed by the application is more comprehensively improved on the excitation mechanism of the system parameters, and usually, the static error model coefficient of the gyroscope is calibrated through the turntable test under gravity. However, the input acceleration in the gravitational field is small and the second order error coefficients of the gyroscope cannot be excited. In practice, gyroscopes typically operate under high acceleration conditions, in which case high-precision navigation cannot ignore the effect of second-order errors on the accuracy of the gyroscope. Therefore, it is very important to calibrate the second order error coefficients of the gyroscope through a high acceleration device. In order to more truly obtain the dynamic characteristics of the system and more vividly restore the working environment of the inertia test element, a frequency scanning signal with high overload and wider frequency domain is selected on the excitation of the system, and high-order parameters in the system are more comprehensively excited, so that the reliability and the authenticity of the identification of high-order term coefficients in an error model of the inertia test element are greatly improved.
Compared with the prior art, the testing method designed by the application has the advantages that the testing operation redundancy, the initial state error introduction and the testing time cost are greatly improved. In the prior art, error model parameters of an inertia test element are often determined through a series of tests combining a multi-position method, a polar axis rolling method and a geographic coordinate axis rolling method under a static condition, the test time can be dozens of hours, and the test method designed by the application can be realized by repeatedly exciting for dozens of seconds. Secondly, to all can have error factors such as measurement noise, alignment deviation and installation error to experimental every time, have certain influence to error model parameter identification precision, and this application can reach the purpose through repeated short-time excitation signal, has realized the purpose of high-efficient test, quick test.
Compared with the prior art, the output data processing mode applied by the method has the advantages that harmonic analysis is carried out on the system model parameter acquisition through the result of Fourier analysis to determine each order parameter of the system at one time or least square fitting is carried out on each attitude data to obtain each order parameter, and the calculation complexity is greatly optimized compared with the traditional method.
The above description is only a preferred embodiment of the present invention, and these embodiments are based on different implementations of the present invention, and the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (3)
1. The method for quickly identifying the inertial element error model based on the frequency scanning excitation signal is characterized by comprising the following specific steps of:
the method comprises the following steps: the excitation signal is designed to be expressed as
b＝2πf0
In the formula (f)cRepresenting a frequency of interest; f. of0Representing an initial frequency; t represents the excitation signal duration; n is0Represents the attenuation coefficient; g represents amplitude gain, t represents a time variable, and n is the order of the time variable;
step two: and (3) solving a first derivative and a second derivative of the excitation signal to obtain the velocity and the acceleration of the excitation signal:
real-time velocity information of the excitation signal:
acceleration information of real-time signals:
step three: by the formula
The method comprises the steps that an input signal obtains time of any frequency and obtains frequency of any time;
step four: and identifying parameters by adopting a harmonic analysis method and an entropy analysis method.
2. The method for fast identification of an inertial element error model based on a swept-frequency excitation signal according to claim 1, wherein n is0、n、f0、fcAll carry out the parameter value setting according to actual need equipment bearing range and components and parts operational environment promptly.
3. The method for rapidly identifying an error model of an inertial element based on a frequency-swept excitation signal according to claim 1, wherein the harmonic analysis method specifically comprises: and respectively obtaining the output of the inertia test element under each attitude condition by adopting a test mode of combining multiple attitudes, carrying out Fourier transform analysis on the output, obtaining a constant term coefficient, a first harmonic term coefficient and a second harmonic term coefficient by comparison, and identifying the error parameter model.
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