CN106503312A - A kind of blade root stress analysis method based on neural network algorithm - Google Patents

A kind of blade root stress analysis method based on neural network algorithm Download PDF

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CN106503312A
CN106503312A CN201610883614.8A CN201610883614A CN106503312A CN 106503312 A CN106503312 A CN 106503312A CN 201610883614 A CN201610883614 A CN 201610883614A CN 106503312 A CN106503312 A CN 106503312A
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blade root
sample point
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neutral net
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CN106503312B (en
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张荻
郭鼎
刘天源
谢永慧
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Xian Jiaotong University
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Abstract

The present invention discloses a kind of blade root stress analysis method based on neural network algorithm, including：The first step, obtains the blade root model sample point set of neural network learning using Quick uniform sequential sampling method；Second step, the sample point set obtained according to the first step complete blade root and correspond to the parametric modeling of wheel rim, and complete the Strength co-mputation of each blade root wheel rim model using finite element software, obtain the corresponding response of each sample point；3rd step, the dimension for reducing sample point using PCA simplify the input vector of neutral net, improve the generalization ability of neutral net；4th step, initializes neuron models, determines the neuron number of hidden layer and the input/output vector of neutral net；Then 5th step, the sampled data training neutral net using parametrization blade root verify accuracy and the generalization ability of model up to stopping criterion is met with test sample.The model set up by the method has the advantages that calculating speed is fast, computational accuracy is high.

Description

A kind of blade root stress analysis method based on neural network algorithm
Technical field
The present invention relates to turbine blade field, more particularly to a kind of blade root stress analysis method.
Background technology
For the steam turbine blade for being constantly in HTHP adverse circumstances during work, blade root position is subject to centrifugal force Main portions, when the stress in blade root somewhere reaches certain numerical value and after certain time, it is possible to leaf destruction can be caused And steam turbine failure is made, so as to cause huge economic loss.
FInite Element is the topmost blade root strength calculation method for being used at present, its pass through by entity division into one be Column unit, then introduces appropriate boundary condition and is solved.The method needs man-made division grid, for blade root intensitometer The solution for calculating this Nonlinear Large Deformation problem generally requires to devote a tremendous amount of time, and the precision of result of calculation can very great Cheng Affected by mesh quality on degree.Accordingly, it would be desirable to set up the high blade root strength model of more quick, solving precision.
Content of the invention
It is an object of the invention to provide a kind of blade root stress analysis method based on neural network algorithm, existing to solve Finite element method three dimensional non-linear large deformation problem excessively slow problem.
To achieve these goals, the present invention is adopted the following technical scheme that：
A kind of blade root stress analysis method based on neural network algorithm, comprises the following steps：
The first step, the blade root model sample point for obtaining neural network learning using space reduction Quick uniform sequential sampling method Collection；
Second step, the sample point set obtained according to the first step complete the parametric modeling of blade root and corresponding wheel rim, and use Finite Element Method completes the Strength co-mputation of each blade root-wheel rim model, obtains the corresponding response of each sample point；
3rd step, the dimension for reducing sample point using PCA simplify the input vector of neutral net, improve god Generalization ability through network；
4th step, initializes neuron models, determines the neuron number of hidden layer and the input/output of neutral net Vector；
5th step, training neutral net until meet stopping criterion, then with test sample verify model accuracy and Generalization ability；If test error has exceeded the scope that receives of engineering calculation, the first step is returned to increase 2n sampled point number, Wherein n is the number of parameters for determining blade root physical dimension.
Further, the first step is specifically included：
For certain needs the blade root of n parameter determination geometry, it is known that there is m training on its design space Sample point；Each sample point contains one group of parameter that can determine that the blade root physical dimension；N parameter is designed at which empty Between on be normalized after, obtain the initial parameter matrix X={ x of the blade root sample1,x2,…,xm}T, whereinFor a sample point；In order to improve the computational accuracy of neutral net, by space reduction Quick uniform sequence Row sampling method obtains more rational sample points；One circulation of sequential sampling method includes procedure below：
Design space after being reduced according to m initial sample point and refusal siding-to-siding block length L first, then in reduction Generate in design space afterwardsIndividual random point, and these points are individually mapped in original design space successively, according to Minimax sampling principle, by space length dminThe maximum random point of value elects new sample point as；Wherein refuse siding-to-siding block lengthI.e. initial sample point concentrates the arithmetic average distance between arbitrary neighborhood sample point；Space Distance
Repeat the process until collecting 4n sample point, wherein n is the number of parameters for determining blade root physical dimension.
Further, second step is specifically included：Sample point according to being gathered in the first step completes corresponding blade root and wheel rim Parametric modeling, make finite element software carry out stress analysis calculating to each blade-wheel rim model after then having divided grid, The stress value and each pair of tooth load for obtaining the blade root key position of each sample blade root model is distributed, and constitutes each sample point The response matrix of a corresponding m` × u, i.e. Y={ y (x1),y(x2),…,y(xm)}T, whereinFor One u dimensional vector.
Further, the 4th step is specifically included：The parameter for initializing neural network model is first had to, and determines hidden layer Neuron number；Hidden layer neuron number is determined using following methods：
Formula 1：
Formula 2：
Formula 3：N1=log2n
Wherein N1Number for hidden layer neuron；N is input vector dimension, i.e., extract through PCA The number of blade root form parameter；M be response vector dimension, i.e., the composition number that blade root stress calculating results include；A for [1, 10] constant between；
3 different N can be calculated respectively according to above 3 formula1, and with middle maximum as the upper limit, minimum of a value is Lower limit, determines the span of hidden layer neuron number, i.e. n1≤N1≤n2, n1For value lower limit, n2For the value upper limit；
Take N1=n1, the artificial nerve network model for solving now is calculated according to training sample, and obtains mean square error now Difference M1, i.e.,Wherein p is the overall number of training sample, y'ijIt is the desired output of network, yij It is the reality output of network；N is taken again1'=n2, obtain mean square error M now2；The mean square error for calculating more twice and receipts Hold back speed, and the span of hidden layer neuron number is reduced by dichotomy, finally work as n2=n1Stop search when+1, And N is determined according to comparative result now1Value；
The activation primitive of hidden layer and output layer chooses sigmoid functions, i.e.,
Using the algorithm of variable learning speed, i.e., when in network training process, if mean square error increases after right value update Add, and more than the increasing value for arranging, then update and be cancelled, learning rate is multiplied by factor ρ, 0.1<ρ<1, by random number Produce；If mean square error is reduced after right value update, right value update is received, and learning rate is multiplied by factor η, 1<η<10, produced by random number；If mean square error increases less than the increasing value for arranging, right value update is received, and is learnt Speed keeps constant.
Further, the 5th step is specifically included：
After the initialization that step 4 completes neural network model, begin through sample point and correspondingly respond to the net Network is trained, if the mean square error of now neutral net output is less than preset value 2 × 10-5Or reach default study number of times The training of neutral net is then completed；
Then one group of design parameter value conduct being not belonging in training sample is chosen from the design space of blade root model again Test sample, and the finite element analysis of the sample is completed according to step 2, obtain the Stress calculation that blade root mainly examines position As a result, i.e., true responseThen using the major parameter of the design of the test sample as the god Through the input vector of network, the stress calculating results that blade root mainly examines position can be equally obtained, that is, calculate responseCalculate the error delta of each in true response and calculating responsei, i.e.,i =1,2 ..., u；
Repeat to choose several design points to be tested, if error is in the range of the acceptance of engineering calculation, i.e.,I=1,2 ..., u then complete the checking to model accuracy and generalization ability, neutral net now Analysis is predicted to the stress situation of actual blade root.
Relative to prior art, the invention has the advantages that：
The strength model set up by the present invention make use of self-study habit and higher robustness of neutral net etc. Feature, after model is set up, need to only provide the input vector for determining the blade root geometry, you can obtain blade root and mainly examine Position stress calculating results.
BP neural network algorithm employed in the present invention by a large amount of neurons and between weighting constitute, including information from The forward-propagating of input layer to output layer and error are constituted from two processes of backpropagation of output layer to input layer.By with adopting The blade root sample for collecting and corresponding stress analysis result training neutral net, adjust the parameter between its each layer, final acquisition The neural network model of blade root stress analysis can be individually completed, that is, provides the input of the design parameter as neutral net of blade root Vector, just can obtain stress analysis result in a short period of time, there are a large amount of pre-treatment works so as to solve Finite Element Method The slower problem of work and calculating speed.
Description of the drawings
Fig. 1 is certain four tooth fir tree blade root of example；Wherein Fig. 1 (a) is front view；Fig. 1 (b) is top view；
Fig. 2 is the general flow chart of the present invention；
Flow charts of the Fig. 3 for rapid serial sampling method；
Fig. 4 is the concrete mode schematic diagram for reducing space in sampling；
Flow charts of the Fig. 5 for Establishment of Neural Model.
Specific embodiment
Embodiments of the present invention are described in detail below in conjunction with accompanying drawing.
Refer to shown in Fig. 1, a kind of blade root stress analysis method based on neural network algorithm of the present invention, including following five Individual step：
First, the blade root model sample point set of neural network learning is obtained using space reduction Quick uniform sequential sampling method.
For certain needs the blade root of n parameter determination geometry, it is known that there is m training on its design space (each sample point contains one group of parameter that can determine that the blade root physical dimension, such as loading end width, blade root to sample point Axial length etc.).After n parameter is normalized on its design space, you can obtain the initial parameter of the blade root sample Matrix X={ x1,x2,…,xm}T, whereinFor a sample point.In order to improve the calculating essence of neutral net Degree, needs to obtain more rational sample points by space reduction Quick uniform sequential sampling method.Fig. 3 is the sequential sampling method Sampling flow chart, one of circulation include procedure below：
Design space after being reduced according to m initial sample point and refusal siding-to-siding block length L first, i.e., set original Determine that feasible interval and refusal is interval according to the position of initial sample point and refusal siding-to-siding block length L in meter space, will move afterwards Except the design space behind refusal interval is reconfigured so as to the design space after being reduced, as shown in Figure 4.Then in reduction Generate in design space afterwards(rounding downwards) individual random point, and these points are individually mapped to original design space successively In, according to minimax sampling principle, by space length dminThe maximum random point of value elects new sample point as.Wherein refuse LengthI.e. initial sample point concentrates the arithmetic average distance between arbitrary neighborhood sample point； Space length
Repeat the process until collecting 4n sample point, wherein n is the number of parameters for determining blade root physical dimension.
By taking the example blade root in Fig. 1 as an example, from the front view and top view of the blade root, the blade root is come by 37 parameters Determine its geometry：b1,b2,…,b8Totally 8 circumferential shape parameters, h1,h2,…,h21Totally 21 radial shape parameters, R1, R2,…,R5Totally 5 radius parameters, θ1,θ2Totally 2 angle parameters and blade root axial length L.
So from above analysis, needing n=37 parameter altogether to determine the physical dimension of the blade root, and handle having this One vector of one group of parameter of sample is referred to as a sample point.
The design space of the example blade root is determined by the span of above-mentioned 37 parameters.Passed through according to engineering design Test, determine the span of each parameter, consider further that the scale of neutral net design, then generated on design space at random M=50 sample point is used as initial sample point.Then all parameters in each sample point are normalized, so as to obtain one Initial parameter matrix of the matrix of individual 50 × 37 (i.e. m × n) as the example blade root, for exampleWherein h1For A blade root form parameter in Fig. 1, h1minFor parameter h1In the value lower limit of design space, h1maxFor parameter h1Empty in design Between the value upper limit.
Take refusal lengthWith reference to Fig. 4, according to the position of initial sample point and refuse Siding-to-siding block length L determines the design space after reduction absolutely, such as sample pointRefusal is interval long Degree L, then refusing interval isDesign space after reduction is25 points are generated afterwards at random in the design space, by this 25 Point is individually mapped to original design space successively, and individually calculates space length of each point in luv space successivelySelect wherein dminMaximum point adds ginseng as the sample point for newly collecting In matrix number.
Repeat this sampling step until the number m`=4n=148 of final sample point, obtains one 148 × 37 (i.e. m` × n) final argument matrix X`.
2nd, the sample point set obtained according to the first step completes the parametric modeling of blade root and corresponding wheel rim, and using limited First method completes the Strength co-mputation of each blade root-wheel rim model, obtains the corresponding response of each sample point.
Sample point according to being gathered in the first step completes the parametric modeling of corresponding blade root and wheel rim, has then divided net Make finite element software stress analysis calculating be carried out to each blade-wheel rim model after lattice, obtain the leaf of each sample blade root model The stress value of root key position and each pair of tooth load distribution, and constitute the response square of the corresponding m` × u of each sample point Battle array, i.e. Y={ y (x1),y(x2),…,y(xm)}T, whereinFor a u dimensional vector.
By taking the example blade root in Fig. 1 as an example, and the then elaboration in step one, the parametrization for completing each sampled point is built Mould.After having chosen the integral radius of blade-wheel rim model, on the basis of front view, selection axle center is the origin of coordinates, according to The coordinate of all key points of the gain of parameter of blade root, and set all key points；Then according to the connection side between key point Formula (line segment connection or circular sliding slopes) sets up the outline model of blade root；Finally fill the outline line to generate face, and along The distance of the normal extension blade root axial length in the face is generating the physical model of whole blade root；Add one above blade root afterwards Individual cuboid entity, produces equivalent centrifugal force to replace above the blade root of real blade.The parametric modeling mode of wheel rim Identical with blade root.
Complete the stress and strain model of the model afterwards, and solve the blade root maximum stress and each pair of tooth for obtaining the sample pattern Load is distributed, that is, complete the solution to a sample point.The finite element solving of all sample points is finally completed, one has been obtained The response matrix Y of m` × u (m`=148, u are the number of the composition that certain sample stress calculating results includes, u=8 in this example) ={ y (x1),y(x2),…,y(xm)}T,Maximum stress value of wherein front 4 dimension for each pair of tooth loading end, 4 dimensions are the load distribution percentage of each pair of tooth afterwards.
Three, the dimension for reducing sample point using PCA simplifies the input vector of neutral net, improves nerve net The generalization ability of network.
The step is used for simplifying the dimension of the sample point obtained by step one to simplify the input variable of neutral net, so as to The training time is reduced, the generalization ability of neutral net is improved.
By taking the example blade root in Fig. 1 as an example, the then elaboration of step one.
Standardize firstly the need of final argument matrix X` (148 × 37) by the example obtained in step one, which is got the bid After standardization, in matrix, each element isWhereinFor primitive elementI-th sample point after normalized J-th parameter, MjAnd SjIt is arithmetic mean of instantaneous value and the standard deviation of j-th parameter of all sample points respectively, i.e.,With(m`=148 in this example).
Then the covariance matrix D=X`` of the final argument matrix X`` after normalizedTX``, and calculate covariance The eigenvalue λ and characteristic vector P of matrix D, i.e. DP=λ P.Obtained 37 eigenvalue λs of characteristic value are arranged out from big to small Come, and itself and its corresponding characteristic vector are considered as λ successively1,λ2,…,λ37And P1,P2,…,P37.
Calculate and work as contribution rate of accumulative totalWhen p value, then can calculate the final principal component of acquisition and pass judgment on vectorEqually by AjArranged from big to small, and calculate and work as contribution rate of accumulative totalWhen selected vectorial A in element position, determine The blade root geometric parameter of worry, that is, the sample point after being simplifiedFor example for above-mentioned inequality, A2, A5,A18,A19,A31Can meet and require, then final blade root parameter matrix X` can be reduced to the matrix of 148 × 5, wherein One sample point can be reduced to
4th, initialize neuron models, determine the neuron number of hidden layer and the input/output of neutral net to Amount.
Flow charts of the Fig. 5 for Establishment of Neural Model.Wherein input vector is the sample point after simplifying in step 3The blade root form parameter that through PCA extract is represented；Output vector is step 2 The middle response vector obtained through finite element analysisThe result of calculation of blade root stress analysis is represented.
The parameter for initializing neural network model is first had to, and determines the neuron number of hidden layer.The present invention using with Lower method determines hidden layer neuron number：
Formula 1：
Formula 2：
Formula 3：N1=log2n
Wherein N1Number for hidden layer neuron；N is input vector dimension, i.e., extract through PCA Number (the i.e. sample point of blade root form parameterDimension)；M should for response vector dimension, i.e. blade root Composition number that power result of calculation includes (i.e. response vectorDimension)；A is normal between [1,10] Number.
3 different N can be calculated respectively according to above 3 formula1, and with middle maximum as the upper limit, minimum of a value is Lower limit, determines the span of hidden layer neuron number, i.e. n1≤N1≤n2, n1For value lower limit, n2For the value upper limit.
Take N1=n1, the artificial nerve network model for solving now is calculated according to training sample, and obtains mean square error now Difference M1, i.e.,Wherein p is the overall number of training sample, y'ijIt is the desired output of network, yij It is the reality output of network；N is taken again1'=n2, obtain mean square error M now2；The mean square error for calculating more twice and receipts Hold back speed, and the span of hidden layer neuron number is reduced by dichotomy, finally work as n2=n1Stop search when+1, And N is determined according to comparative result now1Value.
The activation primitive of hidden layer and output layer chooses sigmoid functions, i.e.,
Algorithm using variable learning speed.I.e. when in network training process, if mean square error increases after right value update Add, and more than the increasing value for arranging, then update and be cancelled, learning rate is multiplied by factor ρ (0.1<ρ<1, by random number Produce)；If mean square error is reduced after right value update, right value update is received, and learning rate is multiplied by factor η (1<η<10, produced by random number)；If mean square error increases less than the increasing value for arranging, right value update is received, and is learned Practise speed and keep constant.
5th, train neutral net and verify accuracy and the generalization ability of model
After the initialization that step 4 completes neural network model, begin through sample point and correspondingly respond to the net Network is trained, if the mean square error of now neutral net output is less than preset value 2 × 10-5Or reach default study number of times The training of neutral net is then completed.
Then choose one group of design parameter value being not belonging in training sample from the design space of blade root model again to make For test sample, and the finite element analysis of the sample is completed according to step 2, obtain the stress that blade root mainly examines position Result of calculation, i.e., true responseThen using the major parameter of the design of the test sample as The input vector of the neutral net, can equally obtain the stress calculating results that blade root mainly examines position, that is, calculate responseCalculate the error delta of each in true response and calculating responsei, i.e.,i =1,2 ..., u.
Repeat to choose several design points to be tested, if (error is 3% in the range of the acceptance of engineering calculation for error Within), i.e.,I=1,2 ..., u then complete the checking to model accuracy and generalization ability, nerve now Network can be predicted analysis to the stress situation of actual blade root；If error is beyond scope is received, return the first step with Increase 2n sampled point number, wherein n is the number of parameters for determining blade root physical dimension.

Claims (5)

1. a kind of blade root stress analysis method based on neural network algorithm, it is characterised in that comprise the following steps：
The first step, the blade root model sample point set for obtaining neural network learning using space reduction Quick uniform sequential sampling method；
Second step, the sample point set obtained according to the first step complete the parametric modeling of blade root and corresponding wheel rim, and using limited First method completes the Strength co-mputation of each blade root-wheel rim model, obtains the corresponding response of each sample point；
3rd step, the dimension for reducing sample point using PCA simplify the input vector of neutral net, improve nerve net The generalization ability of network；
4th step, initialize neuron models, determine the neuron number of hidden layer and the input/output of neutral net to Amount；
Then 5th step, training neutral net verify the accuracy of model and extensive with test sample until meet stopping criterion Ability.
2. a kind of blade root stress analysis method based on neural network algorithm according to claim 1, it is characterised in that One step is specifically included：
For certain needs the blade root of n parameter determination geometry, it is known that there is m training sample on its design space Point；Each sample point contains one group of parameter that can determine that the blade root physical dimension；By n parameter on its design space After being normalized, the initial parameter matrix X={ x of the blade root sample are obtained1,x2,…,xm}T, wherein For a sample point；In order to improve the computational accuracy of neutral net, obtained more by space reduction Quick uniform sequential sampling method Many rational sample points；One circulation of sequential sampling method includes procedure below：
Design space after being reduced according to m initial sample point and refusal siding-to-siding block length L first, then after reduction Generate in design spaceIndividual random point, and these points are individually mapped in original design space successively, according to maximum Minimum sampling principle, by space length dminThe maximum random point of value elects new sample point as；Wherein refuse siding-to-siding block lengthI.e. initial sample point concentrates the arithmetic average distance between arbitrary neighborhood sample point, space Distance
Repeat the process until collecting 4n sample point, wherein n is the number of parameters for determining blade root physical dimension.
3. a kind of blade root stress analysis method based on neural network algorithm according to claim 1, it is characterised in that Two steps are specifically included：Sample point according to being gathered in the first step completes the parametric modeling of corresponding blade root and wheel rim, Ran Houhua Make finite element software stress analysis calculating be carried out to each blade-wheel rim model after dividing good grid, obtain each sample blade root mould The stress value of the blade root key position of type and each pair of tooth load distribution, and constitute the corresponding m` × u's of each sample point Response matrix, i.e. Y={ y (x1),y(x2),…,y(xm)}T, whereinFor a u dimensional vector.
4. a kind of blade root stress analysis method based on neural network algorithm according to claim 1, it is characterised in that Four steps are specifically included：The parameter for initializing neural network model is first had to, and determines the neuron number of hidden layer；Using following Method determines hidden layer neuron number：
Formula 1：
Formula 2：
Formula 3：N1=log2n
Wherein N1Number for hidden layer neuron；N be input vector dimension, i.e., the blade root for extracting through PCA The number of form parameter；M be response vector dimension, i.e., the composition number that blade root stress calculating results include；A be [1,10] it Between constant；
3 different N can be calculated respectively according to above 3 formula1, and with middle maximum as the upper limit, minimum of a value is lower limit, Determine the span of hidden layer neuron number, i.e. n1≤N1≤n2, n1For value lower limit, n2For the value upper limit；
Take N1=n1, the artificial nerve network model for solving now is calculated according to training sample, and obtains mean square error now M1, i.e.,Wherein p is the overall number of training sample, y'ijIt is the desired output of network, yijIt is The reality output of network；N is taken again1'=n2, obtain mean square error M now2；The mean square error for calculating more twice and convergence Speed, and the span of hidden layer neuron number is reduced by dichotomy, finally work as n2=n1Stop search when+1, and N is determined according to comparative result now1Value；
The activation primitive of hidden layer and output layer chooses sigmoid functions, i.e.,
Using the algorithm of variable learning speed, i.e., when in network training process, if mean square error is increased after right value update, And more than the increasing value for arranging, then update and be cancelled, learning rate is multiplied by factor ρ, and 0.1 ＜ ρ ＜ 1 are produced by random number Raw；If mean square error is reduced after right value update, right value update is received, and learning rate is multiplied by factor η, 1 ＜ η ＜ 10, are produced by random number；If mean square error increases less than the increasing value for arranging, right value update is received, and is learnt Speed keeps constant.
5. a kind of blade root stress analysis method based on neural network algorithm according to claim 1, it is characterised in that Five steps are specifically included：
After the initialization that step 4 completes neural network model, begin through sample point and corresponding response is entered to the network Row training, if the mean square error of now neutral net output is less than preset value 2 × 10-5Or it is then complete to reach default study number of times Training into neutral net；
Then one group of design parameter value being not belonging in training sample is chosen from the design space of blade root model again as test Sample, and the finite element analysis of the sample is completed according to step 2, the stress calculating results that blade root mainly examines position are obtained, i.e., True responseThen using the major parameter of the design of the test sample as the neutral net input Vector, can equally obtain the stress calculating results that blade root mainly examines position, that is, calculate responseCalculate The error delta of each in true response and calculating responsei, i.e.,
Repeat to choose several design points to be tested, if error is in the range of the acceptance of engineering calculation, i.e., Checking to model accuracy and generalization ability is then completed, and neutral net now can be to actual blade root Stress situation is predicted analysis.
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CN108170943A (en) * 2017-12-26 2018-06-15 哈尔滨汽轮机厂有限责任公司 Finite-element preprocessing method in steam turbine three dimendional blade design based on Python
CN110851957A (en) * 2019-10-15 2020-02-28 南京航空航天大学 Atmospheric data sensing system resolving method based on deep learning
CN110869728A (en) * 2017-07-19 2020-03-06 林德股份公司 Method for determining the stress level in a material of a process engineering device

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