CN115828139B - Gate structure safety assessment and prediction method and system based on vibration signals - Google Patents
Gate structure safety assessment and prediction method and system based on vibration signals Download PDFInfo
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Abstract
The invention provides a gate structure safety assessment and prediction method based on vibration signals, which comprises the following steps: the method comprises the steps of obtaining a vibration signal of a gate, and putting the vibration signal into a modal feature extraction model to obtain modal information features; the method comprises the steps of placing the modal information features into a mathematical model based on a Bayesian theory, wherein the mathematical model based on the Bayesian theory comprises a convolutional neural network and a support vector machine; the convolutional neural network performs feature extraction on the modal information features, and the support vector machine classifies and regresses the extracted features to obtain feature signals; comparing the characteristic signals with vibration standards to obtain a safety evaluation result of the gate; and (3) a plurality of characteristic signals are put into a mathematical model based on the Bayesian theory to be predicted, a posterior distribution result is obtained, and a structure prediction result of the gate is obtained according to the posterior distribution result. The method shortens the test evaluation period of the gate, improves the gate monitoring precision, and can also predict the future trend of the gate structure.
Description
Technical Field
The invention belongs to the technical field of gate vibration, and particularly relates to a gate structure safety evaluation and prediction method and system based on vibration signals.
Background
The reservoir gate is connected with the upstream and the downstream of the reservoir, and the gate not only has the functions of water blocking and water discharging, but also can adjust and control the water level and the discharge flow of the reservoir, so that the stability of the reservoir gate structure is very important in hydraulic engineering. The reservoir gate can be impacted by various forms of water flow in operation, for example, when the gate is closed in a flood control stage, the water flow is rapidly increased, and the fluctuation of the water flow causes the gate to vibrate; when the gate is opened, vortex, backflow and the like generated by water flow passing through the opening of the gate can also vibrate the gate, and in addition, the gate is also vibrated by other external forces; these vibrations may cause accelerated wear of some parts of the gate, reduced life, excessive stress on some components of the gate, fatigue damage, even damage to the gate and shut down of the operation, and significant safety hazards to the flood control operation of the reservoir.
The gate vibration monitoring methods commonly used in the prior art comprise a prototype monitoring method, a model experiment method and a data analysis method, the methods have higher running cost, long test evaluation period and inaccurate monitoring result. Therefore, a new gate structure monitoring method and system are needed to shorten the test evaluation period and improve the monitoring accuracy of the gate structure.
Disclosure of Invention
The invention aims to at least solve the technical problems in the prior art, and provides a gate structure safety evaluation and prediction method and system based on vibration signals, which shortens the test evaluation period of a gate, improves the gate monitoring precision and can also predict the future trend of the gate structure.
In order to achieve the above object of the present invention, according to a first aspect of the present invention, there is provided a gate structure safety evaluation and prediction method based on vibration signals, comprising the steps of: the method comprises the steps of obtaining a vibration signal of a gate, and putting the vibration signal into a modal feature extraction model to obtain modal information features; the modal information features are put into a mathematical model based on the Bayesian theory, wherein the mathematical model based on the Bayesian theory comprises a convolutional neural network and a support vector machine; the convolutional neural network performs feature extraction on the modal information features, and the support vector machine classifies and regresses the extracted features to obtain feature signals; comparing the characteristic signals with vibration standards, and outputting a safety evaluation result of the gate; and predicting a plurality of characteristic signals to obtain posterior distribution results, and outputting a gate structure prediction result according to the posterior distribution results.
Further, the step of obtaining the vibration signal of the gate and putting the vibration signal into the modal feature extraction model to obtain modal information features comprises the following steps: establishing a discrete time random state space model according to a vibration signal of the gate, generating a covariance matrix, forming a T-shaped matrix according to the covariance matrix, and solving the T-shaped matrix to obtain modal information characteristics; the modal information characteristics include frequency, damping ratio, mode shape, damping and modal participation factors, and are expressed by the following formulas: wherein omega i Represents the frequency of the i-th stage, lambda i The signal complex eigenvalues of the vibration signal state matrix representing the I-th stage, the superscripts Re and I representing the real and imaginary parts, respectively; epsilon i Represents the damping ratio, phi i Representing vibration pattern, C d Representing a discrete output matrix, ψ i A T-matrix representing an i-th stage covariance matrix; zeta type toy i Represents damping, u i Represents the i-th eigenvalue, lnu i Represents u i Is a natural logarithm of Deltat representing the time period after the discretization, & lt>Representing plural->The real part of (2); MP (MP) i Representing modality participation factors, ++>Representing the vibration mode phi i R represents a random vector.
Further, the steps of predicting the plurality of characteristic signals in a mathematical model based on the bayesian theory and obtaining the posterior distribution result specifically include: calculating density distribution functions of a plurality of characteristic signals, integrating sample information and prior information of unknown parameters in the characteristic signals based on Bayesian theory, obtaining estimation of posterior distribution, and further deducing the unknown parameters to obtain posterior distribution results; the density distribution function is specifically:wherein F (x) represents a density distribution function, x represents a priori data, i represents the ith stage, M represents the total number of a priori results x, +.>Weights representing the convolution layer of layer I, b l Representing the offset, x, of the first convolution layer i Representing the i-th a priori data, f (x i ) Represents x i Is a function of the activation function.
Further, a mathematical model based on bayesian theory is as follows: wherein L (theta, x) represents a mathematical model based on Bayesian theory, ρ (theta) is a priori data probability distribution function, P (F (x), theta) represents a likelihood function, and theta represents a modal information feature.
Further, the mathematical model based on the Bayesian theory comprises a first input layer, a second convolution layer, a third sub-sampling layer, a fourth convolution layer, a fifth sub-sampling layer, a support vector machine and a seventh output layer.
Further, the fifth sub-sampling layer and the support vector machine use the relu function as an activation function.
Further, a mathematical model based on the bayesian theory is generated through training of the following steps: collecting vibration signals of a gate to form a data sample; dividing the data samples into a training data set and a test data set; establishing a convolutional neural network; replacing a full connection layer in the convolutional neural network with a support vector machine to generate an initial model; and putting the training data set and the test data set into an initial model for training, and generating a mathematical model based on the Bayesian theory after the model converges.
Further, the step of collecting the data sample composed of the vibration signals of the gate is specifically: the vibration signal of the gate was collected at a sampling frequency of 2000Hz to form a data sample.
Further, the step of placing the modal information features into a mathematical model based on bayesian theory specifically includes: preprocessing the modal information characteristics, and putting the preprocessed modal information characteristics into a mathematical model based on a Bayesian theory; the preprocessing process comprises filtering processing and normalization processing.
In order to achieve the above object of the present invention, according to a second aspect of the present invention, a vibration signal-based gate structure safety evaluation and prediction system, in which any one of the above-described vibration signal-based gate structure safety evaluation and prediction methods is used during operation; the system comprises an acquisition module, an extraction module, a training module and an evaluation prediction module; the acquisition module is used for acquiring a vibration signal of the gate; the extraction module is used for acquiring modal information characteristics according to the vibration signals of the gate; the training module is used for generating and training a mathematical model based on the Bayesian theory; and the evaluation prediction module is used for obtaining the safety evaluation result of the gate and the prediction result of the gate according to the modal information characteristics and the mathematical model based on the Bayesian theory.
The invention has the basic principle and beneficial effects that: according to the scheme, the modal information features are extracted through the vibration signals, the modal information features comprise parameters with characteristics in the vibration signals, the modal information features are input into a Bayesian theory-based mathematical model, the Bayesian theory-based mathematical model is trained by using a deep learning convolutional neural network algorithm and a support vector machine, and the Bayesian theory-based mathematical model monitors and evaluates the vibration signals of the gate according to the modal information features to obtain characteristic signals; comparing the characteristic signals with standard data, and judging whether the vibration signals of the gate are safe vibration signals or not; the mathematical model based on the Bayesian theory adopts the convolutional neural network and the support vector machine, so that the convergence speed is high, the calculation accuracy is high, the detection and monitoring period of the gate vibration signal is shortened, and the monitoring accuracy is improved. The scheme also calculates posterior distribution estimation of a plurality of characteristic signals based on Bayesian theory, and short-term prediction is carried out on the running state of the gate structure according to the posterior distribution estimation result.
Drawings
FIG. 1 is a flow chart of steps of a method for evaluating and predicting the safety of a gate structure based on vibration signals;
FIG. 2 is a schematic diagram of the steps for obtaining the modal information feature of the present invention;
FIG. 3 is a flowchart of a training step of the Bayesian theory-based mathematical model of the present invention;
FIG. 4 is a schematic diagram of a portion of a Bayesian theory-based mathematical model in accordance with the present invention;
fig. 5 is a schematic structural view of the gate structure safety evaluation and prediction system based on vibration signals of the present invention.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the invention.
In the description of the present invention, it should be understood that the terms "longitudinal," "transverse," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like indicate orientations or positional relationships based on the orientation or positional relationships shown in the drawings, merely to facilitate describing the present invention and simplify the description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and therefore should not be construed as limiting the present invention.
In the description of the present invention, unless otherwise specified and defined, it should be noted that the terms "mounted," "connected," and "coupled" are to be construed broadly, and may be, for example, mechanical or electrical, or may be in communication with each other between two elements, directly or indirectly through intermediaries, as would be understood by those skilled in the art, in view of the specific meaning of the terms described above.
As shown in fig. 1, the invention provides a gate structure safety evaluation and prediction method based on vibration signals, which comprises the following steps:
the method comprises the steps of obtaining a vibration signal of a gate, and putting the vibration signal into a modal feature extraction model to obtain modal information features;
the modal information features are put into a mathematical model based on the Bayesian theory, and the mathematical model based on the Bayesian theory comprises a convolutional neural network and a support vector machine; the convolutional neural network performs feature extraction on the modal information features, and the support vector machine classifies and regresses the extracted features to obtain feature signals; comparing the characteristic signals with vibration standards to obtain a safety evaluation result of the gate;
and (3) a plurality of characteristic signals are put into a mathematical model based on the Bayesian theory to be predicted, a posterior distribution result is obtained, and a structure prediction result of the gate is obtained according to the posterior distribution result.
Specifically, the vibration signal of the gate is obtained by online real-time detection of a vibration sensor arranged on the gate, the vibration sensor is preferably arranged at the central position of the gate in order to ensure the accuracy of vibration detection, and the vibration sensor is preferably a capacitive vibration sensor which has the characteristics of simple structure, good environmental adaptability, good dynamic measurement performance and the like.
As shown in fig. 2, the step of obtaining the modal information feature by putting the vibration signal of the gate into the modal feature extraction model specifically includes:
establishing a discrete time random state space model according to a vibration signal of the gate, generating a covariance matrix, forming a T-shaped matrix according to the covariance matrix, and solving the T-shaped matrix to obtain modal information characteristics; specifically, a system discrete time random state space model of the degree of freedom n under environmental excitation is established according to the vibration signal:
X k+1 ＝A d X k +W k
Y k ＝C d X k +V k
wherein X is k And X k+1 Discrete-time state vectors representing the kth time and the kth+1 time, respectively, Y k A vibration signal of the vibration sensor at the kth time; a is that d Is a signal state matrix, A d ∈R 2n×2n ，C d For discrete output matrix, C d ∈R m×2n Wherein R represents real space, m represents the number of output channels, W k Representing zero-mean Gaussian white noise vector caused by model establishment, V k A zero mean white noise vector representing the vibration sensor measurement response;
the discrete vibration signal of the gate, which is measured by the vibration sensor, is Y k ＝{y 1 ，y 2 ，...，y n Utilizing discrete vibration signals to form Hankel matrix and dividing Hankel matrix H into past output matrix Y p And future output matrix Y f Two parts:
where i and j represent the number of rows and columns, respectively, of the Hankel matrix.
The discrete time state vector and the discrete vibration signal can be described by a zero-mean stationary random process, and the covariance matrix R is generated assuming that the vibration signal of the response of the monitoring point of the vibration sensor has an individual state history i The method comprises the following steps:
wherein,,e is a mathematical expectation.
Further, the covariance matrix is formed into a T-matrixFrom singular value decomposition, ψ may be approximated asWherein P and Q each represent an orthogonal matrix, S represents a diagonal matrix, and the elements of the matrix are arranged in order from large to small. Obtaining a state matrix of the gate vibration signal according to the T-shaped matrix:
wherein,,
state matrix a for vibration signal d Decomposing the characteristic value to obtain a signal complex characteristic value lambda i ：
Wherein lambda is i Representing complex eigenvalues, ω i And xi i The frequency and damping ratio of the i-th order modes, respectively. In view of the conversion of discrete-time eigenvalues into continuous-time models, the complex eigenvalues lambda are calculated according to the above-mentioned signals i Extracting and calculating modal information characteristics, wherein the modal information characteristics comprise frequency, damping ratio, vibration mode, damping and modal participation factors, and the modal information characteristics are expressed by the following formulas:
φ i ＝C d Ψ i
wherein omega i Represents the frequency of the i-th stage, lambda i The signal complex eigenvalues of the vibration signal state matrix representing the I-th stage, the superscripts Re and I representing the real and imaginary parts, respectively; epsilon i Represents the damping ratio, phi i Representing vibration pattern, C d Representing a discrete output matrix, ψ i A T-matrix representing an i-th stage covariance matrix; zeta type toy i Represents damping, u i Represents the i-th eigenvalue, lnu i Represents u i Is a natural logarithm of (a), Δt represents a period of time after the discretization,representing plural->The real part of (2); MP (MP) i Representing modality participation factors, ++>Representing the vibration mode phi i R represents a random vector. The modality information characteristics also include amplitude and phase. The mode information feature obtained by the mode feature extraction model has good reliability and high precision.
Further, the step of placing the modal information features into a mathematical model based on bayesian theory specifically includes: preprocessing the modal information characteristics, and putting the preprocessed modal information characteristics into a mathematical model based on a Bayesian theory; the preprocessing process comprises filtering processing and normalization processing. W (W) k In particular to zero-mean Gaussian white noise vector caused by pretreatment process and model establishment. Specifically, a fourth-order band-pass filter of 1MHz-10Hz is used for filtering and noise reduction treatment on the modal information characteristics, and normalization treatment is carried out to ensure that the modal information characteristics are in a certain range, so that the excessive phase difference of the modal information characteristics is avoided, and the dimensional influence between data is eliminated. Specifically, the normalization formula is:
specifically, μ i Sum sigma i Respectively mean and standard deviation, x nij Is x ij Normalized values.
Further, the extracted modal information features are preprocessed and used as input of a mathematical model based on the Bayesian theory, wherein the mathematical model based on the Bayesian theory comprises two convolutions and pooling, and as shown in fig. 4, the mathematical model based on the Bayesian theory comprises a first input layer, a second convolution layer, a third sub-sampling layer, a fourth convolution layer, a fifth sub-sampling layer, a support vector machine and a seventh output layer.
As shown in fig. 3, the mathematical model based on the bayesian theory is generated through training of the following steps: collecting vibration signals of a gate to form a data sample; dividing the data samples into a training data set and a test data set; establishing a convolutional neural network; replacing a full connection layer in the convolutional neural network with a support vector machine to generate an initial model; and putting the training data set and the test data set into an initial model for training, and generating a mathematical model based on the Bayesian theory after the model converges. Preferably, the step of collecting the data sample composed of the vibration signal of the shutter comprises: the vibration signal of the gate was collected at a sampling frequency of 2000HZ to form a data sample. The deep learning network model in fig. 3 is a mathematical model based on bayesian theory.
Specifically, the acquisition frequency of the vibration signals is 2000Hz, each vibration signal is 2560 points, the characteristic size of the mode information extracted by the mode special diagnosis extraction model of the vibration signals is 6×2560, the characteristic size of the second convolution layer is 3×2000 after the primary convolution kernel 4×561 convolution, the characteristic size of the third sub-sampling layer is 3×100 after the primary pooling kernel 1×20 pooling, the characteristic size of the fourth convolution layer is 1×50 after the secondary convolution kernel 3×51 convolution, the characteristic size of the fifth sub-sampling layer is 1×25 after the secondary pooling kernel 1×2 pooling, the one-dimensional data obtained after the twice convolution and pooling are 150, the structural parameters of the convolutional neural network of 6×25 are finally obtained, the characteristic size of 6×25 is input into the support vector machine model for classification, 6 characteristic vectors can be obtained, the 6 characteristic vectors are output as characteristic signals through the seventh output layer, the characteristic signals are compared with standard vectors of vibration standards, whether the vibration sensor acquires the signals safely or not is evaluated, and the vibration history data is set according to the design history data of the reservoir or the vibration history data.
Furthermore, the fifth sub-sampling layer and the support vector machine use the relu function as an activation function, compared with other activation functions, the calculation of the relu function is simpler, meanwhile, the relu function can reduce the dependency of parameters, the sparsity is good, the convergence speed is high, and the gate vibration detection period is shortened. The formula for the relu function to process the data Z is:
f(Z)＝max(0，Z)
further, the bayesian theory analyzes the occurrence probability of various conditions according to all existing evidence conditions, and further obtains the occurrence probability of the interested unknown parameters, so as to predict the occurrence probability of future things.
Specifically, the step of predicting a plurality of characteristic signals in a mathematical model based on bayesian theory to obtain posterior distribution results specifically includes: calculating density distribution functions of a plurality of characteristic signals, and integrating sample information of unknown parameters in the characteristic signals with first based on Bayesian theoryThe posterior information is obtained to estimate posterior distribution, and then unknown parameters are inferred to obtain posterior distribution results; the density distribution function is specifically:wherein F (x) represents a density distribution function, x represents a priori data, i represents the total number of a priori results x in the ith stage M,/v>Weights representing the convolution layer of layer I, b l Representing the offset, x, of the first convolution layer i Representing the i-th a priori data, f (x i ) Represents x i Is a function of the activation function.
Specifically, the mathematical model based on bayesian theory is as follows: wherein L (theta, x) represents a mathematical model based on Bayesian theory, ρ (theta) is a priori data probability distribution function, P (F (x), theta) represents a likelihood function, and theta represents a modal information feature.
In order to achieve the above object of the present invention, according to a second aspect of the present invention, as shown in fig. 5, a vibration signal-based gate structure safety evaluation and prediction system, any one of the above-described vibration signal-based gate structure safety evaluation and prediction methods is used in operation; the system comprises an acquisition module, an extraction module, a training module and an evaluation prediction module; the acquisition module is used for acquiring a vibration signal of the gate; the extraction module is used for acquiring modal information characteristics according to the vibration signals of the gate; the training module is used for generating and training a mathematical model based on the Bayesian theory; and the evaluation prediction module is used for obtaining the safety evaluation result of the gate and the prediction result of the gate according to the modal information characteristics and the mathematical model based on the Bayesian theory.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.
Claims (9)
1. The gate structure safety assessment and prediction method based on the vibration signal is characterized by comprising the following steps of:
the method comprises the steps of obtaining a vibration signal of a gate, and putting the vibration signal into a modal feature extraction model to obtain modal information features;
the modal information features are put into a mathematical model based on the Bayesian theory, wherein the mathematical model based on the Bayesian theory comprises a convolutional neural network and a support vector machine; the convolutional neural network performs feature extraction on the modal information features, and the support vector machine classifies and regresses the extracted features to obtain feature signals; comparing the characteristic signals with vibration standards, and outputting a safety evaluation result of the gate;
predicting a plurality of characteristic signals to obtain posterior distribution results, and outputting a gate structure prediction result according to the posterior distribution results;
the step of predicting the plurality of characteristic signals to obtain posterior distribution results specifically comprises the following steps: calculating density distribution functions of a plurality of characteristic signals, integrating sample information and prior information of unknown parameters in the characteristic signals based on Bayesian theory, obtaining estimation of posterior distribution, and further deducing the unknown parameters to obtain posterior distribution results;
the density distribution function is specifically:
wherein F (x) represents a density distribution function, x represents a priori data, i represents the i-th stage, M represents the total number of a priori results x,weights representing the convolution layer of layer I, b l Representing the offset, x, of the convolution layer of the first layer i Representing the i-th a priori data, f (x i ) Represents x i Is a function of the activation function.
2. The method for evaluating and predicting the safety of a gate structure based on vibration signals according to claim 1, wherein the step of obtaining the characteristics of the modal information by putting the vibration signals of the gate into a model for extracting the characteristics of the modal information comprises the following steps:
establishing a discrete time random state space model according to a vibration signal of the gate, generating a covariance matrix, forming a T-shaped matrix according to the covariance matrix, and solving the T-shaped matrix to obtain modal information characteristics; the modal information characteristics include frequency, damping ratio, mode shape, damping and modal participation factors, and are expressed by the following formulas:
φ i ＝C d Ψ i
wherein omega i Represents the frequency of the i-th stage, lambda i The signal complex eigenvalues of the vibration signal state matrix representing the I-th stage, the superscripts Re and I representing the real and imaginary parts, respectively; epsilon i Represents the damping ratio, phi i Representing vibration pattern, C d Representing a discrete output matrix, ψ i A T-matrix representing an i-th stage covariance matrix; zeta type toy i Represents damping, u i Represents the i-th eigenvalue, lnu i Represents u i Is a natural logarithm of (a), Δt represents a period of time after the discretization,representing plural->The real part of (2); MP (MP) i Representing modality participation factors, ++>Representing the vibration mode phi i R represents a random vector.
3. The method for evaluating and predicting the safety of a gate structure based on a vibration signal according to claim 1, wherein the mathematical model based on the bayesian theory is as follows:
wherein L (theta, x) represents a mathematical model based on Bayesian theory, ρ (theta) is a priori data probability distribution function, P (F (x), theta) represents a likelihood function, and theta represents a modal information feature.
4. A method of evaluating and predicting the safety of a gate structure based on a vibration signal according to claim 1, 2 or 3, wherein the mathematical model based on bayesian theory comprises a first input layer, a second convolution layer, a third sub-sampling layer, a fourth convolution layer, a fifth sub-sampling layer, a support vector machine and a seventh output layer.
5. The method for vibration signal-based gate structure security assessment and prediction according to claim 4, wherein the fifth sub-sampling layer and the support vector machine use a relu function as an activation function.
6. The method for evaluating and predicting the safety of a gate structure based on a vibration signal according to claim 4, wherein the mathematical model based on the bayesian theory is generated by training the following steps:
collecting vibration signals of a gate to form a data sample; dividing the data samples into a training data set and a test data set;
establishing a convolutional neural network; replacing a full connection layer in the convolutional neural network with a support vector machine to generate an initial model;
and putting the training data set and the test data set into an initial model for training, and generating a mathematical model based on the Bayesian theory after the model converges.
7. The method for evaluating and predicting the safety of a gate structure based on vibration signals according to claim 6, wherein the step of collecting the data sample of the vibration signal composition of the gate is specifically: the vibration signal of the gate was collected at a sampling frequency of 2000Hz to form a data sample.
8. The method for evaluating and predicting the safety of a gate structure based on a vibration signal according to claim 1, 2, 3, 5, 6 or 7, wherein: the step of putting the modal information features into a mathematical model based on the Bayesian theory specifically comprises the following steps: preprocessing the modal information characteristics, and putting the preprocessed modal information characteristics into a mathematical model based on a Bayesian theory; the preprocessing process comprises filtering processing and normalization processing.
9. Gate structure safety evaluation and prediction system based on vibration signal, its characterized in that: using any one of the vibration signal-based gate structure safety assessment and prediction methods of claims 1-8 during operation; the system comprises an acquisition module, an extraction module, a training module and an evaluation prediction module;
the acquisition module is used for acquiring a vibration signal of the gate;
the extraction module is used for acquiring modal information characteristics according to the vibration signals of the gate;
the training module is used for generating and training a mathematical model based on the Bayesian theory;
and the evaluation prediction module is used for obtaining the safety evaluation result of the gate and the prediction result of the gate according to the modal information characteristics and the mathematical model based on the Bayesian theory.
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| US8600917B1 (en) * | 2011-04-18 | 2013-12-03 | The Boeing Company | Coupling time evolution model with empirical regression model to estimate mechanical wear |
| US9506836B2 (en) * | 2012-10-09 | 2016-11-29 | The Boeing Company | Methods and systems for structural health monitoring |
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