CN107122520B - Three-dimensional temperature sensing data analysis method based on space-time dynamic coupling - Google Patents

Three-dimensional temperature sensing data analysis method based on space-time dynamic coupling Download PDF

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CN107122520B
CN107122520B CN201710188585.8A CN201710188585A CN107122520B CN 107122520 B CN107122520 B CN 107122520B CN 201710188585 A CN201710188585 A CN 201710188585A CN 107122520 B CN107122520 B CN 107122520B
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王迪
张玺
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Peking University
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Abstract

The invention discloses a three-dimensional temperature sensing data analysis method based on space-time dynamic coupling, which utilizes a temperature field physical model reflecting a heat transfer mechanism and a statistical model based on space-time correlation to establish a mixed effect model and analyze three-dimensional temperature sensing data to obtain a dynamic temperature value of any space position in a space-time three-dimensional temperature field, namely a temperature value of any space position or any moment. According to the technical scheme provided by the invention, a temperature field physical model reflecting a heat transfer mechanism is combined with a statistical model based on space-time correlation to establish a mixed effect model, so that the estimation of a three-dimensional dynamic temperature field is realized, accurate and comprehensive information is provided for real-time monitoring of the temperature field, the optimal configuration of a sensor in the temperature field is facilitated, and the effects of reducing cost and saving energy are achieved.

Description

Three-dimensional temperature sensing data analysis method based on space-time dynamic coupling
Technical Field
The invention provides a dynamic data analysis method of a three-dimensional temperature field, particularly relates to a three-dimensional temperature sensing data analysis method based on space-time dynamic coupling, and belongs to the field of industrial engineering.
Background
The dynamic data analysis technology of the temperature field plays an important role in the engineering field and provides important information for engineering tasks such as improving the product quality and improving the system performance. In recent years, the technology attracts extensive attention of scientific research and engineering personnel, and has been applied to the engineering fields of ecology, meteorology, health care, grain storage and the like. The dynamic data analysis technology of the temperature field can provide comprehensive and accurate information for monitoring of a complex system, and the effect of improving the system performance or the service quality is achieved. Meanwhile, the technology is beneficial to the optimization design of the engineering structure, and the aims of saving resources and reducing cost are fulfilled.
The dynamic data analysis technology of the temperature field aims to realize accurate estimation of the temperature field. The traditional temperature field estimation method is a simulation method based on the heat transfer principle. In documents [1] to [2], the method considers external factors such as environmental factors and internal heat transfer mechanisms affecting the change of the temperature field, establishes a three-dimensional thermodynamic model by setting initial temperature and boundary conditions, and realizes the estimation of the three-dimensional dynamic temperature field. However, the change in the temperature field is affected not only by external factors but also by internal factors and other various uncertain factors. The temperature field can be regarded as a complex heat transfer system that varies in space and time. The traditional temperature field estimation method can only depict the outline and the trend of the temperature field change under the ideal state. For local temperature changes caused by internal factors, which often occur in temperature fields, this method is no longer suitable. Therefore, the conventional temperature field estimation method has a large error, and cannot provide high-precision temperature field information.
With the development of the times, wireless sensor technology is widely applied to the engineering field (such as document [3 ]). The technology collects temperature data through a wireless sensor and establishes a temperature field estimation model by using the data. Due to the limitation of the configuration cost of the sensors, the number of the sensors installed in a temperature field is small at present, and only a small part of sparse observation data can be acquired through the sensors. The sparseness of the observation data can cause the accuracy of the temperature field estimation model to be greatly reduced. Meanwhile, the temperature data acquired by the sensor has measurement errors, which also reduces the accuracy of the temperature field estimation model. Therefore, a method that relies solely on wireless sensor technology in combination with a mathematical model cannot achieve accurate estimation of the temperature field.
In addition, as a complex heat transfer system, the temperature data of adjacent positions or adjacent moments of a three-dimensional temperature field has time and space correlation, and the time and space correlation of the temperature data is interactive, namely, the time correlation, the space correlation and the space and space correlation exist among the data. The description of the characteristic of the temperature field in the existing research is mostly carried out under the assumption that the time correlation and the space correlation are mutually independent, the space-time correlation of data is not considered, and the consideration and the estimation of the space-time correlation of the three-dimensional dynamic temperature field are difficult to realize.
Reference to the literature
[1]D.Wang and X.Zhang,“A prediction method for interior temperatureof grain storage via dynamics model:a simulation study”,Proceed-ings of IEEEInternational Conference of Automation Science and Engineering,pp.1477-1483,2015.
[2]C.Jia,D.Sun and C.Cao,“Finite element prediction of transienttemperature distribution in a grain storage bin”,Journal of AgriculturalEngineering Research,vol.76,no.4,pp.323–330,2000.
[3]Y.Ding,E.A.Elsayed,S.Kumara,J.Lu,F.Niu and J.Shi,“Distributedsensing for quality and productivity improvements”,IEEE Transactions onAutomation Science and Engineering,vol.3,no.4,pp.344–359,2006.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a three-dimensional temperature sensing data analysis method based on space-time dynamic coupling, which combines a temperature field physical model reflecting a heat transfer mechanism and a statistical model based on space-time correlation under the framework of a mixed effect model to realize the estimation of a three-dimensional dynamic temperature field. The invention can solve the problem that accurate and comprehensive temperature field information cannot be obtained due to insufficient sensor data in the engineering field at present, can obtain the comprehensive and accurate information of the temperature field, and provides a basis for monitoring, decision making and other measures in the engineering field.
The technical scheme provided by the invention is as follows:
a three-dimensional temperature sensing data analysis method based on space-time dynamic coupling utilizes a temperature field physical model reflecting a heat transfer mechanism and a statistical model based on space-time correlation to establish a mixed effect model and analyze three-dimensional temperature sensing data to obtain a dynamic temperature value (namely a temperature value at any space position or any moment) at a three-dimensional space position; the method comprises the following steps:
1) establishing a mixed effect model framework by utilizing a temperature field physical model and a statistical model based on space-time correlation, wherein the temperature value of a certain time-space point of a three-dimensional temperature field comprises a mean function term representing the global temperature change of the temperature field, a local change term representing the local temperature change of the temperature field and a random noise term representing the temperature change caused by random or uncontrollable factors;
the mixed effect model framework is established as follows:
assuming that Y (s, t) represents the temperature value of the three-dimensional temperature field at the space-time point (s, t), and s and t represent independent variables of space and time respectively, the framework of the mixed effect model is as follows:
y (s, t) ═ μ (s, t) + w (s, t) + e (s, t) (formula 1)
Wherein, mu (s, t) represents a mean function term at a space-time point (s, t) and is used for describing the global temperature change condition of the temperature field; w (s, t) represents a local variation term at a time-space point (s, t) and is used for describing the local temperature variation condition of the temperature field; e (s, t) represents a random noise term at the point in time space (s, t) to characterize the temperature variation caused by random or uncontrollable factors, which is usually assumed to be white noise. In the following, the mean function term μ (s, t) and the local variation term w (s, t) will be modeled separately.
2) The mean function item mu (s, t) is modeled by the following method:
B1. establishing a mean model:
the change in the temperature field is typically caused by environmental factors. In the invention, the influence of environmental factors is fully considered, and a three-dimensional unsteady Fourier heat transfer model is established for a mean function item mu (s, t) under a Cartesian coordinate system:
Figure GDA0002446187260000031
in equation 2, μ (x, y, Z, t) represents a mean function term in a cartesian coordinate system, where spatial coordinates s ═ x, y, Z, and x, y, and Z represent coordinates in X, Y and Z directions, respectively; ρ represents the density of the substance, c represents the specific heat capacity of the substance, and λx，λyAnd λzWhich represents the thermal conductivity of a substance in the X, Y and Z directions, respectively, in a three-dimensional cartesian coordinate system.
B2. Solving of mean model
Solving equation 2 by using equation 3 by using a finite difference method:
Figure GDA0002446187260000032
wherein, (i, j, k, m) represents a grid position corresponding to the coordinates (x, y, z, t), and Δ x, Δ y, Δ z represent grid intervals in the spatial direction, respectively; Δ t represents a grid interval in the time direction. To ensure the accuracy of the numerical solution, the parameter values are selected to ensure
Figure GDA0002446187260000033
Given initial temperature and boundary conditions, the solution of the mean function can be realized by adopting a finite difference method.
3) The modeling of the local variation term w (s, t) is realized by the following method:
the spatial-temporal correlation of the temperature field is fully considered, and the local temperature change of the temperature field is characterized by adopting a method of combining a Gaussian random field and a Krigin model.
C1. Determining a model framework using Gaussian random fields
Suppose that at time tm(M ═ 1,2, …, M), local temperature changes are spatially smooth, and s is described using a Gaussian random field modeliTemperature of a point in relation to temperature of its adjacent location, i.e. at a given siUnder the condition of temperature values of adjacent points, siThe temperature of the spot is subject to a normal distribution:
Figure GDA0002446187260000041
wherein s isj～siDenotes siAnd sjIn adjacent positions, ω, in a Gaussian random fieldij(tm) Is shown at tmSpatial weight parameter at time, σ2(si,tm) The conditional variance is indicated.
C2. Determining weight parameters using a kriging model
Determining a weight parameter omega by equation 5 using a kriging modelij(tm)：
Figure GDA0002446187260000042
Wherein, C(s)i,sj) Denotes siAnd sjCovariance matrix of C(s)j,sj) Denotes sjThe covariance matrix in between. The covariance matrix is determined by a covariance function, which is expressed as equation 6:
Figure GDA0002446187260000043
wherein s ispAnd sqRespectively representing the spatial coordinates at the p and q points, s being in a Cartesian coordinate systemp＝{xp,yp,zpAnd sq＝{xq,yq,zq}；
Figure GDA0002446187260000044
Is tmThe covariance parameters at all times are represented as η ═ η (t) for the covariance parameters at all times1),η(t2),…,η(tM)}。
C3. Covariance parameter solution
At an initial time t1Solving for t by using maximum likelihood estimation method1A covariance parameter of the time of day. In order to depict the time correlation of the temperature field, a Bayesian estimation method is adopted to carry out on t2To tMThe covariance parameters at the moment are updated. Let it be known that t1To tm-1The time covariance parameter and the temperature data (M2, …, M) are obtained by equation 7 as tmPrediction distribution of covariance parameters at time:
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 (t)m)|Y(s,t1:m-1) Is represented at known t)1To tm-1Time of day temperature data Y (s, t)1:m-1) Under the condition of (1), tmCovariance parameter of time η (t)m) P (η (t)m)|η(tm-1) Is represented at known t)m-1Covariance parameter of time η (t)m-1) Under the condition of (1), tmCovariance parameter of time η (t)m) P (η (t)m-1)|Y(s,t1:m-1) Is represented at known t)1To tm-1Time of day temperature data Y (s, t)1:m-1) Under the condition of (1), tm-1Covariance parameter of time η (t)m-1) The probability density of (c).
And then by equation 8, using tmImplementation of temperature data at time tmUpdating the covariance parameter at that moment, i.e. finding tmPosterior probability density distribution p (η (t) of covariance parameter at timem)|Y(s,t1:m))：
Figure GDA0002446187260000051
Wherein the content of the first and second substances,
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) Is represented at t)mCovariance parameter of time η (t)m) Under the condition of (1), Y (s, t)m) The probability density of (c). Because the distribution of the covariance parameters is abnormal, the iterative calculation of Bayesian estimation is realized by adopting a particle filtering method.
4) The space-time temperature field estimation method comprises the following steps:
after parameter estimation, given the observed data, we can implement the equation 10 for any position s in the temperature fieldiEstimation of temperature value of (a):
Figure GDA0002446187260000052
wherein the content of the first and second substances,
Figure GDA0002446187260000053
at tmTime siAn estimate of the temperature of the spot.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a three-dimensional temperature sensing data analysis method based on space-time dynamic coupling, which is characterized in that a mixed effect model is established by utilizing a temperature field physical model reflecting a heat transfer mechanism and a statistical model based on space-time correlation, and three-dimensional temperature sensing data is analyzed to obtain a dynamic temperature value (namely a temperature value at any space position or any moment) of any space position in a three-dimensional temperature field. According to the technical scheme provided by the invention, a temperature field physical model reflecting a heat transfer mechanism is combined with a statistical model based on space-time correlation to establish a mixed effect model, so that the estimation of a three-dimensional dynamic temperature field is realized, accurate and comprehensive information is provided for real-time monitoring of the temperature field, the optimal configuration of a sensor in the temperature field is facilitated, and the effects of reducing cost and saving energy are achieved.
Drawings
FIG. 1 is a flow chart of a three-dimensional temperature sensing data analysis method based on spatio-temporal dynamic coupling provided by the invention.
FIG. 2 is a result of covariance parameter estimation according to an embodiment of the invention;
wherein, the abscissa is time, and the unit is day; the ordinate is a covariance parameter value at a certain time; (a) is a parameter axAn estimated value of (d); (b) is a parameter ayAn estimated value of (d); (c) is a parameter azAn estimated value of (d); (d) as a parameter
Figure GDA0002446187260000061
An estimate of (d).
FIG. 3 is an estimation result of a grain temperature field according to an embodiment of the present invention;
where the numbers in the legend are the spatial coordinates of the sample points.
Detailed Description
The invention will be further described by way of examples, without in any way limiting the scope of the invention, with reference to the accompanying drawings.
The invention provides a three-dimensional temperature sensing data analysis method based on space-time dynamic coupling, which combines a temperature field physical model reflecting a heat transfer mechanism with a statistical model based on space-time correlation under the framework of a mixed effect model to realize the estimation of a three-dimensional dynamic temperature field. The invention can solve the problem that accurate and comprehensive temperature field information cannot be obtained due to insufficient sensor data in the engineering field at present, can obtain the comprehensive and accurate information of the temperature field, and provides a basis for monitoring, decision making and other measures in the engineering field.
FIG. 1 is a flow chart of a three-dimensional temperature sensing data analysis method based on spatio-temporal dynamic coupling provided by the invention. In the examples, the temperature field was set to (-50 ℃ C., 50 ℃ C.), temperature data was collected by a sensor at a time interval of 7 days, and the collected observation data was expressedIs Yd(s, t). The specific embodiment of analyzing the three-dimensional temperature sensing data by using the method of the present invention is as follows.
1) And establishing a mixed effect model according to the characteristics of the temperature field of the research object.
The research object can be any material temperature field related to a temperature field in the engineering field, such as a grain temperature field in storage, an environment temperature field in a certain area, and a human body temperature field. The framework of the mixed effects model is as follows: assuming that Y (s, t) represents the temperature value of the three-dimensional temperature field at the space-time point (s, t), and s and t represent independent variables of space and time respectively, the framework of the mixed effect model is as follows:
y (s, t) ═ μ (s, t) + w (s, t) + e (s, t) (formula 1)
Wherein, mu (s, t) represents a mean function term at a space-time point (s, t) and is used for describing the global temperature change condition of the temperature field; w (s, t) represents a local variation term at a time-space point (s, t) and is used for describing the local temperature variation condition of the temperature field; e (s, t) represents a random noise term at the point in time space (s, t) to characterize the temperature variation caused by random or uncontrollable factors, which is usually assumed to be white noise. In the following, the mean function term μ (s, t) and the local variation term w (s, t) will be modeled separately.
2) Modeling of mean function term μ (s, t)
And (4) fully considering the physical properties of the research object, establishing a mean value model and solving.
B1. Establishment of mean model
The change in the temperature field is typically caused by environmental factors. In the invention, the influence of environmental factors is fully considered, and a three-dimensional unsteady Fourier heat transfer model is established for a mean function item mu (s, t) under a Cartesian coordinate system:
Figure GDA0002446187260000071
in equation 2, μ (x, y, Z, t) represents a mean function term in a cartesian coordinate system, where spatial coordinates s ═ x, y, Z, and x, y, and Z represent coordinates in X, Y and Z directions, respectively; ρ represents the density of the substance, and c represents the ratio of the substancesHeat capacity, λx，λyAnd λzWhich represents the thermal conductivity of a substance in the X, Y and Z directions, respectively, in a three-dimensional cartesian coordinate system.
B2. Solving of mean model
Solving the formula 2 by using a finite difference method, wherein the implementation method comprises the following steps:
Figure GDA0002446187260000072
wherein (i, j, k, m) represents a grid position corresponding to the coordinates (x, y, z, t), and Δ x, Δ y, Δ z represent grid intervals in the spatial direction, respectively; Δ t represents a grid interval in the time direction. To ensure the accuracy of the numerical solution, the parameters are selected to ensure
Figure GDA0002446187260000073
Given initial temperature value and boundary temperature value, the solution of the mean value function can be realized by adopting a finite difference method.
The mean value model is established based on the physical meaning of the study object, does not relate to the observation data of the temperature field, and is used for describing the global change of the temperature field under the ideal state.
3) Modeling of local variation term w (s, t)
And (3) fully considering the space-time correlation of the temperature field, and establishing a local temperature change model by combining the Gaussian random field and the Kriging model.
C1. Gaussian random field determination model framework
Suppose that at time tm(M ═ 1,2, …, M), local temperature changes are spatially smooth, and s is described using a Gaussian random field modeliTemperature of a point in relation to temperature of its adjacent location, i.e. at a given siUnder the condition of temperature values of adjacent points, siThe temperature of the spot is subject to a normal distribution:
Figure GDA0002446187260000081
wherein s isj～siDenotes siAnd sjIn Gauss randomIn adjacent positions in the field, ωij(tm) Is shown at tmSpatial weight parameter at time, σ2(si,tm) The conditional variance is indicated.
C2. Determining weight parameters by a kriging model
Determining a weight parameter omega using a kriging modelij(tm) The realization method comprises the following steps:
Figure GDA0002446187260000082
wherein, ω isij(tm) Denotes siThe point being in relation to all its neighbours sjWeight parameter of C(s)i,sj) Denotes siAnd sjCovariance matrix of C(s)j,sj) Denotes sjThe covariance matrix in between. The covariance matrix is calculated from a covariance function, which has the following expression:
Figure GDA0002446187260000083
wherein s ispAnd sqRespectively representing the spatial coordinates at the p and q points, s being in a Cartesian coordinate systemp＝{xp,yp,zpAnd sq＝{xq,yq,zq}；
Figure GDA0002446187260000084
Is tmThe covariance parameter at all times is represented as η ═ { η (t) } (t)1),η(t2),…,η(tM)}。
C3. Covariance parameter solution
At an initial time t1Using t1Observation data Y of timed(s,t1) And solving the covariance parameters by adopting a maximum likelihood estimation method. In order to depict the time correlation of the temperature field, a Bayesian estimation method is adopted to carry out on t2To tMThe covariance parameters at the moment are updated. FalseLet known t1To tm-1Time covariance parameter and observation data Yd(s,t1:m-1) (M-2, …, M), and t is obtained by formula 7mPrediction distribution of time covariance parameters:
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 (t)m)|Yd(s,t1:m-1) Is represented at known t)1To tm-1Time of day observation data Yd(s,t1:m-1) Under the condition of (1), tmCovariance parameter of time η (t)m) P (η (t)m)|η(tm-1) Is represented at known t)m-1Covariance parameter of time η (t)m-1) Under the condition of (1), tmCovariance parameter of time η (t)m) P (η (t)m-1)|Yd(s,t1:m-1) Is represented at known t)1To tm-1Time of day observation data Yd(s,t1:m-1) Under the condition of (1), tm-1Covariance parameter of time η (t)m-1) The probability density of (c).
And then by equation 8, using tmObservation data Y of timed(s,tm) Updating of the covariance parameter is achieved by finding the posterior probability density distribution p (η (t)m)|Yd(s,t1:m))：
Figure GDA0002446187260000091
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) Is represented at t)mCovariance parameter of time η (t)m) Under the condition of (A) Yd(s,tm) The probability density of (c). Because the distribution of the covariance parameters is abnormal, the iterative calculation of Bayesian estimation is realized by adopting a particle filtering method.
4) Estimating the temperature of any position in the space-time temperature field
Given the observed data Y after covariance parameter estimationd(s, t), any position s in the temperature field can be realizediIs estimated.
Figure GDA0002446187260000092
Wherein the content of the first and second substances,
Figure GDA0002446187260000093
at tmTime siAn estimate of the temperature of the spot.
The invention is further illustrated by the following examples.
Example (b):
taking a reserve grain depot of a certain country in China as an example, an estimation model of a three-dimensional grain temperature field in the storage process is established. The grain temperature data is acquired by a temperature sensor and recorded as observation data YdIn the example, S is defined as that the specification of a grain temperature field is 26m 46m 6m, the layout of the sensors is 5m in the length direction and the width direction, the interval of the sensors in the height direction is 1.8 m.T, the sampling time of the grain temperature data is 1 month 31 days 2012 to 3 months 4 days 2013, one group of sensor data is collected every 7 days, and 73 groups of data are collected.
Establishing a three-dimensional dynamic grain temperature field estimation model as follows:
(1) framework for establishing mixed effect model
Assuming that Y (s, t) represents the temperature value of the three-dimensional temperature field at the space-time point (s, t), s and t represent independent variables of space and time respectively, the framework of the mixed effect model is
Y (s, t) ═ μ (s, t) + w (s, t) + e (s, t) (formula 1)
Wherein, mu (s, t) represents a mean function term at a space-time point (s, t) and is used for describing the global temperature change condition of the temperature field; w (s, t) represents a local variation term at a time-space point (s, t) and is used for describing the local temperature variation condition of the temperature field; e (s, t) represents a random noise term at the point in time space (s, t) to characterize the temperature variation caused by random or uncontrollable factors, which is usually assumed to be white noise. In the following, the mean function term μ (s, t) and the local variation term w (s, t) will be modeled separately.
(2) Establishment and solution of mean function mu (s, t) model
The change of the grain temperature field is related to the external environment temperature and the heat transfer of the grain. Here, the influence of the external environment temperature on the grain temperature is to establish a three-dimensional unsteady fourier heat transfer model for the mean function term μ (s, t) in a cartesian coordinate system:
Figure GDA0002446187260000101
in equation 2, μ (x, y, Z, t) represents a mean function term in a cartesian coordinate system, where spatial coordinates s ═ x, y, Z, and x, y, and Z represent coordinates in X, Y and Z directions, respectively; ρ represents the density of the substance, c represents the specific heat capacity of the substance, and λx，λyAnd λzWhich represents the thermal conductivity of a substance in the X, Y and Z directions, respectively, in a three-dimensional cartesian coordinate system. The grain variety in this example is wheat with a density ρ of 750kg/m2The specific heat capacity c is 0.15W/(m.K), and the thermal conductivity lambda isx，λy，λzThe ratio was 2000J/(kg. K).
Solving the Fourier heat transfer model by adopting a finite difference method, wherein the realization method comprises the following steps:
Figure GDA0002446187260000102
where, (i, j, k, m) represents a grid position corresponding to a space-time coordinate (x, y, z, t), and Δ x, Δ y, Δ z, and Δ t represent grid intervals in a space-time direction, respectively, that is, Δ x is 0.5m, Δ y is 0.5m, Δ z is 0.3m, and Δ t is 24 h. Given initial grain temperature and temperature value of boundary condition (the change of the boundary temperature of the granary is caused by the external environment temperature), the solution of the mean value function can be realized by adopting a finite difference method.
(3) Establishment of local variation term w (s, t) and covariance parameter solution
The Gaussian random field determination model framework is as follows: suppose that at time tm(M ═ 1,2, …, M), local temperature changes are spatially smooth, and s is described using a Gaussian random field modeliTemperature of a point in relation to temperature of its adjacent location, i.e. at a given siUnder the condition of temperature values of adjacent points, siThe temperature of the spot is subject to a normal distribution:
Figure GDA0002446187260000111
wherein s isj～siDenotes siAnd sjPosition of nearest sensor in granary, ωij(tm) Is shown at tmSpatial weight parameter at time, σ2(si,tm) The conditional variance is indicated.
Determining a weight parameter omega using a kriging modelij(tm) The realization method comprises the following steps:
Figure GDA0002446187260000112
wherein, ω isij(tm) Denotes siPosition s of a point relative to its nearest sensor in the grain binjWeight parameter of C(s)i,sj) Denotes siAnd sjCovariance matrix of C(s)j,sj) Denotes sjThe covariance matrix in between. The covariance matrix is calculated from a covariance function, which has the following expression:
Figure GDA0002446187260000113
wherein s ispAnd sqRespectively representing the spatial coordinates at the p and q points, s being in a Cartesian coordinate systemp＝{xp,yp,zpAnd sq＝{xq,yq,zq}；
Figure GDA0002446187260000114
Is tmThe covariance parameter at all times is represented as η ═ { η (t) } (t)1),η(t2),…,η(tM)}。
At an initial time t1Using t1Observation data Y of timed(s,t1) And solving the covariance parameters by adopting a maximum likelihood estimation method. In order to depict the time correlation of the temperature field, a Bayesian estimation method is adopted to carry out on t2To tMThe covariance parameters at the moment are updated. Let it be known that t1To tm-1Time covariance parameter and observation data Yd(s,t1:m-1) (M-2, …, M), and t is obtained by formula 7mPrediction distribution of time covariance parameters:
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 (t)m)|Yd(s,t1:m-1) Is represented at known t)1To tm-1Time of day observation data Yd(s,t1:m-1) Under the condition of (1), tmCovariance parameter of time η (t)m) P (η (t)m)|η(tm-1) Is represented at known t)m-1Covariance parameter of time η (t)m-1) Under the condition of (1), tmCovariance parameter of time η (t)m) P (η (t)m-1)|Yd(s,t1:m-1) Is represented at known t)1To tm-1Time of day observation data Yd(s,t1:m-1) Under the condition of (1), tm-1Covariance parameter of time η (t)m-1) The probability density of (c).
And then by equation 8, using tmObservation data Y of timed(s,tm) Realization of tmUpdating the covariance parameter at that moment, i.e. finding tmPosterior probability density distribution p (η (t) of covariance parameter at timem)|Yd(s,t1:m))：
Figure GDA0002446187260000121
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) Is represented at t)mCovariance parameter of time η (t)m) Under the condition of (A) Yd(s,tm) The probability density of (c). Because the distribution of the covariance parameters is abnormal, the iterative calculation of Bayesian estimation is realized by adopting a particle filtering method. The result of the covariance parameter estimation is shown in fig. 2.
(4) Spatio-temporal temperature field estimation
Given the observed data Y after covariance parameter estimationd(s, t), any position s in the temperature field can be realizediIs estimated.
Figure GDA0002446187260000122
Wherein the content of the first and second substances,
Figure GDA0002446187260000123
at tmTime siAn estimate of the temperature of the spot. Fig. 3 is a graph of the variation of grain temperature illustrating the estimation of a portion of the grain temperature field, wherein the numbers in the legend are the spatial coordinates of the sampling points. Fig. 3 shows that the temperature of any spatial position dynamically changes with time, and the temperature change law of adjacent spatial positions is similar.
It is noted that the disclosed embodiments are intended to aid in further understanding of the invention, but those skilled in the art will appreciate that: various substitutions and modifications are possible without departing from the spirit and scope of the invention and appended claims. Therefore, the invention should not be limited to the embodiments disclosed, but the scope of the invention is defined by the appended claims.

Claims (4)

1. A three-dimensional temperature sensing data analysis method based on space-time dynamic coupling utilizes a temperature field physical model reflecting a heat transfer mechanism and a statistical model based on space-time correlation to establish a mixed effect model, analyzes three-dimensional temperature sensing data and obtains a dynamic temperature value of any space position in a three-dimensional temperature field; the method comprises the following steps:
1) establishing a mixed effect model to represent a temperature value of a space-time point (s, t) by utilizing a temperature field physical model and a statistical model based on space-time correlation; the temperature value Y (s, t) for a time bin (s, t) is represented by: a mean function term μ (s, t) representing the global temperature variation of the temperature field, a local variation term w (s, t) representing the local temperature variation of the temperature field, and a random noise term e (s, t) representing the temperature variation caused by random or uncontrollable factors;
2) modeling and solving the mean function term μ (s, t): establishing a three-dimensional thermodynamic model as a mean model, and solving the mean model by adopting a finite difference method to obtain a mean value of the global temperature change of the temperature field;
3) adopting a Gaussian random field and a Krigin model to represent local temperature change of a temperature field, modeling and solving the local change item w (s, t) to obtain model parameters; the method comprises the following steps:
C1. determining a model by adopting a Gaussian random field:
suppose that at time tm(M ═ 1, 2.. said., M), local temperature variations are spatially smooth, and s is described using a gaussian random field modeliTemperature of a point in relation to temperature of its adjacent location, i.e. at a given siUnder the condition of temperature values of adjacent points, siTemperature of point and obedience of formulaNormal distribution of 4:
Figure FDA0002457751210000011
wherein s isj～siDenotes siAnd sjIn adjacent positions, ω, in a Gaussian random fieldij(tm) Denotes si～sjAt tmSpatial weight parameter at time, σ2(si，tm) Represents a conditional variance; w(s)i，tm) Representing a point of space-time(s)i，tm) A local variation term of the local temperature variation of (a);
C2. determining weight parameters by adopting a kriging model:
determining a weight parameter omega by equation 5 using a kriging modelij(tm)：
Figure FDA0002457751210000012
Wherein the content of the first and second substances,
Figure FDA0002457751210000013
represents tmTime siAnd sjThe covariance matrix of (a) is determined,
Figure FDA0002457751210000014
represents tmTime sjA covariance matrix between; the covariance matrix is determined by the covariance function of equation 6:
Figure FDA0002457751210000015
wherein s ispAnd sqRespectively representing the spatial coordinates at the p and q points, s being in a Cartesian coordinate systemp＝{xp，yp，zpAnd sq＝{xq，yq，zq}；
Figure FDA0002457751210000021
Is at tmThe covariance parameters at all the time points are recorded as η ═ η (t)1)，η(t2)，...，η(tM)}；
C3. Solving covariance parameters:
at an initial time t1Solving for the time t by using a maximum likelihood estimation method1A covariance parameter of (a); using Bayesian estimation method to pair t2To tMUpdating the covariance parameters of the moment;
let it be known that t1To tm-1The covariance parameter and temperature data at time (M ═ 2.., M) are obtained by equation 7 as tmPrediction distribution of time covariance parameters:
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 (t)m)|Y(s，t1：m-1) Is represented at known t)1To tm-1Time of day temperature data Y (s, t)1：m-1) Under the condition of (1), tmCovariance parameter of time η (t)m) P (η (t)m)|η(tm-1) Is represented at known t)m-1Covariance parameter of time η (t)m-1) Under the condition of (1), tmCovariance parameter of time η (t)m) P (η (t)m-1)|Y(s，t1：m-1) Is represented at known t)1To tm-1Time of day temperature data Y (s, t)1：m-1) Under the condition of (1), tm-1Covariance parameter of time η (t)m-1) The probability density of (d);
and then by equation 8, using tmImplementation of temperature data at time tmUpdating the covariance parameter at that moment, i.e. finding tmPosterior probability density distribution p (η (t) of covariance parameter at timem)|Y(s，t1：m))：
Figure FDA0002457751210000022
Wherein the content of the first and second substances,
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) Is represented at t)mCovariance parameter of time η (t)m) Under the condition of (1), Y (s, t)m) The probability density of (d);
4) estimating temperature values of the spatiotemporal temperature field:
given the observation data Y, the calculation is carried out by the formula 10 to obtain the position s of any position in the temperature fieldiEstimation of temperature value of (a):
Figure FDA0002457751210000023
wherein the content of the first and second substances,
Figure FDA0002457751210000024
at tmTime siAn estimate of the temperature of the spot; mu(s)i，tm) Is tmTime siAverage of global temperature variation of the points; omegaij(tm) Denotes sj～siAt tmSpatial weight of a time instant; y(s)j，tm) For a given tmTime sjA temperature value of the point; mu(s)j，tm) Is tmTime sjThe mean function term of the global temperature variation of the point.
2. The method for analyzing temperature sensing data according to claim 1, wherein the temperature value Y (s, t) at the certain time slot (s, t) in step 1) is specifically represented by formula 1:
y (s, t) ═ μ (s, t) + w (s, t) + e (s, t) (formula 1)
The temperature value Y (s, t) of the certain time null point (s, t) is obtained by adding a mean function term μ (s, t) representing the global temperature variation of the temperature field, a local variation term w (s, t) representing the local temperature variation of the temperature field, and a random noise term e (s, t) representing the temperature variation caused by random or uncontrollable factors.
3. The method for analyzing temperature sensing data according to claim 1, wherein the step 2) of modeling and solving the mean function term μ (s, t) comprises the following steps:
B1. establishing a mean model: considering the influence of environmental factors, a three-dimensional unsteady Fourier heat transfer model is established for a mean function term mu (s, t) under a Cartesian coordinate system as follows:
Figure FDA0002457751210000031
in equation 2, μ (x, y, Z, t) represents a mean function term in a cartesian coordinate system, where spatial coordinates s ═ x, y, Z, and x, y, and Z represent coordinates in X, Y and Z directions, respectively; p represents the density of the substance, c represents the specific heat capacity of the substance, lambdax，λyAnd λzRespectively representing the thermal conductivity of the substance along X, Y and Z directions under a three-dimensional Cartesian coordinate system;
B2. solving a mean value model:
and (3) solving the mean model of the formula 2 by adopting a finite difference method and giving initial temperature and boundary conditions by using a formula 3:
Figure FDA0002457751210000032
wherein, (i, j, k, m) represents a grid position corresponding to the coordinates (x, y, z, t), and Δ x, Δ y, Δ z represent grid intervals in the spatial direction, respectively; Δ t represents a grid interval in the time direction.
4. The method for analyzing temperature sensing data according to claim 3, wherein the parameter value in formula 3 of step B2 is selected to satisfy
Figure FDA0002457751210000041
Where ρ represents the density of a substance, c represents the specific heat capacity of the substance, and λx，λyAnd λzRespectively representing the thermal conductivity of the substance along X, Y and Z directions under a three-dimensional Cartesian coordinate system; Δ x, Δ y, Δ z respectively represent grid intervals in the spatial direction; Δ t represents a grid interval in the time direction.
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