Confirmed reliability modeling and analysis method for high-precision fiber-optic gyroscope

Abstract

The invention belongs to the technical field of reliability modeling of fiber-optic gyroscopes, and particularly relates to a definite reliability modeling and analysis method of a high-precision fiber-optic gyroscope, which is based on performance margin and considers a degradation mechanism and uncertainty, and can accurately evaluate the reliability of the fiber-optic gyroscope. The problem that degradation and uncertainty are not considered in the prior art is solved. The method comprises the following steps: S1, performing function, performance and margin analysis on the fiber-optic gyroscope, and determining key performance parameters and threshold values of the fiber-optic gyroscope; determining the type of the key performance parameter in combination with the threshold value of the key performance parameter and a product design specification; s2, aiming at key performance parameters of the fiber-optic gyroscope, establishing a disciplinary cross equation of performance, internal dependent variables, external dependent variables and reversible time; s3, establishing a corresponding margin equation according to the type of the key performance parameter; s4, constructing a performance margin degradation equation based on the margin equation; and S5, on the basis of a performance margin degradation equation, considering internal and external cause uncertainty, and further constructing a definite reliability model.

Description

Technical Field

[0001] This invention belongs to the field of reliability modeling technology for fiber optic gyroscopes, and specifically relates to a reliable modeling and analysis method for high-precision fiber optic gyroscopes. Background Technology

[0002] Fiber optic gyroscopes (FOGs) are high-precision angular velocity sensors based on the Sagnac effect. Due to their advantages such as no moving parts, high shock resistance, and large dynamic range, they have become core inertial devices in the field of inertial navigation, widely used in aerospace, intelligent vehicles, and industrial automation. However, under extreme environments (such as drastic temperature changes, vibration, shock, and electromagnetic interference) and long-term continuous operation, the performance of the optical components (such as erbium-doped fiber light sources, fiber loops, and Y-waveguides) and electronic control systems of FOGs may degrade, leading to decreased accuracy or even failure. For example, wavelength drift of the light source directly affects the stability of the scaling factor, the temperature sensitivity of the fiber loop may introduce zero-bias errors, and the failure of the closed-loop control circuit may cause cumulative deviations in navigation information. These potential risks pose a severe challenge to high-reliability applications (such as satellite attitude control). Therefore, reliability modeling of fiber optic gyroscopes has become a key research direction for ensuring their performance throughout their entire lifecycle.

[0003] Currently, scholars have conducted extensive research on the performance models and degradation mechanisms of fiber optic gyroscopes. Most of these studies rely on accelerated degradation tests and reliability tests to obtain actual product data for modeling and compensation. However, this black-box modeling method cannot provide information on the relationship between system reliability and internal physical properties and external factors, thus failing to support product design improvements. Therefore, developing a "white-box" performance modeling method based on the internal component parameter information is a key research direction for ensuring the performance throughout the entire lifecycle of fiber optic gyroscopes. Summary of the Invention

[0004] To address the shortcomings of the existing technologies, this invention proposes a reliable modeling and analysis method for high-precision fiber optic gyroscopes. This method is based on reliable modeling with performance margins and considers degradation mechanisms and uncertainties to establish a reliability model, which can accurately evaluate the reliability of fiber optic gyroscopes and provide important guidance for product design and optimization.

[0005] This invention provides a reliable modeling method for high-precision fiber optic gyroscopes, the specific steps of which are as follows: S1 performs functional, performance, and margin analysis on the fiber optic gyroscope to determine the key performance parameters and thresholds of the fiber optic gyroscope; and, in conjunction with the thresholds of the key performance parameters and product design specifications, determines the types of key performance parameters. S2 establishes interdisciplinary equations for the key performance parameters of fiber optic gyroscopes, relating performance to internal variables, external variables, and reversible time. S3 establishes the corresponding margin equation based on the type of key performance parameters; S4 constructs a performance margin degradation equation based on the margin equation; S5 is based on the performance margin degradation equation, taking into account internal and external uncertainties, and thus constructs a certainty reliability model.

[0006] Optionally, the functional analysis in step S1 is used to determine the impact of the fiber optic gyroscope's zero bias, scaling factor error, and zero bias stability on the fiber optic gyroscope's angular velocity measurement error; based on the impact results of the functional analysis on the fiber optic gyroscope's angular velocity measurement error, a performance analysis is performed to determine the key performance parameters of the fiber optic gyroscope; based on the key performance parameters obtained from the performance analysis, and in conjunction with the product design specifications, the types and thresholds of the key performance parameters of the fiber optic gyroscope are determined.

[0007] Optionally, the specific steps of step S2 are as follows: Based on the working principle and structural composition of the fiber optic gyroscope, S21 establishes a control system model for the fiber optic gyroscope. S22 analyzes and quantifies the impact of the internal physical properties and external stress conditions of fiber optic gyroscopes on the performance of key components of fiber optic gyroscopes. Based on the impact analysis of the key components of the fiber optic gyroscope in step S22, S23 adds a disturbance term to the control system model of the fiber optic gyroscope to obtain an interdisciplinary model of the fiber optic gyroscope.

[0008] Optionally, internal physical property parameters include the polarization error of the fiber optic gyroscope, the polarization crosstalk error of the Y-waveguide, and the gyroscope optical path noise; external stress conditions include temperature and vibration.

[0009] Optionally, in step S3, the polarization error of the fiber optic gyroscope and the polarization error of the Y-waveguide are used as phase difference disturbance terms, the gyroscope optical path noise is used as parameter disturbance terms, and the temperature-induced zero-bias drift is used as output disturbance terms. These are added to the fiber optic gyroscope control system model, and the influence on the parameters of the fiber optic ring and the Y-waveguide is substituted into the control system performance model to obtain the fiber optic gyroscope interdisciplinary model.

[0010] Optionally, the specific steps of step S4 are as follows: S41 analyzes the degradation mechanism and causes of fiber optic gyroscopes, identifies the performance parameters that are degraded, and obtains the degradation equations corresponding to the degraded performance parameters; S42 combines the threshold values ​​of key performance parameters and substitutes the degradation equation into the margin equation to obtain the performance margin degradation equation.

[0011] Optionally, the specific steps of step S5 are as follows: The intrinsic and extrinsic parameters of the model, including physical properties and external conditions, are obtained based on the performance margin degradation model of the fiber optic gyroscope. Uncertainty in determining physical properties; To determine the uncertainty of external conditions; Based on the uncertainties of physical properties and external conditions, a certainty reliability model is established.

[0012] In another aspect, the present invention discloses a method for analyzing the certainty reliability of a high-precision fiber optic gyroscope, which uses the aforementioned certainty reliability model to analyze the certainty reliability of the high-precision fiber optic gyroscope.

[0013] Compared with the prior art, the present invention has at least the following beneficial effects: (1) The present invention adopts a “white box” performance modeling method based on the internal component parameter information, which breaks through the limitations of the traditional “black box” modeling of accelerated degradation test and can clearly reveal the intrinsic correlation mechanism between the reliability of fiber optic gyroscope and its internal physical properties and external environmental factors. (2) Based on the sure-reliability theory, this invention integrates the physical degradation mechanism and parameter uncertainty of optical components and electronic control systems into the modeling framework, and establishes a sure-reliability model that considers environmental stresses such as temperature and vibration. It can predict the degradation trend of key performance parameters such as zero bias stability and scaling factor error, and realize quantitative assessment of reliability throughout the entire life cycle. (3) This invention can quantitatively analyze the sensitivity and contribution of each component parameter to the system reliability, and can guide designers to prioritize the improvement of weak links, thereby significantly improving R&D efficiency and cost-effectiveness; (4) The accelerated degradation model of the present invention establishes a quantitative relationship between temperature and degradation rate, and can accurately extrapolate long-term performance under normal operating temperature using high-temperature accelerated test data, which greatly shortens the reliability verification cycle. (5) This invention supports customized reliability design for different application scenarios, and can optimize cost and performance while ensuring reliability. Attached Figure Description

[0014] Figure 1 The following is the simulation calculation process for the fiber optic gyroscope in this invention; Figure 2 This is a block diagram illustrating the working principle of the fiber optic gyroscope of the present invention. Figure 3 This is a block diagram of the fiber optic gyroscope algorithm control principle of the present invention; Figure 4 This is a model of the high-precision closed-loop fiber optic gyroscope control system of the present invention; Figure 5 This invention presents an interdisciplinary model of fiber optic gyroscopes. Figure 6This is the fiber optic gyroscope performance degradation model of the present invention; Figure 7 This is the zero-bias stability-temperature-time three-dimensional surface of the present invention; Figure 8 The scaling factor error-temperature-time three-dimensional surface of this invention; Figure 9 This is the zero-bias stability degradation curve and range of the present invention; Figure 10 The scaling factor error degradation curve and interval of this invention; Figure 11 This is the reliability curve of the present invention; Figure 12 This invention illustrates the effect of parameter variations on zero-bias stability. Figure 13 This describes the effect of changes in various parameters of the present invention on the scaling factor error. Detailed Implementation

[0015] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0016] A specific embodiment of the present invention, such as Figure 1-13 This paper discloses a reliable modeling and analysis method for high-precision fiber optic gyroscopes. Based on performance margin and considering degradation mechanisms and uncertainties, a reliable model is established. A reliability analysis of the fiber optic gyroscope is completed using a Monte Carlo simulation-based reliability assessment method. Specific steps include: S1 performs functional, performance, and margin analysis on the fiber optic gyroscope to determine the key performance parameters and thresholds of the fiber optic gyroscope; combined with the thresholds of the key performance parameters and product design specifications, it determines the types of key performance parameters.

[0017] Furthermore, the types of key performance parameters include large-scale, small-scale, and target-type.

[0018] Preferably, the fiber optic gyroscope is a high-precision three-axis fiber optic gyroscope, whose main function is to convert the sensitive carrier angular motion information into a digital signal proportional to the carrier angular increment, and transmit it externally through an RS-422 communication interface.

[0019] Further, (1) functional analysis is used to determine the effects of the fiber optic gyroscope's zero bias, scaling factor error, and zero bias stability on the fiber optic gyroscope's angular velocity measurement error.

[0020] Specifically, a high-precision three-axis fiber optic gyroscope is used to sense the angular velocity of the carrier in three directions: yaw, pitch, and roll. Its working principle is as follows: the light beam emitted from the light source enters the coupler and is split into two beams, which are coupled into the fiber optic sensing loop from both ends and propagate in clockwise and counterclockwise directions, respectively. When the fiber optic sensing loop is stationary, the optical path difference between the two beams exiting from the two ends of the fiber optic sensing loop is zero. However, when the fiber optic sensing loop moves at an angular velocity... When rotating, due to the Sagnac effect, two beams of light propagating in clockwise and counterclockwise directions produce an optical path difference. This leads to a phase difference, and the angular rate can be obtained by detecting the phase difference. Information.

[0021] During this process, fiber optic gyroscopes will generate errors due to environmental factors such as temperature and rapid temperature changes. These errors will affect the accuracy of the angular velocity measurement of the fiber optic gyroscope, ultimately affecting the navigation accuracy of the system and causing a decline in the performance of the integrated inertial navigation system. The functional analysis of fiber optic gyroscopes includes angular velocity measurement errors.

[0022] Furthermore, the angular velocity measurement error of the fiber optic gyroscope The expression is: (1) In the formula, This is the fiber optic gyroscope scaling factor error matrix; Indicates the fiber optic gyroscope carrier system Frame of reference relative to inertial frame The rotational angular velocity of the system; The constant error of the gyroscope is represented by the zero bias constant value; The random error of the gyroscope is represented by zero-bias stability.

[0023] (2) Performance analysis: Based on the influence results of the fiber optic gyroscope angular velocity measurement error obtained from the fiber optic gyroscope function analysis in (1), it can be seen that the zero bias, scale factor error and zero bias stability of the fiber optic gyroscope have a significant impact on its angular velocity measurement accuracy. Since the zero bias focuses more on high-precision measurement in a short time, it is not considered as a key performance parameter. Only the scale factor error and zero bias stability are selected as the key performance parameters of the fiber optic gyroscope. (3) Margin analysis: Based on the key performance parameters obtained from the performance analysis and combined with the product design specifications, determine the type and threshold of the key performance parameters of the fiber optic gyroscope, in order to prepare for the subsequent construction of the margin equation.

[0024] For example, the parameter scaling factor error of the product design specification and zero bias stability The threshold values ​​are 5 ppm and 0.004° / h, respectively, and the key performance parameters are classified as small parameters.

[0025] S2 establishes interdisciplinary equations relating performance to internal variables, external variables, and reversible time for key performance parameters of fiber optic gyroscopes.

[0026] Based on the working principle and structural composition of fiber optic gyroscopes, S21 establishes a control system model for fiber optic gyroscopes.

[0027] S211 defines the working principle and structural composition of the fiber optic gyroscope.

[0028] Furthermore, the working principle of a fiber optic gyroscope is as follows: the light beam emitted by the light source enters the coupler and is split into two beams, which are coupled into the fiber optic sensing loop from both ends and propagate in clockwise and counterclockwise directions, respectively. When the fiber optic sensing loop is stationary, the optical path difference between the two beams exiting from the two ends of the fiber optic sensing loop is zero. However, when the fiber optic sensing loop moves at an angular velocity... When rotating, due to the Sagnac effect, two beams of light propagating in clockwise and counterclockwise directions produce an optical path difference. This leads to a phase difference, and the angular rate can be obtained by detecting the phase difference. Information.

[0029] Further, see Figure 2 The structure of a fiber optic gyroscope includes a shared erbium-doped fiber light source, with a 1×3 fiber coupler splitting the output light into three equal paths. In addition, the optical path section also includes three 2×2 couplers, three multi-energy integrated Y-waves, three fiber loops, and three detectors, which respectively form three axial sensing optical paths to sense angular motion in each direction and convert interference light signals into electrical signals. The gyroscope processing circuit is a single unit that simultaneously processes signals in the three axes and generates three output data channels.

[0030] Specifically, the light source is an erbium-doped fiber light source, and the output light is divided into three optical paths equally by a 1×3 fiber coupler.

[0031] Furthermore, each optical path includes a 2×2 coupler, a multi-energy integrated Y waveguide, an optical fiber ring, and a detector. The three optical paths constitute three axial sensing optical paths, used to sense angular motion in each direction and convert interference optical signals into electrical signals. Specifically, the gyroscope processing circuit consists of one unit, which simultaneously processes signals from the three axial sensing optical paths and generates three output data streams.

[0032] Furthermore, the Sagnac interferometer consists of a light source, a coupler, a Y-waveguide, and an optical fiber loop, and generates an optical path difference from two beams of light propagating in clockwise and counterclockwise directions. Caused phase difference The angular velocity Ω is obtained by the following expression: (2) In the formula, L 0 represents the circumference of the fiber optic ring. λ is the wavelength of light in a vacuum. c The speed of light in a vacuum. D 0 represents the diameter of the fiber optic loop. Let... , Indicates the scale factor.

[0033] After the interfering light enters the photodetector, the light intensity signal illuminates the photodiode integrated into the photodetector, converting the optical signal into an electrical signal, as expressed by: (3) In the formula, The electrical signal representing time t; H The photoelectric conversion responsivity of the photodetector; This is a light intensity signal.

[0034] Furthermore, the electrical signal is converted into a voltage signal via the transimpedance within the photodetector. The expression is: (4) In the formula, R f This is the transimpedance of the photodetector.

[0035] Furthermore, considering this photoelectric conversion stage as a proportional stage, its proportionality factor is determined by the parameters of the photodetector itself, expressed as: (5) In the formula, The scaling factor represents the photoelectric conversion ratio.

[0036] Then, the voltage signal transmitted by the photodetector The amplified electrical signal is then transmitted to the gyroscope processing circuit. The high-precision fiber optic gyroscope used in this invention employs a closed-loop digital processing circuit scheme, and its control principle is as follows: Figure 4 As shown.

[0037] By biasing and modulating, the intensity of the interference light is controlled within a high-sensitivity region. The interference light intensity is converted into an electrical signal by a photodetector, then acquired by an A / D converter and converted into a digital quantity. The demodulated digital data is used as the change in angular velocity and fed into the accumulator of a digital integrator. After accumulation, the gyroscope angular velocity data is obtained. This data is processed and placed into the output register, and then output through the rate register as the gyroscope output. Simultaneously, the data is output through the rate register and fed into the feedback modulation generator for closed-loop modulation of the gyroscope.

[0038] The data entering the feedback modulation generator is accumulated twice. The accumulated result is superimposed with the value of the bias modulation signal. After D / A conversion, the corresponding modulation voltage signal is generated. After being amplified by amplifier 2, it is applied to the phase modulator of the Y waveguide to compensate for the Sagnac phase shift, so that the gyroscope's operating point is always stable in a very small area near the desired operating point.

[0039] The Y-waveguide phase modulator functions by using the delay of the fiber optic loop and an applied voltage to create a phase difference between two pairs of counter-propagating light beams. Therefore, when the feedback voltage output from the gyroscope processing circuit is applied to the Y-waveguide phase modulator, a feedback phase difference is generated. The expression is: (6) In the formula, The modulation gain of the phase modulator. The half-wave voltage of the phase modulator; V(t) Let be the derivative of the modulated signal at time t.

[0040] Based on the obtained working principle and structural composition of the fiber optic gyroscope, S212 establishes a control system model for the fiber optic gyroscope, such as... Figure 5 As shown.

[0041] In the control system model of a fiber optic gyroscope, the reciprocal of the fiber optic gyroscope's scaling factor... This is used to convert digital angular velocity quantities into angular velocity values, and its expression is: (7) In the formula, This indicates the gain of the D / A converter.

[0042] Based on the above analysis of the functional principle of fiber optic gyroscopes and combined with control theory, this invention constructs a control system model for fiber optic gyroscopes, as shown in Figure 5. K 1 and K 2 represents the multiples of amplifier 1 and amplifier 2, respectively; This represents the integrator in Simulink.

[0043] S22 analyzes and quantifies the impact of internal physical properties of fiber optic gyroscopes, such as polarization error, Y-waveguide polarization crosstalk error, and gyroscope noise, as well as external stress conditions such as temperature and vibration, on the performance of key components of fiber optic gyroscopes (such as Y-waveguides and fiber optic rings).

[0044] S221 obtains the polarization error of the fiber optic gyroscope; Furthermore, when the optical signal in a fiber optic gyroscope propagates through an optical path spanning kilometers, its phase, polarization, and other characteristics may change due to the influence of physical fields, thus causing measurement errors. Among these errors, the presence of polarization coupling points in the optical path leads to cross-coupled light waves. Since the interference phase difference between these cross-coupled light waves differs from the interference phase difference between the main wave and the main wave, this results in gyroscope measurement errors; these errors are called fiber optic gyroscope polarization errors. Fiber optic gyroscope polarization errors can be categorized into two types: intensity-based polarization errors and amplitude-based polarization errors.

[0045] Specifically, the expression for intensity-type polarization error is: (8) In the formula, Intensity-type polarization phase error Standard deviation; The amplitude suppression ratio of the Y-waveguide; h The average rate of optical power conversion; L This is the length of the fiber optic loop; N This represents the number of polarization coupling points in the optical path. ; This is the depolarization length of the fiber optic ring; , C T This refers to the polarization crosstalk of the fiber optic loop.

[0046] Specifically, the expression for amplitude-type polarization error is: (9) In the formula, This refers to amplitude-type polarization phase shift error; d The degree of polarization of the light source. This indicates the coherence of the light beam emitted from the light source after it enters the coupler and is split into two coupled light waves that return to the beam splitter and interfere. This represents the time difference between the return of the two light waves to the beam splitter. and These represent the strength coupling rates of the two coupling points, respectively.

[0047] S222 Obtains the Y-waveguide polarization crosstalk error; It is understandable that when a Y-waveguide is coupled to an optical fiber, polarization crosstalk occurs due to the alignment angle error between their polarization principal axes. This is called Y-waveguide pigtail polarization crosstalk, which is the main source of gyroscope polarization crosstalk.

[0048] Specifically, this invention addresses the polarization error of the Y-waveguide. As a phase disturbance term, it is added to the fiber optic gyroscope control system model to reflect the stationary phase error caused by Y-waveguide polarization crosstalk. The impact of optical path phase difference on fiber optic gyroscopes.

[0049] Specifically, the polarization crosstalk at the output end of the Y-waveguide pigtail is obtained by the following expression: (10) In the formula, The amplitude ratio of the output light wave from the optical fiber. This is for Y-waveguide pigtail polarization crosstalk.

[0050] Static phase error caused by Y-waveguide polarization crosstalk The expression is: (11) S223 acquires the optical path noise of the fiber optic gyroscope; The detection noise of a fiber optic gyroscope affects its measurement accuracy. This noise primarily consists of two parts: optical noise and circuit noise. Optical noise includes thermal noise from the photodetector, shot noise from the photoelectric converter, and relative intensity noise caused by the light source's beat frequency. Circuit noise includes input current and voltage noise from the operational amplifier, noise from the A / D sampling conversion, and quantization noise. Of these, circuit noise has a smaller impact on the gyroscope compared to optical noise. Therefore, this patent only models the optical noise of the fiber optic gyroscope.

[0051] Furthermore, the optical path noise of a fiber optic gyroscope includes relative intensity noise, shot noise, and thermal noise.

[0052] Specifically, relative intensity noise The expression is: (12) In the formula, Indicates photocurrent; This indicates the spectral width of the light source.

[0053] Furthermore, The expression representing the spectral width of a light source is: (13) In the formula, λ is the wavelength of light in a vacuum. c y is the speed at which light travels in a vacuum.

[0054] Furthermore, photocurrent The expression is: (14) In the formula, H The photoelectric conversion responsivity of the photodetector To resist strong light signals, For the bias phase, take . Specifically, shot noise is random noise generated when photons are converted into electrons. Shot noise is related to the optical power injected into the detector, and its expression is: (15) In the formula, e is the charge of a single electron, taken as . Specifically, the thermal noise originates from the detector's dark current and the Johnson thermal noise of the detector's transimpedance amplifier feedback resistor. The expression is: (16) In the formula, k Let Boltzmann constant be used here. ; For the transimpedance of a photodetector; It is dark current.

[0055] S224 temperature-induced zero-bias drift; For fiber optic gyroscopes operating in variable temperature environments, two beams of light propagating in opposite directions within the fiber optic loop will experience different phase changes. This non-reciprocal phase shift caused by temperature results in an error in the gyroscope's output, known as the Shupe error.

[0056] Temperature-induced zero-bias drift directly affects the fiber optic gyroscope output. When added to the output of the fiber optic gyroscope control system model, the expression for the Shupe error caused by temperature-induced zero-bias drift is: (17) In the formula, express Non-reciprocal phase error caused by Shupe error at time step; This represents the rate of temperature change of the fiber optic loop at position z; express Time Fiber The temperature of the segment; n represents the refractive index of the optical fiber; D represents the diameter of the optical fiber loop; L Indicates the length of the fiber optic loop; T Indicates temperature; It can be seen that the greater the rate of temperature change, the greater the drift error, and the relationship between the resulting Shupe error and the rate of ambient temperature change exhibits a non-linear characteristic. Due to fiber thermal stress, the influence of the adhesive coating, and the non-uniformity of the heat conduction process, the fiber optic gyroscope experiences temperature drift error, and the magnitude of this error is related to the rate of temperature change. Relevant experimental data show that the relationship between the rate of change of external temperature and the gyroscope's thermal drift error is a parabolic non-linear relationship, which can be described using a parabolic function: (18) In the formula, Indicates the rate of temperature change. This represents the zero bias standard deviation of the fiber optic gyroscope over a period of time. , and All of these are parameters to be fitted.

[0057] Due to the thermal stress of the optical fiber, the effects of the adhesive coating, and the non-uniformity of the heat conduction process, the fiber optic gyroscope experiences temperature drift error, the magnitude of which is related to the rate of temperature change. The relationship between the external temperature change rate and the gyroscope's thermal drift error is non-linear, similar to a parabola, and can be described using a parabolic function. When the temperature change rate is 1℃ / min, the zero-bias stability is assumed to be 0.001(°) / h(1 The expression for the zero-bias stability of a fiber optic gyroscope is: (19) In the formula, (°C / min) represents the rate of temperature change. (° / h) represents the zero-bias stability of the fiber optic gyroscope.

[0058] S225 Temperature-Induced Fiber Ring Parameters (Fiber Ring Diameter) D and fiber length L and the change in the half-wave voltage of the Y-waveguide; ① Changes in fiber optic ring parameters The thermal expansion and contraction of materials such as optical fibers, fiber optic ring skeletons, and adhesives within the fiber optic ring under varying temperatures all cause changes in the average diameter of the fiber optic ring, and there is a fixed proportional relationship between the average diameter of the fiber optic ring and the fiber length. Specifically, due to the stretching effect of the expansion of the average diameter of the fiber optic ring under temperature conditions, the change in fiber length within the fiber optic ring over the entire temperature range is approximately four times the change in fiber length under free conditions. The expression for the temperature-induced changes in fiber optic ring parameters is: (20) (twenty one) (twenty two) In the formula, This is the linear expansion coefficient of the optical fiber. D The diameter of the fiber optic ring. L This refers to the length of the optical fiber. This indicates the change in the diameter of the fiber optic ring; This indicates the change in fiber length; Indicates the initial diameter of the fiber optic ring; Indicates the initial length of the fiber optic loop; It represents the amount of temperature change.

[0059] Therefore: (twenty three) In the formula, This indicates how the scaling factor changes with temperature.

[0060] ②Y-waveguide half-wave voltage variation; Furthermore, using lithium niobate crystal (LiNbO3) as the substrate, a model was established to describe the temperature variation of the half-wave voltage of the Y-waveguide, expressed as: (twenty four) (25) In the formula, For the Y-waveguide half-wave voltage, The scaling factor for the half-wave voltage of the Y-waveguide as a function of temperature; This represents the initial value of the Y-waveguide half-wave voltage; A model representing the change of half-wave voltage of a Y-waveguide with temperature.

[0061] Therefore: (26) In the formula, This indicates how the modulation gain of the phase modulator changes with temperature.

[0062] Based on the impact analysis of the key components of the fiber optic gyroscope in step S22, S23 adds a disturbance term to the control system model of the fiber optic gyroscope to obtain an interdisciplinary model of the fiber optic gyroscope.

[0063] Based on the above analysis, intensity-type polarization error, amplitude-type polarization error, and Y-waveguide polarization error are taken as phase difference disturbance terms, optical path noise is taken as photodetector parameter disturbance terms of the fiber optic gyroscope, and temperature-induced zero-bias drift is taken as output disturbance terms. These are added to the fiber optic gyroscope control system model, and the influence of environmental factors (external stress conditions) on the fiber optic ring and Y-waveguide parameters is substituted into the control system performance model. Thus, the interdisciplinary model of the fiber optic gyroscope shown in Figure 6 can be obtained.

[0064] In summary, the interdisciplinary equation for the zero-bias stability of a fiber optic gyroscope is: (27) In the formula, Indicates zero-bias stability; This is the initial value for the zero-bias stability of the fiber optic gyroscope; Temperature-induced zero-bias drift.

[0065] The interdisciplinary equation for the scaling factor error is: (28) In the formula, Indicates the scale factor error; Indicates the amplifier's gain; Indicates the gain of the D / A converter; The scaling factor is the measured value. for initial value, for The initial value.

[0066] S3 establishes the corresponding margin equation based on the type of key performance parameters, with the expression as follows: (29) In the formula, Indicates performance margin; Represent the margin equation; Indicates key performance parameters; Thresholds representing key performance parameters; This indicates the function that takes the smaller value.

[0067] S4 constructs a performance margin degradation equation based on the margin equation; S41 analyzes the degradation mechanism and causes of fiber optic gyroscopes, identifies the performance parameters that are degraded, and obtains the degradation equations corresponding to the degraded performance parameters.

[0068] Specifically, during use, fiber optic gyroscopes mainly experience phenomena such as decreased light source output power, decreased photodetector responsivity, and increased polarization crosstalk in the Y-waveguide and fiber optic loops. However, existing long-term high-temperature stability test data for fiber optic gyroscopes shows that the change in photodetector output power within 2000 hours is no more than 5%, and its degradation is negligible. Furthermore, related experimental results show that the erbium-doped fiber optic light source used in high-precision fiber optic gyroscopes also exhibits good long-term stability in output power. Since the main parameter studied in this invention is the optical power reaching the detector, which is relatively small compared to the light source output power, the impact of light source output power degradation on the fiber optic gyroscope is also negligible.

[0069] Therefore, in the performance degradation modeling of fiber optic gyroscopes, this invention mainly focuses on modeling the polarization crosstalk degradation of Y-waveguides and fiber optic rings.

[0070] S411 constructs a Y-waveguide polarization crosstalk degradation model, the expression of which is: (30) (31) In the formula, Initial polarization crosstalk for the Y-waveguide; A 1 represents the coefficient to be estimated; The activation energy for the degradation response of the Y-waveguide; k Boltzmann's constant; T Thermodynamic temperature; This refers to the degradation time.

[0071] Combining equation (12), the degradation model of Y-waveguide polarization crosstalk error can be obtained as follows: (32) S412 constructs a fiber optic ring polarization crosstalk degradation model, with the following expression: (33) (34) In the formula, This is the initial polarization crosstalk of the fiber optic loop; A 2 represents the coefficient to be estimated; The activation energy for the degradation reaction of the optical fiber ring; k Boltzmann's constant; T Thermodynamic temperature; This represents the degradation time. Combining the section analysis results, the intensity-type polarization error can be obtained. Standard deviation The degradation model is as follows: (35) Right now . S42 combines the threshold values ​​of key performance parameters and substitutes the degradation equation into the margin equation to obtain the performance margin degradation equation, which derives from the expression: (36) In the formula, Indicates performance margin; This represents the margin equation.

[0072] For example, the expression for the scaling factor performance degradation equation of a fiber optic gyroscope is: (37) In the formula, This represents the activation energy, preferably 0.6 eV; k is a constant. These are unknown parameters; they are obtained through data fitting. This represents the initial value of the scaling factor error.

[0073] Substituting the performance degradation equation into the margin equation, we obtain the performance margin degradation equation for the fiber optic gyroscope, which is expressed as follows: .

[0074] In the formula, The threshold representing zero-bias stability; The performance degradation equation representing zero-biased stability; The threshold representing the scaling factor error; The performance degradation equation representing the scaling factor error; The performance margin representing zero-bias stability; This represents the performance margin for scaling factor error.

[0075] S5 is based on the performance margin degradation equation, taking into account internal and external uncertainties, and then constructs a certainty reliability model; Specifically, the uncertainties in the performance margin degradation equation of fiber optic gyroscopes are analyzed from two aspects: physical properties and external conditions. These uncertainties are then quantified, and a reliable model of the fiber optic gyroscope is constructed.

[0076] S51 determines the internal and external parameters with uncertainties and their distribution.

[0077] In practical applications, the performance margin of fiber optic gyroscopes may be affected by various uncertainties during their operation. This invention analyzes and quantifies the uncertainties in the performance margin degradation equations of various components in a fiber optic gyroscope from both physical properties and external conditions, thereby determining the uncertain internal and external parameters and their distribution, and ultimately constructing a reliable model for the fiber optic gyroscope.

[0078] Step 511: Obtain the internal and external parameters of the model based on the performance margin degradation model of the fiber optic gyroscope, including physical properties and external conditions.

[0079] Specifically, the physical properties (intrinsic parameters) are expressed as follows: ; External conditions (external factors), expressed as: ; During the production process, variations in manufacturing processes can affect the initial length of the fiber optic ring. L 0 and fiber ring diameter D Inconsistencies exist; furthermore, manufacturing defects can also affect the wavelength of light. The responsivity of photodetectors H Transimpedance of photodetectors Y-waveguide half-wave voltage Y-waveguide initial polarization crosstalk and the initial polarization crosstalk of the fiber optic ring Inconsistencies in parameters, etc. P 0 represents the optical power reaching the photodetector. Since its impact on the fiber optic gyroscope's performance is relatively small, its uncertainty is not considered here. Additionally, Indicates the amplitude suppression ratio of the Y-waveguide. Indicates the fiber loop depolarization length. Indicates the degree of polarization of the light source. Indicates the coherence of the coupled optical waves. Both represent the strength coupling rate. Indicates spectral width, This represents the wavelength of light. Furthermore, the various noises inherent in fiber optic gyroscopes also exhibit uncertainty.

[0080] The performance degradation margin model of fiber optic gyroscopes also shows that their performance is affected by temperature. T and rate of temperature change V T The impact of these parameters is significant, and in actual use, these two parameters also contain uncertainties.

[0081] S512 determines the uncertainty of physical properties; (1) Physical parameters of fiber optic ring Due to manufacturing errors, the length of the fiber optic ring... L 0. Diameter D 0. The wavelength of light transmitted in the fiber optic ring and initial polarization crosstalk All of them have uncertainty, and their uncertainty can be quantified as follows: (38) in, express The mean; express Standard deviation; express The mean; express Standard deviation; express The mean; express Standard deviation; express The mean; express Standard deviation; (2) Physical parameters of photodetector The detector used in this invention is a PIN photodetector, and its responsivity is... Hand transimpedance R f Both involve uncertainty, which can be quantified as follows: (39) in, express The mean; express Standard deviation; express The mean; express Standard deviation; (3) Physical parameters of Y-waveguide Polarization crosstalk and half-wave voltage are key parameters of Y-waveguides. However, due to errors in manufacturing processes, the initial polarization crosstalk of a Y-waveguide can vary. and initial half-wave voltage It has uncertainty, and its uncertainty is quantified as follows: (40) in,; express The mean; express Standard deviation; express The mean; express Standard deviation; (4) Fiber optic gyroscope noise Relative intensity noise of fiber optic gyroscopes I RIN Shot noise I shot and thermal noise I ther All of these can be considered white noise, quantized as a normal distribution with a mean of 0, and their uncertainty quantification results are as follows: (41) in, express The variance; express The variance; express The variance; (5) Intensity-type polarization error Intensity-type polarization error It can be considered as a normal distribution with a mean of 0. The uncertainty quantification result is: (42) in, express The standard deviation; (6) Temperature-induced zero-bias drift Zero-bias drift of fiber optic gyroscope caused by temperature changes Generally, it is quantified as a normal distribution with a mean of 0, and its standard deviation is given by the aforementioned formula. The uncertainty quantification result is as follows: (43) in, express The standard deviation; S513 Determines the uncertainty of external conditions In real-world applications, the performance degradation of fiber optic gyroscopes is affected by ambient temperature. T and the rate of change of ambient temperature V T The impact, and its uncertainty quantification result is: (44) in, express Standard deviation; express The standard deviation; S52 establishes a certainty reliability model based on the uncertainty of physical properties and external conditions.

[0082] (45) In the formula, Indicates a high degree of certainty regarding reliability; Represents a probability measure; This indicates a performance margin that takes into account uncertainties; Indicates the internal variable; This represents an external variable.

[0083] Another embodiment of the present invention discloses a method for analyzing the certainty reliability of a high-precision fiber optic gyroscope. Using the certainty reliability model described in the foregoing claims, the method analyzes the certainty reliability of the high-precision fiber optic gyroscope. The specific steps are as follows: S101 determines the model parameters of the fiber optic gyroscope; The distributions of deterministic and uncertain parameters, as well as their distributed parameters, of the degradation model of the fiber optic gyroscope were obtained. The model parameter values ​​for a certain type of fiber optic gyroscope were derived from product design specifications and experimental data.

[0084] S102 obtains the performance degradation curve and confidence interval curve of the fiber optic gyroscope based on the model parameters; Furthermore, the 95% confidence interval curve of the fiber optic gyroscope was obtained.

[0085] S103 uses the confidence reliability model obtained in step S5 to obtain the reliability; S104 sensitivity analysis; Based on the degradation model parameter information of the fiber optic gyroscope, the sensitivity of each parameter of the fiber optic gyroscope is analyzed, the sensitivity parameters are determined, and suggestions are provided for product design and use.

[0086] Taking a certain type of fiber optic gyroscope as an example, we model its key performance parameters and analyze the performance degradation and degradation range to complete the reliability analysis of the fiber optic gyroscope.

[0087] First, model-based reliability analysis of fiber optic gyroscopes. The parameter values ​​for the degradation model of the fiber optic gyroscope are shown in Table 1.

[0088] Table 1 Parameters of the fiber optic gyroscope performance degradation model

[0089] It should be noted that the above list of the types and quantities of parameters in this invention is only a hypothetical example. In actual implementation, the corresponding parameters can be set as needed.

[0090] Then, the deterministic degradation law Under the parameters of the fiber optic gyroscope performance degradation model in Table 1, the zero-bias stability of the fiber optic gyroscope is obtained according to the performance margin degradation model. Scale factor error dKF 1. Relationship between temperature and time. Six temperature points were selected between 10℃ and 70℃, and the results are shown in Figures 8 and 9. It can be seen that the zero-bias stability and scaling factor error of the fiber optic gyroscope both increase with the increase of degradation time, and the degradation rate is affected by temperature, with the degradation rate being faster at higher temperatures.

[0091] Next, we will quantify the uncertainty. The results of uncertainty quantification are shown in Table 2.

[0092] Table 2 Uncertainty Quantification Parameters

[0093] It should be noted that the above list of the types and quantities of parameters in this invention is only a hypothetical example. In actual implementation, the corresponding parameters can be set as needed.

[0094] Then, the performance degradation range of the fiber optic gyroscope. Under the parameters of the fiber optic gyroscope performance degradation model in Table 1, the relationship between the performance degradation of the fiber optic gyroscope and time can be calculated based on the performance margin degradation model and its uncertainty quantification results. The corresponding temperature conditions are alternating hot and cold days with a temperature change rate of 1℃ / min. After the simulation is completed, the 95% confidence intervals of the degradation of each performance parameter of the fiber optic gyroscope during the mission can be statistically obtained, as shown in the figure below.

[0095] Next, reliability assessment Based on the fiber optic gyroscope metric model, the parameters in Table 2 were substituted into the confidence reliability model. The Monte Carlo simulation method was used for random sampling to simulate and solve the probability that the margin is greater than 0. The reliability change curve of the fiber optic gyroscope after 10 years was calculated, and the confidence reliability assessment results were obtained, as shown in Figure 12.

[0096] The results above show that, due to environmental factors and error accumulation, zero-bias stability gradually degrades over time, especially in the later stages, where the degradation rate accelerates, and its impact on the overall reliability of the fiber optic gyroscope becomes more significant in the later stages. The scaling factor error performance is very stable, consistently maintaining high reliability, and plays a strong supporting role in the overall performance stability of the fiber optic gyroscope.

[0097] Finally, sensitivity analysis Based on the degradation model parameter information of the fiber optic gyroscope, the zero bias constant value of the fiber optic gyroscope is determined. Scale factor error and zero bias stability The deterministic degradation law with respect to the initial sagnac coefficients Initial Y-waveguide coefficients Y-waveguide initial polarization crosstalk Initial polarization crosstalk of fiber ring Photoelectric converter responsivity H and transimpedance The sensitivity of the data is analyzed to determine the sensitivity parameters, providing recommendations for product design and use.

[0098] The above analysis results show that: (1) the Sagnac coefficient, fiber ring polarization crosstalk and photodetector responsivity have a significant impact on the scaling factor error of the fiber optic gyroscope; (2) the Sagnac coefficient, Y waveguide coefficient, photodetector responsivity and transimpedance have a significant impact on the zero-bias stability of the fiber optic gyroscope.

[0099] Therefore, based on the above sensitivity analysis results, the following suggestions can be made for the design and control of fiber optic gyroscopes: (1) Suppress fiber optic loop polarization crosstalk and Y-waveguide polarization crosstalk; (2) On the basis of meeting the design requirements, the longer the fiber optic length, the larger the fiber optic loop diameter, and the shorter the optical wavelength, the higher the accuracy of the fiber optic gyroscope; (3) On the basis of meeting the design requirements, the smaller the Y-waveguide half-wave voltage, the smaller the zero-bias stability of the fiber optic gyroscope; (4) On the basis of meeting the design requirements, the smaller the responsivity of the optical detector and the smaller the transimpedance, the smaller the zero-bias stability of the fiber optic gyroscope.

[0100] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A reliable modeling method for high-precision fiber optic gyroscopes, characterized in that, The specific steps are as follows: S1 performs functional, performance, and margin analysis on the fiber optic gyroscope to determine the key performance parameters and thresholds of the fiber optic gyroscope; and, in conjunction with the thresholds of the key performance parameters and product design specifications, determines the types of key performance parameters. S2 establishes interdisciplinary equations relating performance to internal variables, external variables, and reversible time for key performance parameters of fiber optic gyroscopes. S3 establishes the corresponding margin equation based on the type of key performance parameters; S4 constructs a performance margin degradation equation based on the margin equation; S5 is based on the performance margin degradation equation, taking into account internal and external uncertainties, and then constructs a certainty reliability model.

2. The confidence reliability modeling method according to claim 1, characterized in that, The functional analysis in step S1 is used to determine the impact of the fiber optic gyroscope's zero bias, scale factor error, and zero bias stability on the fiber optic gyroscope's angular velocity measurement error. Based on the impact of the fiber optic gyroscope angular velocity measurement error obtained from the functional analysis, a performance analysis is conducted to determine the key performance parameters of the fiber optic gyroscope. Based on the key performance parameters obtained from performance analysis and in conjunction with product design specifications, the types and thresholds of key performance parameters for fiber optic gyroscopes are determined.

3. The confidence reliability modeling method according to claim 1, characterized in that, The specific steps of step S2 are as follows: Based on the working principle and structural composition of fiber optic gyroscopes, S21 establishes a control system model for fiber optic gyroscopes. S22 analyzes and quantifies the impact of the internal physical properties and external stress conditions of fiber optic gyroscopes on the performance of key components of fiber optic gyroscopes. Based on the impact analysis of the key components of the fiber optic gyroscope in step S22, S23 adds a disturbance term to the control system model of the fiber optic gyroscope to obtain an interdisciplinary model of the fiber optic gyroscope.

4. The confidence reliability modeling method according to claim 3, characterized in that, Internal physical properties include the polarization error of the fiber optic gyroscope, the polarization crosstalk error of the Y-waveguide, and the optical path noise of the gyroscope. External stress conditions include temperature and vibration.

5. The confidence reliability modeling method according to claim 4, characterized in that, In step S3, the polarization error of the fiber optic gyroscope and the polarization error of the Y-waveguide are used as phase difference perturbation terms, the gyroscope optical path noise is used as parameter perturbation terms, and the temperature-induced zero-bias drift is used as output perturbation terms. These are added to the fiber optic gyroscope control system model, and the influence on the parameters of the fiber optic loop and the Y-waveguide is substituted into the control system performance model to obtain the fiber optic gyroscope interdisciplinary model.

6. The confidence reliability modeling method according to claim 4, characterized in that, The specific steps of step S4 are as follows: S41 analyzes the degradation mechanism and causes of fiber optic gyroscopes, identifies the performance parameters that are degraded, and obtains the degradation equations corresponding to the degraded performance parameters; S42 combines the threshold values ​​of key performance parameters and substitutes the degradation equation into the margin equation to obtain the performance margin degradation equation.

7. The confidence reliability modeling method according to claim 1, characterized in that, The specific steps of step S5 are as follows: The intrinsic and extrinsic parameters of the model, including physical properties and external conditions, are obtained based on the performance margin degradation model of the fiber optic gyroscope. Uncertainty in determining physical properties; To determine the uncertainty of external conditions; Based on the uncertainties of physical properties and external conditions, a certainty reliability model is established.

8. A method for analyzing the certainty reliability of a high-precision fiber optic gyroscope, using the certainty reliability model described in any one of claims 1-7 to analyze the certainty reliability of the high-precision fiber optic gyroscope.

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