Robustness analysis method and device for health status assessment of laser gyroscopes

Abstract

This application relates to a robustness analysis method and apparatus for assessing the health status of a laser gyroscope. The method includes: performing uncertainty modeling on the health assessment evidence of the laser gyroscope; calculating the confidence interval, interval weight, and reliability of the input health assessment evidence based on the established uncertainty model; establishing interval evidence inference rules based on two pieces of health assessment evidence; constructing an optimization model based on the interval evidence inference rules; outputting the optimal interval for the health assessment evidence of the laser gyroscope based on the optimization model, the confidence interval, interval weight, and reliability of the health assessment evidence; calculating a robustness coefficient to further evaluate robustness to disturbances; finding the disturbance range based on the robustness coefficient and optimizing it to obtain a disturbance threshold. This method can improve the accuracy of laser gyroscope health status assessment while ensuring robustness.

Description

Technical Field

[0001] This application relates to the field of health assessment technology, and in particular to a robust analysis method and apparatus for assessing the health status of a laser gyroscope. Background Technology

[0002] In recent years, the rapid development of next-generation information technologies such as the Internet of Things, big data, digital twins, and artificial intelligence has brought a wealth of decision-making information. The challenge to timely and accurate decision-making is no longer a lack of information, but rather the inherent risk of uncertainty arising from unreliable, incomplete, deceptive, and conflicting information. Therefore, a deep understanding of uncertainty is a crucial prerequisite for achieving scientific and rational decision-making.

[0003] Due to differing understandings of uncertainty and its properties, people's interpretations of uncertainty vary. From a cognitive perspective, it can be divided into a priori uncertainty and cognitive uncertainty. From an attribute dimension perspective, it includes randomness, fuzziness, incompleteness, emptiness, ambiguity, inaccuracy, incoherence, nonspecificity, and complex uncertainty. To address various uncertainties in decision-making, several representative methods have been developed, such as probability theory, fuzzy set theory, rough set theory, evidence theory, decision theory, and machine / deep learning-related theories. It is worth noting that these theories have excellent applications in various fields.

[0004] Regarding independent evidence combinations, the Dempster-Shafer evidence theory was first proposed by Dempster in 1967 and by Shafer in 1976. However, the Dempster-Shafer rule suffers from a serious "counterintuitive" problem when dealing with highly contradictory evidence, assuming that the evidence is completely important and reliable. In 1994, Yang and Singh proposed the Evidence-Based Reasoning (ER) method, which improved upon the Dempster-Shafer rule and was well applied to multi-attribute decision-making problems under uncertainty. To enhance the ER method's ability to handle interval uncertainty, two types of Interval Evidence-Based Reasoning (IER) methods were proposed, modeling interval propositions and interval confidence levels, respectively. In 2013, Yang and Xu proposed an ER rule with evidence weights and reliability, extending the Dempster-Shafer rule and the ER method. Using likelihood analysis, the ER rule has been proven to be a generalized form of the traditional Bayesian rule.

[0005] Regarding the combination of relevant evidence, Yang and Xu proposed Maximum Likelihood Evidential Reasoning (MAKER), introducing marginal probability and joint probability to obtain the relevance coefficient of evidence. In subsequent studies, MAKER has been improved and applied in different fields. For example, Kong et al. constructed a clinical decision support system for trauma management based on MAKER. He et al. designed a MAKER-based data classifier in conjunction with principal component analysis.

[0006] However, when faced with a large amount of evidence, experts, limited by their personal experience and knowledge, often tend to provide evidence parameters in the form of intervals rather than clear values. Furthermore, interval uncertainty manifests in a wide range of forms, including interval propositions, interval reference values, interval confidence levels, and other interval evidence parameters. Secondly, the definitions of evidence relevance vary, with representative relevance measures including the Pearson coefficient, cosine similarity, Spearman coefficient, Kendall correlation coefficient, and mutual information. Analyzing evidence relevance when interval uncertainty exists is still in its early stages. Moreover, in the context of time series, evidence should be dynamic, posing a significant challenge to the design of evidence combination rules. Summary of the Invention

[0007] Therefore, it is necessary to provide a robust analysis method and apparatus for assessing the health status of a laser gyroscope, addressing the aforementioned technical problems.

[0008] A robust analysis method for assessing the health status of a laser gyroscope, the method comprising:

[0009] Uncertainty modeling is performed on the health assessment evidence of the laser gyroscope. Based on the established uncertainty model, the input health assessment evidence is calculated to obtain the confidence interval, interval weight, and reliability of the health assessment evidence.

[0010] An interval evidence reasoning rule is established based on two health assessment pieces of evidence; the interval evidence reasoning rule is the interval confidence distribution and mixed probability quality representation obtained by fusion of the two health assessment pieces of evidence.

[0011] Based on the interval evidence reasoning rules, an optimization model is constructed. Based on the optimization model and the confidence interval, interval weight, and reliability of the health assessment evidence, the optimal interval of the laser gyroscope's health assessment evidence is output, thereby obtaining the health status of the laser gyroscope.

[0012] Obtain the perturbation data of the health assessment evidence, and output the first output trajectory and the second output trajectory of the two perturbation data according to the interval evidence inference rule;

[0013] Based on the first output trajectory and the second output trajectory, the robustness coefficient of the interval evidence reasoning rule is calculated;

[0014] Based on the robustness coefficient, a first threshold and a second threshold for the disturbance amount of the two disturbance data are obtained, as well as a first threshold interval and a second threshold interval corresponding to the first threshold and the second threshold.

[0015] Based on the first threshold interval, the second threshold interval, the interval weights, and the reliability, an objective function is established, and the objective function is solved to obtain the disturbance amount of the two disturbance data.

[0016] In one embodiment, the method further includes: obtaining a confidence interval for the health assessment evidence based on the reference range of the identification framework for health assessment evidence and the observed range of the health assessment evidence.

[0017] When the observed value interval is within the reference value interval, the expression for the interval confidence level is:

[0018]

[0019] Among them, h i,n-1 h i,n+1 h represents the upper and lower bounds of the reference value interval, respectively. i,n Indicates a reference value. Let represent the upper and lower bounds of the observation interval, respectively; let n represent the nth level in the identification frame; and let N(i) represent the number of levels in the identification frame. and They represent x respectively i Belongs to level θ i,n The upper and lower bounds of the confidence level. and They represent x respectively i Belongs to level θ i,n+1 The upper and lower bounds of the confidence level;

[0020] Evidence e i The confidence distribution is expressed as:

[0021] e i ={(θ n ,β i,n ),(θ n+1 ,β i,n+1 ),(θ j ,0);j≠n,n+1;j∈[1,N(i)]}

[0022] in,

[0023] When the observed value interval crosses the reference value interval, the expression for the interval confidence level is:

[0024]

[0025] in, and They represent x respectively i Belongs to level θ i,n-1 The upper and lower bounds of the confidence level;

[0026] Evidence e i The confidence distribution is expressed as:

[0027] e i ={(θ n-1 ,β i,n-1 ),(θ n ,β i,n ),(θ n+1 ,β i,n+1 )}

[0028] in,

[0029] In one embodiment, it also includes: evidence e i The mean and variance within time T in the k-th sampling are respectively:

[0030]

[0031] in, This indicates that the evidence e at time t in the k-th sampling is from... i Data, This represents the mean. Indicates variance;

[0032] The evidence e was calculated using the coefficient of variation method and Monte Carlo simulation. i The interval weights within time T in the k-th sampling are:

[0033]

[0034] in, and These represent the upper and lower bounds of the interval evidence weights, respectively.

[0035] In one embodiment, it further includes: obtaining evidence e i The number of observation data that meet the threshold requirement within time T in the k-th sampling. Calculate evidence e i The reliability is:

[0036]

[0037] Where, r i k (T) represents reliability;

[0038] Based on all sampling results within time T, the reliability is calculated as follows:

[0039]

[0040] in, and These represent the upper and lower bounds of reliability, respectively.

[0041] In one embodiment, it further includes: calculating evidence e i (t) and e j The interval similarity of (t) is:

[0042]

[0043] Where, q i yes and The i-th largest number in the array, sgn(·) is the sign function;

[0044] All evidence is ranked according to its reliability. Based on the ranking result, the relevance matrix of L pieces of evidence is obtained as follows:

[0045]

[0046] Based on the correlation matrix, calculate evidence e. i The interval correlation coefficient between (t) and other evidence is:

[0047]

[0048] in, α i (t) is a time variable, and α i (t)∈[0,1].

[0049] In one embodiment, the method further includes: modeling any piece of health assessment evidence as follows:

[0050]

[0051] Where Θ represents the recognition frame, θ represents the level of the recognition frame, and β i,θ (t) represents the evidence e at time t. i (t) The interval confidence level assigned to the level θ.

[0052] Calculate evidence e i The mixture probability mass of (t) is:

[0053]

[0054] Where, m i,θ (t) represents the mixed probability mass. Indicates mixed weights;

[0055] Mixed weights The expression is:

[0056]

[0057] In one embodiment, the method further includes: constructing an optimized model based on the interval evidence reasoning rule as follows:

[0058]

[0059] r i - (t)≤r i (t)≤r i + (t); u - (θ)≤u(θ)≤u + (θ)

[0060] in, and These represent the interval weights w, respectively. i The lower and upper bounds of (t), r i - (t) and r i + (t) represents the reliability r. i The lower and upper bounds of (t), u - (θ) and u + (θ) denote the lower and upper bounds of u(θ), respectively, and u(θ) denotes the utility of θ.

[0061] In one embodiment, it further includes: based on the first output trajectory u(e) ij (t))∈[u - ,u + ] and the second output trajectory u′(e ij (t))∈[u′ - ,u′ + The robustness coefficient of the interval evidence reasoning rule is calculated as follows:

[0062]

[0063] in,

[0064] In one embodiment, the method further includes: establishing an objective function based on the first threshold interval, the second threshold interval, the interval weights, and the reliability:

[0065]

[0066] r i - (t)≤r i (t)≤r i + (t)

[0067] Where, f(Δx) i ,Δx j ) is the objective function, st represents the constraint condition, and δ is the threshold of the robustness coefficient.

[0068] A robust analysis device for assessing the health status of a laser gyroscope, the device comprising:

[0069] The uncertainty modeling module is used to perform uncertainty modeling on the health assessment evidence of the laser gyroscope. Based on the established uncertainty model, it calculates the confidence interval, interval weight, and reliability of the health assessment evidence.

[0070] The interval evidence reasoning rule establishment module is used to establish interval evidence reasoning rules based on two health assessment pieces of evidence; the interval evidence reasoning rules are interval confidence distributions and mixed probability quality representations obtained by fusion of interval evidence from the two health assessment pieces of evidence.

[0071] The status assessment module is used to construct an optimization model based on the interval evidence reasoning rules, and output the optimal interval of the health assessment evidence of the laser gyroscope based on the optimization model and the confidence interval, interval weight and reliability of the health assessment evidence, so as to obtain the health status of the laser gyroscope.

[0072] The robustness coefficient calculation module is used to acquire the perturbation data of the health assessment evidence, and output a first output trajectory and a second output trajectory of two perturbation data according to the interval evidence inference rule; and calculate the robustness coefficient of the interval evidence inference rule according to the first output trajectory and the second output trajectory.

[0073] The robustness analysis module is used to obtain a first threshold and a second threshold for the disturbance amount of two disturbance data points based on the robustness coefficient, as well as a first threshold interval and a second threshold interval corresponding to the first threshold and the second threshold; and to establish an objective function based on the first threshold interval, the second threshold interval, the interval weight, and the reliability, and to solve the objective function to obtain the disturbance amount of the two disturbance data points.

[0074] The robustness analysis method and apparatus for the aforementioned laser gyroscope health status assessment first calculates the input health assessment evidence based on the established uncertainty model, obtaining the confidence interval, interval weight, and reliability of the health assessment evidence, thus achieving unified modeling of interval uncertainty. Second, it establishes interval evidence inference rules based on two health assessment pieces of evidence and realizes the interval confidence distribution and mixed probability quality representation obtained from interval evidence fusion. Based on these interval evidence inference rules, an optimization model is constructed. To further verify the robustness of the interval evidence inference rules, the robustness coefficients under both no-disturbance and disturbed conditions are established by analyzing disturbed observation data. This allows for the calculation of the threshold for the disturbance amount, ultimately yielding robustness analysis results. Attached Figure Description

[0075] Figure 1 This is a flowchart illustrating a robustness analysis method for assessing the health status of a laser gyroscope in one embodiment.

[0076] Figure 2 This is a schematic diagram illustrating the relationship between the observed value interval and the reference value interval in one embodiment; where (a) indicates that the observed value interval is within the reference value interval, and (b) indicates that the observed value interval crosses the reference value interval;

[0077] Figure 3 Here is a flowchart of the robustness analysis process in one embodiment;

[0078] Figure 4 This is a structural block diagram of a robust analysis device for assessing the health status of a laser gyroscope in one embodiment;

[0079] Figure 5 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0080] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0081] In one embodiment, such as Figure 1 As shown, a robust analysis method for assessing the health status of a laser gyroscope is provided, the method comprising the following steps:

[0082] Step 102: Perform uncertainty modeling on the health assessment evidence of the laser gyroscope, and calculate the confidence interval, interval weight, and reliability of the health assessment evidence based on the established uncertainty model.

[0083] Step 104: Establish interval evidence reasoning rules based on two health assessment pieces of evidence.

[0084] The interval evidence reasoning rule is the interval confidence distribution and mixed probability quality representation obtained by fusing interval evidence from two health assessment evidences.

[0085] Step 106: Construct an optimization model based on the interval evidence reasoning rules. Based on the optimization model and the confidence interval, interval weight, and reliability of the health assessment evidence, output the optimal interval of the laser gyroscope's health assessment evidence to obtain the health status of the laser gyroscope.

[0086] Step 108: Obtain perturbation data of health assessment evidence, and output the first output trajectory and the second output trajectory of the two perturbation data according to the interval evidence reasoning rules.

[0087] Step 110: Calculate the robustness coefficient of the interval evidence reasoning rule based on the first output trajectory and the second output trajectory.

[0088] Step 112: Based on the robustness coefficient, obtain the first threshold and the second threshold of the disturbance amount of the two disturbance data, as well as the first threshold interval and the second threshold interval corresponding to the first threshold and the second threshold.

[0089] Step 114: Based on the first threshold interval, the second threshold interval, the interval weight, and the reliability, establish an objective function, solve the objective function, and obtain the disturbance amount of the two disturbance data.

[0090] The robustness analysis method for the health status assessment of the aforementioned laser gyroscope first calculates the input health assessment evidence based on the established uncertainty model, obtaining the confidence interval, interval weight, and reliability of the health assessment evidence, thus achieving unified modeling of interval uncertainty. Secondly, it establishes interval evidence inference rules based on two health assessment pieces of evidence and realizes the interval confidence distribution and mixed probability quality representation obtained by fusion of interval evidence. Based on these interval evidence inference rules, an optimization model is constructed. To further verify the robustness of the interval evidence inference rules, the rules are analyzed on perturbed observation data to establish robustness coefficients under both perturbed and unperturbed conditions. This allows for the calculation of the threshold for the perturbed amount, ultimately yielding the robustness analysis results.

[0091] First, considering that precise values ​​are difficult to obtain, interval values ​​may be more suitable for expressing quantitative input information of evidence. Assume there are L pieces of evidence e1, e2, ..., e L The i-th piece of evidence is represented as e i And i∈[1,L]. According to the research of Wang et al., if the evidence e i The observed data is x iIt can then be described as similar to x is in interval form. i The upper and lower limits are respectively and e i The identification framework or hypothesis space is represented as Θ i ={θ i,1 ,θ i,2 ,…,θ i,N(i)}, where θ i,n It is the nth proposition or reference level, and n∈[1,N(i)], where N(i) depends on i. θ i,n The reference value is represented as h. i,n Without loss of generality, assume h i,n-1 <h i,n <h i,n+1 Then we should discuss two possible scenarios.

[0092] In one embodiment, Figure 2 As shown, Figure 2 (a) gives the case where the observed value interval is within the reference value interval. In this case, the expression for the interval confidence is:

[0093]

[0094] Among them, h i,n-1 h i,n+1 h represents the upper and lower bounds of the reference value interval, respectively. i,n Indicates a reference value. Let represent the upper and lower bounds of the observation interval, respectively; let n represent the nth level in the identification frame; and let N(i) represent the number of levels in the identification frame. and They represent x respectively i Belongs to level θ i,n The upper and lower bounds of the confidence level. and They represent x respectively i Belongs to level θ i,n+1 The upper and lower bounds of the confidence level;

[0095] Evidence e i The confidence distribution is expressed as:

[0096] e i ={(θ n ,β i,n ),(θ n+1 ,β i,n+1 ),(θ j ,0);j≠n,n+1;j∈[1,N(i)]}

[0097] in,

[0098] exist Figure 2 In (b), the expression for the interval confidence score is given when the observed value interval crosses the reference value interval:

[0099]

[0100] in, and They represent x respectively i Belongs to level θ i,n-1 The upper and lower bounds of the confidence level;

[0101] Evidence e i The confidence distribution is expressed as:

[0102] e i ={(θ n-1 ,β i,n-1 ),(θ n ,β i,n ),(θ n+1 ,β i,n+1 )}

[0103] in,

[0104] In one embodiment, suppose x i It is an interval number In the context of time series, x i It can be described as x i (t). To reduce the impact of random errors, Monte Carlo simulations are used to resample the data. Assume the time length is T, and sampling is performed K times. In the k-th sampling, data from e... i Time series data can be represented as And k∈[1,K]. Evidence e i The mean and variance within time T in the k-th sampling are respectively:

[0105]

[0106] in, This indicates that the evidence e at time t in the k-th sampling is from... i Data, This represents the mean. Variance is expressed; the evidence e is calculated using the coefficient of variation method and Monte Carlo simulation. i The interval weights within time T in the k-th sampling are:

[0107]

[0108] in, and These represent the upper and lower bounds of the interval evidence weights, respectively.

[0109] In one embodiment, assume e i The observation data at time t in the k-th sampling is The threshold can be determined by experts based on industry standards, such as... if If the threshold is exceeded, the data may contain noise and become unreliable. Obtain evidence e i The number of observation data that meet the threshold requirement within time T in the k-th sampling. Calculate evidence e i The reliability is:

[0110]

[0111] in, Reliability is expressed as follows: Based on all sampling results within time T, the reliability is calculated as follows:

[0112]

[0113] in, and These represent the upper and lower bounds of reliability, respectively.

[0114] In one embodiment, e i and e j The observation data at time t can be represented as x i (t) and x j (t), and have and Accordingly, the evidence can be represented as e. i (t) and e j (t). To perform interval correlation analysis, it is first necessary to normalize the interval values ​​to the interval [0,1]. Therefore, x i (t) and x j The normalized upper and lower bounds of (t) are calculated as follows:

[0115]

[0116] Calculate evidence e i (t) and e j The interval similarity of (t) is:

[0117]

[0118] Where, q i yes and The i-th largest number in the set, sgn(·) is the sign function.

[0119] It is worth noting that if and Then we have α i,j (t) = 1. Clearly, α i,j (t)∈[0,1]. α i,j The larger the value of (t), the better. i (t) and e j (t) are more similar. If α i,j (t) = 1, interval and They will completely overlap.

[0120] In another embodiment, when the evidence is relevant, the fusion of evidence no longer satisfies the commutative law. This means that the reasoning outcome depends on the order in which the evidence is fused. Since the reliability of evidence reflects the quality of the evidence source, it can be used to determine the fusion order. The greater the reliability of the evidence, the earlier it should be fused. Without loss of generality, assume that L pieces of evidence are ordered in descending order of reliability as e1(t), e2(t), ..., e L (t). The correlation matrix can be constructed as follows:

[0121]

[0122] The interval correlation coefficient can be expressed as follows: the interval similarity between any two pieces of evidence can be represented by the following formula:

[0123]

[0124] The correlation matrix can be represented by the following formula:

[0125]

[0126] So, evidence e i The interval correlation coefficient between (t) and other evidence is:

[0127]

[0128] in, α i (t) is a time variable, and α i (t)∈[0,1].

[0129] In one embodiment, in a time-series context, any two pieces of evidence e i (t) and e j (t) can all be modeled as a dynamic interval confidence distribution in the following form:

[0130] e i(t)={(θ,β i,n (t)); n∈[1,N(i)]}

[0131] e j (t)={(θ j,m ,β j,m (t)); m∈[1,N(j)]}

[0132] Where, β i,n (t) and β j,m (t) respectively represent e i (t) and e j (t) is assigned to proposition θ at time t. i,n and θ j,m The interval confidence levels are equivalent to β. i,n and β j,m ,

[0133] It should be emphasized that e i (t) and e j (t) may be modeled under different recognition frameworks. That is, Θ i and Θ j The types and number of propositions are not entirely the same. Taking the health status assessment of a laser gyroscope as an example, navigation accuracy and drift coefficient can usually be used as two pieces of evidence. In this case, Θ1 and Θ2 are different.

[0134] In this embodiment, any piece of health assessment evidence is modeled as follows:

[0135]

[0136] Where Θ represents the recognition frame, θ represents the level of the recognition frame, and β i,θ (t) represents the evidence e at time t. i (t) The interval confidence level assigned to the level θ.

[0137] Calculate evidence e i The mixture probability mass of (t) is:

[0138]

[0139] Where, m i,θ (t) represents the mixed probability mass. Indicates mixed weights; mixed weights The expression is:

[0140]

[0141] In another embodiment, the interval evidence reasoning rule is as follows: assuming the identification frame is Θ = {θ1, θ2, ..., θ...} N Any two pieces of evidence at time t can be represented as e i (t) and e j (t), whose interval confidence distribution and mixed probability quality are determined by the above equation. Therefore, the interval evidence reasoning rule based on two pieces of evidence can be described as:

[0142]

[0143] Where, β ij,θ (t) represents e i (t) and e j (t) assigns the combined interval confidence score to proposition θ, and m ij,θ (t) represents the unnormalized combinatorial probability mass of θ. i,φ (t) and They represent e respectively i (t) and e j (t) is assigned to φ and The combinatorial probability mass, m i,θ (t)=w i (t)β i,θ (t) and m j,θ (t)=w j (t)β j,θ (t),

[0144] Based on the above analysis, the inference results can be described as the following confidence distribution:

[0145]

[0146] Assuming the utility of θ is u(θ), the expected utility of the inference result is determined by the following formula:

[0147]

[0148] In one embodiment, under the interval evidence reasoning rule, some evidence parameters are uncertain. On the one hand, the initial utility values ​​of all propositions in Θ are set by experts based on experience and may not be precise values. On the other hand, confidence, evidence weight, and reliability are described in interval form, which includes interval uncertainty. Therefore, it is necessary to optimize the evidence parameters.

[0149] Therefore, the optimization model is constructed as follows:

[0150]

[0151] r i- (t)≤r i (t)≤r i + (t); u - (θ)≤u(θ)≤u + (θ)

[0152] in, and These represent the interval weights w, respectively. i The lower and upper bounds of (t), r i - (t) and r i + (t) represents the reliability r. i The lower and upper bounds of (t), u - (θ) and u + (θ) denote the lower and upper bounds of u(θ), respectively, and u(θ) denotes the utility of θ.

[0153] Furthermore, how can we measure the stability of interval outputs under perturbation conditions to quantitatively analyze the robustness of interval evidence reasoning rules, such as... Figure 3 As shown, the difference between the nominal sample trajectory and the perturbed sample trajectory lies in whether the perturbation is introduced into the observed data. The expected utility is denoted as u(t) and u′(t), respectively. Interval similarity is used as a robustness measure for interval evidence reasoning rules, and the perturbation threshold is obtained by establishing a parameter estimation model.

[0154] Specifically, based on the first output trajectory u(e) ij (t))∈[u - ,u + ] and the second output trajectory u′(e ij (t))∈[u′ - ,u′ + The robustness coefficient of the interval evidence reasoning rule is calculated as follows:

[0155]

[0156] in,

[0157] Specifically, based on evidence e i (t) and e j (t) is used for illustration. Assume the disturbed observation data are represented as x. i x′(t) and x′ j (t), calculated as x i ′(t)=x i (t)+Δx i (t) and x′ j (t)=x j(t)+Δx j (t). Although the evidence is described in interval form, the parameters of the evidence involved in the fusion exist in the form of exact values, and are constrained by upper and lower bounds. The following perturbed evidence can be obtained by using a utility-based interval confidence calculation method:

[0158]

[0159] The perturbation effect of the inference result is calculated by the following formula:

[0160]

[0161] Suppose there are two pieces of evidence e on the nominal sample trajectory. i (t) and e j (t), the evidence on the perturbed sample trajectory is e i ′(t) and e′ j (t). Using the IER rule, the outputs of the two trajectories are denoted as u(e). ij (t))∈[u - ,u + ] and u′(e ij (t))∈[u′ - ,u′ + ].

[0162] In another embodiment, it should be in Find Δx when it reaches a certain value i and Δx j The threshold. Assume Δx i ∈[Δx i,min ,Δx i,max ], Δx j ∈[Δx j,min ,Δx j,max According to the first threshold interval [Δx] i,min ,Δx i,max ], second threshold interval [Δx j,min ,Δx j,max Based on the interval weights and the aforementioned reliability, the objective function is established as follows:

[0163]

[0164] r i - (t)≤r i (t)≤r i + (t)

[0165] Where, f(Δx) i ,Δx j) is the objective function, st represents the constraint condition, and δ is the threshold of the robustness coefficient.

[0166] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. In addition, Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0167] In one embodiment, such as Figure 4 As shown, a robustness analysis device for assessing the health status of a laser gyroscope is provided, comprising: an uncertainty modeling module 402, an interval evidence reasoning rule establishment module 404, a status assessment module 406, a robustness coefficient calculation module 408, and a robustness analysis module 410, wherein:

[0168] Uncertainty modeling module 402 is used to perform uncertainty modeling on the health assessment evidence of the laser gyroscope. Based on the established uncertainty model, it calculates the confidence interval, interval weight and reliability of the health assessment evidence.

[0169] The interval evidence reasoning rule establishment module 404 is used to establish interval evidence reasoning rules based on two health assessment evidences; the interval evidence reasoning rules are interval confidence distributions and mixed probability quality representations obtained by fusion of interval evidences from two health assessment evidences.

[0170] The status assessment module 406 is used to construct an optimization model based on the interval evidence reasoning rules, and output the optimal interval of the health assessment evidence of the laser gyroscope based on the optimization model and the confidence interval, interval weight and reliability of the health assessment evidence, so as to obtain the health status of the laser gyroscope.

[0171] The robustness coefficient calculation module 408 is used to acquire the perturbation data of the health assessment evidence, and output a first output trajectory and a second output trajectory of two perturbation data according to the interval evidence inference rule; and calculate the robustness coefficient of the interval evidence inference rule according to the first output trajectory and the second output trajectory.

[0172] The robustness analysis module 410 is used to obtain a first threshold and a second threshold for the disturbance amount of two disturbance data points, as well as a first threshold interval and a second threshold interval corresponding to the first threshold and the second threshold, based on the robustness coefficient; establish an objective function based on the first threshold interval, the second threshold interval, the interval weight, and the reliability, solve the objective function, and obtain the disturbance amount of the two disturbance data points.

[0173] In one embodiment, the uncertainty modeling module 402 is further configured to obtain the confidence interval of the health assessment evidence based on the reference value interval of the identification framework of the health assessment evidence and the observed value interval of the health assessment evidence:

[0174] When the observed value interval is within the reference value interval, the expression for the interval confidence level is:

[0175]

[0176] Among them, h i,n-1 h i,n+1 h represents the upper and lower bounds of the reference value interval, respectively. i,n Indicates a reference value. Let represent the upper and lower bounds of the observation interval, respectively; let n represent the nth level in the identification frame; and let N(i) represent the number of levels in the identification frame. and They represent x respectively i Belongs to level θ i,n The upper and lower bounds of the confidence level. and They represent x respectively i Belongs to level θ i,n+1 The upper and lower bounds of the confidence level;

[0177] Evidence e i The confidence distribution is expressed as:

[0178] e i ={(θ n ,β i,n ),(θ n+1 ,β i,n+1 ),(θ j ,0);j≠n,n+1;j∈[1,N(i)]}

[0179] in,

[0180] When the observed value interval crosses the reference value interval, the expression for the interval confidence level is:

[0181]

[0182] in, and They represent x respectively i Belongs to level θ i,n-1 The upper and lower bounds of the confidence level;

[0183] Evidence e i The confidence distribution is expressed as:

[0184] e i ={(θ n-1 ,β i,n-1 ),(θ n ,β i,n ),(θ n+1 ,β i,n+1 )}

[0185] in,

[0186] In one embodiment, the uncertainty modeling module 402 is also used for evidence e i The mean and variance within time T in the k-th sampling are respectively:

[0187]

[0188] in, This indicates that the evidence e at time t in the k-th sampling is from... i Data, This represents the mean. Indicates variance;

[0189] The evidence e was calculated using the coefficient of variation method and Monte Carlo simulation. i The interval weights within time T in the k-th sampling are:

[0190]

[0191] in, and These represent the upper and lower bounds of the interval evidence weights, respectively.

[0192] In one embodiment, the uncertainty modeling module 402 is also used to obtain evidence e. i The number of observation data that meet the threshold requirement within time T in the k-th sampling. Calculate evidence e i The reliability is:

[0193]

[0194] in, Indicates reliability;

[0195] Based on all sampling results within time T, the reliability is calculated as follows:

[0196]

[0197] in, and These represent the upper and lower bounds of reliability, respectively.

[0198] In one embodiment, the interval evidence reasoning rule establishment module 404 is also used to calculate evidence e. i (t) and e j The interval similarity of (t) is:

[0199]

[0200] Where, q i yes and The i-th largest number in the array, sgn(·) is the sign function;

[0201] All evidence is ranked according to its reliability. Based on the ranking result, the relevance matrix of L pieces of evidence is obtained as follows:

[0202]

[0203] Based on the correlation matrix, calculate evidence e. i The interval correlation coefficient between (t) and other evidence is:

[0204]

[0205] in, α i (t) is a time variable, and α i (t)∈[0,1].

[0206] In one embodiment, the interval evidence reasoning rule establishment module 404 is further used to model any piece of health assessment evidence as follows:

[0207]

[0208] Where Θ represents the recognition frame, θ represents the level of the recognition frame, and β i,θ (t) represents the evidence e at time t. i (t) The interval confidence level assigned to the level θ.

[0209] Calculate evidence e i The mixture probability mass of (t) is:

[0210]

[0211] Where, m i,θ(t) represents the mixed probability mass. Indicates mixed weights;

[0212] Mixed weights The expression is:

[0213]

[0214] In one embodiment, the state evaluation module 406 is further configured to construct an optimized model based on the interval evidence reasoning rule:

[0215]

[0216] r i - (t)≤r i (t)≤r i + (t); u - (θ)≤u(θ)≤u + (θ)

[0217] in, and These represent the interval weights w, respectively. i The lower and upper bounds of (t), r i - (t) and r i + (t) represents the reliability r. i The lower and upper bounds of (t), u - (θ) and u + (θ) denote the lower and upper bounds of u(θ), respectively, and u(θ) denotes the utility of θ.

[0218] In one embodiment, the robustness coefficient calculation module 408 is further configured to calculate the robustness coefficient based on the first output trajectory u(e) ij (t))∈[u - ,u + ] and the second output trajectory u′(e ij (t))∈[u′ - ,u′ + The robustness coefficient of the interval evidence reasoning rule is calculated as follows:

[0219]

[0220] in,

[0221] In one embodiment, the robustness analysis module 410 is further configured to establish an objective function based on the first threshold interval, the second threshold interval, the interval weights, and the reliability:

[0222]

[0223] r i - (t)≤r i (t)≤r i + (t)

[0224] Where, f(Δx) i ,Δx j ) is the objective function, st represents the constraint condition, and δ is the threshold of the robustness coefficient.

[0225] Specific limitations regarding the robustness analysis device for laser gyroscope health status assessment can be found in the limitations of the robustness analysis method for laser gyroscope health status assessment described above, and will not be repeated here. Each module in the aforementioned robustness analysis device for laser gyroscope health status assessment can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0226] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 5 As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When executed by the processor, the computer program implements a robust analysis method for assessing the health status of a laser gyroscope. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0227] Those skilled in the art will understand that Figure 5 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0228] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0229] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0230] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art could make various modifications and improvements without departing from the spirit of the present application, all of which fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

Claims

1. A robustness analysis method for assessing the health status of a laser gyroscope, characterized in that, The method includes: Uncertainty modeling is performed on the health assessment evidence of the laser gyroscope. Based on the established uncertainty model, the input health assessment evidence is calculated to obtain the confidence interval, interval weight, and reliability of the health assessment evidence. The health assessment evidence includes navigation accuracy and drift coefficient. An interval evidence reasoning rule is established based on two health assessment pieces of evidence; the interval evidence reasoning rule is the interval confidence distribution and mixed probability quality representation obtained by fusion of the two health assessment pieces of evidence. Based on the interval evidence reasoning rules, an optimization model is constructed, and based on the optimization model, the confidence interval of the health assessment evidence, the interval weight, and the reliability, the optimal interval of the health assessment evidence of the laser gyroscope is output. Obtain the perturbation data of the health assessment evidence, and output the first output trajectory and the second output trajectory of the two perturbation data according to the interval evidence inference rule; Based on the first output trajectory and the second output trajectory, the robustness coefficient of the interval evidence reasoning rule is calculated; Based on the robustness coefficient, a first threshold and a second threshold for the disturbance amount of the two disturbance data are obtained, as well as a first threshold interval and a second threshold interval corresponding to the first threshold and the second threshold. Based on the first threshold interval, the second threshold interval, the interval weight, and the reliability, an objective function is established, and the objective function is solved to obtain the perturbation amount of the two perturbation data. The interval confidence distribution and mixed probability quality representation obtained after interval evidence fusion based on two health assessment evidences include: Modeling any piece of health assessment evidence as follows: ； in, Represents the identification framework. Indicates the level of the identification frame. express t Evidence at all times Assigned to level The interval confidence level, ; Calculation evidence The mixture probability mass is: ； in, Indicates mixed probability mass. Indicates mixed weights, It is a time variable, and ; Mixed weights The expression is: ； Indicates the interval weight.

2. The method according to claim 1, characterized in that, Based on the established uncertainty model, the confidence intervals of the input health assessment evidence are calculated, including: Based on the reference range of the health assessment evidence identification framework and the observed range of the health assessment evidence, the confidence interval for the health assessment evidence is as follows: When the observed value interval is within the reference value interval, the expression for the interval confidence level is: ； in, These represent the upper and lower bounds of the reference value interval, respectively. Indicates a reference value. These represent the upper and lower bounds of the observation interval, respectively, and n represents the nth level in the identification frame. This indicates the number of levels in the identification frame. and They represent Belonging to a rank The upper and lower bounds of the confidence level. and They represent Belonging to a rank The upper and lower bounds of the confidence level; evidence The confidence distribution is expressed as: in, , , ; When the observed value interval crosses the reference value interval, the expression for the interval confidence level is: ； in, and They represent Belonging to a rank The upper and lower bounds of the confidence level; evidence The confidence distribution is expressed as: ； in, , .

3. The method according to claim 2, characterized in that, Based on the established uncertainty model, the input health assessment evidence is calculated to obtain the interval weights of the health assessment evidence, including: evidence In the Time in the second sampling The mean and variance within the range are as follows: ； ； in, Indicates the first The evidence at time t in the second sampling Data, This represents the mean. Indicates variance; The coefficient of variation method and Monte Carlo simulation were used to calculate the evidence. In the Time in the second sampling The interval weights within are: ； in, and These represent the upper and lower bounds of the interval evidence weights, respectively.

4. The method according to claim 3, characterized in that, The reliability of the input health assessment evidence is calculated based on the established uncertainty model, including: Obtaining evidence In the Time in the second sampling The number of observations that meet the threshold requirement within the range Calculate evidence The reliability is: ； in, Indicates reliability; According to time The reliability of all sampling results is calculated as follows: ； in, and These represent the upper and lower bounds of reliability, respectively.

5. The method according to claim 3, characterized in that, The method further includes: Calculation evidence and The interval similarity is: ； in, yes , , and The Middle Large numbers, It is a symbolic function; All evidence is ranked according to the aforementioned reliability, and based on the ranking result, the following is obtained: L The relevance matrix of the evidence is as follows: ； Based on the correlation matrix, calculate the evidence. The interval correlation coefficient with other evidence is: ； in, , .

6. The method according to claim 5, characterized in that, Based on the interval evidence reasoning rules, an optimized model is constructed, including: Based on the interval evidence reasoning rules, the optimized model is constructed as follows: ； in, and Representing the interval weights respectively The lower and upper bounds, and Representing reliability respectively The lower and upper bounds, and They represent The lower and upper bounds, express Its effectiveness.

7. The method according to claim 6, characterized in that, Based on the first output trajectory and the second output trajectory, the robustness coefficient of the interval evidence reasoning rule is calculated, including: According to the first output trajectory and the second output trajectory The robustness coefficient of the interval evidence reasoning rule is calculated as follows: ； in, .

8. The method according to claim 7, characterized in that, Based on the first threshold interval, the second threshold interval, the interval weights, and the reliability, an objective function is established, and the objective function is solved to obtain the perturbation amounts of the two perturbation data points, including: Based on the first threshold interval, the second threshold interval, the interval weights, and the reliability, the objective function is established as follows: ； in, It is the objective function. Indicates constraints. It is the threshold of the robustness coefficient.

9. A robust analysis device for assessing the health status of a laser gyroscope, characterized in that, The apparatus for implementing the robust analysis method for assessing the health status of a laser gyroscope according to any one of claims 1 to 8 comprises: The uncertainty modeling module is used to perform uncertainty modeling on the health assessment evidence of the laser gyroscope. Based on the established uncertainty model, it calculates the confidence interval, interval weight, and reliability of the health assessment evidence. The interval evidence reasoning rule establishment module is used to establish interval evidence reasoning rules based on two health assessment pieces of evidence; the interval evidence reasoning rules are interval confidence distributions and mixed probability quality representations obtained by fusion of interval evidence from the two health assessment pieces of evidence. The status assessment module is used to construct an optimization model based on the interval evidence reasoning rules, and output the optimal interval of the health assessment evidence of the laser gyroscope based on the optimization model and the confidence interval, interval weight and reliability of the health assessment evidence, so as to obtain the health status of the laser gyroscope. The robustness coefficient calculation module is used to acquire the perturbation data of the health assessment evidence, and output a first output trajectory and a second output trajectory of two perturbation data according to the interval evidence inference rule; and calculate the robustness coefficient of the interval evidence inference rule according to the first output trajectory and the second output trajectory. The robustness analysis module is used to obtain a first threshold and a second threshold for the disturbance amount of two disturbance data points based on the robustness coefficient, as well as a first threshold interval and a second threshold interval corresponding to the first threshold and the second threshold; and to establish an objective function based on the first threshold interval, the second threshold interval, the interval weight, and the reliability, and to solve the objective function to obtain the disturbance amount of the two disturbance data points.

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