Hemispherical resonator gyroscope service life prediction method of gray support vector machine
By using a grey support vector machine model to screen the lifetime characteristic factors of hemispherical resonant gyroscopes and establishing a lifetime prediction model, the problems of long time consumption and high cost of traditional methods are solved, and efficient lifetime prediction is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIJING AUTOMATION CONTROL EQUIP INST
- Filing Date
- 2025-12-31
- Publication Date
- 2026-05-15
AI Technical Summary
In the existing technology, the life prediction method for hemispherical resonant gyroscopes is time-consuming, costly, and highly dependent on the number of samples, which leads to increased time and economic costs.
A grey support vector machine model was adopted, and data was obtained through accelerated reliability tests of hemispherical resonant gyroscopes. A classification hyperplane dual optimization equation and model decision function based on Lagrange multipliers were constructed, lifetime characteristic factors were screened, and a grey support vector machine lifetime prediction model was established. Lifetime prediction was performed using limited test data.
This method enables effective and reliable prediction of the lifetime of hemispherical resonant gyroscopes, reduces the test cycle and cost, and provides an effective evaluation method for the reliability and lifetime prediction of hemispherical resonant gyroscopes.
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Figure CN122045969A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of hemispherical resonator gyroscope technology, and in particular to a method for predicting the lifetime of a hemispherical resonator gyroscope using a gray support vector machine. Background Technology
[0002] High reliability and long lifespan of gyroscopes have become development goals and urgent requirements for major equipment and engineering projects. Hemispherical resonant gyroscopes are solid-state wave gyroscopes that use the precession of the standing wave along the circumferential direction of a hemispherical harmonic oscillator to sense the angular motion of the base. They possess unique advantages such as high precision, radiation resistance, low power consumption, small size, high reliability, long lifespan, and maintenance-free operation throughout their lifespan. They also exhibit excellent environmental adaptability, highly meeting the development needs of new equipment. my country's research and development of hemispherical resonant gyroscopes is still in its initial stage. Research on key issues in engineering applications, such as failure mechanisms, reliable manufacturing processes, reliability testing, and evaluation, is limited. Therefore, how to achieve lifespan assessment of hemispherical resonant gyroscopes is a critical problem that urgently needs to be solved.
[0003] A hemispherical resonator gyroscope mainly consists of a hemispherical resonator, planar electrodes, gyroscope circuitry, application software, meter structure, sealed casing, electrical connections, and adhesive bonding assembly. All these components together constitute a complete functional system of the hemispherical resonator gyroscope. If any component or part of the hemispherical resonator gyroscope malfunctions, the entire hemispherical resonator gyroscope will fail.
[0004] Traditional lifetime distribution theories and normal distribution theories, among other estimation and prediction methods, fall under the categories of statistics and probability, and are highly dependent on the sample size. If these methods are used to study lifetime prediction technology for hemispherical resonator gyroscopes, a large number of samples would be required for long-term experiments, undoubtedly increasing both time and economic costs. Therefore, this paper proposes a lifetime prediction technology based on a grey support vector machine model, incorporating key data from accelerated testing. This method can effectively predict the reliability and lifetime of samples using limited test data. Summary of the Invention
[0005] This invention provides a method for predicting the lifetime of a hemispherical resonant gyroscope using a gray support vector machine, which can solve the technical problems of long time consumption and high cost of traditional lifetime prediction methods in the prior art.
[0006] According to one aspect of the present invention, a method for predicting the lifetime of a hemispherical resonant gyroscope using a grey support vector machine is provided, the method comprising:
[0007] S1. Conduct accelerated reliability tests on hemispherical resonant gyroscopes to obtain raw test data, and construct training and test sample sets based on the raw test data;
[0008] S2, construct the classification hyperplane dual optimization equation and model decision function based on Lagrange multipliers. Based on the classification hyperplane dual optimization equation, model decision function, training sample set and test sample set, search and filter the feature vector of the hemispherical resonant gyroscope. Use the feature vector obtained after searching and filtering as the lifetime feature factor of the hemispherical resonant gyroscope.
[0009] S3. Based on the hemispherical resonant gyroscope lifetime characteristic factors obtained in S2, a grey support vector machine hemispherical resonant gyroscope lifetime prediction model is established.
[0010] S4. Based on the grey support vector machine hemispherical resonator gyroscope lifetime prediction model and the original experimental data corresponding to the lifetime characteristic factors of each hemispherical resonator gyroscope, the predicted value of the lifetime characteristic factor of each hemispherical resonator gyroscope is calculated, and the lifetime of the hemispherical resonator gyroscope is predicted according to the predicted value.
[0011] Furthermore, the dual optimization equation for the classification hyperplane is:
[0012]
[0013] 0≤a i ≤C,i=1,2,...,l
[0014] In the above formula, a i a j All are Lagrange multipliers, where i represents the i-th sample, j represents the j-th sample, and l represents the total number of samples. i ,y i ) represents the training sample set {(x i ,y i The i-th training sample in the sequence {x,i=1,2,...,l} j ,y j ) represents the test sample set {(x j ,y j Let ),j=1,2,...,l} be the j-th test sample, and let <·,·> denote the dot product of vectors, where C is a constant greater than 0.
[0015] Furthermore, the model decision function is:
[0016] f(x) = sign(<ω,x>+b)
[0017] In the above formula, f(x) represents the model decision function, x represents the input parameters, ω is an adjustable weight vector, and ω∈R n b is the bias, b∈R, R n Let R represent an n-dimensional vector space, and let R represent the set of real numbers.
[0018] Furthermore, based on the grey support vector machine hemispherical resonator gyroscope lifetime prediction model and the original experimental data corresponding to each hemispherical resonator gyroscope lifetime feature factor, the predicted values of each hemispherical resonator gyroscope lifetime feature factor are calculated, including:
[0019] The original experimental data corresponding to the lifetime characteristic factor of each hemispherical resonant gyroscope constitute the corresponding original nonlinear data sequence.
[0020] The original nonlinear data sequence of the lifetime characteristic factor of each hemispherical resonant gyroscope is processed by gray accumulation to obtain the corresponding new sequence;
[0021] The new sequence of lifetime characteristic factors for each hemispherical resonant gyroscope is input into the hemispherical resonant gyroscope lifetime prediction model based on grey support vector machine to obtain the predicted value of each hemispherical resonant gyroscope lifetime characteristic factor.
[0022] Furthermore, the hemispherical resonator gyroscope lifetime prediction model based on grey support vector machine is as follows:
[0023]
[0024] x 0 (k)=x 1 (k)-x 1 (k-1), 2≤k≤n
[0025] a * =(a1 a1) * … a N-m a N-m * ) T i = 1, 2, ..., Nm
[0026]
[0027] In the above formula, The value represents the predicted value at step l of the sequence generated by gray accumulation, N represents the length of the data sequence, m represents the embedding dimension of the phase space reconstruction, and a * Represents the sequence of Lagrange multipliers. Let K(.,.) represent the i-th Lagrange multiplier, and K(.,.) be the kernel function. This represents the sequence generated by gray accumulation. This represents the gray cumulative generation sequence generated in prediction step l, x 0 (k) represents the k-th predicted value of the inverse accumulation generation sequence, x 1 (k) represents the k-th data in the sequence generated by gray accumulation, x 1 (k-1) represents the (k-1)th data point in the sequence generated by gray accumulation, where k represents the order in the sequence. This represents the j-th data point in the generated gray cumulative sequence. The expression represents the generation of a gray cumulative sequence from 1 to j, and ε represents the error tolerance.
[0028] Furthermore, the prediction of the hemispherical resonator gyroscope lifetime based on the predicted value includes: when the predicted value of any hemispherical resonator gyroscope lifetime characteristic factor exceeds the set threshold, it is considered that the hemispherical resonator gyroscope lifetime has been reached.
[0029] This invention provides a method for predicting the lifetime of a hemispherical resonant gyroscope (BRG) using a grey support vector machine. This method constructs a classification hyperplane dual optimization equation and model decision function based on Lagrange multipliers, searches and filters to obtain BRG lifetime feature factors, establishes a grey support vector machine BRG lifetime prediction model based on these feature factors, and obtains the predicted values of the feature factors. Thus, the lifetime of the BRG is predicted based on these predicted values. This method can achieve effective and reliable prediction of the BRG lifetime using limited test data, reducing the experimental cycle and cost, and providing an effective evaluation means for the reliability and lifetime prediction of hemispherical resonant gyroscopes. Attached Figure Description
[0030] The accompanying drawings, which form part of this specification, are provided to further illustrate embodiments of the invention and, together with the textual description, explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.
[0031] Figure 1 A partial flowchart of a hemispherical resonator gyroscope lifetime prediction method according to a specific embodiment of the present invention is shown.
[0032] Figure 2 A schematic diagram of a grey support vector machine prediction model provided according to a specific embodiment of the present invention is shown. Detailed Implementation
[0033] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0034] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0035] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values of the components and steps set forth in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.
[0036] According to a specific embodiment of the present invention, a method for predicting the lifetime of a hemispherical resonant gyroscope using a grey support vector machine is provided, the method comprising:
[0037] S1. Conduct accelerated reliability tests on hemispherical resonant gyroscopes to obtain raw test data, and construct training and test sample sets based on the raw test data;
[0038] S2, construct the classification hyperplane dual optimization equation and model decision function based on Lagrange multipliers. Based on the classification hyperplane dual optimization equation, model decision function, training sample set and test sample set, search and filter the feature vector of the hemispherical resonant gyroscope. Use the feature vector obtained after searching and filtering as the lifetime feature factor of the hemispherical resonant gyroscope.
[0039] S3. Based on the hemispherical resonant gyroscope lifetime characteristic factors obtained in S2, a grey support vector machine hemispherical resonant gyroscope lifetime prediction model is established.
[0040] S4. Based on the grey support vector machine hemispherical resonator gyroscope lifetime prediction model and the original experimental data corresponding to the lifetime characteristic factors of each hemispherical resonator gyroscope, the predicted value of the lifetime characteristic factor of each hemispherical resonator gyroscope is calculated, and the lifetime of the hemispherical resonator gyroscope is predicted according to the predicted value.
[0041] This method, employing a grey support vector machine (SVM) approach, provides a method for predicting the lifetime of a hemispherical resonant gyroscope (HNR). This method constructs a classification hyperplane dual optimization equation and model decision function based on Lagrange multipliers, searches and filters to obtain hemispherical resonant gyroscope lifetime feature factors, and establishes a grey SVM hemispherical resonant gyroscope lifetime prediction model based on these feature factors. The predicted values of these feature factors are then used to predict the lifetime of the hemispherical resonant gyroscope. This method achieves effective and reliable prediction of hemispherical resonant gyroscope lifetime with limited test data, reducing experimental time and cost, and providing an effective evaluation method for hemispherical resonant gyroscope reliability and lifetime prediction. Compared with existing technologies, the technical solution of this invention solves the technical problems of long time consumption and high cost in traditional lifetime prediction methods.
[0042] Further, in this embodiment of the invention, based on the grey support vector machine hemispherical resonator gyroscope lifetime prediction model and the original experimental data corresponding to each hemispherical resonator gyroscope lifetime feature factor, the predicted value of each hemispherical resonator gyroscope lifetime feature factor is calculated, including:
[0043] The original experimental data corresponding to the lifetime characteristic factor of each hemispherical resonant gyroscope constitute the corresponding original nonlinear data sequence.
[0044] The original nonlinear data sequence of the lifetime characteristic factor of each hemispherical resonant gyroscope is processed by gray accumulation to obtain the corresponding new sequence;
[0045] The new sequence of lifetime characteristic factors for each hemispherical resonant gyroscope is input into the hemispherical resonant gyroscope lifetime prediction model based on grey support vector machine to obtain the predicted value of each hemispherical resonant gyroscope lifetime characteristic factor.
[0046] Furthermore, in this embodiment of the invention, the prediction of the lifetime of the hemispherical resonator gyroscope based on the predicted value includes: when the predicted value of any hemispherical resonator gyroscope lifetime characteristic factor exceeds a set threshold, it is considered that the lifetime of the hemispherical resonator gyroscope has been reached.
[0047] Furthermore, in this embodiment of the invention, the dual optimization equation for the classification hyperplane is:
[0048]
[0049] 0≤a i ≤C,i=1,2,...,l
[0050] In the above formula, a i a j All are Lagrange multipliers, where i represents the i-th sample, j represents the j-th sample, and l represents the total number of samples. i ,y i ) represents the training sample set {(xi ,y i The i-th training sample in the sequence {x,i=1,2,...,l} j ,y j ) represents the test sample set {(x j ,y j Let ),j=1,2,...,l} be the j-th test sample, and let <·,·> denote the dot product of vectors, where C is a constant greater than 0.
[0051] The model decision function is:
[0052] f(x) = sign(<ω,x>+b)
[0053] In the above formula, f(x) represents the model decision function, x represents the input parameters, ω is an adjustable weight vector, and ω∈R n b is the bias, b∈R, R n Let R represent an n-dimensional vector space, and let R represent the set of real numbers.
[0054] Furthermore, in this embodiment of the invention, the hemispherical resonant gyroscope lifetime prediction model based on gray support vector machine is as follows:
[0055]
[0056] x 0 (k)=x 1 (k)-x 1 (k-1), 2≤k≤n
[0057] a * =(a1 a1) * … a N-m a N-m * ) T i = 1, 2, ..., Nm
[0058]
[0059] In the above formula, The value represents the predicted value at step l of the sequence generated by gray accumulation, N represents the length of the data sequence, m represents the embedding dimension of the phase space reconstruction, and a * Represents the sequence of Lagrange multipliers. Let K(.,.) represent the i-th Lagrange multiplier, and K(.,.) be the kernel function. This represents the sequence generated by gray accumulation. This represents the gray cumulative generation sequence generated in prediction step l, x 0 (k) represents the k-th predicted value of the inverse accumulation generation sequence, x 1 (k) represents the k-th data in the sequence generated by gray accumulation, x 1(k-1) represents the (k-1)th data point in the sequence generated by gray accumulation, where k represents the order in the sequence. This represents the j-th data point in the generated gray cumulative sequence. The expression represents the generation of a gray cumulative sequence from 1 to j, and ε represents the error tolerance.
[0060] To facilitate a clearer understanding of the hemispherical resonator gyroscope lifetime prediction method based on gray support vector machines provided by this invention, the following will use practical application examples to illustrate the above processes in detail. Those skilled in the art will understand that this example is only for the purpose of facilitating a clearer understanding of the hemispherical resonator gyroscope lifetime prediction method based on gray support vector machines provided by this invention, and does not impose any technical limitations on it.
[0061] This invention mainly comprises two parts: one is the extraction of lifetime characteristic factors of hemispherical resonant gyroscopes, and the other is the establishment of a lifetime prediction model and lifetime prediction. The specific contents are as follows:
[0062] 1. Extraction of lifetime characteristic factors of hemispherical resonant gyroscope
[0063] Extracting the characteristic factors that influence and characterize the performance and lifespan of a hemispherical resonator gyroscope (BRG) is crucial for gyroscope lifespan prediction and evaluation, directly impacting the accuracy of the lifespan prediction model. Due to the large amount of data collected during accelerated lifespan testing of BRGs, some of this data is insensitive to the BRG's lifespan characteristics and difficult to use for reliable lifespan prediction. Therefore, dimensionality reduction of the collected raw feature data is necessary. This invention employs a heuristic search strategy based on support vector machines (SVMs), using the cross-validation error rate of the feature set of lifespan characteristic parameters such as the resonator's vibration signal, angular rate output, and control signal as the evaluation metric. This strategy learns to identify and select characteristic factors that characterize the lifespan of the BRG, providing accurate feature data for BRG lifespan prediction.
[0064] The feature factor extraction model algorithm for hemispherical resonant gyroscope lifetime constructs a series of support vector machine classification problems based on a given training sample set. It utilizes the weight vector decision contribution ranking criterion and uses the cross-validation error rate of the classifier on the test sample set as the evaluation metric to heuristically search and filter gyroscope variable features, removing features irrelevant to decision-making, thereby optimizing the selection and extraction of variable feature subsets. The basic principle of the feature factor extraction model algorithm is as follows:
[0065] 1) Input the original training set, construct and solve the optimization problem.
[0066] In the case of linearly inseparable classification, an additional cost function needs to be allocated to the objective function for the classification error, i.e., a misclassification penalty component is introduced, so as to find an optimal hyperplane that minimizes the probability of the average classification error over the entire training sample set.
[0067] Assume that a classification hyperplane exists:
[0068] <ω,x>+b=0 (1)
[0069] The constraints are satisfied:
[0070] y i (<ω,x>+b)-1≥0,i=1,2,...,l (2)
[0071] In the formula, <·,·> denote the inner product of vectors, and ω∈R n Let b be an adjustable weight vector, b∈R be the bias, and {(x i y i Let {i = 1, 2, ..., l} be the training sample set. The hyperplane with the largest distance to the classification hyperplane is the optimal hyperplane, and the decision function can be obtained from this.
[0072] f(x)=sign(<ω,x>+b) (3)
[0073] Solving the above optimal hyperplane problem can be transformed into a constrained optimization problem. Using the Lagrange multiplier method, the dual optimization problem of the classification hyperplane problem can be obtained, namely:
[0074]
[0075] 0≤a i ≤C,i=1,2,...,l (4)
[0076] In the formula, the auxiliary variable a i is the Lagrange multiplier; C is a constant greater than 0, which controls the degree of punishment for misclassified samples, that is, controls the balance between the complexity of the learning machine and the number of inseparable sample points. The larger C is, the heavier the punishment for errors. The decision function f of the model can be obtained from the above formula.
[0077] 2) Given the corresponding test set, the corresponding risk R[f] can be calculated based on the model function f.
[0078] 3) Update the weight vector ω = ([ω]1,[ω]2,...,[ω]) constructed in step 1). l The component of )|[ω] i1 |≤|[ω] i2 |≤...≤|[ω] in|, where, [ω]1,[ω]2,...,[ω] l Let [ω] represent the weights of the first variable, the second variable, ..., the l-th variable, respectively. i1 ,[ω] i2 ...[ω] in Let each represent the weight corresponding to the i-th variable, the weight corresponding to the i-th variable, ..., the weight corresponding to the n-th variable, in that order.
[0079] 4) If n = 1, proceed to step (5); otherwise, set k = 1 and proceed to the following steps:
[0080] a. Remove [ω] from the original training set. ik Corresponding feature [x] ik Update the given input training and test sets;
[0081] b. Based on the updated input training set in step a, reconstruct and solve the optimization problem to obtain the model decision function f′;
[0082] c. Calculate the corresponding risk R[f′] based on the updated input test set in step a;
[0083] d. If R[f′] < R[f], then set ω = ω′, R[f′] = R[f], n = n-1, and go to step (3);
[0084] e. If k = n, go to step 5; otherwise, set k = k + 1 and go to step a.
[0085] 5) Output ω (ω component [ω]) i The corresponding feature [x] i (Features extracted for the model).
[0086] The lifetime feature factors of a hemispherical resonant gyroscope can be extracted using the above algorithm. While maintaining overall risk, the number of variable features is minimized to achieve key feature extraction. The basic strategy of this feature extraction model is as follows: A series of support vector machine classification problems are constructed using a given training sample set. The weight vector decision contribution ranking criterion is utilized, and the cross-validation error rate of the classifier on the test sample set is used as the evaluation metric. Heuristic search and filtering of system variable features are then performed to remove variable features irrelevant to system decisions, thereby optimizing the selection and extraction of variable feature subsets.
[0087] The specific extraction process is as follows:
[0088] From the 300-day gyroscope parameter data, 100 days of data from the beginning and end were selected as samples for different performance states of the gyroscope. Based on the feature extraction model described above, a corresponding 50-day training sample set and a 150-day test sample set were constructed. Gyroscope angular rate, quadrature amplitude, antinode amplitude, amplitude stabilization control voltage, quadrature control voltage, temperature, and high voltage were selected as candidate feature sets. Zero bias of the angular rate output by the hemispherical resonator gyroscope was used as the core performance indicator of the hemispherical resonator gyroscope.
[0089] To eliminate the impact of differences in the numerical values of various feature variables (angular velocity, orthogonal amplitude, antinode amplitude, amplitude stabilization control voltage, orthogonal control voltage, temperature, and high voltage) in the sample set on the performance of the classifier model, it is necessary to normalize each feature variable in the sample set when heuristically searching and filtering the gyroscope performance feature variables. This facilitates the subsequent unified differentiation of the contribution of different feature vectors to the model. The normalization method adopted in this paper is as follows: all feature vectors are unified to the range [0,1].
[0090]
[0091] First, construct the feature vector X = [x w ,x a ,x q ,x fa ,x fq ,x T ,x V ], where x w Represents the normalized angular velocity, x a Represents the normalized orthogonal amplitude, x q x represents the normalized amplitude of the antinode. fa Represents the normalized amplitude control voltage, x fq Represents the normalized quadrature control voltage, x T Represents the normalized temperature, x V This represents normalized high voltage. The model predicts the target Y as a hemispherical resonant gyroscope with zero bias angular rate.
[0092] Using formulas (1) to (4), the dual optimization problem of the classification hyperplane can be obtained through the Lagrange multiplier method. The model decision function f is solved, and the corresponding weight vector ω = [ω] is obtained from the feature vector. w ,ω a ,ω q ,ω fa ,ω fq ,ω T ,ω V Table 2 shows the values of the weight vectors corresponding to the seven feature vectors of the first support vector machine model.
[0093] Table 2 Feature vector weights of the Support Vector Machine model
[0094] <![CDATA[ω w ]]> <![CDATA[ω a ]]> <![CDATA[ω q ]]> <![CDATA[ω fa ]]> <![CDATA[ω fq ]]> <![CDATA[ω T ]]> <![CDATA[ω V ]]> 0.31 0.07 0.09 0.25 0.24 0.025 0.015
[0095] Where, ω V <ω T <ω a <ω q <ω fq <ω fa <ω w We can see that high pressure contributes the least to the model. Next, we remove the feature vector that contributes the least to the model (i.e., high pressure) and construct a new feature vector X2 = [x w ,x a ,x q ,x fa ,x fq ,x T Solve for the corresponding weight vector ω2=[ω w ,ω a ,ω q ,ω fa ,ω fq ,ω T Cross-validation is also performed on the test sample set. The feature vector x with the smallest weight in this test is removed. T We devise new feature vectors until the model's validation error on the test sample set no longer decreases.
[0096] Finally, a model decision function was constructed using the support vector machine formula. From the seven feature vectors mentioned above, angular rate, amplitude stabilization control voltage, and quadrature control voltage were selected as key feature factors characterizing the lifetime performance of the hemispherical resonator gyroscope. In the entire algorithm extraction process, the selected hemispherical resonator gyroscope factors were, in order: high voltage, temperature, quadrature amplitude, antinode amplitude, quadrature control voltage, amplitude stabilization control voltage, and angular rate. The corresponding cross-validation errors of the test sample sets are shown in the table below.
[0097] Table 3 Cross-validation error of the test sample set
[0098]
[0099] 2. Grey Support Vector Machine Hemispherical Resonant Gyroscope Lifetime Prediction Model
[0100] After obtaining the characteristic factors, a lifetime prediction model for the hemispherical resonant gyroscope can be established through statistical learning. By predicting the lifetime characteristic factors using the model, the divergence law of the lifetime characteristic factors is obtained. When the lifetime characteristic factors exceed a set threshold, the lifetime of the hemispherical resonant gyroscope is considered to have been reached. The prediction results of the three lifetime characteristic factors are compared, and the minimum value is taken as the final lifetime prediction result of the hemispherical resonant gyroscope. The model establishment method is illustrated below using angular rate as an example.
[0101] To meet the lifetime prediction requirements of hemispherical resonant gyroscopes under small sample conditions, this scheme employs a grey support vector machine (SVM) prediction model. This aims to improve the model's prediction accuracy, efficiency, robustness, and adaptability / self-learning capabilities. The grey SVM prediction model uses a cascaded structure. First, grey preprocessing (cumulative generation) is applied to the input data to reduce or weaken the randomness of the data sequence. Then, an SVM prediction model is built on the generated regularized data sequence. Finally, a grey inverse cumulative generation operation is used to reconstruct the prediction output of the original data sequence. The grey SVM prediction model execution algorithm is as follows: Figure 2 As shown, the specific steps include:
[0102] Given the original nonlinear data sequence:
[0103] X N ,X N ={x1,x2,…,x N},x i ∈R, i=1,2,...,N (6)
[0104] Where, x i X represents the angular velocity, which is the lifetime characteristic factor of the hemispherical resonant gyroscope mentioned above. N It is the corresponding angular rate time series.
[0105] The gray accumulation generation operation is defined as follows:
[0106]
[0107] By analyzing the original sequence X N Performing a gray accumulation generation operation can produce a new sequence:
[0108]
[0109] For the newly generated sequence By reconstructing the phase space, we can obtain:
[0110]
[0111] Among them, X 1 Y represents the input sequence after phase space reconstruction. 1 This represents the target sequence after phase space reconstruction.
[0112] By choosing the support vector machine model parameters ε, C and the kernel function K(.,.), we can obtain the support vector machine prediction regression estimation function:
[0113]
[0114] Where x(t) represents the prediction result of the support vector machine. This represents the support vector machine prediction regression estimation function. This represents the input sequence.
[0115] Lagrange multipliers The bias b is obtained by solving the following quadratic programming problem, namely:
[0116]
[0117] in, Let represent the normal vector of the hyperplane to be solved. Represents the Lagrange multipliers. and Both are input sequences.
[0118] From the above formula, we can obtain:
[0119]
[0120] Support Vector Machine Prediction Model:
[0121]
[0122] Calculate the newly generated sequence Predicted sequence Modeling and predicting sequences Perform a reverse accumulation generation operation:
[0123] x 0 (k)=x 1 (k)-x 1 (k-1), 2≤k≤n (14)
[0124] The original sequence X can then be obtained. N The predicted value—the predicted result of the hemispherical resonant gyroscope angular rate—is considered to have reached its lifespan when the predicted result exceeds the threshold.
[0125] The reliability and lifespan of a hemispherical resonant gyroscope can be predicted using the algorithm described above. When sufficient accelerated life test data is available, the accuracy of the model can also be verified through comparison, as follows: Figure 1 As shown, it includes:
[0126] Step 1: Conduct accelerated reliability tests on the hemispherical resonant gyroscope and obtain test data;
[0127] Step 2: Based on the experimental data, perform a heuristic search for the lifetime characteristic factor of the hemispherical resonant gyroscope using support vector machines to obtain the lifetime characteristic factor of the hemispherical resonant gyroscope.
[0128] Step 3: Using the hemispherical resonant gyroscope lifetime characteristic factors obtained in Step 2, establish a grey support vector machine hemispherical resonant gyroscope lifetime prediction model;
[0129] Step 4: Conduct accelerated lifetime tests on the hemispherical resonant gyroscope to verify the accuracy of the model.
[0130] In summary, this invention provides a method for predicting the lifetime of a hemispherical resonant gyroscope (HNR) using a grey support vector machine. This method constructs a classification hyperplane dual optimization equation and model decision function based on Lagrange multipliers, searches and filters to obtain hemispherical resonant gyroscope lifetime feature factors, establishes a grey support vector machine-based hemispherical resonant gyroscope lifetime prediction model based on these feature factors, and obtains the predicted values of the feature factors. Thus, the lifetime of the hemispherical resonant gyroscope is predicted based on these predicted values. This method can achieve effective and reliable prediction of the hemispherical resonant gyroscope lifetime with limited test data, reducing the experimental cycle and cost, and providing an effective evaluation means for the reliability and lifetime prediction of hemispherical resonant gyroscopes. Compared with existing technologies, the technical solution of this invention can solve the technical problems of long time consumption and high cost in traditional lifetime prediction methods.
[0131] For ease of description, spatial relative terms such as "above," "on top of," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation beyond the orientation of the device as described in the figures. For example, if the device in the figures were inverted, a device described as "above" or "on top of" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.
[0132] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.
[0133] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for predicting the lifetime of a hemispherical resonant gyroscope using a grey support vector machine, characterized in that, The method includes: S1. Conduct accelerated reliability tests on hemispherical resonant gyroscopes to obtain raw test data, and construct training and test sample sets based on the raw test data; S2, construct the classification hyperplane dual optimization equation and model decision function based on Lagrange multipliers, and search and filter the feature vectors of the hemispherical resonant gyroscope based on the classification hyperplane dual optimization equation, the model decision function, the training sample set and the test sample set, and use the feature vectors obtained after searching and filtering as the lifetime feature factors of the hemispherical resonant gyroscope. S3. Based on the hemispherical resonant gyroscope lifetime characteristic factors obtained in S2, a grey support vector machine hemispherical resonant gyroscope lifetime prediction model is established. S4. Based on the grey support vector machine hemispherical resonator gyroscope lifetime prediction model and the original experimental data corresponding to the lifetime characteristic factor of each hemispherical resonator gyroscope, the predicted value of the lifetime characteristic factor of each hemispherical resonator gyroscope is calculated, and the lifetime of the hemispherical resonator gyroscope is predicted according to the predicted value.
2. The method according to claim 1, characterized in that, The dual optimization equation for the classification hyperplane is: 0≤a i ≤C,i=1,2,...,l In the above formula, a i a j All are Lagrange multipliers, where i represents the i-th sample, j represents the j-th sample, and l represents the total number of samples. i ,y i ) represents the training sample set {(x i ,y i The i-th training sample in the sequence {x,i=1,2,...,l} j ,y j ) represents the test sample set {(x j ,y j Let ),j=1,2,...,l} be the j-th test sample, and let <·,·> denote the dot product of vectors, where C is a constant greater than 0.
3. The method according to claim 2, characterized in that, The model decision function is: f(x) = sign(<ω,x>+b) In the above formula, f(x) represents the model decision function, x represents the input parameters, ω is an adjustable weight vector, and ω∈R n b is the bias, b∈R, R n Let R represent an n-dimensional vector space, and let R represent the set of real numbers.
4. The method according to claim 3, characterized in that, Based on the grey support vector machine hemispherical resonator gyroscope lifetime prediction model and the original experimental data corresponding to each hemispherical resonator gyroscope lifetime characteristic factor, the predicted values of each hemispherical resonator gyroscope lifetime characteristic factor are calculated, including: The original experimental data corresponding to the lifetime characteristic factor of each hemispherical resonant gyroscope constitute the corresponding original nonlinear data sequence. The original nonlinear data sequence of the lifetime characteristic factor of each hemispherical resonant gyroscope is processed by gray accumulation to obtain the corresponding new sequence; The new sequence of lifetime characteristic factors for each hemispherical resonant gyroscope is input into the hemispherical resonant gyroscope lifetime prediction model based on grey support vector machine to obtain the predicted value of each hemispherical resonant gyroscope lifetime characteristic factor.
5. The method according to any one of claims 1 to 4, characterized in that, The hemispherical resonant gyroscope lifetime prediction model based on grey support vector machine is as follows: x 0 (k)=x 1 (k)-x 1 (k-1),2≤k≤n a * =(a1 a1 * …a N-m a N-m * ) T ,i=1,2,…,N-m In the above formula, The value represents the predicted value at step l of the sequence generated by gray accumulation, N represents the length of the data sequence, m represents the embedding dimension of the phase space reconstruction, and a * Represents the sequence of Lagrange multipliers. Let K(.,.) represent the i-th Lagrange multiplier, and K(.,.) be the kernel function. This represents the sequence generated by gray accumulation. This represents the gray cumulative generation sequence generated in prediction step l, x 0 (k) represents the k-th predicted value of the inverse accumulation generation sequence, x 1 (k) represents the k-th data in the sequence generated by gray accumulation, x 1 (k-1) represents the (k-1)th data point in the sequence generated by gray accumulation, where k represents the order in the sequence. This represents the j-th data point in the generated gray cumulative sequence. The expression represents the generation of a gray cumulative sequence from 1 to j, and ε represents the error tolerance.
6. The method according to claim 5, characterized in that, Predicting the lifetime of a hemispherical resonator gyroscope based on the predicted value includes: when the predicted value of any hemispherical resonator gyroscope lifetime characteristic factor exceeds a set threshold, the lifetime of the hemispherical resonator gyroscope is considered to have been reached.