CN107122520A - A kind of three dimensional temperature sensing data analysis method coupled based on space-time dynamic - Google Patents
A kind of three dimensional temperature sensing data analysis method coupled based on space-time dynamic Download PDFInfo
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Abstract
The invention discloses a kind of three dimensional temperature sensing data analysis method coupled based on space-time dynamic, utilize the temperature field physical model and the statistical model based on temporal correlation for reflecting heat-transfer mechanism, set up Mixed effect model, three dimensional temperature sensing data is analyzed, obtain the temperature value of the dynamic temperature value of any locus in space-time three-dimensional temperature field, i.e., any locus or any instant.Pass through technical scheme provided by the present invention, the temperature field physical model for reflecting heat-transfer mechanism is combined with the statistical model based on temporal correlation, set up Mixed effect model, realize the estimation to Three-Dimensional Dynamic temperature field, accurate, comprehensive information is provided for the real-time monitoring in temperature field, help to realize the allocation optimum of sensor in temperature field, reach the effect for reducing cost, saving the energy.
Description
Technical field
The present invention provides a kind of dynamic data analysis method of three-dimensional temperature field, and in particular to one kind is based on space-time dynamic coupling
The three dimensional temperature sensing data analysis method of conjunction, belongs to Industrial Engineering field.
Background technology
The dynamic data analytical technology in temperature field is played an important role in engineering field, to improving product quality, lifting
The engineering duties such as systematic function provide important information.In recent years, this technology causes scientific research and the extensive concern of engineering staff,
Through being applied in engineering fields such as ecology, meteorology, health care, grain storages.The dynamic data analytical technology energy in temperature field
Comprehensively and accurately information is provided for the monitoring of complication system, the effect for improving systematic function or service quality is reached.Meanwhile, should
Technology contributes to the optimization design of engineering structure, realizes the target for the cost that economizes on resources, reduces.
The dynamic data analytical technology in temperature field aims at the accurate estimation to temperature field.Traditional temperature field estimation side
Method is a kind of emulation mode based on heat transfer principle.Described in document [1]~[2], this method considers the change in influence temperature field
The external factor of change, such as environmental factor, internal heat transfer mechanism, by given initial temperature and boundary condition, set up three-dimensional heating power
Model is learned, the estimation to Three-Dimensional Dynamic temperature field is realized.However, the change in temperature field is not only influenceed by external factor, also
Influenceed by internal factor and other a variety of uncertain factors.Temperature field can be considered as one with the complexity of change in time and space
Heat transfer system.Traditional temperature field method of estimation is only capable of portraying the profile and trend of change of temperature field in the ideal situation.It is right
The change of the local temperature as caused by internal factor often occurred in temperature field, this method is no longer applicable.Therefore, traditional temperature
Spend field method of estimation error larger, it is impossible to provide high-precision temperature field information.
With the development in epoch, wireless sensor technology is widely used in engineering field (such as document [3]).The technology is led to
Wireless senser collecting temperature data are crossed, and temperature field estimation model is set up using these data.Due to sensor configuration cost
Limitation, the number of sensors installed at present in temperature field is less, and the sparse sight of a small part can only be obtained by sensor
Survey data.The openness of observation data can cause temperature field to estimate that model accuracy is substantially reduced.Meanwhile, gathered by sensor
There is measurement error in temperature data, can equally reduce the accuracy that model is estimated in temperature field.Therefore, wireless senser skill is only relied on
Art can not realize the accurate estimation to temperature field with the method that mathematical modeling is combined.
In addition, as a complicated heat transfer system, the temperature data of three-dimensional temperature field adjacent position or adjacent moment is deposited
Correlation in time and space, and temperature data when, empty correlation be interaction, i.e., both existence time phase between data
, there is temporal correlation again in Guan Xing, spatial coherence.Existing research be mostly to the description of this characteristic of temperature field in the time and
Spatial coherence is carried out under separate assumed condition, does not account for the temporal correlation of data, it is difficult to realized to three
The temporal correlation of dimension dynamic temperature field is considered and estimated.
Bibliography
[1]D.Wang and X.Zhang,“A prediction method for interior temperature
of grain storage via dynamics model:a simulation study”,Proceed-ings of IEEE
International Conference of Automation Science and Engineering,pp.1477-1483,
2015.
[2]C.Jia,D.Sun and C.Cao,“Finite element prediction of transient
temperature distribution in a grain storage bin”,Journal of Agricultural
Engineering Research,vol.76,no.4,pp.323–330,2000.
[3]Y.Ding,E.A.Elsayed,S.Kumara,J.Lu,F.Niu and J.Shi,“Distributed
sensing for quality and productivity improvements”,IEEE Transactions on
Automation Science and Engineering,vol.3,no.4,pp.344–359,2006.
The content of the invention
The deficiency existed for above-mentioned prior art, the present invention provides a kind of three dimensional temperature biography coupled based on space-time dynamic
Data analysing method is felt, under the framework of Mixed effect model, during by reflecting the temperature field physical model of heat-transfer mechanism with being based on
The statistical model of empty correlation is combined, and realizes the estimation to Three-Dimensional Dynamic temperature field.It can solve the problem that and exist at present by the present invention
Present in engineering field due to sensing data deficiency can not obtain accurately, full temperature information the problem of, can obtain
The comprehensive and accurate information in temperature field, foundation is provided for the measure such as monitoring, decision-making in engineering field.
The technical scheme that the present invention is provided is as follows：
A kind of three dimensional temperature sensing data analysis method coupled based on space-time dynamic, utilizes the temperature for reflecting heat-transfer mechanism
Field physical model and the statistical model based on temporal correlation, set up Mixed effect model, and three dimensional temperature sensing data is carried out
Analysis, obtains the dynamic temperature value (i.e. any locus or any instant temperature value) on three-dimensional space position；Including as follows
Step：
1) using temperature field physical model and the statistical model based on temporal correlation, Mixed effect model framework is set up,
The temperature value of three-dimensional temperature field event includes representing the mean value function of the global temperature change in temperature field, represents temperature field
Local temperature change localized variation and represent the random noise of the temperature change as caused by random or uncontrollable factor；
Set up Mixed effect model framework as follows：
Assuming that Y (s, t) represents temperature value of the three-dimensional temperature field in event (s, t), s and t difference representation spaces and time
Independent variable, the framework of Mixed effect model is：
Y (s, t)=μ (s, t)+w (s, t)+∈ (s, t) (formula 1)
Wherein, μ (s, t) represents the mean value function at event (s, t) place, for portraying the global temperature change in temperature field
Change situation；W (s, t) represents the localized variation at event (s, t) place, for portraying the local temperature change feelings in temperature field
Condition；∈ (s, t) represents the random noise at event (s, t) place, warm as caused by random or uncontrollable factor for portraying
Situation of change is spent, it is white noise to usually assume that it.Below, by respectively to mean value function μ (s, t) and localized variation w (s, t)
Set up model.
2) mean value function μ (s, t) modeling, implementation method is：
B1. mean value model is set up：
The change in temperature field is typically as caused by environmental factor.In the present invention, the influence of environmental factor is taken into full account,
Under cartesian coordinate system, three-dimensional unstable state Fourier's heat transfer model is set up to mean value function μ (s, t)：
In formula 2, mean value function of μ (x, y, z, the t) expressions under cartesian coordinate system, its spatial coordinates s=x, y,
Z }, x, y and z are illustrated respectively in X, Y and the coordinate of Z-direction；ρ represents the density of material, and c represents the specific heat capacity of material, λx, λyWith
λzIt is illustrated respectively in thermal conductivity of the material along x, y and z directionss under three Cartesian coordinates.
B2. the solution of mean value model
Using finite difference calculus, formula 2 is solved using formula 3：
Wherein, the corresponding grid position of (i, j, k, m) denotation coordination (x, y, z, t), Δ x, Δ y, Δ z and Δ t difference tables
Show space, the grid interval of time orientation.To ensure the accuracy of this numerical solution, the selection of parameter value should ensure that Given initial temperature and boundary condition, are that can be achieved to mean value function using finite difference calculus
Solution.
3) localized variation w (s, t) modeling, implementation method is：
The temporal correlation in temperature field is taken into full account, is carved using Gaussian random field with the method that Kriging model is combined
Draw the local temperature change in temperature field.
C1. model framework is determined using Gaussian random field
Assuming that in moment tm(m=1,2 ..., M), local temperature change has spatial stationarity property, using Gaussian random field mould
Type describes siThe relation of the temperature position temperature adjacent thereto of point, i.e., in given siUnder conditions of point adjacent position temperature value, siPoint
Temperature and submit to normal distribution：
Wherein, sj~siRepresent siAnd sjAdjacent position, ω are in Gaussian random fieldij(tm) represent in tmThe sky at moment
Between weight parameter, σ2(si,tm) represent conditional variance.
C2. weight parameter is determined using Kriging model
Using Kriging model, weight parameter ω is determined by formula 5ij(tm)：
Wherein, C (si,sj) represent siWith sjCovariance matrix, C (sj,sj) represent sjBetween covariance matrix.Association side
Poor matrix determines by covariance function, the expression formula such as formula 6 of covariance function：
Wherein spAnd sqThe space coordinate at p and q points, under cartesian coordinate system, s are represented respectivelyp={ xp,yp,zpAnd
sq={ xq,yq,zq}；For in tmWhen inscribe the ginseng of covariance function
Number, by η={ { η (t1),η(t2),…,{η(tM) it is designated as covariance parameter.
C3. covariance parameter is solved
In initial time t1, covariance parameter is solved using Maximum Likelihood Estimation.In order to portray the time in temperature field
Correlation, using Bayesian Estimation method to t2To tMThe covariance parameter at moment is updated.Assuming that known t1To tm-1Moment
Covariance parameter and temperature data (m=2 ..., M), t is obtained by formula 7mThe prediction distribution of moment covariance parameter：
p(η(tm)|Y(s,t1:m-1))=∫ p (η (tm)|η(tm-1))p(η(tm-1)|Y(s,t1:m-1))dη(tm) (formula 7)
Wherein, p (η (tm)|Y(s,t1:m-1)) represent in known t1To tm-1Moment temperature data Y (s, t1:m-1) condition
Under, tmCovariance parameter η (the t at momentm) probability density；p(η(tm)|η(tm-1)) represent in known tm-1The covariance at moment
Parameter η (tm-1) under conditions of, tmCovariance parameter η (the t at momentm) probability density；p(η(tm-1)|Y(s,t1:m-1)) represent
In known t1To tm-1Moment temperature data Y (s, t1:m-1) under conditions of, tm-1Covariance parameter η (the t at momentm-1) probability it is close
Degree.
Again by formula 8, t is utilizedmThe temperature data at moment realizes the renewal of covariance parameter, that is, asks after covariance parameter
Test probability density distribution p (η (tm)|Y(s,t1:m))：
Wherein,
p(Y(s,tm)|Y(s,t1:m-1))=∫ p (Y (s, tm)|η(tm))p(η(tm)|Y(s,t1:m-1))dη(tm) (formula 9)
p(Y(s,tm)|η(tm)) represent in tmCovariance parameter η (the t at momentm) under conditions of, Y (s, tm) probability it is close
Degree.Because the distribution of parameter is nonnormal, therefore use particle filter method realizes the iterative calculation of Bayesian Estimation.
4) space-time temperature field is estimated, implementation method is：
After parameter Estimation, observation data are given, are realized by formula 10 to any position in temperature fieldTemperature value
Estimation：
Wherein,In tmMomentThe Temperature estimate value of point.
Compared with prior art, the beneficial effects of the invention are as follows：
The present invention provides a kind of three dimensional temperature sensing data analysis method coupled based on space-time dynamic, is conducted heat using reflection
The temperature field physical model of mechanism and the statistical model based on temporal correlation, set up Mixed effect model, and three dimensional temperature is passed
Sense data are analyzed, and obtain dynamic temperature value (i.e. any locus or any of any locus in three-dimensional temperature field
Moment temperature value).By technical scheme provided by the present invention, during by reflecting the temperature field physical model of heat-transfer mechanism with being based on
The statistical model of empty correlation is combined, and sets up Mixed effect model, is realized the estimation to Three-Dimensional Dynamic temperature field, is temperature field
Real-time monitoring accurate, comprehensive information is provided, help to realize the allocation optimum of sensor in temperature field, reaching reduces into
Originally the effect of the energy, is saved.
Brief description of the drawings
Fig. 1 is the flow chart element for the three dimensional temperature sensing data analysis method coupled based on space-time dynamic that the present invention is provided
Figure.
Fig. 2 is the covariance parameter estimated result of the embodiment of the present invention；
Wherein, abscissa is the time, and unit is day；Ordinate is covariance parameter value；(a) it is parameter axEstimate；
(b) it is parameter ayEstimate；(c) it is parameter azEstimate；(d) it is parameterEstimate.
Fig. 3 is the estimated result of the cereal temperature of the embodiment of the present invention；
Wherein, numeral is the space coordinate of sampled point in legend.
Embodiment
Below in conjunction with the accompanying drawings, the present invention, the model of but do not limit the invention in any way are further described by embodiment
Enclose.
The present invention provides a kind of three dimensional temperature sensing data analysis method coupled based on space-time dynamic, in melange effect mould
Under the framework of type, the temperature field physical model for reflecting heat-transfer mechanism is combined with the statistical model based on temporal correlation, it is real
Now to the estimation in Three-Dimensional Dynamic temperature field.It is can solve the problem that by the present invention at present present in engineering field due to sensor number
According to deficiency can not obtain accurately, full temperature information the problem of, temperature field comprehensive can be obtained and accurate information, be work
The measure such as monitoring, decision-making provides foundation in journey field.
Fig. 1 is the flow chart element for the three dimensional temperature sensing data analysis method coupled based on space-time dynamic that the present invention is provided
Figure.Embodiment design temperature scope is (- 50 DEG C, 50 DEG C), and using sensor collecting temperature data, acquisition time is at intervals of 7
My god, the observation data collected are expressed as Yd(s,t).Three dimensional temperature sensing data is analyzed using the inventive method
Embodiment is as follows.
1) according to the feature in the temperature field of research object, Mixed effect model is set up.
Research object can be any mass temperature relevant with temperature field, such as grain in storing in a warehouse in engineering field
Temperature field, a certain regional environment temperature, body thermal field.The framework of Mixed effect model is as follows：Assuming that Y (s, t) is represented
Temperature value of the three-dimensional temperature field in event (s, t), s and t difference representation spaces and the independent variable of time, Mixed effect model
Framework is：
Y (s, t)=μ (s, t)+w (s, t)+∈ (s, t) (formula 1)
Wherein, μ (s, t) represents the mean value function at event (s, t) place, for portraying the global temperature change in temperature field
Change situation；W (s, t) represents the localized variation at event (s, t) place, for portraying the local temperature change feelings in temperature field
Condition；∈ (s, t) represents the random noise at event (s, t) place, warm as caused by random or uncontrollable factor for portraying
Situation of change is spent, it is white noise to usually assume that it.Below, by respectively to mean value function μ (s, t) and localized variation w (s, t)
Set up model.
2) mean value function μ (s, t) modeling
The physical attribute of research object is taken into full account, mean value model is set up and solves.
B1. the foundation of mean value model
The change in temperature field is typically as caused by environmental factor.In the present invention, the influence of environmental factor is taken into full account,
Under cartesian coordinate system, three-dimensional unstable state Fourier's heat transfer model is set up to mean value function μ (s, t)：
In formula 2, mean value function of μ (x, y, z, the t) expressions under cartesian coordinate system, its spatial coordinates s=x, y,
Z }, x, y and z are illustrated respectively in X, Y and the coordinate of Z-direction；ρ represents the density of material, and c represents the specific heat capacity of material, λx, λyWith
λzIt is illustrated respectively in thermal conductivity of the material along x, y and z directionss under three Cartesian coordinates.
B2. the solution of mean value model
Formula 2 is solved using finite difference calculus, implementation method is：
The wherein corresponding grid position of (i, j, k, m) denotation coordination (x, y, z, t), Δ x, Δ y, Δ z and Δ t are represented respectively
Space, the grid interval of time orientation.To ensure the accuracy of this numerical solution, the selection of parameter should ensure thatGiven initial temperature value and boundary temperature value, are that can be achieved to average using finite difference calculus
The solution of function.
Mean value model is what the physical significance based on research object was set up, is not related to the observation data in temperature field, for retouching
State the global change in ideally temperature field.
3) localized variation w (s, t) modeling
The temporal correlation in temperature field is taken into full account, local temperature change is set up with reference to Gaussian random field and Kriging model
Model.
C1. Gaussian random field determines model framework
Assuming that in moment tm(m=1,2 ..., M), local temperature change has spatial stationarity property, using Gaussian random field mould
Type describes siThe relation of the temperature position temperature adjacent thereto of point, i.e., in given siUnder conditions of point adjacent position temperature value, siPoint
Temperature and submit to normal distribution：
Wherein, sj~siRepresent siAnd sjAdjacent position, ω are in Gaussian random fieldij(tm) represent in tmThe sky at moment
Between weight parameter, σ2(si,tm) represent conditional variance.
C2. Kriging model determines weight parameter
Weight parameter ω is determined using Kriging modelij(tm), implementation method is：
Wherein, ωij(tm) represent siIts relative all adjacent position s of pointjWeight parameter, C (si,sj) represent siWith sj's
Covariance matrix, C (sj,sj) represent sjBetween covariance matrix.Covariance matrix is to be calculated to obtain by covariance function, is assisted
The expression formula of variance function is as follows：
Wherein spAnd sqThe space coordinate at p and q points, under cartesian coordinate system, s are represented respectivelyp={ xp,yp,zpAnd
sq={ xq,yq,zq}；For in tmWhen inscribe the ginseng of covariance function
Number, by η={ { η (t1),η(t2),…,{η(tM) it is designated as covariance parameter.
C3. covariance parameter is solved
In initial time t1, use t1The observation data Y at momentd(s,t1), association side is solved using Maximum Likelihood Estimation
Poor parameter.In order to portray the temporal correlation in temperature field, using Bayesian Estimation method to t2To tMThe covariance parameter at moment enters
Row updates.Assuming that known t1To tm-1The covariance parameter and observation data Y at momentd(s,t1:m-1) (m=2 ..., M), pass through formula 7
Obtain tmThe prediction distribution of moment covariance parameter：
p(η(tm)|Yd(s,t1:m-1))=∫ p (η (tm)|η(tm-1))p(η(tm-1)|Yd(s,t1:m-1))dη(tm) (formula 7)
Wherein, p (η (tm)|Yd(s,t1:m-1)) represent in known t1To tm-1Moment observation data Yd(s,t1:m-1) condition
Under, tmCovariance parameter η (the t at momentm) probability density；p(η(tm)|η(tm-1)) represent in known tm-1The covariance at moment
Parameter η (tm-1) under conditions of, tmCovariance parameter η (the t at momentm) probability density；p(η(tm-1)|Yd(s,t1:m-1)) represent
In known t1To tm-1Moment observation data Yd(s,t1:m-1) under conditions of, tm-1Covariance parameter η (the t at momentm-1) probability it is close
Degree.
Again by formula 8, t is utilizedmThe observation data Y at momentd(s,tm) realize the renewal of covariance parameter, that is, seek covariance
The posterior probability Density Distribution p (η (t of parameterm)|Yd(s,t1:m))：
Wherein：
p(Yd(s,tm)|Yd(s,t1:m-1))=∫ p (Yd(s,tm)|η(tm))p(η(tm)|Yd(s,t1:m-1))dη(tm) (formula 9)
p(Yd(s,tm)|η(tm)) represent in tmCovariance parameter η (the t at momentm) under conditions of, Yd(s,tm) probability it is close
Degree.Because the distribution of parameter is nonnormal, therefore use particle filter method realizes the iterative calculation of Bayesian Estimation.
4) estimation obtains the temperature of any position in space-time temperature field
After covariance parameter estimation, observation data Y is givend(s, t), just can be realized to any position in temperature field's
The estimation of temperature.
Wherein,In tmMomentThe Temperature estimate value of point.
Below by example, the present invention will be further described.
Embodiment：
By taking Chinese Central China's a state grain storehouse as an example, the estimation of three-dimensional cereal temperature in storage process is set up
Model.Grain temperature data are collected by temperature sensor, are designated as observation data Yd(s, t), s ∈ S, t ∈ T, wherein S is represented
The space independent variable s of data span is observed, T represents to observe the time independent variable t of data span.In this example
In, S is defined as follows：The specification of cereal temperature is 26m*46m*6m, and the layout of sensor is in length and width direction neighboring sensor
Device at intervals of 5m, in short transverse adjacent sensors at intervals of 1.8m.T is defined as follows：The sampling time of grain temperature data
For on March 4,31 days to 2013 January in 2012, one group of sensing data was gathered every 7 days, totally 73 groups of data.
Three-Dimensional Dynamic cereal temperature estimation model is established below：
(1) framework of Mixed effect model is set up
Assuming that Y (s, t) represents temperature value of the three-dimensional temperature field in event (s, t), s and t difference representation spaces and time
Independent variable, the framework of Mixed effect model is
Y (s, t)=μ (s, t)+w (s, t)+∈ (s, t) (formula 1)
Wherein, μ (s, t) represents the mean value function at event (s, t) place, for portraying the global temperature change in temperature field
Change situation；W (s, t) represents the localized variation at event (s, t) place, for portraying the local temperature change feelings in temperature field
Condition；∈ (s, t) represents the random noise at event (s, t) place, warm as caused by random or uncontrollable factor for portraying
Situation of change is spent, it is white noise to usually assume that it.Below, by respectively to mean value function μ (s, t) and localized variation w (s, t)
Set up model.
(2) foundation and solution of mean value function μ (s, t) model
The change of cereal temperature is relevant with ambient temperature and grain itself heat transfer.Here, ambient temperature pair
The influence of cereal temperature, under cartesian coordinate system, three-dimensional unstable state Fourier heat transfer mould is set up to mean value function μ (s, t)
Type：
In formula 2, mean value function of μ (x, y, z, the t) expressions under cartesian coordinate system, its spatial coordinates s=x, y,
Z }, x, y and z are illustrated respectively in X, Y and the coordinate of Z-direction；ρ represents the density of material, and c represents the specific heat capacity of material, λx, λyWith
λzIt is illustrated respectively in thermal conductivity of the material along x, y and z directionss under three Cartesian coordinates.Grain variety in this example is small
Wheat, its density p is 750kg/m2, specific heat capacity c is 0.15W/ (mK), thermal conductivity λx, λy, λzFor 2000J/ (kgK).
Above-mentioned Fourier heat transfer model is solved using finite difference calculus, implementation method is：
Wherein, (i, j, k, m) represents t points of the corresponding grid position of spacetime coordinate (x, y, z, t), Δ x, Δ y, Δ z and Δ
Not Biao Shi space-time direction grid interval, i.e. Δ x=0.5m, Δ y=0.5m, Δ z=0.3m, Δ t=24h.Give initial grain
The temperature value (change of silo boundary temperature is as caused by ambient temperature) of temperature and boundary condition is eaten, using finite difference
Point-score is that the solution to mean value function can be achieved.
(3) localized variation w (s, t) foundation is solved with covariance parameter
Gaussian random field determines that model framework is：Assuming that in moment tm(m=1,2 ..., M), local temperature change has sky
Between stationarity, s is described using gaussian random field modeliThe relation of the temperature position temperature adjacent thereto of point, i.e., in given siPoint phase
Ortho position is put under conditions of temperature value, siThe temperature of point is with submitting to normal distribution：
Wherein, sj~siRepresent siAnd sjThe position of closest sensor in silo, ωij(tm) represent in tmWhen
The space weight parameter at quarter, σ2(si,tm) represent conditional variance.
Weight parameter ω is determined using Kriging modelij(tm), implementation method is：
Wherein, ωij(tm) represent siThe position s of its relative closest sensor in silo of pointjWeight ginseng
Number, C (si,sj) represent siWith sjCovariance matrix, C (sj,sj) represent sjBetween covariance matrix.Covariance matrix be by
Covariance function is calculated and obtained, and the expression formula of covariance function is as follows：
Wherein spAnd sqThe space coordinate at p and q points, under cartesian coordinate system, s are represented respectivelyp={ xp,yp,zpAnd
sq={ xq,yq,zq}；For in tmWhenThe parameter of covariance function is inscribed,
By η={ { η (t1),η(t2),…,{η(tM) it is designated as covariance parameter.
In initial time t1, use t1The observation data Y at momentd(s,t1), association side is solved using Maximum Likelihood Estimation
Poor parameter.In order to portray the temporal correlation in temperature field, using Bayesian Estimation method to t2To tMThe covariance parameter at moment enters
Row updates.Assuming that known t1To tm-1The covariance parameter and observation data Y at momentd(s,t1:m-1) (m=2 ..., M), pass through formula 7
Obtain tmThe prediction distribution of moment covariance parameter：
p(η(tm)|Yd(s,t1:m-1))=∫ p (η (tm)|η(tm-1))p(η(tm-1)|Yd(s,t1:m-1))dη(tm) (formula 7)
Wherein, p (η (tm)|Yd(s,t1:m-1)) represent in known t1To tm-1Moment observation data Yd(s,t1:m-1) condition
Under, tmCovariance parameter η (the t at momentm) probability density；p(η(tm)|η(tm-1)) represent in known tm-1The covariance at moment
Parameter η (tm-1) under conditions of, tmCovariance parameter η (the t at momentm) probability density；p(η(tm-1)|Yd(s,t1:m-1)) represent
In known t1To tm-1Moment observation data Yd(s,t1:m-1) under conditions of, tm-1Covariance parameter η (the t at momentm-1) probability it is close
Degree.
Again by formula 8, t is utilizedmThe observation data Y at momentd(s,tm) realize the renewal of covariance parameter, that is, seek covariance
The posterior probability Density Distribution p (η (t of parameterm)|Yd(s,t1:m))：
Wherein：
p(Yd(s,tm)|Yd(s,t1:m-1))=∫ p (Yd(s,tm)|η(tm))p(η(tm)|Yd(s,t1:m-1))dη(tm) (formula 9)
p(Yd(s,tm)|η(tm)) represent in tmCovariance parameter η (the t at momentm) under conditions of, Yd(s,tm) probability it is close
Degree.Because the distribution of parameter is nonnormal, therefore use particle filter method realizes the iterative calculation of Bayesian Estimation.Association side
The result of poor parameter Estimation is as shown in Figure 2.
(4) space-time temperature field is estimated
After covariance parameter estimation, observation data Y is givend(s, t), just can be realized to any position in temperature field's
The estimation of temperature.
Wherein,In tmMomentThe Temperature estimate value of point.Fig. 3 is cereal temperature change curve, lists one
Divide the estimated result of cereal temperature, wherein, numeral is the space coordinate of sampled point in legend.Fig. 3 shows, any locus
Temperature be generation dynamic change over time, and the temperature changing regularity of adjacent space position is close.
It should be noted that the purpose for publicizing and implementing example is that help further understands the present invention, but the skill of this area
Art personnel are appreciated that：Do not departing from the present invention and spirit and scope of the appended claims, various substitutions and modifications are all
It is possible.Therefore, the present invention should not be limited to embodiment disclosure of that, and the scope of protection of present invention is with claim
The scope that book is defined is defined.
Claims (5)
1. a kind of three dimensional temperature sensing data analysis method coupled based on space-time dynamic, utilizes the temperature field for reflecting heat-transfer mechanism
Physical model and the statistical model based on temporal correlation, set up Mixed effect model, three dimensional temperature sensing data are divided
Analysis, obtains the dynamic temperature value of any locus in three-dimensional temperature field；Comprise the following steps：
1) using temperature field physical model and the statistical model based on temporal correlation, set up Mixed effect model and represent event
The temperature value of (s, t)；The temperature value Y (s, t) of certain event (s, t) represents to include：Represent the global temperature change in temperature field
Mean value function μ (s, t), represent temperature field local temperature change localized variation w (s, t) and represent by random or can not
The random noise ∈ (s, t) of temperature change caused by control factor；
2) mean value function μ (s, t) is modeled and solved：Three-dimensional thermodynamical model is set up as mean value model, using having
Limit calculus of finite differences is solved to the mean value model, obtains the average of temperature field global temperature change；
3) local temperature for representing temperature field using Gaussian random field and Kriging model changes, to the localized variation w (s,
T) model and solve, obtain model parameter；
4) temperature value in estimation space-time temperature field：
Given observation data Y, is calculated by formula 10, obtained to any position in temperature fieldTemperature value estimation：
Wherein,In tmMomentThe Temperature estimate value of point；For tmMomentThe global temperature change of point
Average；ωi*j(tm) represent in tmThe space weight at moment；Y(sj,tm) it is given tmMoment sjThe temperature value of point；μ(sj,tm)
For tmMoment sjThe average of office's temperature change of point.
2. temperature sensing data analysis method as claimed in claim 1, it is characterized in that, step 1) certain event (s, t)
Temperature value Y (s, t) is embodied as formula 1：
Y (s, t)=μ (s, t)+w (s, t)+∈ (s, t) (formula 1)
The temperature value Y (s, t) of certain event (s, t) by represent the global temperature change in temperature field mean value function μ (s,
T), represent the localized variation w (s, t) of the local temperature change in temperature field and represent warm as caused by random or uncontrollable factor
Random noise ∈ (s, the t) additions for spending change are obtained.
3. temperature sensing data analysis method as claimed in claim 1, it is characterized in that, step 2) to the mean value function μ (s,
T) model and solve, specifically include following steps：
B1. mean value model is set up：Consider the influence of environmental factor, under cartesian coordinate system, mean value function μ (s, t) is built
Vertical three-dimensional unstable state Fourier's heat transfer model is as follows：
In formula 2, mean value function of μ (x, y, z, the t) expressions under cartesian coordinate system, its spatial coordinates s={ x, y, z },
X, y and z are illustrated respectively in X, Y and the coordinate of Z-direction；ρ represents the density of material, and c represents the specific heat capacity of material, λx, λyAnd λzPoint
Thermal conductivity of the material along x, y and z directionss under three Cartesian coordinates is not represented；
B2. mean value model is solved：
Using finite difference calculus, using formula 3, initial temperature and boundary condition are given, the mean value model of above-mentioned formula 2 is asked
Solution：
Wherein, the corresponding grid position of (i, j, k, m) denotation coordination (x, y, z, t), Δ x, Δ y, Δ z and Δ t represent empty respectively
Between, the grid interval of time orientation.
4. temperature sensing data analysis method as claimed in claim 3, it is characterized in that, in step B2, parameter valueWherein, ρ represents the density of material, and c represents the specific heat capacity of material, λx, λyAnd λzRepresent respectively
Thermal conductivity of the material along x, y and z directionss under three Cartesian coordinates；Δ x, Δ y, Δ z and Δ t difference representation space, when
Between direction grid interval.
5. temperature sensing data analysis method as claimed in claim 1, it is characterized in that, step 3) to the localized variation w (s,
T) model and solve, comprise the following steps：
C1. model is determined using Gaussian random field：
Assuming that in moment tm(m=1,2 ..., M), local temperature change has spatial stationarity property, is retouched using gaussian random field model
State siThe relation of the temperature position temperature adjacent thereto of point, i.e., in given siUnder conditions of point adjacent position temperature value, siThe temperature of point
Spend and submit to the normal distribution of formula 4：
Wherein, sj~siRepresent siAnd sjAdjacent position, ω are in Gaussian random fieldij(tm) represent in tmThe space right at moment
Weight parameter, σ2(si,tm) represent conditional variance；
C2. weight parameter is determined using Kriging model
Using Kriging model, weight parameter ω is determined by formula 5ij(tm)：
Wherein, C (si,sj) represent siWith sjCovariance matrix, C (sj,sj) represent sjBetween covariance matrix；Covariance square
Battle array is determined by the covariance function of formula 6：
Wherein, spAnd sqThe space coordinate at p and q points, under cartesian coordinate system, s are represented respectivelyp={ xp,yp,zqAnd sq=
{xq,yq,zq}；For in tmWhen inscribe the parameter of covariance function；By η
={ { η (t1),η(t2),…,{η(tM) it is designated as covariance parameter；
C3. the covariance parameter is solved：
In initial time t1, covariance parameter is solved using Maximum Likelihood Estimation；Using Bayesian Estimation method to t2To tM
The covariance parameter at moment is updated；
Assuming that known t1To tm-1The covariance parameter and temperature data at (m=2 ..., M) moment, t is obtained by formula 7mMoment association side
The prediction distribution of poor parameter：
p(η(tm)|Y(s,t1:m-1))=∫ p (η (tm)|η(tm-1))p(η(tm-1)|Y(s,t1:m-1))dη(tm) (formula 7)
Wherein, p (η (tm)|Y(s,t1:m-1)) represent in known t1To tm-1Moment temperature data Y (s, t1:m-1) under conditions of, tmWhen
Covariance parameter η (the t at quarterm) probability density；p(η(tm)|η(tm-1)) represent in known tm-1The covariance parameter η at moment
(tm-1) under conditions of, tmCovariance parameter η (the t at momentm) probability density；p(η(tm-1)|Y(s,t1:m-1)) represent known
t1To tm-1Moment temperature data Y (s, t1:m-1) under conditions of, tm-1Covariance parameter η (the t at momentm-1) probability density；
Again by formula 8, t is utilizedmThe temperature data at moment realizes the renewal of covariance parameter, that is, asks the posteriority of covariance parameter general
Rate Density Distribution p (η (tm)|Y(s,t1:m))：
Wherein,
p(Y(s,tm)|Y(s,t1:m-1))=∫ p (Y (s, tm)|η(tm))p(η(tm)|Y(s,t1:m-1))dη(tm) (formula 9)
p(Y(s,tm)|η(tm)) represent in tmCovariance parameter η (the t at momentm) under conditions of, Y (s, tm) probability density.
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