CN110763441B - Engine turbine disk detection method based on single-class maximum vector angle region interval - Google Patents
Engine turbine disk detection method based on single-class maximum vector angle region interval Download PDFInfo
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Abstract
The invention relates to a method for detecting an engine turbine disk based on single-class maximum vector angle region interval, which is characterized by comprising the following steps of: step one, utilizing a maximized vector angle mean value and a minimized vector angle variance frame; and step two, adopting an unsupervised single-class maximum vector angle region interval classification method. The beneficial effects of the invention are: according to the method for detecting the abnormality of the engine turbine disk at the interval of the single-class maximum vector angle areas, a new detection model can be established only by normal training samples, and the method can be better applied to project practice; the proposed method searches for an optimized vector in the feature space by maximizing the vector angle mean while minimizing the vector angle variance, which can achieve better detection performance in a multi-modal process; the algorithm can construct an abnormal detection model only by acquiring experimental data of a detection object in a normal running state, and engineering implementation is easy. The technology can be further popularized and applied to the abnormality detection of general industrial parts.
Description
Technical Field
The invention relates to the technical field of fault Prediction and Health Management (PHM), in particular to an engine turbine disk abnormality detection method based on single-class maximum vector angle region intervals.
Background
The existing abnormal detection is a technical method for learning a detection model from normal data so as to effectively identify abnormal behaviors. In the real world, anomaly detection has wide practical applications, such as machine fault detection, industrial process monitoring, aviation safety, and the like. In general, anomaly detection can be considered a classification problem. In the classification-based anomaly detection method, a detection model is extracted from labeled training data, and whether a test sample is normal or abnormal can be predicted. In actual anomaly detection applications, normal training patterns are easy to acquire, but anomalous samples are difficult to acquire. In order to effectively solve the problem, a classification method capable of effectively detecting fault signals only by normal samples is provided.
In recent years, the kernel-based method is widely used in the field of anomaly detection, such as kernel Principal Component Analysis (PCA), one-class support vector machine (ocsvvm), and Support Vector Data Description (SVDD). The KPCA algorithm is an extension of Principal Component Analysis (PCA) using kernel-method techniques. The PCA is subjected to original linear operation in a regenerative kernel Hilbert space by utilizing a kernel function. In practical applications, however, the dimensionality of the kernel matrix becomes larger as the data set becomes larger. Therefore, when the data set is large, computation and storage become the bottleneck of the KPCA-based anomaly detection method. Simon Gunter et al introduced a gain-adaptive approach to improve the computational efficiency of KPCA algorithms, which were accelerated by iterative kernels.
The OCSVM is an unsupervised learning method, and in order to improve generalization capability, the OCSVM constructs a hyperplane in a feature space, and the hyperplane can separate normal samples and abnormal samples in the feature space. The SVDD algorithm is a single classification method based on the minimum boundary sphere theory, and establishes a single SVDD minimum volume hypersphere by using normal sample data in a feature space, so that fault detection is realized.
In the aspect of a maximum vector angle interval classifier, hu Wenjun et al proposes a two-class maximum vector angle boundary classifier. In the aspect of interval distribution optimization of the support vector machine, teng Zhang et al propose a double-class maximum interval distribution support vector machine. When the two methods are applied to the aspect of fault detection, a fault sample needs to be introduced for model training, and in the actual application of anomaly detection, the fault data sample is difficult to obtain or cannot be obtained at all.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, applies a maximum vector angle mean value and a minimum vector angle variance frame to the abnormality detection of the engine turbine disk, and provides a detection method of the engine turbine disk based on single-class maximum vector angle region intervals.
The invention is realized by the following technical scheme:
the engine turbine disk detection method based on the single-class maximum vector angle region interval is characterized by comprising the following steps of:
step one, utilizing a maximized vector angle mean value and a minimized vector angle variance frame;
step two, adopting an unsupervised single-class maximum vector angle region interval classification method;
wherein, the frame of utilizing the maximum vector angle mean and the minimum vector angle variance in the step one is:
given an original training matrix
Wherein +>
Represents input data, <' > based on>
Is a feature mapping function that can ≥ be input data from a given input space>
Mapping to a high-dimensional feature space pick>
Training sample
And vector angle mean between vector v>
And vector angle mean square deviation->
Can be expressed as:
wherein the content of the first and second substances,
e＝[1,...,1] T ；
the maximize vector angle mean and minimize vector angle variance framework may be expressed as:
according to the above technical solution, preferably, the unsupervised single-class maximum vector angular region interval classification method in step two is:
under the framework of maximizing the vector angular mean and minimizing the variance thereof, the unsupervised single-class maximum vector angular region interval classification method is constructed as follows:
wherein e = [1,.. 1, 1.)] T V denotes an optimal vector, ρ denotes a vector angular region interval, ξ = [ ξ = 1 ，...，ξ n ] T Vector representing relaxation variables, v and λ represent two normal constants;
the optimal vector in equation (4) is expressed as follows:
thus, X can be obtained T v＝X T X α = K α, wherein K = X T X represents a kernel matrix, and equation (4) can be expressed as follows:
s.t.α T K ：i ≥ρ-ξ i ，i＝1，...，l
ξ i ≥0，i＝1，...，l(6)
wherein Q =4 λ (lK) T K-(Ke)(Ke) T )/l 2 ，q＝-λ(Ke)/l，K ：i I-th column representing K;
to investigate the constraint problem as described in (6), the lagrangian function was constructed as follows:
wherein, β = [ β = 1 ，...，β l ] T And η = [ η ] 1 ，...，η l ] T Representing the lagrange multiplier, by making the partial derivative of L (ρ, α, ξ, β, η) zero by the lagrange multiplier method, the following equation can be derived:
wherein, H = KQ -1 K，p＝-λ(He)/l，Q -1 Representing the inverse matrix of Q.
The beneficial effects of the invention are:
1. according to the method for detecting the abnormality of the engine turbine disk at the interval of the single-class maximum vector angle areas, a new detection model can be established only by normal training samples, and the method can be better applied to project practice;
2. the proposed method searches for an optimized vector in the feature space by maximizing the vector angle mean while minimizing the vector angle variance, which can achieve better detection performance in a multi-modal process;
3. the algorithm can construct an abnormal detection model only by acquiring experimental data of a detected object in a normal running state, and is easy for engineering realization. The technology can be further popularized and applied to the abnormity detection of common industrial parts.
Drawings
Fig. 1 (a) shows the influence of the parameter v on the accuracy in experiment 1.
Fig. 1 (b) shows the effect of the parameter v on the recall ratio in experiment 1.
FIG. 2 (a) shows the effect of the parameter λ on the accuracy in experiment 2.
FIG. 2 (b) is a graph showing the effect of parameter λ on recall in experiment 2.
FIG. 3 (a) is a graph comparing the accuracy of the three algorithms OCSVM, one-class SVDD and one-class LARM at 3000RPM for case 1.
FIG. 3 (b) is a graph comparing the recall rates of the three algorithms OCSVM, one-class SVDD, and one-class LARM at 3000RPM for case 1.
FIG. 3 (c) is a graph comparing the average training times of the three algorithms OCSVM, one-class SVDD, and one-class LARM at 3000RPM for case 1.
FIG. 3 (d) is a graph comparing the average test times of the three algorithms OCSVM, one-class SVDD and one-class LARM at a rotation speed of 3000RPM in case 1.
FIG. 4 (a) is a graph comparing the accuracy of the three algorithms OCSVM, one-class SVDD and one-class LARM at 4000RPM for case 2.
FIG. 4 (b) is a graph comparing the recall rates of the three algorithms OCSVM, one-class SVDD and one-class LARM at 4000RPM for case 2.
FIG. 4 (c) is a graph comparing the average training times of the three algorithms OCSVM, one-class SVDD and one-class LARM at 4000RPM for case 2.
FIG. 4 (d) is a graph comparing the average test times of the three algorithms OCSVM, one-class SVDD and one-class LARM at 4000RPM for case 2.
FIG. 5 (a) is a graph comparing the accuracy of the three algorithms OCSVM, one-class SVDD and one-class LARM at 5000RPM for case 3.
FIG. 5 (b) is a graph comparing recall rates of the three algorithms OCSVM, one-class SVDD, and one-class LARM at 5000RPM for case 3.
FIG. 5 (c) is a graph comparing the average training times of the three algorithms OCSVM, one-class SVDD, and one-class LARM at 5000RPM for case 3.
FIG. 5 (d) is a graph comparing the average test times of the three algorithms OCSVM, one-class SVDD and one-class LARM at 5000RPM for case 3.
FIG. 6 (a) is a comparison graph of the accuracy of the three algorithms OCSVM, one-class SVDD, and one-class LARM in case 4 multi-mode process.
FIG. 6 (b) is a graph comparing recall rates of three algorithms, namely OCSVM, one-class SVDD and one-class LARM, in case 4 in the multi-mode process.
FIG. 6 (c) is a comparison graph of the average training time of the three algorithms OCSVM, one-class SVDD and one-class LARM in case 4 multi-mode process.
FIG. 6 (d) is a comparison graph of the average test time of the three algorithms OCSVM, one-class SVDD and one-class LARM in case 4 multi-mode process.
FIG. 7 (a) is a comparison graph of the average accuracy results of the three algorithms OCSVM, one-class SVDD and one-class LARM in different mode processes.
FIG. 7 (b) is a comparison graph of the average recall rate results of the three algorithms OCSVM, one-class SVDD and one-class LARM during different modes.
FIG. 7 (c) is a comparison graph of the average training time results of the three algorithms OCSVM, one-class SVDD, and one-class LARM in different modes.
FIG. 7 (d) is a comparison graph of the average test time results of the three algorithms OCSVM, one-class SVDD, and one-class LARM in different modes.
Detailed Description
In order to make the technical solutions of the present invention better understood by those skilled in the art, the present invention will be further described in detail with reference to the accompanying drawings and preferred embodiments.
As shown in the figure, the engine turbine disk detection method based on the single-type maximum vector angle region interval is characterized by comprising the following steps of:
step one, utilizing a maximized vector angle mean value and a minimized vector angle variance frame;
step two, adopting an unsupervised single-class maximum vector angle region interval classification method;
wherein, the frame using the maximum vector angle mean and the minimum vector angle variance in the step one is:
given an original training matrix
Wherein->
Represents input data, <' > based on>
Is a feature mapping function that can combine input data from a given input space +>
Mapping to a high-dimensional feature space pick>
Training sample
And the mean value of the vector angle between the vector v>
And vector angle mean square deviation->
Can be expressed as:
wherein the content of the first and second substances,
e＝[1,...,1] T ；
the maximize vector angle mean and minimize vector angle variance framework may be expressed as:
according to the above technical solution, preferably, the unsupervised single-class maximum vector angular region interval classification method in step two is:
under the framework of maximizing the vector angle mean and minimizing the variance, the unsupervised single-class maximum vector angle region interval classification method is constructed and can be represented as follows:
wherein e = [1,. -, 1] T V denotes an optimal vector, ρ denotes a vector angular region interval, ξ = [ ξ = 1 ,...,ξ n ] T Vector representing relaxation variable, v and λ represent two normal numbers;
the optimal vector in equation (4) is expressed as follows:
thus, X can be obtained T v＝X T X α = K α, wherein K = X T X represents a kernel matrix, and formula (4) can be expressed as follows:
s.t.α T K :i ≥ρ-ξ i ,i＝1,...,l
ξ i ≥0,i＝1,...,l(6)
wherein Q =4 λ (lK) T K-(Ke)(Ke) T )/l 2 ，q＝-λ(Ke)/l，K :i I-th column representing K;
to investigate the constraint problem as described in (6), the lagrangian function was constructed as follows:
wherein β = [ β ] 1 ，..，β l ] T And η = [ η ] 1 ，...，η l ] T Representing the lagrange multiplier, by making the partial derivative of L (ρ, α, ξ, β, η) zero by the lagrange multiplier method, the following equation can be derived:
wherein, H = KQ -1 K，p＝-λ(He)/l，Q -1 Representing the inverse matrix of Q.
The single-class maximum vector angular region interval (one-class LARM: one-class 1 specific vector-oriented region and margin) algorithm provided by the invention is an unsupervised classification method, and only needs an original training matrix
The anomaly detection model may be trained, where l represents the number of training samples.
In order to verify the effectiveness of the engine turbine disk abnormality detection method based on the single-class maximum vector angular region interval, the inventor conducts experiments on the method, and the process is as follows:
in order to further prove the performance of the engine turbine disk abnormality detection method based on the single-class maximum vector angular region interval, a data set provided by a rotor dynamics laboratory of the national aeronautics and astronautics administration (NASA) gurney research center is selected in the following experiments to evaluate the performance of the proposed abnormality detection algorithm. In the experimental test system, the fault was placed on the edge region of the turbine disk of the engine. Three states (normal, small scratch and large scratch) of three different rotation speeds (3000 Revolutions Per Minute (RPM), 4000RPM and 5000 RPM) were recorded in the engine turbine disk abnormality data.
All experiments were performed on a computer with Xeon (R) E5-1630v4 and 16-GB main memory with a 3.70GHz CPU. The accuracy and the recall ratio are used as indexes for evaluating the experimental results, and the formula is as follows:
where TP represents the true number of samples, TN represents the true negative number of samples, FP represents the false positive number of samples, and FN represents the false negative number of samples.
Experiment 1: parameter influence and selection
All experiments in the present invention, using Radial Basis Function (RBF) as kernel function:
κ(x i ,x j )＝exp(-γ||x i -x j || 2 ),0＜γ＜+∞ (10)
wherein gamma represents the nuclear parameter of RBF, gamma is in the set { alpha ] through a 5-fold cross validation method 0 /32,α 0 /16,α 0 /8,α 0 /4,α 0 /2,α 0 Selected from (i) }, in which α 0 The average norm of the training examples is shown. For a single-class LARM algorithm, v and λ are two parameters that affect the detection performance, so the following experiment is performed to understand the effect of the parameters v and λ more.
The first experiment was used to measure the effect of a parameter v on assay performance, where the parameter v was selected in the set {0.01k,0.1k }, k =1,3,5,7,9 by a 5-fold cross-validation method. In the present experiment, training and test data were randomly selected from disk defect data at each RPM condition, the number of training data was set to 45, 60, 75, 90 and 105 (15, 20, 25, 30 and 35 normal samples were independently collected at each RPM condition, and the number of test data was set to 6000 (1000 normal samples and 1000 abnormal samples were independently collected at each RPM condition). All experiments were repeated 10 times, and the average accuracy and recall were as shown in fig. 1 (a) and 1 (b).
The second experiment was used to measure the effect of a parameter λ on detection performance, where the parameter λ was selected by the data cross-validation method in the set {0.1k }, k =1,2, \8230;, 9. The setup of the training and testing samples was the same as that of the first experiment. All experiments were repeated 10 times, with average accuracy and recall as shown in fig. 2 (a) and 2 (b).
As can be seen from FIGS. 1 (a), 1 (b), 2 (a) and 2 (b), the influence of the parameters v and λ on the accuracy and recall is weak, and in order to reduce the training time, the parameters v and λ in the subsequent experiments are selected by the method of influencing cross-validation in the sets {0.1,0.3,0.6,0.9} and {0.01,0.05,0.1,0.5,0.9} respectively. The above experiments show that the selection ranges of v and λ are suitable for the subsequent experiments.
Experiment 2: performance of a one-class LARM algorithm
In the experiment, the performance comparison of the small scratch detection of the single-class LARM and the OCSVM and the single-class SVDD in the failure data set of the engine turbine disk is carried out. In order to ensure the fairness and the accuracy of the experiment, the three algorithms are realized by an LIBSVM software package.
For OCSVM, the parameter v is chosen in the set {0.01k,0.1k }, k =1,2, \8230, 9.
For a single class of SVDD, the parameter C is selected in the set {1/l + k δ }, k =0,1,2, \ 8230, 17, where δ = (l-1)/17 l and l represent the number of training samples.
(1) Case 1: small scratch detection at 3000RPM
In case 1, the engine turbine disk was operated in a single mode process, with 3000RPM. The engine turbine disk is firstly operated normally to collect 5000 samples, and then the small scratch state is switched to collect other 5000 samples. To ensure the accuracy of the experiment, the experiment was repeated 20 times, with both training and test data randomly selected from the engine turbine disk failure data set. A comparison graph of the detection results based on the three algorithms of ocsvvm, SVDD and LARM is shown in fig. 3 (a), 3 (b), 3 (c) and 3 (d).
As can be seen from fig. 3 (a), when the number of training samples is greater than 30, the single-class LARM has a significant advantage in terms of accuracy. The recall rate of the single type of LARM (see fig. 3 (b)) is significantly better than that of the OCSVM and the single type of SVDD. However, as shown in fig. 3 (c), the training speed of the single-class LARM algorithm is inferior to that of the OCSVM and SVDD algorithms. This is because solving the QP problem for a single type of LARM requires computing the inverse matrix for Q. As training samples increase, matrix inversion becomes very time consuming. As a result, as shown in FIG. 3 (d), the OCSVM, the single-type SVDD and the single-type LARM have a small difference in test time. When the number of training is 105 and the number of test samples is 10000, the average test time of the single type of LARM is about 0.05 seconds.
(2) Case 2: small scratch detection at 4000RPM
In case 2, the engine turbine disk was operated in a single mode process at 4000RPM. The engine turbine disk firstly runs normally to collect 5000 samples, and then switches to a small scratch state to collect other 5000 samples. The setup of training and testing samples was the same as that of the case 1 experiment. Comparative graphs of detection results based on three algorithms of the ocsvvm, the single SVDD and the single LARM are shown in fig. 4 (a), fig. 4 (b), fig. 4 (c) and fig. 4 (d).
The results shown in fig. 4 (a), 4 (b), 4 (c) and 4 (d) show that when the number of training samples is greater than 45, the single-class LARMs have significant advantages in accuracy and recall, respectively. Similar to case 1, fig. 4 (c) shows that the training time of OCSVM and single class SVDD is better than that of single class LARM algorithm. As can be seen from fig. 4 (d), the testing time of OCSVM and SVDD class is slightly better than that of LARM algorithm class. When the number of training is 105 and the number of test samples is 10000, the longest time interval of the single type of LARM is about 0.01 second.
(3) Case 3: small scratch detection at 5000RPM
In case 3, the engine turbine disk was operated in a single mode process with a speed of 5000RPM. The engine turbine disk is firstly operated normally to collect 5000 samples, and then the small scratch state is switched to collect other 5000 samples. The setup of training and testing samples was the same as that of the case 1 experiment. Comparative graphs of the detection results based on the three algorithms of the ocsvvm, the single SVDD and the single LARM are shown in fig. 5 (a), fig. 5 (b), fig. 5 (c) and fig. 5 (d).
As can be seen from fig. 5 (a), the proposed single-class LARM has a significant advantage in terms of accuracy when the number of training samples is greater than 60. The recall rate of the single-class LARM (see fig. 5 (b)) is significantly better than that of the OCSVM and the single-class SVDD. Similar to case 1, fig. 5 (c) shows that the training time of OCSVM and SVDD class is better than that of LARM class. As can be seen from fig. 5 (d), the testing time of ocsvvm, SVDD of single type and LARM of single type is not very different.
(4) Case 4: small scratch detection under multi-mode process
In case 4, the turbine disk of the turbine engine operates in a multimode process with speeds of 3000RPM,4000RPM and 5000RPM, respectively. The method comprises the steps that a turbine disk of the turbine engine normally runs in a 3000RPM mode to collect 1000 samples, then is switched to a 4000RPM mode to collect 1000 samples, finally is switched to a 5000RPM mode to collect 1000 samples, after 3000 normal samples are collected totally, a small scratch state is switched to run in the 5000RPM mode to collect 1000 normal samples, then is switched to the 4000RPM mode to collect 1000 normal samples, and then is switched to the 3000RPM mode to collect 1000 normal samples. The training samples consisted of the same number of normal samples of 3000RPM,4000RPM and 5000RPM. The setup of training and testing samples was the same as that of the case 1 experiment. A comparison graph of the detection results based on the three algorithms of ocsvvm, SVDD and LARM is shown in fig. 6 (a), 6 (b), 6 (c) and 6 (d).
As a result, as shown in fig. 6 (a), 6 (b), 6 (c) and 6 (d), the proposed single-type LARM has significant advantages in terms of accuracy and recall. Similar to case 1, fig. 6 (c) shows that the training time of OCSVM and SVDD is better than that of the LARM algorithm. As can be seen from fig. 6 (d), the testing time of ocsvvm, SVDD of single type and LARM of single type is not very different.
In conjunction with the above experimental results, the average accuracy, average recall, average training time and average testing time for the different model processes are recorded in fig. 7 (a), fig. 7 (b), fig. 7 (c) and fig. 7 (d), respectively. Fig. 7 (a) and 7 (b) are results of detection performances including accuracy and recall in different mode detection processes, respectively. Fig. 7 (c) and 7 (d) show the computation costs including training and detection times, respectively, in the different modes. We summarize the experimental results of all experimental modes into fig. 7 (a), fig. 7 (b), fig. 7 (c) and fig. 7 (d), where the detection performance of algorithms that distinguish OCSVM, SVDD and LARM of a single type can be visually checked and compared.
The accuracy and recall shown in fig. 7 (a) and 7 (b) for all detection modes indicate that a single class of LARMs compares favorably to a single class of SVDD and OCSVM. A single type of LARM typically achieves the best detection performance in all methods, especially with turbine engine disks operating in multiple modes. The mean and covariance of the sampled data at multiple modes will vary significantly, which will affect the accuracy of the detection model. The homogeneous LARM algorithm attempts to maximize the vector angle mean while minimizing the vector angle variance in the feature space. Thus, the single-class LARM algorithm achieves better detection performance in a multi-mode process.
As can be seen from fig. 7 (c), the training time of OCSVM and SVDD class is better than that of LARM class. This is because solving the QP problem for a single type of LARM requires computing the inverse of the matrix Q. As the training samples increase, solving the inverse matrix transform can be very time consuming. The training time of the single class LARMs limits their applicability to medium and large datasets. When the number of training samples is relatively small, the training time difference between ocsvvm, SVDD and LARM of single class is not large, but LARM of single class has significant advantages in detection performance, including accuracy and recall, especially for multimodal processes.
As can be seen from fig. 7 (d), the testing time gap between ocsvvm, SVDD of single type and LARM of single type is not large. A single class of LAR takes approximately 0.05-0.06 seconds to detect 10000 samples in a single modality process and approximately 0.03 seconds to detect 6000 samples in a multi-modality process.
Combining the experimental results of experiments 1 to 2, the following conclusions can be drawn:
1) From the results, the fault sample is difficult to obtain and even can not be used at all, so that the single-class maximum vector angular region interval engine turbine disk abnormity detection method provided by the invention can construct a new detection model only by normal training samples, and can be better applied to project practice;
2) Furthermore, the proposed method searches for an optimized vector in the feature space by maximizing the vector angle mean while minimizing the vector angle variance, which may achieve better detection performance in a multi-modal process.
Claims (1)
1. The engine turbine disk detection method based on the single-class maximum vector angle region interval is characterized by comprising the following steps of:
step one, utilizing a maximized vector angle mean value and a minimized vector angle variance frame;
step two, adopting an unsupervised single-class maximum vector angular region interval classification method;
wherein, the frame using the maximum vector angle mean and the minimum vector angle variance in the step one is: given an original training matrix X = [ phi (X) 1 )，...，φ(x i )]In which
Representing input data, l representing the number of training samples, phi (x) i ) Is a feature mapping function for basing input data on a given input space ≧ or>
Mapping to a high-dimensional feature space pick>
Training sample phi (x) i ) Vector angular mean between i = 1.. 1, l and vector v
And vector angle mean square error>
Can be expressed as:
wherein, X = [ phi (X) 1 )，φ(x 2 )，…，φ(x 1 )]，e＝[1，...，1] T ；
The maximize vector angle mean and minimize vector angle variance framework is represented as:
in the second step, the unsupervised single-class maximum vector angular region interval classification method comprises the following steps:
under the framework of maximizing the vector angle mean and minimizing the variance, an unsupervised single-class maximum vector angle region interval classification method is constructed and expressed as follows:
wherein e = [1,.. 1, 1.)] T V denotes an optimal vector, ρ denotes a vector angular region interval, ξ = [ ξ = 1 ，...，ξ n ] T Vector representing relaxation variable, v and λ represent two normal constants;
the optimal vector in equation (4) is expressed as follows:
thus, X is obtained T v＝X T X α = K α, wherein K = X T X represents a kernel matrix, and formula (4) can be expressed as follows:
wherein the content of the first and second substances,
K ：i i-th column representing K;
to study the constraint problem as (6), the lagrangian function was constructed as follows:
wherein the content of the first and second substances,
and &>
Representing the lagrange multiplier, by making the partial derivative of L (ρ, α, ξ, β, η) zero by the lagrange multiplier method, the following equation can be derived:
wherein, H = KQ -1 K，p＝-λ(He)/l，Q -1 ，Q -1 An inverse matrix representing Q;
the engine turbine disk detection method is used for searching for an optimized vector in a feature space by maximizing a vector angle average value and minimizing a vector angle variance at the same time, and performing engine turbine disk abnormality detection.
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Application publication date: 20200207 Assignee: Xi'an Xingyuan Digital Technology Co.,Ltd. Assignor: CIVIL AVIATION University OF CHINA Contract record no.: X2024980002853 Denomination of invention: Engine turbine disk detection method based on single class maximum vector angle region interval Granted publication date: 20230407 License type: Common License Record date: 20240314 |