An inertial platform accelerometer fault injection simulation method

Abstract

The application provides an inertial platform and accelerometer fault injection simulation method, which adopts a transfer function method to establish a gyroscope measurement model, adopts a fault injection function mode, and gives simulation methods of an accelerometer bias voltage unstable drift fault, an accelerometer large measurement signal distortion fault, an inertial platform jitter fault, an output signal and high frequency harmonic wave frequency superposition fault, and a piezoelectric coefficient attenuation fault of a sensor sensitive core, so as to complete equivalent functions of testing, can replace a real inertial platform and accelerometer system, and comprehensively simulate one or more faults of the accelerometer, so that the whole simulation function is detailed and accurate.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aircraft inertial navigation and platform inertial navigation test equivalence and fault injection, in particular to an inertial platform accelerometer fault injection simulation method. BACKGROUND

[0002] With the development of high-precision inertial navigation technology, the matching installation of inertial platform and accelerometer has been widely used to provide autonomous position solving mode for aircraft. The accelerometer is installed on the inertial platform, and the stability of the inertial platform provides an invariable accelerometer measurement axis, thereby providing accurate positioning solution. Due to the complexity of the inertial platform and the navigation device, it is necessary to test and align before use. The test equipment for the inertial platform test is also very complex, which mainly tests and analyzes the fault states that the platform and the platform inertial navigation device may encounter. However, the teaching and use training of the test system using real inertial platform and accelerometer is very uneconomical in economy. Because the real system is expensive, the test of multiple power-on will inevitably cause damage and failure, and also damage its reliability. On the other hand, since the occurrence of failure is a small probability event, the teaching and training effect is poor when the real system is used for test teaching and training. At the same time, if a fault system is used, it can only test and simulate one kind of fault. Based on the above background reasons, it is considered that it has very practical value to research the function of injecting and simulating the acceleration fault and completing the test equivalence. At present, the fault simulation of acceleration is relatively simple, mainly focusing on the simulation of on-off fault, normal state or not. Based on the above reasons, the present application simulates five types of faults, including the instability drift fault of the bias voltage of the accelerometer, the distortion fault of the large measurement signal of the accelerometer, the inertial platform jitter fault, the superposition fault of the output signal and the high-frequency harmonic wave frequency, and the piezoelectric coefficient attenuation fault of the sensor sensitive core. Thus, it has good engineering practical value.

[0003] It should be noted that the information disclosed in the above background section is only used to strengthen the understanding of the background of the present application, and therefore can include information that does not constitute prior art known to those skilled in the art. SUMMARY

[0004] The present application aims to provide an inertial platform accelerometer fault injection simulation method, thereby overcoming the problems of inaccurate, comprehensive, in-depth and meticulous accelerometer fault simulation caused by the limitations and defects of the related art.

[0005] According to one aspect of the present application, an inertial platform accelerometer fault injection simulation method is provided, comprising the following steps:

[0006] Step S10, according to the accelerometer bias voltage unstable drift fault condition, first set the bias voltage drift amplitude and drift frequency, and then generate the bias voltage drift signal using the sine function; then the absolute value and sign function are used to obtain the bias voltage absolute value signal and the bias voltage sign signal; then the natural frequency and damping ratio parameters of the accelerometer are set, the measurement model of the accelerometer is established using the transfer function, the vertical acceleration signal of the inertial platform vertical motion is set as the input of the accelerometer, and the vertical acceleration measurement signal of the inertial platform is obtained; then the normal measurement range parameters of the accelerometer are set, and the vertical acceleration measurement signal of the inertial platform considering the saturation condition is obtained according to the vertical acceleration measurement signal of the inertial platform; then the accelerometer range parameters under the bias voltage drift fault are calculated according to the bias voltage absolute value signal and the bias voltage sign signal and the normal measurement range parameters of the accelerometer; then the vertical acceleration measurement signal under the bias voltage drift fault is calculated according to the vertical acceleration measurement signal of the inertial platform; finally, the injection time function of the bias voltage drift fault is designed, and the vertical acceleration comprehensive measurement signal under the bias voltage drift fault injection is obtained by combining the vertical acceleration measurement signal under the bias voltage drift fault and the vertical acceleration measurement signal of the inertial platform considering the saturation condition.

[0007] Step S20, according to the accelerometer large measurement signal distortion fault condition, first set the vertical acceleration signal of the inertial platform large acceleration vertical motion as the input of the accelerometer, then obtain the vertical large acceleration motion acceleration measurement signal according to the accelerometer measurement model established using the transfer function; then the absolute value is obtained to obtain the vertical large acceleration motion acceleration absolute value signal; then the fault acceleration threshold parameter and the maximum acceleration parameter and the overload protection parameter are set, and the large acceleration distortion gain coefficient signal is solved; then the time constant of the distortion fault is set, and the distortion amplitude signal is calculated using the first-order transfer function, and the vertical acceleration measurement signal under the large signal distortion fault is further calculated; then the time injection function of the large measurement signal distortion fault is set, and the vertical acceleration comprehensive measurement signal under the large measurement signal distortion fault injection is obtained by combining the vertical large acceleration motion acceleration measurement signal and the vertical acceleration measurement signal under the large signal distortion fault.

[0008] Step S30, according to the inertial platform jitter fault condition, first set the accelerometer normal vertical input signal under the inertial platform jitter; then the accelerometer transfer function model is solved under the normal vertical acceleration measurement signal of the inertial platform jitter; again set the base frequency parameter of the inertial platform jitter and the base frequency jitter amplitude parameter, the frequency jitter amplitude parameter, the half frequency jitter amplitude parameter, and then combine to obtain the jitter angular velocity signal of the inertial platform; again set the equivalent jitter arm parameter of the accelerometer installation point, and solve the jitter acceleration signal of the inertial platform; then the normal vertical acceleration measurement signal under the inertial platform jitter and the jitter acceleration signal of the inertial platform are superimposed to obtain the acceleration measurement signal under the jitter fault; finally, the injection time function of the inertial platform jitter fault is designed, and the vertical acceleration comprehensive measurement signal under the inertial platform jitter fault injection is obtained by combining the acceleration measurement signal under the jitter fault and the normal vertical acceleration measurement signal under the inertial platform jitter.

[0009] Step S40, according to the output signal and the high frequency harmonic wave frequency superposition fault, first set the high frequency vertical input signal as the high frequency input signal of the inertial platform accelerometer; then the accelerometer measurement signal under the high frequency vertical input is solved through the accelerometer transfer function model; again set the initial value of the resonance drift frequency, then compare it with the natural frequency parameter of the accelerometer to obtain the accelerometer frequency error signal; then the resonance drift frequency signal is obtained by amplifying and integrating according to the accelerometer frequency error signal; then the accelerometer frequency error signal is established under the high frequency harmonic wave frequency superposition fault, and the high frequency input signal of the inertial platform accelerometer is input to obtain the acceleration measurement signal under the high frequency harmonic wave frequency superposition fault; finally, the injection time function of the high frequency harmonic wave frequency superposition fault is designed, and the acceleration measurement signal under the high frequency harmonic wave frequency superposition fault and the accelerometer measurement signal under the high frequency vertical input are superimposed to obtain the acceleration comprehensive measurement signal under the high frequency harmonic wave frequency superposition fault.

[0010] Step S50, according to the piezoelectric coefficient attenuation fault of the sensor sensitive core; first set the accelerometer input signal under the piezoelectric coefficient attenuation fault; then the accelerometer measurement signal under no fault is solved by using the transfer function model of the accelerometer; again set the piezoelectric coefficient initial value, and compare it with the constant 1 to obtain the piezoelectric coefficient error signal; again, the piezoelectric coefficient signal is obtained by amplifying and integrating; again, the accelerometer measurement signal under the piezoelectric coefficient attenuation fault is solved according to the piezoelectric coefficient error signal and the transfer function model of the accelerometer; finally, the piezoelectric coefficient attenuation fault injection time function is designed, and the accelerometer comprehensive measurement signal under the piezoelectric coefficient attenuation fault is obtained by combining the accelerometer measurement signal under no fault.

[0011] Step S60, according to the accelerometer bias voltage unstable drift fault, accelerometer large measurement signal distortion fault, inertial platform jitter fault, output signal and high frequency harmonic wave frequency superposition fault, piezoelectric coefficient attenuation fault of sensor sensitive core, select one or several cases for fault injection, calculate the accelerometer measurement signal under fault, realize the fault injection simulation of inertial platform and accelerometer, complete the equivalent function of inertial platform and accelerometer test.

[0012] In an example embodiment of the application, according to the accelerometer bias voltage unstable drift fault, first set the bias voltage drift amplitude and drift frequency, then generate the bias voltage drift signal using the sine function; Then use the absolute value and sign function to obtain the bias voltage absolute value signal and bias voltage sign signal; Then set the natural frequency and damping ratio parameters of the accelerometer, use the transfer function to establish the measurement model of the accelerometer, set the vertical acceleration signal of the inertial platform as the input of the accelerometer, and obtain the vertical acceleration measurement signal of the inertial platform; Set the normal measurement range parameters of the accelerometer, and obtain the vertical acceleration measurement signal of the inertial platform considering the saturation according to the vertical acceleration measurement signal of the inertial platform; According to the bias voltage absolute value signal and the bias voltage sign signal and the normal measurement range parameters of the accelerometer, calculate the accelerometer range parameters under the bias voltage drift fault; Then calculate the vertical acceleration measurement signal under the bias voltage drift fault according to the vertical acceleration measurement signal of the inertial platform; Finally, design the injection time function of the bias voltage drift fault, and combine the vertical acceleration measurement signal under the bias voltage drift fault and the vertical acceleration measurement signal of the inertial platform considering the saturation to obtain the vertical acceleration comprehensive measurement signal under the bias voltage drift fault injection, including:

[0013] u p =r1 sin(ω1t);

[0014] u p1 =|u p |;

[0015] u p2 =sign(u p );

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] a c2 = a c1 h1+(1-h1)a c3 ;

[0022] wherein r1 is the bias voltage drift amplitude, a constant parameter; ω1 is the drift frequency, a constant parameter; u p is the bias voltage drift signal; u p1 is the bias voltage absolute value signal, sign() is the sign function; u p2 is the bias voltage sign signal; ω2 is the natural frequency of the accelerometer, a constant parameter; ε2 is the damping ratio parameter of the accelerometer, a constant parameter; s is the differential operator of the measurement model transfer function of the accelerometer; a h is the acceleration signal of the vertical motion of the inertial platform; a c is the vertical acceleration measurement signal of the inertial platform; r a0 is the normal measurement range parameter of the accelerometer, a constant parameter; a c3 is the vertical acceleration measurement signal of the inertial platform considering the saturation condition; k0, ε0 are constant parameters; r a1 is the accelerometer measurement range parameter under the bias voltage drift fault; a c1 is the vertical acceleration measurement signal under the bias voltage drift fault; h1 is the injection time function of the bias voltage drift fault, t 1s is the injection start time of the bias voltage drift fault; t 1e is the injection end time of the bias voltage drift fault; a c2 is the vertical acceleration comprehensive measurement signal under the bias voltage drift fault injection.

[0023] In an example embodiment of the application, according to the large measurement signal distortion fault condition of the accelerometer, first, the acceleration signal of the large acceleration vertical motion of the inertial platform is set as the input of the accelerometer, and then according to the measurement model of the accelerometer established by the transfer function, the vertical large acceleration motion acceleration measurement signal is obtained; then the absolute value thereof is obtained to obtain the vertical large acceleration motion acceleration absolute value signal; then the fault acceleration threshold parameter, the maximum acceleration parameter and the overload protection parameter are set to solve the large acceleration distortion gain coefficient signal; then the time constant of the distortion fault is set, a first-order transfer function is used to solve the distortion amplitude signal, and the vertical acceleration measurement signal under the large signal distortion fault is further solved; then the time injection function of the large measurement signal distortion fault is set, and the vertical acceleration comprehensive measurement signal under the large measurement signal distortion fault injection is obtained by synthesizing the vertical large acceleration motion acceleration measurement signal and the vertical acceleration measurement signal under the large signal distortion fault, including:

[0024]

[0025] a d2 = |a d | - h1a

[0026]

[0027]

[0028]

[0029]

[0030] a d4 = (1 - h2)a d + h2a d3 ;

[0031] where a h1 is the acceleration signal of the inertial platform large acceleration vertical motion, a d is the vertical large acceleration motion acceleration measurement signal; a d2 is the vertical large acceleration motion acceleration absolute value signal; a d0 is the fault acceleration threshold parameter, which is a constant; a max is the maximum acceleration parameter, which is a constant; ε1 is the overload protection parameter, which is a constant; k0 is the large acceleration distortion gain coefficient signal; T w is the distortion fault time constant, which is a constant; a d1 is the distortion amplitude signal, a d3 is the vertical acceleration measurement signal under large signal distortion fault; h2 is the large measurement signal distortion fault time injection function, t 2s is the large measurement signal distortion fault injection start time; t 2e is the large measurement signal distortion fault injection end time; a d4 is the vertical acceleration integrated measurement signal under large measurement signal distortion fault injection.

[0032] In one example embodiment of the present invention, based on the inertial platform jitter fault condition, firstly, a normal vertical input signal of the accelerometer under inertial platform jitter is set; then, the normal vertical acceleration measurement signal under inertial platform jitter is calculated using the accelerometer transfer function model; next, the fundamental frequency parameter, fundamental frequency jitter amplitude parameter, harmonic frequency jitter amplitude parameter, and half-frequency jitter amplitude parameter of the inertial platform jitter are set, and then combined to obtain the jitter angular velocity signal of the inertial platform; next, the equivalent jitter lever arm parameter of the accelerometer mounting point is set, and the jitter acceleration signal of the inertial platform is calculated; then, the normal vertical acceleration measurement signal under inertial platform jitter and the jitter acceleration signal of the inertial platform are superimposed to obtain the acceleration measurement signal under jitter fault; finally, the injection time function of the inertial platform jitter fault is designed, and the combined vertical acceleration measurement signal under inertial platform jitter fault and normal vertical acceleration measurement signal under inertial platform jitter is obtained, including:

[0033]

[0034] ω=l1 sin(ω3t)+l2 sin(2ω3t)+l3 sin(ω3t / 2);

[0035] a b1 =ωr;

[0036] a b2 =a b1 +a b ;

[0037]

[0038] a b3 =h3a b2 +(1-h3)a b ;

[0039] Where a h2 This provides the normal vertical input signal of the accelerometer under inertial platform jitter; a b ω is the normal vertical acceleration measurement signal under inertial platform jitter; ω3 is the fundamental frequency parameter of the inertial platform jitter, which is a constant; l1 is the fundamental frequency jitter amplitude parameter, l2 is the harmonic frequency jitter amplitude parameter, and l3 is the half-frequency jitter amplitude parameter, all of which are constant; ω is the jitter angular velocity signal of the inertial platform; r is the equivalent jitter lever arm parameter of the accelerometer mounting point, and a b1 The jitter acceleration signal of the inertial platform; a b2 h3 represents the acceleration measurement signal under jitter fault; h3 is the injection time function of the inertial platform jitter fault, and t... 3s The injection start time for the inertial platform jitter fault; t 3e The injection end time for inertial platform jitter fault; ab3 The vertical acceleration comprehensive measurement signal is injected to address the inertial platform jitter fault.

[0040] In one exemplary embodiment of the present invention, based on the output signal and high-frequency harmonic frequency superposition fault, the high-frequency vertical input signal is first set as the high-frequency input signal of the inertial platform accelerometer; then, the accelerometer measurement signal under high-frequency vertical input is calculated through the accelerometer transfer function model; next, the initial value of the resonant drift frequency is set, and then compared with the natural frequency parameter of the accelerometer to obtain the accelerometer frequency error signal; then, the resonant drift frequency signal is obtained by amplification and integration based on the accelerometer frequency error signal; then, the gyroscope transfer function under the high-frequency harmonic frequency superposition fault is established based on the accelerometer frequency error signal, and the high-frequency input signal of the inertial platform accelerometer is input to obtain the acceleration measurement signal under the high-frequency harmonic frequency superposition fault; finally, the injection time function of the high-frequency harmonic frequency superposition fault is designed, and the acceleration measurement signal under the high-frequency harmonic frequency superposition fault and the accelerometer measurement signal under the high-frequency vertical input are superimposed to obtain the comprehensive acceleration measurement signal under the high-frequency harmonic frequency superposition fault, including:

[0041]

[0042] e w =ω2-ω 31 ;

[0043]

[0044]

[0045]

[0046] a d1 =h4a d +(1-h4)a d0 ;

[0047] Where a h3 For the high-frequency input signal of the inertial platform accelerometer; a d0 The accelerometer measurement signal is obtained from a high-frequency vertical input; then, the initial value of the resonant drift frequency, e, is set. w For accelerometer frequency error signal; ω 30 ω is a constant parameter related to the initial value of the resonant drift frequency signal; 31 The resonant drift frequency signal, Here, T is the gyroscope transfer function under a high-frequency harmonic frequency superposition fault, and T is a constant integral parameter, where a is a constant. d h4 represents the acceleration measurement signal under a high-frequency harmonic superposition fault; h4 is the injection time function of the high-frequency harmonic superposition fault, and t4s The injection start time for the high-frequency harmonic superposition fault; t 4e The injection end time for the high-frequency harmonic superposition fault; a d1 This is a comprehensive acceleration measurement signal under a fault with superimposed high-frequency harmonics.

[0048] In one exemplary embodiment of the present invention, based on the piezoelectric coefficient attenuation fault of the sensor sensing core; firstly, the accelerometer input signal under the piezoelectric coefficient attenuation fault is set; then, the accelerometer measurement signal under the fault-free condition is calculated using the accelerometer transfer function model; next, the initial value of the piezoelectric coefficient is set and compared with a constant 1 to obtain the piezoelectric coefficient error signal; then, the piezoelectric coefficient signal is obtained by amplification and integration; then, the accelerometer measurement signal under the piezoelectric coefficient attenuation fault is calculated based on the piezoelectric coefficient error signal and the accelerometer transfer function model; finally, the injection time function for the piezoelectric coefficient attenuation fault is designed, and combined with the accelerometer measurement signal under the fault-free condition, the comprehensive accelerometer measurement signal under the piezoelectric coefficient attenuation fault is obtained, including:

[0049]

[0050] e k (n) = 1 - k0(n);

[0051]

[0052]

[0053]

[0054] a e2 =h5a e1 +(1-h5)a e ;

[0055] Where a h4 For accelerometer input signal under piezoelectric coefficient decay fault; a e For accelerometer measurement signals under fault-free conditions; e k This is the piezoelectric coefficient error signal; k a0 Let T be the initial value of the piezoelectric coefficient, and k0(n) be the piezoelectric coefficient signal; b is the time constant for the decay of the piezoelectric coefficient, and is a constant parameter; a e1 h5 represents the accelerometer measurement signal under piezoelectric coefficient decay fault conditions; h5 is the injection time function of the piezoelectric coefficient decay fault, t 5s t represents the injection start time of the piezoelectric coefficient decay fault; 5e The injection end time for the piezoelectric coefficient decay fault; a e2 This is the comprehensive measurement signal of the accelerometer under piezoelectric coefficient decay fault.

[0056] Beneficial effects

[0057] This invention provides a method for simulating fault injection in inertial platform accelerometers, with the following five main innovations. The first is that the unstable drift fault of the accelerometer bias voltage is equivalent to the impact on the accelerometer's measurement range under positive and negative feedback conditions, demonstrating good innovation and simulation equivalence.

[0058] Secondly, regarding the large-signal distortion fault of the accelerometer, a method is proposed to simulate large-signal distortion by setting fault acceleration threshold parameters, maximum acceleration parameters, and overload protection parameters, solving the large-acceleration distortion gain coefficient signal, setting the time constant of the distortion fault, and using the first-order transfer function to solve the distortion amplitude signal. This method has great innovation and accuracy.

[0059] Thirdly, for inertial platform jitter faults, three signals—fundamental frequency, double frequency, and half frequency—are used to simulate the jitter acceleration of the inertial platform. At the same time, the equivalent jitter force arm parameters of the accelerometer mounting point are used to calculate the jitter acceleration signal of the inertial platform. This method has the advantages of being equivalent and ingenious, and simplifies the acceleration calculation process while still being able to equivalently represent the impact of platform jitter on the accelerometer output.

[0060] Fourthly, for the fault caused by the superposition of the output signal and the high-frequency harmonic frequency, a method is proposed to simulate the resonance fault caused by the superposition of the output signal and the high-frequency harmonic frequency. The accelerometer frequency error signal is obtained by comparing the resonant drift frequency with the natural frequency parameter of the accelerometer. Then, the resonant drift frequency signal is obtained by amplifying and integrating the accelerometer frequency error signal. This method is very innovative.

[0061] Fifthly, regarding the piezoelectric coefficient attenuation fault of the sensor's sensitive core, a method is proposed to obtain the piezoelectric coefficient error signal by comparing the piezoelectric coefficient with a constant 1, and then amplifying and integrating it to obtain the piezoelectric coefficient signal. This method allows for easy setting of values ​​for calculation, and by combining the piezoelectric coefficient error signal with the accelerometer's transfer function model to calculate the accelerometer measurement signal under the piezoelectric coefficient attenuation fault, it has great innovation and can accurately approximate the piezoelectric coefficient attenuation phenomenon.

[0062] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0063] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0064] Figure 1 This is a flowchart of an inertial platform accelerometer fault injection simulation method provided by the present invention;

[0065] Figure 2 This is the normal vertical input signal curve of the accelerometer under inertial platform jitter (unit: meters per second squared) provided in the embodiments of the present invention;

[0066] Figure 3 This is the normal vertical acceleration measurement signal curve (unit: meters per second squared) of the inertial platform under shaking according to the method provided in the embodiments of the present invention.

[0067] Figure 4 This is the jitter angular velocity signal curve (unit: radians per second) of the inertial platform provided by the method in the embodiments of the present invention;

[0068] Figure 5 This is the jitter acceleration signal curve (unit: meters per second squared) of the inertial platform provided by the method in the embodiments of the present invention;

[0069] Figure 6 It is the injection time function (unitless) for the inertial platform jitter fault of the method provided in the embodiments of the present invention;

[0070] Figure 7 It is the comprehensive vertical acceleration measurement signal (unit: meters per second) under the inertial platform jitter fault injection method provided in the embodiments of the present invention. Detailed Implementation

[0071] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided to make the invention more comprehensive and complete, and to fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a full understanding of embodiments of the invention. However, those skilled in the art will recognize that the technical solutions of the invention may be practiced with one or more of these specific details omitted, or other methods, components, apparatus, steps, etc., may be employed. In other instances, well-known technical solutions are not shown or described in detail to avoid obscuring various aspects of the invention.

[0072] This invention provides a method for simulating accelerometer fault injection on an inertial platform. It establishes a gyroscope measurement model using the transfer function method and employs a fault injection function to simulate faults such as accelerometer bias voltage instability and drift, large measurement signal distortion, inertial platform jitter, superposition of output signal and high-frequency harmonic frequencies, and attenuation of the piezoelectric coefficient of the sensor's sensitive core. This method achieves equivalent testing functionality, can replace a real inertial platform and accelerometer system, and comprehensively simulates one or more accelerometer faults, resulting in a detailed and accurate simulation. It also avoids the economic losses and reliability degradation associated with using a real platform and accelerometer system, and can repeatedly reproduce the aforementioned faults.

[0073] The following will further explain and illustrate the inertial platform accelerometer fault injection simulation method of the present invention with reference to the accompanying drawings. (Reference) Figure 1 As shown, this inertial platform accelerometer fault injection simulation method may include the following steps:

[0074] Step S10: Based on the accelerometer bias voltage instability and drift fault, firstly, set the bias voltage drift amplitude and drift frequency, then generate the bias voltage drift signal using a sine function; next, use absolute value and sign functions to obtain the absolute value signal and sign signal of the bias voltage; then set the accelerometer's natural frequency and damping ratio parameters, establish the accelerometer's measurement model using a transfer function, set the acceleration signal of the inertial platform's vertical motion as the accelerometer's input, and obtain the inertial platform's vertical acceleration measurement signal; then set the accelerometer's normal measurement range parameters, and obtain the saturation-considered measurement signal based on the inertial platform's vertical acceleration measurement signal. The system first measures the vertical acceleration of the inertial platform under the specified conditions. Then, based on the absolute value signal of the bias voltage, the sign signal of the bias voltage, and the normal measurement range parameters of the accelerometer, it calculates the accelerometer range parameters under the bias voltage drift fault. Next, it calculates the vertical acceleration measurement signal under the bias voltage drift fault based on the vertical acceleration measurement signal of the inertial platform. Finally, it designs the injection time function for the bias voltage drift fault and combines the vertical acceleration measurement signal under the bias voltage drift fault and the vertical acceleration measurement signal of the inertial platform considering saturation to obtain the comprehensive vertical acceleration measurement signal under the bias voltage drift fault injection.

[0075] Specifically, this can be broken down into the following four steps. First, set the bias voltage drift amplitude and drift frequency, then use a sine function to generate the bias voltage drift signal; finally, use absolute value and sign functions to obtain the absolute value and sign signals of the bias voltage, as follows:

[0076] u p = r1 sin(ω1t);

[0077] u p1 =|u p |;

[0078] u p2 =sign(u p );

[0079] Where r1 is the bias voltage drift amplitude, a constant parameter; ω1 is the drift frequency, a constant parameter; u p This is the bias voltage drift signal; u p1 The absolute value signal of the bias voltage is given by sign(), which is the sign function; u p2 This is the bias voltage symbol signal.

[0080] The second step involves setting the natural frequency and damping ratio parameters of the accelerometer, establishing the accelerometer's measurement model using a transfer function, and setting the vertical acceleration signal of the inertial platform as the input to the accelerometer to obtain the vertical acceleration measurement signal of the inertial platform. Then, the normal measurement range parameters of the accelerometer are set, and the vertical acceleration measurement signal of the inertial platform considering saturation is obtained as follows:

[0081]

[0082]

[0083] Where ω2 is the natural frequency of the accelerometer, a constant parameter; ε2 is the damping ratio parameter of the accelerometer, a constant parameter; s is the differential operator of the transfer function of the accelerometer's measurement model; a h This is the acceleration signal for the vertical motion of the inertial platform; a c For the vertical acceleration measurement signal of the inertial platform; r a0 These are the normal measurement range parameters of the accelerometer, and are constant parameters; a c3 The vertical acceleration measurement signal of the inertial platform under saturation conditions is considered.

[0084] The third step involves calculating the accelerometer range parameters under bias voltage drift fault based on the absolute value signal and sign signal of the bias voltage, and the normal measurement range parameters of the accelerometer. Then, based on the vertical acceleration measurement signal of the inertial platform, the vertical acceleration measurement signal under bias voltage drift fault is calculated as follows:

[0085]

[0086]

[0087] Where k0 and ε0 are constant parameters; r a1 Accelerometer range parameters under bias voltage drift fault;

[0088] a c1 This is the vertical acceleration measurement signal under bias voltage drift fault.

[0089] The fourth step is to design the injection time function for the bias voltage drift fault. Based on the vertical acceleration measurement signal under the bias voltage drift fault and the vertical acceleration measurement signal of the inertial platform considering saturation, the comprehensive vertical acceleration measurement signal under the bias voltage drift fault injection is obtained as follows:

[0090]

[0091] a c2 =a c1h1+(1-h1)a c3 ;

[0092] Where h1 is the injection time function of the bias voltage drift fault, t 1s The injection start time for the bias voltage drift fault; t 1e The injection end time for bias voltage drift fault; a c2 The vertical acceleration comprehensive measurement signal is injected under bias voltage drift fault.

[0093] Step S20: Based on the accelerometer's large measurement signal distortion fault, firstly, the acceleration signal of the inertial platform's large acceleration vertical motion is set as the accelerometer input. Then, based on the accelerometer measurement model established using a transfer function, the vertical large acceleration motion acceleration measurement signal is obtained. Next, its absolute value is calculated to obtain the absolute value signal of the vertical large acceleration motion acceleration. Then, the fault acceleration threshold parameter, maximum acceleration parameter, and overload protection parameter are set, and the large acceleration distortion gain coefficient signal is solved. Next, the time constant of the distortion fault is set, and the distortion amplitude signal is solved using a first-order transfer function. The vertical acceleration measurement signal under the large signal distortion fault is further solved. Then, the time injection function of the large measurement signal distortion fault is set, and the vertical large acceleration motion acceleration measurement signal and the vertical acceleration measurement signal under the large signal distortion fault are combined to obtain the vertical acceleration comprehensive measurement signal under the injection of the large measurement signal distortion fault.

[0094] Specifically, this can be broken down into the following three steps. First, the acceleration signal of the inertial platform's large-acceleration vertical motion is set as the input to the accelerometer. Then, based on the accelerometer measurement model established using a transfer function, the vertical large-acceleration motion acceleration measurement signal is obtained. Finally, its absolute value is calculated to obtain the absolute value signal of the vertical large-acceleration motion acceleration, as follows:

[0095]

[0096] a d2 =|a d |;

[0097] Where a h1 For the acceleration signal of the large acceleration vertical motion of the inertial platform, a d For vertical acceleration measurement signals; a d2 This is the absolute value signal of vertical acceleration during large acceleration motion.

[0098] The second step involves setting the fault acceleration threshold parameters, maximum acceleration parameters, and overload protection parameters, and then solving for the large acceleration distortion gain coefficient signal. Next, the time constant for the distortion fault is set, and the distortion amplitude signal is calculated using a first-order transfer function. Finally, the vertical acceleration measurement signal under a large-signal distortion fault is calculated as follows:

[0099]

[0100]

[0101]

[0102] Where a d0 This is the fault acceleration threshold parameter, which is a constant; a max ε1 is the maximum acceleration parameter, which is a constant; ε2 is the overload protection parameter, which is a constant; k0 is the large acceleration distortion gain coefficient signal; T w The time constant for the distortion fault is a constant value; d1 For the distorted amplitude signal, a d3 This is the vertical acceleration measurement signal under large signal distortion fault conditions.

[0103] The third step is to set the time injection function for the large measurement signal distortion fault, and to combine the vertical acceleration measurement signal under the large acceleration motion and the vertical acceleration measurement signal under the large signal distortion fault to obtain the combined vertical acceleration measurement signal under the large measurement signal distortion fault injection.

[0104]

[0105] a d4 =(1-h2)a d +h2a d3 ;

[0106] Where h2 is the time injection function for large measurement signal distortion fault, t 2s The injection start time for large measurement signal distortion faults; t 2e The injection end time for a large measurement signal distortion fault; a d4 The vertical acceleration integrated measurement signal is injected under the condition of large measurement signal distortion fault.

[0107] Step S30: Based on the inertial platform jitter fault situation, firstly, set the normal vertical input signal of the accelerometer under inertial platform jitter; then, calculate the normal vertical acceleration measurement signal under inertial platform jitter using the accelerometer transfer function model; next, set the fundamental frequency parameter, fundamental frequency jitter amplitude parameter, harmonic frequency jitter amplitude parameter, and half-frequency jitter amplitude parameter of the inertial platform jitter, and then combine them to obtain the jitter angular velocity signal of the inertial platform; next, set the equivalent jitter force arm parameter of the accelerometer mounting point, and calculate the jitter acceleration signal of the inertial platform; then, superimpose the normal vertical acceleration measurement signal under inertial platform jitter and the jitter acceleration signal of the inertial platform to obtain the acceleration measurement signal under jitter fault; finally, design the injection time function of the inertial platform jitter fault, and combine the acceleration measurement signal under jitter fault and the normal vertical acceleration measurement signal under inertial platform jitter to obtain the comprehensive vertical acceleration measurement signal under inertial platform jitter fault injection.

[0108] Specifically, this can be broken down into the following four steps. The first step is to set the normal vertical input signal of the accelerometer under inertial platform jitter; then, the normal vertical acceleration measurement signal under inertial platform jitter is calculated using the accelerometer transfer function model as follows:

[0109]

[0110] Where a h2 This provides the normal vertical input signal of the accelerometer under inertial platform jitter; a b This is the normal vertical acceleration measurement signal under inertial platform vibration.

[0111] The second step is to set the fundamental frequency parameter, fundamental frequency jitter amplitude parameter, harmonic frequency jitter amplitude parameter, and half-frequency jitter amplitude parameter of the inertial platform jitter, and then combine them to obtain the jitter angular velocity signal of the inertial platform as follows:

[0112] ω=l1 sin(ω3t)+l2 sin(2ω3t)+l3sin(ω3t / 2);

[0113] Where ω3 is the fundamental frequency parameter of the inertial platform jitter, which is a constant; l1 is the fundamental frequency jitter amplitude parameter, l2 is the harmonic frequency jitter amplitude parameter, and l3 is the half-frequency jitter amplitude parameter, all of which are constant; ω is the jitter angular velocity signal of the inertial platform.

[0114] The third step is to set the equivalent jitter arm parameters at the accelerometer mounting point and calculate the jitter acceleration signal of the inertial platform. Then, the acceleration measurement signal under jitter fault is obtained by superimposing the normal vertical acceleration measurement signal under jitter of the inertial platform with the jitter acceleration signal of the inertial platform.

[0115] a b1 =ωr;

[0116] a b2 =a b1 +a b ;

[0117] Where r is the equivalent jitter arm parameter of the accelerometer mounting point, and a b1 The jitter acceleration signal of the inertial platform; a b2 This is the acceleration measurement signal under jitter fault conditions;

[0118] The fourth step is to design the injection time function for the inertial platform jitter fault. By combining the acceleration measurement signal under jitter fault and the normal vertical acceleration measurement signal under inertial platform jitter, the comprehensive vertical acceleration measurement signal under inertial platform jitter fault injection is obtained as follows:

[0119]

[0120] a b3 =h3a b2 +(1-h3)a b ;

[0121] Where h3 is the injection time function for the inertial platform jitter fault, t 3s The injection start time for the inertial platform jitter fault; t 3e The injection end time for inertial platform jitter fault; a b3 The vertical acceleration comprehensive measurement signal is injected to address the inertial platform jitter fault.

[0122] Step S40: Based on the output signal and the high-frequency harmonic frequency superposition fault, firstly, the high-frequency vertical input signal is set as the high-frequency input signal of the inertial platform accelerometer; then, the accelerometer measurement signal under the high-frequency vertical input is calculated through the accelerometer transfer function model; next, the initial value of the resonant drift frequency is set, and then compared with the natural frequency parameter of the accelerometer to obtain the accelerometer frequency error signal; then, the resonant drift frequency signal is obtained by amplification and integration based on the accelerometer frequency error signal; then, the gyroscope transfer function under the high-frequency harmonic frequency superposition fault is established based on the accelerometer frequency error signal, and the high-frequency input signal of the inertial platform accelerometer is input to obtain the acceleration measurement signal under the high-frequency harmonic frequency superposition fault; finally, the injection time function of the high-frequency harmonic frequency superposition fault is designed, and the acceleration measurement signal under the high-frequency harmonic frequency superposition fault and the accelerometer measurement signal under the high-frequency vertical input are superimposed to obtain the comprehensive acceleration measurement signal under the high-frequency harmonic frequency superposition fault.

[0123] Specifically, this can be broken down into the following four steps. Step 1: Set the high-frequency vertical input signal as the high-frequency input signal of the inertial platform accelerometer; then, calculate the accelerometer measurement signal under the high-frequency vertical input signal using the accelerometer transfer function model as follows:

[0124]

[0125] Where a h3 For the high-frequency input signal of the inertial platform accelerometer; a d0 The accelerometer measurement signal is obtained under high-frequency vertical input; then the initial value of the resonant drift frequency is set.

[0126] The second step is to set the initial value of the resonant drift frequency and then compare it with the natural frequency parameter of the accelerometer to obtain the accelerometer frequency error signal. Then, based on the accelerometer frequency error signal, amplification and integration are performed to obtain the resonant drift frequency signal as follows:

[0127] e w =ω2-ω 31 ;

[0128]

[0129] Where e w For accelerometer frequency error signal; ω 30 ω is a constant parameter related to the initial value of the resonant drift frequency signal; 31 The resonant drift frequency signal, Let T be the gyroscope transfer function under a high-frequency harmonic frequency superposition fault, where T is a constant integral parameter and is constant.

[0130] The third step involves establishing the gyroscope transfer function under high-frequency harmonic frequency superposition fault based on the accelerometer frequency error signal, and inputting the high-frequency input signal from the inertial platform accelerometer to obtain the acceleration measurement signal under high-frequency harmonic frequency superposition fault as follows:

[0131]

[0132] Where a d This is the acceleration measurement signal under a fault caused by the superposition of high-frequency harmonics.

[0133] The fourth step involves designing the injection time function for a high-frequency harmonic frequency superposition fault, and then superimposing the acceleration measurement signal under the high-frequency harmonic frequency superposition fault with the accelerometer measurement signal under high-frequency vertical input to obtain the comprehensive acceleration measurement signal under the high-frequency harmonic frequency superposition fault as follows:

[0134]

[0135] a d1=h4a d +(1-h4)a d0 ;

[0136] Where h4 is the injection time function of the high-frequency harmonic superposition fault, t 4s The injection start time for the high-frequency harmonic superposition fault; t 4e The injection end time for the high-frequency harmonic superposition fault; a d1 This is a comprehensive acceleration measurement signal under a fault with superimposed high-frequency harmonics.

[0137] Step S50: Based on the piezoelectric coefficient attenuation fault of the sensor sensitive core; firstly, set the accelerometer input signal under the piezoelectric coefficient attenuation fault; then, use the accelerometer transfer function model to calculate the accelerometer measurement signal under fault-free conditions; then set the initial value of the piezoelectric coefficient and compare it with constant 1 to obtain the piezoelectric coefficient error signal; then, perform amplification and integration to obtain the piezoelectric coefficient signal; then, based on the piezoelectric coefficient error signal and the accelerometer transfer function model, calculate the accelerometer measurement signal under the piezoelectric coefficient attenuation fault; finally, design the injection time function for the piezoelectric coefficient attenuation fault, and combine it with the accelerometer measurement signal under fault-free conditions to obtain the comprehensive accelerometer measurement signal under the piezoelectric coefficient attenuation fault.

[0138] Specifically, this can be broken down into the following four steps. First, set the accelerometer input signal under piezoelectric coefficient attenuation fault conditions; then, use the accelerometer transfer function model to calculate the accelerometer measurement signal under fault-free conditions as follows:

[0139]

[0140] Where a h4 For accelerometer input signal under piezoelectric coefficient decay fault; a e This is the accelerometer measurement signal under fault-free conditions.

[0141] The second step is to set an initial value for the piezoelectric coefficient and compare it with a constant 1 to obtain the piezoelectric coefficient error signal; then, amplify and integrate the result to obtain the piezoelectric coefficient signal as follows:

[0142] e k (n) = 1 - k0(n);

[0143]

[0144] Where e k This is the piezoelectric coefficient error signal; k a0 Let T be the initial value of the piezoelectric coefficient, and k0(n) be the piezoelectric coefficient signal; b is the time constant for the decay of the piezoelectric coefficient, and is a constant parameter.

[0145] The third step involves calculating the accelerometer measurement signal under piezoelectric coefficient attenuation fault based on the piezoelectric coefficient error signal and the accelerometer transfer function model, as follows:

[0146]

[0147] Where a e1 This is the accelerometer measurement signal under piezoelectric coefficient decay fault conditions.

[0148] The fourth step involves designing the injection time function for the piezoelectric coefficient decay fault. Combined with the accelerometer measurement signal under fault-free conditions, the comprehensive accelerometer measurement signal under the piezoelectric coefficient decay fault condition is obtained as follows:

[0149]

[0150] a e2 =h5a e1 +(1-h5)a e ;

[0151] Where h5 is the injection time function of the piezoelectric coefficient decay fault, t 5s t represents the injection start time of the piezoelectric coefficient decay fault; 5e The injection end time for the piezoelectric coefficient decay fault; a e2 This is the comprehensive measurement signal of the accelerometer under piezoelectric coefficient decay fault.

[0152] Step S60: Based on the accelerometer bias voltage instability drift fault, accelerometer large measurement signal distortion fault, inertial platform jitter fault, output signal superposition with high-frequency harmonic frequency fault, and sensor sensitive core piezoelectric coefficient attenuation fault, select one or more of these faults for fault injection, calculate the accelerometer measurement signal under the fault, realize the fault injection simulation of inertial platform and accelerometer, and complete the equivalent function of inertial platform and accelerometer testing.

[0153] Case Implementation and Computer Simulation Results Analysis

[0154] In step S10, ω2 is selected as the natural frequency of the accelerometer, and is a constant parameter; ε = 0.2, ω n =5000. In step S30, select a h2 =6 + 0.1sin(5t), ω3 = 40, l1 = 0.5, l2 = 0.3, l2 = 0.2, r = 0.2. Choose t 3s =10, t 3e =15. The final accelerometer vertical input signal under inertial platform jitter is as follows: Figure 2 As shown; the normal vertical acceleration measurement signal under inertial platform vibration is as follows: Figure 3As shown; the jitter angular velocity signal of the inertial platform is as follows Figure 4 As shown; the jitter acceleration signal of the inertial platform is as follows Figure 5 As shown; the injection time function for inertial platform jitter fault is as follows: Figure 6 As shown; the comprehensive measurement signal of vertical acceleration under inertial platform jitter fault injection is as follows: Figure 7 As shown. First, it should be noted that the probability of all five faults occurring simultaneously is very small. Therefore, the fault selection in steps S10, S20, and S40, S50 was not conducted experimentally; otherwise, the five faults would interfere with each other, which would be detrimental to fault analysis. Figure 6 It can be seen that the fault injection time is 10s to 15s, from Figure 7 It was clearly noticeable that the inertial platform's jitter during this period introduced high-frequency errors and chatter effects into the accelerometer measurements, which was quite similar to real-world conditions. Of course, if... Figure 4 A further increase in the jittery angular velocity signal will have a more detrimental effect on the accelerometer measurement. The above experimental results demonstrate the correctness of the method provided by this invention and its high engineering application value.

Claims

1. A method for simulating fault injection in an inertial platform accelerometer, characterized by the following steps: Step S10: Based on the accelerometer bias voltage instability and drift fault, firstly, set the bias voltage drift amplitude and drift frequency, then generate the bias voltage drift signal using a sine function; then, use absolute value and sign functions to obtain the absolute value signal and sign signal of the bias voltage; then, set the natural frequency and damping ratio parameters of the accelerometer, establish the accelerometer measurement model using a transfer function, set the acceleration signal of the vertical motion of the inertial platform as the input of the accelerometer, and obtain the vertical acceleration measurement signal of the inertial platform; then, set the normal measurement range parameters of the accelerometer, and obtain the vertical acceleration measurement signal of the inertial platform considering saturation based on the vertical acceleration measurement signal of the inertial platform; finally, calculate the accelerometer measurement range parameters under the bias voltage drift fault based on the aforementioned absolute value signal and sign signal of the bias voltage and the normal measurement range parameters of the accelerometer. Then, the vertical acceleration measurement signal under the bias voltage drift fault is calculated based on the vertical acceleration measurement signal of the inertial platform. Finally, the injection time function of the bias voltage drift fault is designed, and the combined vertical acceleration measurement signal under the bias voltage drift fault and the vertical acceleration measurement signal of the inertial platform considering saturation are obtained as follows: and p =r1sin(ω1t); in p1 =|in p |; in p2 =sign(u p ); has c2 =a c1 h1+(1-h1)a c3 ; Where r1 is the bias voltage drift amplitude, a constant parameter; ω1 is the drift frequency, a constant parameter; u p This is the bias voltage drift signal; u p1 The absolute value signal of the bias voltage is given by sign(), which is the sign function; u p2 ω2 is the bias voltage symbol; ω2 is the natural frequency of the accelerometer, a constant parameter; ε2 is the damping ratio parameter of the accelerometer, a constant parameter; s is the differential operator of the transfer function of the accelerometer's measurement model; a h This is the acceleration signal for the vertical motion of the inertial platform; a c For the vertical acceleration measurement signal of the inertial platform; r a0 These are the normal measurement range parameters of the accelerometer, and are constant parameters; a c3 To consider the vertical acceleration measurement signal of the inertial platform under saturation conditions; k0 and ε0 are constant parameters; r a1 For accelerometer range parameters under bias voltage drift fault; a c1 h1 is the vertical acceleration measurement signal under bias voltage drift fault; h1 is the injection time function of bias voltage drift fault, t 1s The injection start time for bias voltage drift fault; t 1e The injection end time for bias voltage drift fault; a c2 The comprehensive measurement signal of vertical acceleration injected under bias voltage drift fault; Step S20: Based on the accelerometer's large measurement signal distortion fault, firstly, the acceleration signal of the inertial platform's large acceleration vertical motion is set as the input of the accelerometer. Then, based on the accelerometer measurement model established using the transfer function, the vertical large acceleration motion acceleration measurement signal is obtained. Finally, its absolute value is calculated to obtain the absolute value signal of the vertical large acceleration motion acceleration. Next, set the fault acceleration threshold parameter, maximum acceleration parameter, and overload protection parameter, and solve for the large acceleration distortion gain coefficient signal; then set the time constant of the distortion fault, use the first-order transfer function to solve the distortion amplitude signal, and further solve the vertical acceleration measurement signal under the large signal distortion fault; then set the time injection function for the large measurement signal distortion fault, and combine the vertical large acceleration motion acceleration measurement signal and the vertical acceleration measurement signal under the large signal distortion fault to obtain the comprehensive vertical acceleration measurement signal under the injection of the large measurement signal distortion fault as follows: a d2 =|a d |; a d4 =(1-h2)a d +h2a d3 ; Where a h1 For the acceleration signal of the large acceleration vertical motion of the inertial platform, a d For vertical acceleration measurement signals; a d2 This is the absolute value signal of vertical acceleration during large acceleration motion; a d0 This is the fault acceleration threshold parameter, which is a constant; a max This is the maximum acceleration parameter, which is a constant. ε1 is the overload protection parameter, which is a constant; k0 is the large acceleration distortion gain coefficient signal; T w The time constant for the distortion fault is a constant value; d1 For the distorted amplitude signal, a d3 h1 represents the vertical acceleration measurement signal under large signal distortion fault; h2 represents the time injection function under large measurement signal distortion fault; t represents the vertical acceleration measurement signal. 2s The injection start time for large measurement signal distortion faults; t 2e The injection end time for a large measurement signal distortion fault; a d4 The vertical acceleration integrated measurement signal is injected under the condition of large measurement signal distortion fault; Step S30: Based on the inertial platform jitter fault situation, firstly, set the normal vertical input signal of the accelerometer under inertial platform jitter; then, calculate the normal vertical acceleration measurement signal under inertial platform jitter using the accelerometer transfer function model; next, set the fundamental frequency parameters, fundamental frequency jitter amplitude parameters, harmonic frequency jitter amplitude parameters, and half-frequency jitter amplitude parameters of the inertial platform jitter, and then combine them to obtain the jitter angular velocity signal of the inertial platform; next, set the equivalent jitter force arm parameters of the accelerometer mounting point, and calculate the jitter acceleration signal of the inertial platform; then, superimpose the normal vertical acceleration measurement signal under inertial platform jitter with the jitter acceleration signal of the inertial platform to obtain the acceleration measurement signal under jitter fault; finally, design the injection time function for inertial platform jitter fault, and combine the acceleration measurement signal under jitter fault and the normal vertical acceleration measurement signal under inertial platform jitter to obtain the comprehensive vertical acceleration measurement signal under inertial platform jitter fault injection as follows: ω=l1sin(ω3t)+l2sin(2ω3t)+l3sin(ω3t / 2); a b1 =ωr; a b2 =a b1 +a b ; a b3 =h3a b2 +(1-h3)a b ; Where a h2 This provides the normal vertical input signal of the accelerometer under inertial platform jitter; a b ω is the normal vertical acceleration measurement signal under inertial platform jitter; ω3 is the fundamental frequency parameter of the inertial platform jitter, which is a constant; l1 is the fundamental frequency jitter amplitude parameter, l2 is the harmonic frequency jitter amplitude parameter, and l3 is the half-frequency jitter amplitude parameter, all of which are constant; ω is the jitter angular velocity signal of the inertial platform; r is the equivalent jitter lever arm parameter of the accelerometer mounting point, and a b1 The jitter acceleration signal of the inertial platform; a b2 h3 represents the acceleration measurement signal under jitter fault; h3 is the injection time function of the inertial platform jitter fault, and t 3s The injection start time for inertial platform jitter fault; t 3e The injection end time for inertial platform jitter fault; a b3 The vertical acceleration comprehensive measurement signal injected under the inertial platform jitter fault; Step S40: Based on the output signal and the high-frequency harmonic frequency superposition fault, firstly, the high-frequency vertical input signal is set as the high-frequency input signal of the inertial platform accelerometer; then, the accelerometer measurement signal under the high-frequency vertical input is calculated through the accelerometer transfer function model; next, the initial value of the resonant drift frequency is set, and then compared with the natural frequency parameter of the accelerometer to obtain the accelerometer frequency error signal; then, the resonant drift frequency signal is obtained by amplification and integration based on the accelerometer frequency error signal; then, the gyroscope transfer function under the high-frequency harmonic frequency superposition fault is established based on the accelerometer frequency error signal, and the high-frequency input signal of the inertial platform accelerometer is input to obtain the acceleration measurement signal under the high-frequency harmonic frequency superposition fault; finally, the injection time function of the high-frequency harmonic frequency superposition fault is designed, and the acceleration measurement signal under the high-frequency harmonic frequency superposition fault and the accelerometer measurement signal under the high-frequency vertical input are superimposed to obtain the comprehensive acceleration measurement signal under the high-frequency harmonic frequency superposition fault as follows: e w =ω2-ω 31 ; a d1 =h4a d +(1-h4)a d0 ; Where a h3 For the high-frequency input signal of the inertial platform accelerometer; a d0 The accelerometer measurement signal is obtained from a high-frequency vertical input; then, the initial value of the resonant drift frequency, e, is set. w For accelerometer frequency error signal; ω 30 ω is a constant parameter related to the initial value of the resonant drift frequency signal; 31 This is the resonant drift frequency signal. Here, T is the gyroscope transfer function under a high-frequency harmonic frequency superposition fault, and T is a constant integral parameter, where a is a constant. d h4 represents the acceleration measurement signal under a high-frequency harmonic superposition fault; h4 is the injection time function of the high-frequency harmonic superposition fault, and t 4s The injection start time for the high-frequency harmonic superposition fault; t 4e The injection end time for the high-frequency harmonic superposition fault; a d1 This is a comprehensive acceleration measurement signal under a fault with superimposed high-frequency harmonics. Step S50: Based on the piezoelectric coefficient attenuation fault of the sensor's sensitive core, first set the accelerometer input signal under the piezoelectric coefficient attenuation fault. Then, the accelerometer transfer function model is used to solve the accelerometer measurement signal under fault-free conditions; Then, set an initial value for the piezoelectric coefficient and compare it with a constant 1 to obtain the piezoelectric coefficient error signal; The piezoelectric coefficient signal is then obtained through amplification and integration. Next, the accelerometer measurement signal under piezoelectric coefficient attenuation fault is calculated based on the piezoelectric coefficient error signal and the accelerometer transfer function model. Finally, the injection time function for the piezoelectric coefficient attenuation fault is designed, and combined with the accelerometer measurement signal under fault-free conditions, the comprehensive accelerometer measurement signal under the piezoelectric coefficient attenuation fault is obtained as follows: e k (n)=1-k0(n); the e2 =h5a e1 +(1-h5)a e ; Where a h4 For accelerometer input signal under piezoelectric coefficient decay fault; a e For accelerometer measurement signals under fault-free conditions; e k This is the piezoelectric coefficient error signal; k a0 Let T be the initial value of the piezoelectric coefficient, and k0(n) be the piezoelectric coefficient signal; b is the time constant for the decay of the piezoelectric coefficient, and is a constant parameter; a e1 h5 represents the accelerometer measurement signal under piezoelectric coefficient decay fault conditions; h5 is the injection time function of the piezoelectric coefficient decay fault, t 5s The injection start time for the piezoelectric coefficient decay fault; t 5e The injection end time for the piezoelectric coefficient decay fault; a e2 This is the comprehensive measurement signal of the accelerometer under piezoelectric coefficient decay fault. Step S60: Based on the accelerometer bias voltage instability drift fault, accelerometer large measurement signal distortion fault, inertial platform jitter fault, output signal superposition with high-frequency harmonic frequency fault, and sensor sensitive core piezoelectric coefficient attenuation fault, select one or more of these faults for fault injection, calculate the accelerometer measurement signal under the fault, realize the fault injection simulation of inertial platform and accelerometer, and complete the equivalent function of inertial platform and accelerometer testing.

Images