CN107831482A - Sea clutter optimal soft survey instrument and method based on improved free searching algorithm optimization RBF neural - Google Patents
Sea clutter optimal soft survey instrument and method based on improved free searching algorithm optimization RBF neural Download PDFInfo
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- CN107831482A CN107831482A CN201711117144.5A CN201711117144A CN107831482A CN 107831482 A CN107831482 A CN 107831482A CN 201711117144 A CN201711117144 A CN 201711117144A CN 107831482 A CN107831482 A CN 107831482A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
- G01S7/417—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section involving the use of neural networks
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/004—Artificial life, i.e. computing arrangements simulating life
- G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/02—Neural networks
Abstract
The invention discloses a kind of sea clutter optimal soft survey instrument and method based on improved free searching algorithm optimization RBF neural, including radar, field intelligent instrument, control station, the spot database for depositing data, optimal hard measurement host computer and forecast hard measurement value display instrument based on improved drosophila optimized algorithm optimization RBF neural, the described optimal hard measurement host computer based on improved free searching algorithm optimization RBF neural, including data preprocessing module, RBF neural module, model modification module.The present invention realizes the online optimal hard measurement of sea clutter, and randomness caused by overcoming human factor influences, and improves the stability of model prediction, reduces the possibility that model prediction is absorbed in local optimum.
Description
Technical field
The present invention relates to optimal soft survey instrument and method field, is specifically a kind of excellent based on improved free searching algorithm
Change the sea clutter optimal soft survey instrument and method of RBF neutral nets.
Background technology
The echo-signal reflected from seawater surface is called sea clutter, sea clutter and sea condition, agitation, radar in field of radar
The many factors such as parameter are relevant.Worked in for seaward detector, shipborne radar etc. for the radar of marine environment, serious
Sea surface reflection echo will influence the detection to sea-surface target and tracking performance, grasp the property of sea clutter, and it is miscellaneous to establish accurately sea
Wave pattern is analysis and the premise for improving radar performance.The statistical property of sea clutter includes amplitude characteristic and correlation properties.Sea is miscellaneous
The correlation properties of ripple include temporal correlation and spatial coherence.Temporal correlation is also referred to as pulse-to-pulse correlation, and it is miscellaneous to reflect sea
Wave amplitude can be represented equivalently with the fluctuating of time with power spectrum.The spatial coherence of sea clutter is divided into attitude corrections
And distance correlation.The dynamic characteristic that sea clutter can study ocean for us provides help, still, if will be from sea clutter background
Lower detection target, such as floating ice, ship, it just turns into very big obstacle, it is necessary to suppresses as much as possible to weaken or eliminate these
Interference.Study the main purpose of sea clutter：On the one hand it is that the natural mechanism of sea clutter is explained, and then proposes rational mould
Type；On the other hand, it is interference of the sea clutter to be reduced to detection target, finds out and how will drown out the target in strong sea clutter background
The method that signal extraction comes out.The foundation of accurate sea clutter model is to realize the key of above-mentioned each purpose
The research work on the Modeling and Prediction of sea clutter is largely all concentrated on above artificial neural network in recent years, is taken
Obtained good effect.But artificial neural network the shortcomings that also having its own, such as the interstitial content of over-fitting, hidden layer and
The bad determination of parameter.Secondly, the data that observation site collects are not also because noise, manual operation error etc. be with necessarily true
Error is determined, so not strong using the general Generalization Ability of forecasting model of the strong artificial neural network of certainty.SVMs, by
Vapnik introduced in 1998, due to its good Generalization Ability, was widely used in pattern-recognition, fitting and classification problem
In.Because standard SVMs is sensitive to isolated point and noise, so having also been proposed RBF neural later.RBF nerve nets
Network can preferably handle the sample data with noise compared to standard SVMs, be used for modeling here.It is improved from
By searching algorithm, i.e. Fruit Fly Optimization Algorithm, carried by TaiWan, China Wen-Tsao professors Pan
A kind of a kind of biological intelligence optimizing algorithm deduced out based on drosophila foraging behavior from you out, abbreviation FOA.The algorithm passes through
It is interparticle in colony to influence each other, reduce the risk that searching algorithm is absorbed in locally optimal solution, there is good global search
Performance.Improved free searching algorithm is used to search for the best parameter group of RBF neural, to reach the mesh of Optimized model
's.
The content of the invention
In order to overcome the shortcomings of the measurement accuracy of existing radar it is not high, it is low to noise sensitivity, promote poor performance, this hair
It is bright a kind of on-line measurement is provided, calculating speed is fast, model automatically updates, noise resisting ability is strong, it is good based on improvement to promote performance
Free searching algorithm optimization RBF neural sea clutter optimal soft survey instrument and method.
The purpose of the present invention is achieved through the following technical solutions：One kind is based on improved free searching algorithm optimization
The sea clutter optimal soft survey instrument of RBF neural, including radar, the field intelligent instrument for measuring easy survey variable, use
The spot database and sea clutter forecast hard measurement value display instrument of control station, storage data in measurement performance variable, it is described
Field intelligent instrument, control station and propylene polymerization production process connect, the field intelligent instrument, control station and spot database
Connection, the soft measuring instrument are also included on the optimal hard measurement based on improved free searching algorithm optimization RBF neural
Position machine, the spot database are optimized on the optimal hard measurement of RBF neural with described based on improved free searching algorithm
The input connection of position machine, the optimal hard measurement host computer based on improved free searching algorithm optimization RBF neural
Output end be connected with sea clutter hard measurement value display instrument, it is described based on improved free searching algorithm optimization RBF neural
Optimal hard measurement host computer include：
Data preprocessing module, for the model training inputted from spot database sample to be pre-processed, to training
Center of a sample, that is, the average value of sample is subtracted, then it is standardized：
Calculate average：
Calculate variance：
Standardization：
Wherein, TX is training sample, and N is number of training,For the average of training sample, X is the training after standardization
Sample, σxTo calculate variance.
" base " of the RBF neural by the use of RBF as hidden unit forms implicit sheaf space, and defeated people's vector is direct
It is linear to be mapped to mapping of the implicit sheaf spaces of implicit sheaf space to output space.In general, network is defeated by being input to
The mapping gone out is nonlinear, and network output for adjustable parameter but is linear.Theory is it has been proved that RBF networks
It is that the optimal network of mapping function is completed in feedforward neural network with global and optimal approximation capability.As long as have enough
Hidden neuron, RBF can be with the approximate any continuous functions of arbitrary accuracy.Using feedforward network topological structure, hidden layer it is each
Unit exports:
hi=Ri(X)=Ri(||X-C||/σi) (4)
I=1,2,3 ..., L
Wherein, X is N-dimensional input vector, CiIt is the vector with X with dimension, RiFor Radial basis kernel function.
Ri() generally use Gaussian function, wherein σ are kernel function width, i.e.,：
Therefore the output of network output layer is
Wherein w is connection weight, and h is the unit output of hidden layer.
Improved free searching algorithm optimization module, for using improved free searching algorithm to RBF neural
Kernel function width optimizes, and comprises the following steps that：
Improved free search algorithm module, for the core letter using improved free searching algorithm to RBF neural
SerComm degree optimizes, and comprises the following steps that：
(1) the scale n and dimension m, [X of population are initializedmini, Xmaxi] excursion as i-th dimension, greatest iteration time
Number is Maxgen, and exploration step number is T, and the variable neighborhood value of i-th of body jth dimension is Rji∈[Rmin,Rmax].It is according to these settings
Initialize installation can be carried out to population position：
xtji=x0ji-Δxtji+2Δxtji*randomtji(0,1) (7)
X0jiIt is the initial value randomly generated：
Δxtji=Rji*(Xmax-Xmin)*randomtji(0,1) (8)
(2) each individual is gone into action, and individual i carries out T step detections every time, and the renewal of position is determined by following formula：
x0ji=Xmini+(Xmaxi-Xmini)*randomji(0,1) (9)
In exploration behavior once, individual exploration behavior is represented by：
F (x in formulatji) it is the position that each individual is completed to mark after search.
Pheromones are defined as follows：
And sensitivity updates according to equation below：
S in formulaminAnd SmaxIt is the minimum value and maximum of sensitivity respectively, the minimum value and maximum of pheromones are respectively
PminAnd Pmax, and P is provided hereinmin=SminAnd Pmin=Smax。
After the search of epicycle terminates, according to the starting point of equation below renewal next round search：
(3) set meet the individual of conditional (13) asIt is and corresponding first
Beginning position and each survey position beWithDefining individual density is：
Thus defining individual relative density is：
Obvious pj∈(0,1).The strategy of catastrophe is：Relative density pjIt is bigger, then individual survey position Relatively centralized, easily
Local optimum is absorbed in, the probability for now carrying out catastrophe is bigger.Therefore, catastrophe will be produced according to following steps：
(a) j=1 is made.
(b) for individual j, r is producedl=random (0,1).
If (c) rl≤pl, then initial position of the new original position as next iteration is regenerated；Otherwise, it is necessary to fromMiddle random selection position enters the initial position of next iteration as the individual.
(d) j=j+1 is made, if meeting j≤m, repeats step (2), otherwise terminates the process.
It is described based on the optimal soft of improved free searching algorithm optimization RBF neural as a kind of preferable scheme
Measurement host computer also includes：Model modification module, for the online updating of model, offline analysis data is periodically input to training
Concentrate, update RBF neural network model.
A kind of optimal hard measurement instrument of sea clutter described above based on improved free searching algorithm optimization RBF neural
The flexible measurement method that table is realized, the flexible measurement method comprise the following steps：
1), to radar object, according to specificity analysis and climatic analysis, selection operation variable and easily survey variable are as model
Input, performance variable and easily survey variable are obtained by spot database；
2), the model training sample inputted from spot database is pre-processed, to training sample centralization, that is, subtracted
The average value of sample, is then standardized to it so that its average is 0, variance 1.The processing uses following formula process
To complete：
2.1) average is calculated：
2.2) variance is calculated：
2.3) standardize：Wherein, TX is
Training sample, N are number of training,For the average of training sample, X is the training sample after standardization.3), to from data
Pretreatment module is transmitted through the training sample come, is modeled using RBF neural.RBF neural is made with RBF
Implicit sheaf space is formed for " base " of hidden unit, defeated people's vector is mapped directly into implicit sheaf space implies sheaf space to output
The mapping in space is linear.In general, network is nonlinear by the mapping for being input to output, and network output pair can
For tune parameter but it is linear.It is theoretical it has been proved that RBF networks have global and optimal approximation capability, be feed forward neural
The optimal network of mapping function is completed in network.As long as there is enough hidden neurons, RBF can be any with arbitrary accuracy approximation
Continuous function.Using feedforward network topological structure, each unit output of hidden layer is:
hi=Ri(X)=Ri(||X-C||/σi) (4)
I=1,2,3 ..., L
Wherein, X is N-dimensional input vector, CiIt is the vector with X with dimension, RiThe characteristics of with local experiences.
Ri() generally use Gaussian function, wherein σ are kernel function width, i.e.,：
Therefore the output of network output layer is
Wherein w is connection weight, and h is the unit output of hidden layer.
4), the penalty factor and error margin value of RBF neural are optimized using improved free searching algorithm,
Comprise the following steps that：
(1) the scale n and dimension m, [X of population are initializedmini, Xmaxi] excursion as i-th dimension, greatest iteration time
Number is Maxgen, and exploration step number is T, and the variable neighborhood value of i-th of body jth dimension is Rji∈[Rmin,Rmax].It is according to these settings
Initialize installation can be carried out to population position：
xtji=x0ji-Δxtji+2Δxtji*randomtji(0,1) (7)
X0jiIt is the initial value randomly generated：
Δxtji=Rji*(Xmax-Xmin)*randomtji(0,1) (8)
(2) each individual is gone into action, and individual i carries out T step detections every time, and the renewal of position is determined by following formula：
x0ji=Xmini+(Xmaxi-Xmini)*randomji(0,1) (9)
In exploration behavior once, individual exploration behavior is represented by：
F (x in formulatji) it is the position that each individual is completed to mark after search.
Pheromones are defined as follows：
And sensitivity updates according to equation below：
S in formulaminAnd SmaxIt is the minimum value and maximum of sensitivity respectively, the minimum value and maximum of pheromones are respectively
PminAnd Pmax, and P is provided hereinmin=SminAnd Pmin=Smax。
After the search of epicycle terminates, according to the starting point of equation below renewal next round search：
(3) set meet the individual of conditional (13) asIt is and corresponding first
Beginning position and each survey position beWithDefining individual density is：
Thus defining individual relative density is：
Obvious pj∈(0,1).The strategy of catastrophe is：Relative density pjIt is bigger, then individual survey position Relatively centralized, easily
Local optimum is absorbed in, the probability for now carrying out catastrophe is bigger.Therefore, catastrophe will be produced according to following steps：
(a) j=1 is made.
(b) for individual j, r is producedl=random (0,1).
If (c) rl≤pl, then initial position of the new original position as next iteration is regenerated；Otherwise, it is necessary to fromMiddle random selection position enters the initial position of next iteration as the individual.
(d) j=j+1 is made, if meeting j≤m, repeats step (2), otherwise terminates the process.
As a kind of preferable scheme：The flexible measurement method is further comprising the steps of：5), periodically by offline analysis data
It is input in training set, updates RBF neural network model.
The present invention technical concept be：Online optimal hard measurement is carried out to sea clutter, overcomes existing sea clutter measuring instrument
Table stability is poor, is easily absorbed in the deficiency of local optimum, introduces improved free searching algorithm and RBF neural network model is carried out certainly
Dynamic optimization, it is not necessary to which artificial experience repeatedly to adjust the parameter of RBF neural, to obtain optimal hard measurement result.This mould
Type has the advantage that relative to existing sea clutter soft-sensing model：It is modeled, is had higher by RBF neural network model
Forecast precision；Existing model parameter typically determined by the experience of operative employee, have it is certain restricted and uncertain,
If once value is improper, concussion and bigger prediction error that model prediction exports can be caused, and model passes through improvement
Free searching algorithm automatic optimal is carried out to the parameter of model, obtain optimal soft-sensing model.
Beneficial effects of the present invention are mainly manifested in：Realize the online optimal hard measurement of sea clutter, overcome it is artificial because
Randomness caused by element influences, and improves the stability of model prediction, reduces the possibility that model prediction is absorbed in local optimum.
Brief description of the drawings
Fig. 1 is the topology diagram of RBF neural；
Fig. 2 is the optimal hard measurement of sea clutter modeling process based on improved free searching algorithm optimization RBF neural
The basic structure schematic diagram of instrument and method；
Fig. 3 is the optimal hard measurement host computer structural representation based on improved free searching algorithm optimization RBF neural
Figure.
Embodiment
The invention will be further described below in conjunction with the accompanying drawings.The embodiment of the present invention is used for illustrating the present invention, without
It is to limit the invention, in the protection domain of spirit and claims of the present invention, any is repaiied to what the present invention made
Change and change, both fall within protection scope of the present invention.
Embodiment 1
Reference picture 1, Fig. 2 and Fig. 3, a kind of sea clutter based on improved free searching algorithm optimization RBF neural is most
Excellent soft measuring instrument, including radar 1, the field intelligent instrument 2 for measuring easy survey variable, the control for measuring performance variable
Stand 3, deposit the spot database 4 and sea clutter hard measurement value display instrument 6 of data, the field intelligent instrument 2, control station 3
It is connected with radar 1, the field intelligent instrument 2, control station 3 are connected with spot database 4, and the soft measuring instrument also includes changing
The optimal hard measurement host computer 5 for the free searching algorithm optimization RBF neural entered, the spot database 4 are based on described
The input connection of the optimal hard measurement host computer 5 of improved free searching algorithm optimization RBF neural, it is described based on improvement
Output end and the sea clutter hard measurement value of optimal hard measurement host computer 5 of free searching algorithm optimization RBF neural show
Instrument 6 connects.The easy survey variable of the instrumentation radar object of field intelligent instrument 2, easy variable of surveying is transferred to spot database 4；Control
Stand the performance variables of 3 control radar objects, performance variable is transferred to spot database 4.The variable recorded in spot database 4
Input of the data as the optimal hard measurement host computer 5 based on improved free searching algorithm optimization RBF neural, hard measurement
It is worth display instrument 6 to be used to show the optimal hard measurement host computer 5 based on improved free searching algorithm optimization RBF neural
Output, i.e. hard measurement value.The optimal hard measurement host computer 5 based on improved free searching algorithm optimization RBF neural,
Including following 4 parts：
Data preprocessing module 7, for the model training inputted from spot database sample to be pre-processed, to training
Center of a sample, that is, the average value of sample is subtracted, then it is standardized：
Calculate average：
Calculate variance：
Standardization：
Wherein, TX is training sample, and N is number of training,For the average of training sample, X is the training after standardization
Sample, σxFor variance.
" base " of the RBF neural by the use of RBF as hidden unit forms implicit sheaf space, and defeated people's vector is direct
It is linear to be mapped to mapping of the implicit sheaf spaces of implicit sheaf space to output space.In general, network is defeated by being input to
The mapping gone out is nonlinear, and network output for adjustable parameter but is linear.Theory is it has been proved that RBF networks
It is that the optimal network of mapping function is completed in feedforward neural network with global and optimal approximation capability.As long as have enough
Hidden neuron, RBF can be with the approximate any continuous functions of arbitrary accuracy.Using feedforward network topological structure, hidden layer it is each
Unit exports:
hi=Ri(X)=Ri(||X-C||/σi) (4)
I=1,2,3 ..., L
Wherein, X is N-dimensional input vector, CiIt is the vector with X with dimension, RiFor Radial basis kernel function.
Ri() generally use Gaussian function, wherein σ are kernel function width, i.e.,：
Therefore the output of network output layer is
Wherein w is connection weight, and h is the unit output of hidden layer.
Improved free search algorithm module 9, for using punishment of the improved free searching algorithm to RBF neural
The factor and error margin value optimize, and comprise the following steps that：
(1) the scale n and dimension m, [X of population are initializedmini, Xmaxi] excursion as i-th dimension, greatest iteration time
Number is Maxgen, and exploration step number is T, and the variable neighborhood value of i-th of body jth dimension is Rji∈[Rmin,Rmax].It is according to these settings
Initialize installation can be carried out to population position：
xtji=x0ji-Δxtji+2Δxtji*randomtji(0,1) (7)
X0jiIt is the initial value randomly generated：
Δxtji=Rji*(Xmax-Xmin)*randomtji(0,1) (8)
(2) each individual is gone into action, and individual i carries out T step detections every time, and the renewal of position is determined by following formula：
x0ji=Xmini+(Xmaxi-Xmini)*randomji(0,1) (9)
In exploration behavior once, individual exploration behavior is represented by：
F (x in formulatji) it is the position that each individual is completed to mark after search.
Pheromones are defined as follows：
And sensitivity updates according to equation below：
S in formulaminAnd SmaxIt is the minimum value and maximum of sensitivity respectively, the minimum value and maximum of pheromones are respectively
PminAnd Pmax, and P is provided hereinmin=SminAnd Pmin=Smax。
After the search of epicycle terminates, according to the starting point of equation below renewal next round search：
(3) set meet the individual of conditional (13) asIt is and corresponding first
Beginning position and each survey position beWithDefining individual density is：
Thus defining individual relative density is：
Obvious pj∈(0,1).The strategy of catastrophe is：Relative density pjIt is bigger, then individual survey position Relatively centralized, easily
Local optimum is absorbed in, the probability for now carrying out catastrophe is bigger.Therefore, catastrophe will be produced according to following steps：
(a) j=1 is made.
(b) for individual j, r is producedl=random (0,1).
If (c) rl≤pl, then initial position of the new original position as next iteration is regenerated；Otherwise, it is necessary to fromMiddle random selection position enters the initial position of next iteration as the individual.
(d) j=j+1 is made, if meeting j≤m, repeats step (2), otherwise terminates the process.
It is described based on the optimal soft of improved free searching algorithm optimization RBF neural as a kind of preferable scheme
Measurement host computer also includes：Model modification module 10, for the online updating of model, offline analysis data is periodically input to instruction
Practice and concentrate, update RBF neural network model.
Embodiment 2
Reference picture 1, Fig. 2 and Fig. 3, a kind of sea clutter based on improved free searching algorithm optimization RBF neural is most
Excellent flexible measurement method, the flexible measurement method comprise the following steps：
1), to radar object, according to industrial analysis and Operations Analyst, selection operation variable and easily survey variable are as model
Input, performance variable and easily survey variable are obtained by spot database；
2), the model training sample inputted from spot database is pre-processed, to training sample centralization, that is, subtracted
The average value of sample, is then standardized to it so that its average is 0, variance 1.The processing uses following formula process
To complete：
2.1) average is calculated：
2.2) variance is calculated：
2.3) standardize：
Wherein, TX is training sample, and N is number of training,For the average of training sample, X is the training sample after standardization
This, σxTo calculate variance.
3), to the training sample for being transmitted through coming from data preprocessing module, it is modeled using RBF neural.RBF nerves
" base " of the network by the use of RBF as hidden unit forms implicit sheaf space, and defeated people's vector is mapped directly into hidden layer sky
Between imply sheaf space to export space mapping be linear.In general, network is non-thread by the mapping for being input to output
Property, and network output for adjustable parameter but is linear.It is theoretical it has been proved that RBF networks have it is global and optimal
Approximation capability, it is that the optimal network of mapping function is completed in feedforward neural network.As long as there are enough hidden neurons, RBF
Can be with the approximate any continuous function of arbitrary accuracy.Using feedforward network topological structure, each unit output of hidden layer is:
hi=Ri(X)=Ri(||X-C||/σi) (4)
I=1,2,3 ..., L
Wherein, X is N-dimensional input vector, CiIt is the vector with X with dimension, RiThe characteristics of with local experiences.
Ri() generally use Gaussian function, wherein σ are kernel function width, i.e.,：
Therefore the output of network output layer is
Wherein w is connection weight, and h is the unit output of hidden layer.
4), the kernel function width of RBF neural is optimized using improved free searching algorithm, specific steps are such as
Under：
(1) the scale n and dimension m, [X of population are initializedmini, Xmaxi] excursion as i-th dimension, greatest iteration time
Number is Maxgen, and exploration step number is T, and the variable neighborhood value of i-th of body jth dimension is Rji∈[Rmin,Rmax].It is according to these settings
Initialize installation can be carried out to population position：
xtji=x0ji-Δxtji+2Δxtji*randomtji(0,1) (7)
X0jiIt is the initial value randomly generated：
Δxtji=Rji*(Xmax-Xmin)*randomtji(0,1) (8)
(2) each individual is gone into action, and individual i carries out T step detections every time, and the renewal of position is determined by following formula：
x0ji=Xmini+(Xmaxi-Xmini)*randomji(0,1) (9)
In exploration behavior once, individual exploration behavior is represented by：
F (x in formulatji) it is the position that each individual is completed to mark after search.
Pheromones are defined as follows：
And sensitivity updates according to equation below：
S in formulaminAnd SmaxIt is the minimum value and maximum of sensitivity respectively, the minimum value and maximum of pheromones are respectively
PminAnd Pmax, and P is provided hereinmin=SminAnd Pmin=Smax。
After the search of epicycle terminates, according to the starting point of equation below renewal next round search：
(3) set meet the individual of conditional (13) asIt is and corresponding first
Beginning position and each survey position beWithDefining individual density is：
Thus defining individual relative density is：
Obvious pj∈(0,1).The strategy of catastrophe is：Relative density pjIt is bigger, then individual survey position Relatively centralized, easily
Local optimum is absorbed in, the probability for now carrying out catastrophe is bigger.Therefore, catastrophe will be produced according to following steps：
(a) j=1 is made.
(b) for individual j, r is producedl=random (0,1).
If (c) rl≤pl, then initial position of the new original position as next iteration is regenerated；Otherwise, it is necessary to fromMiddle random selection position enters the initial position of next iteration as the individual.
(d) j=j+1 is made, if meeting j≤m, repeats step (2), otherwise terminates the process.
As a kind of preferable scheme：The flexible measurement method is further comprising the steps of：4), periodically by offline analysis data
It is input in training set, updates RBF neural network model.
The method specific implementation step of the present embodiment is as follows：
Step 1：To radar object 1, according to specificity analysis and climatic analysis, selection operation variable and easily survey variable are as mould
The input of type.Performance variable and easily survey variable are obtained by spot database 4.
Step 2：Sample data is pre-processed, completed by data preprocessing module 7.
Step 3：Initial R BF neural network models 8 are established based on model training sample data.Input data such as step 2 institute
Acquisition is stated, output data is obtained by offline chemical examination.
Step 4：Optimize the parameter of Initial R BF neural network models by improved free search algorithm module 9.
Step 5：Offline analysis data is periodically input in training set by model modification module 10, updates RBF neural
Model, the optimal hard measurement host computer 5 based on improved free searching algorithm optimization RBF neural network model, which is established, to be completed.
Step 6：The display of sea clutter hard measurement value display instrument 6 is based on improved free searching algorithm optimization RBF neural
The output of the optimal hard measurement host computer 5 of model, completes the display to the optimal hard measurement of sea clutter.
Located in advance based on the optimal hard measurement host computer of improved free searching algorithm optimization RBF neural, including data
Module, RBF neural module, model modification module are managed, and provides a kind of hard measurement side realized with soft measuring instrument
Method.The present invention realizes the online optimal hard measurement of sea clutter, and randomness caused by overcoming human factor influences, and improves mould
The stability of type forecast, reduces the possibility that model prediction is absorbed in local optimum.
Claims (2)
1. a kind of sea clutter optimal soft survey instrument based on improved free searching algorithm optimization RBF neural, described
Optimal soft survey instrument, including radar, the field intelligent instrument for measuring easy survey variable, the control for measuring performance variable
Stand, deposit the spot database and sea clutter hard measurement value display instrument of data；The field intelligent instrument, control station and radar
Connection, the field intelligent instrument, control station and spot database connect, it is characterised in that：The soft measuring instrument also includes
Based on the optimal hard measurement host computer of improved free searching algorithm optimization RBF neural, the spot database with it is described
The input connection of optimal hard measurement host computer based on improved free searching algorithm optimization RBF neural, it is described to be based on
The output end of the optimal hard measurement host computer of improved free searching algorithm optimization RBF neural shows with sea clutter hard measurement value
Show that instrument connects；The optimal hard measurement host computer based on improved free searching algorithm optimization RBF neural includes：
Data preprocessing module, for the model training inputted from spot database sample to be pre-processed, to training sample
Centralization, that is, the average value of sample is subtracted, then it is standardized：
Calculate average：
Calculate variance：
Standardization：
Wherein, TX is training sample, and N is number of training,For the average of training sample, X is the training sample after standardization,
σxTo calculate variance.
Using feedforward network topological structure, each unit output h of hidden layer is:
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<mi>h</mi>
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</msub>
<mo>=</mo>
<msub>
<mi>R</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>X</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>R</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<mo>|</mo>
<mo>|</mo>
<mi>X</mi>
<mo>-</mo>
<mi>C</mi>
<mo>|</mo>
<mo>|</mo>
<mo>/</mo>
<msub>
<mi>&sigma;</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mn>3</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mi>L</mi>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, X is N-dimensional input vector, CiIt is the vector with X with dimension, RiFor Radial basis kernel function.
Ri() generally use Gaussian function, wherein σ are kernel function width, i.e.,：
<mrow>
<msub>
<mi>R</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>X</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mo>|</mo>
<mo>|</mo>
<mi>X</mi>
<mo>-</mo>
<msub>
<mi>C</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mo>/</mo>
<msubsup>
<mi>&sigma;</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
Therefore the output y of network output layer is
<mrow>
<mi>y</mi>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>l</mi>
</munderover>
<msub>
<mi>w</mi>
<mi>j</mi>
</msub>
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein w is connection weight, and h is the unit output of hidden layer.
Improved free search algorithm module, for wide to the kernel function of RBF neural using improved free searching algorithm
Degree optimizes, and comprises the following steps that：
(1) the scale n and dimension m, [X of population are initializedmini, Xmaxi] excursion as i-th dimension, maximum iteration is
Maxgen, exploration step number are T, and the variable neighborhood value of i-th of body jth dimension is Rji∈[Rmin,Rmax].Can be right according to these settings
Population position x carries out Initialize installation：
xtji=x0ji-Δxtji+2Δxtji*randomtji(0,1) (7)
X0jiIt is the initial value randomly generated：
Δxtji=Rji*(Xmax-Xmin)*randomtji(0,1) (8)
(2) each individual is gone into action, and individual i carries out T step detections every time, and the renewal of position is determined by following formula：
x0ji=Xmini+(Xmaxi-Xmini)*randomji(0,1) (9)
In exploration behavior once, individual exploration behavior is represented by：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>f</mi>
<mrow>
<mi>t</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>t</mi>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>f</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<mi>max</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>f</mi>
<mrow>
<mi>t</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
F (x in formulatji) it is the position that each individual is completed to mark after search.
Pheromones P is defined as follows：
<mrow>
<msub>
<mi>P</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mi>f</mi>
<mi>j</mi>
</msub>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>f</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
And sensitivity S updates according to equation below：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>S</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<msub>
<mi>S</mi>
<mi>min</mi>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;S</mi>
<mi>j</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&Delta;S</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>S</mi>
<mi>max</mi>
</msub>
<mo>-</mo>
<msub>
<mi>S</mi>
<mi>min</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>*</mo>
<msub>
<mi>random</mi>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>,</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
S in formulaminAnd SmaxIt is the minimum value and maximum of sensitivity respectively, the minimum value and maximum of pheromones are respectively Pmin
And Pmax, and P is provided hereinmin=SminAnd Pmin=Smax。
After the search of epicycle terminates, according to the starting point of equation below renewal next round search：
<mrow>
<msubsup>
<mi>x</mi>
<mrow>
<mn>0</mn>
<mi>j</mi>
<mi>i</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>x</mi>
<mrow>
<mn>0</mn>
<mi>j</mi>
<mi>i</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<mo><</mo>
<msub>
<mi>S</mi>
<mi>j</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>x</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<mo>&GreaterEqual;</mo>
<msub>
<mi>S</mi>
<mi>j</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
(3) assume that the individual for meeting conditional (13) isIt is and corresponding initial
Position and each survey position areWithDefining individual density p is：
<mrow>
<msub>
<mi>&rho;</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<mn>1</mn>
<mo>/</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>t</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>T</mi>
</munderover>
<msup>
<mrow>
<mo>(</mo>
<mo>|</mo>
<mo>|</mo>
<msubsup>
<mi>x</mi>
<mi>j</mi>
<mn>0</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>x</mi>
<mi>j</mi>
<mi>t</mi>
</msubsup>
<mo>|</mo>
<mo>|</mo>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>14</mn>
<mo>)</mo>
</mrow>
</mrow>
Thus defining individual relative density p is：
<mrow>
<msub>
<mi>p</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mi>&rho;</mi>
<mi>j</mi>
</msub>
<mrow>
<munderover>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<mrow>
<mo>(</mo>
<msub>
<mi>&rho;</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
Obvious pj∈(0,1).The strategy of catastrophe is：Relative density pjBigger, then individual survey position Relatively centralized, is easily absorbed in
Local optimum, the probability for now carrying out catastrophe are bigger.Therefore, catastrophe r will be produced according to following steps：
(a) j=1 is made.
(b) for individual j, r is producedl=random (0,1).
If (c) rl≤pl, then initial position of the new original position as next iteration is regenerated；Otherwise, it is necessary to fromMiddle random selection position enters the initial position of next iteration as the individual.
(d) j=j+1 is made, if meeting j≤m, repeats step (2), otherwise terminates the process.
Model modification module, for the online updating of model, periodically offline analysis data is input in training set, updates RBF
Neural network model.
2. a kind of sea clutter as claimed in claim 1 based on improved free searching algorithm optimization RBF neural is optimal
The flexible measurement method that soft measuring instrument is realized, it is characterised in that：The flexible measurement method comprises the following steps：
1), to radar object, according to specificity analysis and climatic analysis, selection operation variable and easily survey variable are as the defeated of model
Enter, performance variable and easily survey variable are obtained by spot database；
2), the model training sample inputted from spot database is pre-processed, to training sample centralization, that is, subtracts sample
Average value, then it is standardized so that its average be 0, variance 1.The processing is using following formula process come complete
Into：
2.1) average is calculated：
2.2) variance is calculated：
2.3) standardize：
Wherein, TX is training sample, and N is number of training,For the average of training sample, X is the training sample after standardization,
σxTo calculate variance.
3) to the training sample for being transmitted through coming from data preprocessing module, built using RBF neural.RBF neural is used
RBF forms implicit sheaf space as " base " of hidden unit, and defeated people's vector is mapped directly into implicit sheaf space and implied
The mapping in sheaf space to output space is linear.In general, network is nonlinear by the mapping for being input to output, and
Network output is for adjustable parameter but is linear.Theory is it has been proved that RBF networks have global and optimal Approximation
Can, it is that the optimal network of mapping function is completed in feedforward neural network.As long as there is enough hidden neurons, RBF can with appoint
The approximate any continuous function of precision of anticipating.Using feedforward network topological structure, each unit output h of hidden layer is:
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>h</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<msub>
<mi>R</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>X</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>R</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<mo>|</mo>
<mo>|</mo>
<mi>X</mi>
<mo>-</mo>
<mi>C</mi>
<mo>|</mo>
<mo>|</mo>
<mo>/</mo>
<msub>
<mi>&sigma;</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mn>3</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mi>L</mi>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, X is N-dimensional input vector, CiIt is the vector with X with dimension, RiThe characteristics of with local experiences.
Ri() generally use Gaussian function, wherein σ are kernel function width, i.e.,：
<mrow>
<msub>
<mi>R</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>X</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>exp</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mo>|</mo>
<mo>|</mo>
<mi>X</mi>
<mo>-</mo>
<msub>
<mi>C</mi>
<mi>i</mi>
</msub>
<mo>|</mo>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mo>/</mo>
<msubsup>
<mi>&sigma;</mi>
<mi>i</mi>
<mn>2</mn>
</msubsup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
Therefore the output y of network output layer is
<mrow>
<mi>y</mi>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>l</mi>
</munderover>
<msub>
<mi>w</mi>
<mi>j</mi>
</msub>
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein w is connection weight, and h is the unit output of hidden layer.
4), the kernel function width of RBF neural is optimized using improved free searching algorithm, comprised the following steps that：
(1) the scale n and dimension m, [X of population are initializedmini, Xmaxi] excursion as i-th dimension, maximum iteration is
Maxgen, exploration step number are T, and the variable neighborhood value of i-th of body jth dimension is Rji∈[Rmin,Rmax].Can be right according to these settings
Population position carries out Initialize installation：
xtji=x0ji-Δxtji+2Δxtji*randomtji(0,1) (7)
X0jiIt is the initial value randomly generated：
Δxtji=Rji*(Xmax-Xmin)*randomtji(0,1) (8)
(2) each individual is gone into action, and individual i carries out T step detections every time, and the renewal of position is determined by following formula：
x0ji=Xmini+(Xmaxi-Xmini)*randomji(0,1) (9)
In exploration behavior once, individual exploration behavior is represented by：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>f</mi>
<mrow>
<mi>t</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>t</mi>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>f</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>f</mi>
<mrow>
<mi>t</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
F (x in formulatji) it is the position that each individual is completed to mark after search.
Pheromones P is defined as follows：
<mrow>
<msub>
<mi>P</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mi>f</mi>
<mi>j</mi>
</msub>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>f</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
And sensitivity S updates according to equation below：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>S</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<msub>
<mi>S</mi>
<mi>min</mi>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;S</mi>
<mi>j</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&Delta;S</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>S</mi>
<mi>max</mi>
</msub>
<mo>-</mo>
<msub>
<mi>S</mi>
<mi>min</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>*</mo>
<msub>
<mi>random</mi>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>,</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
S in formulaminAnd SmaxIt is the minimum value and maximum of sensitivity respectively, the minimum value and maximum of pheromones are respectively Pmin
And Pmax, and P is provided hereinmin=SminAnd Pmin=Smax。
After the search of epicycle terminates, according to the starting point of equation below renewal next round search：
<mrow>
<msubsup>
<mi>x</mi>
<mrow>
<mn>0</mn>
<mi>j</mi>
<mi>i</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>x</mi>
<mrow>
<mn>0</mn>
<mi>j</mi>
<mi>i</mi>
</mrow>
<mo>&prime;</mo>
</msubsup>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<mo><</mo>
<msub>
<mi>S</mi>
<mi>j</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>x</mi>
<mrow>
<mi>j</mi>
<mi>i</mi>
</mrow>
</msub>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<mo>&GreaterEqual;</mo>
<msub>
<mi>S</mi>
<mi>j</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
(3) set meet the individual of conditional (13) asAnd corresponding initial bit
Put and be with each survey positionWithDefining individual density p is：
<mrow>
<msub>
<mi>&rho;</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<mn>1</mn>
<mo>/</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>t</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>T</mi>
</munderover>
<msup>
<mrow>
<mo>(</mo>
<mo>|</mo>
<mo>|</mo>
<msubsup>
<mi>x</mi>
<mi>j</mi>
<mn>0</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>x</mi>
<mi>j</mi>
<mi>t</mi>
</msubsup>
<mo>|</mo>
<mo>|</mo>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>14</mn>
<mo>)</mo>
</mrow>
</mrow>
Thus defining individual relative density p is：
<mrow>
<msub>
<mi>p</mi>
<mi>j</mi>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mi>&rho;</mi>
<mi>j</mi>
</msub>
<mrow>
<munderover>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>m</mi>
</munderover>
<mrow>
<mo>(</mo>
<msub>
<mi>&rho;</mi>
<mi>j</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
Obvious pj∈(0,1).The strategy of catastrophe is：Relative density pjBigger, then individual survey position Relatively centralized, is easily absorbed in
Local optimum, the probability for now carrying out catastrophe are bigger.Therefore, catastrophe will be produced according to following steps：
(a) j=1 is made.
(b) for individual j, r is producedl=random (0,1).
If (c) rl≤pl, then initial position of the new original position as next iteration is regenerated；Otherwise, it is necessary to fromMiddle random selection position enters the initial position of next iteration as the individual.
(d) j=j+1 is made, if meeting j≤m, repeats step (2), otherwise terminates the process.
Periodically offline analysis data is input in training set, updates RBF neural network model.
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