CN108376186A - A kind of stored grain temperature field method of estimation based on transfer learning - Google Patents
A kind of stored grain temperature field method of estimation based on transfer learning Download PDFInfo
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Abstract
The storage three-dimensional cereal temperature field method of estimation based on transfer learning that the invention discloses a kind of, establishes the Mixed effect model frame that thermodynamical model is combined with transfer learning model, by three-dimensional cereal temperature field event (s, t) temperature value ym(s, t) it is expressed as the adduction of the global temperature variation item in temperature field, local temperature the variation item and the noise item caused by random or uncontrollable factor in temperature field, the global change of cereal temperature field is described and estimated by thermodynamical model, by the localized variation for being combined the description of transfer learning model and estimation cereal temperature field of establishing space-time temperature field by multi-task learning and auto-correlation Time Series Method, the accurate estimation to storage three-dimensional cereal temperature field is realized, thus to obtain stored grain temperature.The present invention, which can solve the problems, such as that sensing data is insufficient, observation data portion lacks, can not obtain accurate cereal temperature field information, obtain the comprehensive and accurate information in cereal temperature field.
Description
Technical Field
The invention provides a temperature field estimation method, particularly relates to a method for obtaining the temperature of stored grains through grain temperature field estimation based on transfer learning, and belongs to the field of industrial engineering.
Background
With the increasing world population, the worldwide demand for food has increased. In order to meet the supply of grains, the Chinese government establishes a large number of grain depots around the country for storing the grains. The grains are deteriorated due to various reasons in the storage process, and finally the loss of the grains is caused. Loss of grain in storage has become a concern worldwide. As reported by the food and agriculture organizations of united nations, about 8% of food is damaged by the presence of pests every year around the world. The monitoring of the grain quality in the storage process is of great importance, and the most common grain quality monitoring index is the temperature of the grain. The development of the grain temperature field estimation technology is beneficial to monitoring the global change condition of the grain quality, and accurate and comprehensive information is provided for real-time monitoring of the grain quality.
The existing temperature field estimation technology collects temperature data through wireless sensing equipment, and establishes a temperature field estimation model by using the data to realize the estimation of a temperature field. In engineering application, due to the limitation of the configuration cost of the sensor, the number of the sensing devices installed in a temperature field is small, and only a small part of sparse data can be acquired through the sensing devices. Meanwhile, the sensing equipment is easy to damage, and partial sensor data is lost or unavailable. The lack of sensor data results in a significant reduction in the accuracy of existing temperature field estimation techniques.
The existing temperature field estimation methods mainly have two categories: thermodynamic models based on heat transfer principles and statistical models based on data. The thermodynamic model is a description of the temperature field changes that are ideally based on the heat transfer mechanism. And establishing a three-dimensional thermodynamic model by giving an initial temperature and boundary conditions, and realizing the estimation of a three-dimensional dynamic temperature field. The model does not consider local changes generated by the influence of other factors on the change of the temperature field in the actual engineering application, and the estimation error of the temperature field is large. The statistical model is based on the existing estimation of the sensor data on the temperature field, and comprises a regression analysis model, a kriging model, a gaussian random field model and the like. Due to the insufficiency of sensor data, the accuracy of the model estimation is low.
In addition, as a complex heat transfer system, the temperature data of adjacent positions or adjacent moments of a three-dimensional grain temperature field has time and space correlation, and the time and space correlation of the temperature data is interactive. The characteristic of the grain temperature field is mostly described in the prior art under the assumption that time and space correlations are mutually independent, the time-space correlation of data is not considered, accurate estimation of a storage three-dimensional grain temperature field is difficult to realize, and more accurate storage grain temperature is difficult to obtain.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides the storage three-dimensional grain temperature field estimation method based on the transfer learning, the storage grain temperature is obtained through the storage grain three-dimensional temperature field estimation, and the comprehensive and accurate information of the grain temperature field can be obtained.
According to the method, the space-time correlation of the grain temperature field is fully considered, a thermodynamic model and a migration learning model are combined under a mixed effect model framework, the thermodynamic model is adopted to describe the global change of the grain temperature field, the migration learning model of the space-time temperature field is established to describe the local change of the grain temperature field through the combination of multi-task learning and an autocorrelation time sequence method, and the accurate estimation of the storage three-dimensional grain temperature field is realized. In order to solve the problem of insufficient sensor data in the current granary, the invention adopts a transfer learning technology, simultaneously considers a plurality of granary sensor data with similar attributes, and realizes the accurate estimation of a three-dimensional grain temperature field in the storage process. The invention can solve the problem that the accurate grain temperature field information cannot be obtained due to insufficient sensor data and partial missing of observation data in the storage at present, can obtain the comprehensive and accurate information of the grain temperature field, and provides the comprehensive and accurate information for monitoring the grain quality.
The technical scheme provided by the invention is as follows:
a method for estimating a three-dimensional grain storage temperature field based on transfer learning comprises the steps of establishing a mixed effect model framework combining a thermodynamic model and a transfer learning model, describing and estimating global change of the grain temperature field through the thermodynamic model, and describing and estimating local change of the grain temperature field through the transfer learning model combining a multi-task learning method and an autocorrelation time sequence method, so that accurate estimation of the three-dimensional grain storage temperature field is realized, and the grain storage temperature is obtained; the method comprises the following steps:
1) establishing a mixed effect model framework by utilizing a thermodynamic model and a migration learning model, and enabling a temperature value y of a three-dimensional grain temperature field at a space-time point (s, t)m(s, t) is expressed as the sum of the global temperature variation term of the temperature field, the local temperature variation term of the temperature field, and the noise term caused by random or uncontrollable factors.
The estimation of a certain grain temperature field is defined as a task, and M grain temperature fields to be estimated are assumed to be in total, namely M tasks are in total. For task M (M is 1, …, M), the temperature values of the three-dimensional grain temperature field are composed of an average function term representing global temperature variation, a local variation term representing local temperature variation, and a random noise term. The mixed effect model framework is established as follows:
for task M (M equals 1, …, M), assume ym(s, t) represents the temperature value of the three-dimensional grain temperature field at the space-time point (s, t), s and t represent independent variables of space and time respectively, and the framework of the mixed effect model is represented as formula 1:
ym(s,t)＝um(s,t)+bm(s,t)+εm(s, t) (formula 1)
Wherein u ism(s, t) represents a mean function term of the task m at a space-time point (s, t) and is used for describing the global temperature change condition of the temperature field; bm(s, t) represents a local variation item of the task m at a space-time point (s, t) and is used for describing the local temperature variation condition of the temperature field; epsilonm(s, t) represents a random noise term at the point in time space (s, t) for task m to characterize temperature variations due to random or uncontrollable factors. It is generally assumed that ∈1(s,t),…,,…,εM(s, t) } are mutually independent in the time dimension, taking into account only their spatial correlation, i.e. assuming εm(s, t) (M1, …, M) obeys a normal distribution at any time Denotes the time epsilon at tm(s, t) (M ═ 1, …, M) obeys the variance of the normal distribution.
Next, the mean function term μ (s, t) and the local variation term w (s, t) are modeled separately.
2) For mean function term mu in mixed effect modelm(s, t) (global temperature change term of the temperature field) is modeled, and the implementation method is as follows:
variations in the temperature field of the grain are typically caused by environmental factors. In the invention, the influence of environmental factors is fully considered, and the mean function term u is subjected to the Cartesian coordinate systemm(s, t) establishing a three-dimensional unsteady Fourier heat transfer model:
in the formula 2, um(x, y, Z, t) represents the mean function term of task m in a cartesian coordinate system, where the spatial coordinates s ═ x, y, Z, and x, y, and Z represent the coordinates in X, Y and Z directions, respectively; rho represents the density of the grain, c represents the specific heat capacity of the grain, and lambdax，λyAnd λzWhich respectively represent the thermal conductivity of grains in x, y and z directions under a three-dimensional cartesian coordinate system. Given initial grain temperature and boundary conditions, equation 2 is solved by using a finite difference method.
3) For local variation term b in mixed effect modelm(s, t) (local temperature change term of the temperature field) is modeled, and the realization method is as follows:
the time-space correlation of the grain temperature field is fully considered, a multi-task learning and autocorrelation time sequence method is combined to establish a transfer learning model of the time-space temperature field, and the local temperature change of the grain temperature field is described. For task M (M ═ 1, …, M), the following model was established:
in equation 3, for the convenience of understanding, the local variation item b of the task m at the space-time point (s, t) is definedm(s, t) is represented byAn autocorrelation time series model is adopted to depict the time correlation of the local variation item at the time t and the local variation item in the L time before the time t,a correlation parameter representing the local variation item at the t moment and the local variation item at the t-l moment;representing the change produced by the local change term at time t compared to the previous t-L, assumingIs a Gaussian process with the mean value of zero, and adopts a multi-task learning model to describe the relation between a task M and other M-1 tasksThe spatial correlation of (a). Firstly, based on multi-task learning method pairModeling, and estimating to obtain parameters of a multi-task learning and autocorrelation time series model; the following operations are specifically executed:
C1. obtained by a multitask learning method
For task m, limited sensor data does not enable accurate temperature field estimation. In order to estimate the temperature field more accurately, the present invention considers M grains with similar propertiesThe food temperature field, such as the geographical position, the granary specification, the external environment and the type of the stored food are the same. Grain temperature sensing data in the M tasks are used as observation data, and accurate estimation of the M grain temperature fields is achieved. At time T (T equal to 0, …, T), let us assumeWith similar model structure, parameters of their correlation are drawn instantlyObeying the same Gaussian process with the mean vector of mutThe covariance matrix is Ct. Suppose μtAnd CtThe prior distribution of (a) follows a normal-inverse weixate distribution:
in formula 4, μtHas a prior mean vector of 0 and a covariance matrix ofPi represents the precision of the function; ctHas a prior scale matrix of κ-1The precision is τ. The calculation steps of the multi-task learning model are as follows:
step one, generating mu from formula 4tAnd CtAn initial value of (1);
step two, for all tasks M (M is 1, …, M), parameters
Step three, giving an arbitrary space position s,wherein κ(s)iS) represents the sum of position siAnd s-related kernel functions.
The invention describes the spatial correlation κ between two different positions in the grain temperature field using the following kernel function:
in formula 5, s and s' represent two different spatial positions, δ2Representing a parameter related to spatial distance.
The technology adopts the maximum Expectation-maximization (EM) algorithm to estimate the parameters in the multi-task learning modelAndfirst, mu is obtained by using formula 4tAnd CtOf the initial prior value, mutAnd CtThe posterior estimate of (c) is obtained by two steps (the expectation step and the maximum step) as follows:
the step of (E) is desirably: based on phitEstimates the current estimated value of each task M (M is 1, …, M)And
wherein κmA spatial location kernel function matrix representing task m;indicating the observation data corresponding to the task m at the time t.
Maximum (M) step: updating mu based on the result of step Et、CtAndposterior estimates of (a):
in equation 9, κ denotes a kernel function matrix of spatial location points included in the M tasks, and tr (-) denotes a trace of the matrix. The two steps of the EM algorithm are repeated until the parameters sought converge. Using estimated values of parametersAndsubstituting into the third step to obtainEstimated value of (a):
C2. parameter estimation for spatiotemporal temperature field migration learning model
The space-time temperature field migration learning model comprises three parameters: a priori parameters Ψ ═ { π, τ, δ }, parameters for multitask learningAnd parameters of an autocorrelation time series modelThe training data is defined as the difference between the grain temperature sensor data and the mean function term corresponding to its time and space position, i.e. the difference The prior parameter psi can be determined by engineering knowledge, and the invention adopts an iterative algorithm to estimate the parameterAnd βm. The process of the parameter iterative estimation algorithm is shown in fig. 2, and the initial values of the two types of parameters are set to be zero, that is, when the iteration number k is equal to 1,filling missing data of the positions of some sensors in the training data set by using a linear interpolation method to form a new training data setThe parameter iterative estimation algorithm comprises two steps:
step one, estimating parameters of an autocorrelation time series model
First, based on the existing parameter values, the values are obtained using equation 11Is estimated value ofThe training dataset is then calculated using equation 12Andthe difference of (a):
data is obtained about an autocorrelation time series model. I.e. the expression of the autocorrelation time series model is The data isObtaining estimates of parameters from a correlation time series model using a least squares method
Step two, estimating the parameters of the multi-task learning model
Estimation of parameters based on time series modelObtaining data on a multitask learning model, i.e.
Obtaining parameter estimation values of a multi-task learning model by adopting a maximum expectation algorithm in C1And
when both types of parameters are estimated, the iteration number k is updated to k + 1. The current parameter estimated value is brought into a multi-task learning technology and an autocorrelation time sequence model to fill in missing data of the positions of some sensors in a training data set to form a new training data set
And repeating the first step and the second step until the algorithm converges. Is defined asThe algorithm terminates with e representing a positive number approaching zero.
4) The space-time temperature field estimation method comprises the following steps:
after the parameter estimation, for task M (M is 1, …, M), the estimation of the temperature value at time t and space s in the grain temperature field is implemented by equation 15:
wherein,andrespectively representing autocorrelation time series models and multi-taskingParameter estimates for the business learning model.
Thereby obtaining a grain temperature value with space-time properties.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a storage three-dimensional grain temperature field estimation method based on transfer learning. In order to solve the problem of insufficient data of sensors in the current grain temperature field, the invention adopts a transfer learning technology and simultaneously considers the data of a plurality of granary sensors with similar attributes to estimate the storage three-dimensional grain temperature field. Meanwhile, the method fully considers the time-space correlation of the temperature field, adopts a thermodynamic model to describe the global change of the grain temperature field under a mixed effect model frame, and adopts a time-space temperature field migration learning model based on multi-task learning and autocorrelation time sequence technology to describe the local change of the grain temperature field, thereby realizing the accurate estimation of the storage three-dimensional grain temperature field. The invention can solve the problem that the accurate grain temperature field information cannot be obtained due to insufficient sensor data and partial missing of observation data in the storage at present, can obtain the comprehensive and accurate information of the grain temperature field, and provides the comprehensive and accurate information for monitoring the grain quality.
Drawings
Fig. 1 is a flow chart of a method for estimating a temperature field of stored three-dimensional grains based on transfer learning according to the present invention.
FIG. 2 is a flow diagram of the parameter iterative estimation method of the present invention.
FIG. 3 shows the estimation results of the grain temperature variation curves of some spatial positions in three grain temperature fields according to the embodiment of the present invention;
wherein, the numbers in the legend are the spatial coordinates of the sampling points; (a) showing the grain temperature change curve of the granary # 1; (b) showing the grain temperature change curve of grain bin # 2; (c) shows the grain temperature profile for grain bin # 3.
Fig. 4 is a visualization diagram of an estimation result of the grain temperature field according to the embodiment of the present invention.
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 storage three-dimensional grain temperature field estimation method based on transfer learning. In order to solve the problem of insufficient sensor data in the current granary, the invention adopts a transfer learning technology, simultaneously considers a plurality of granary sensor data with similar attributes, and realizes the accurate estimation of a three-dimensional grain temperature field in the storage process. The invention can solve the problem that the accurate grain temperature field information cannot be obtained due to insufficient sensor data and partial missing of observation data in the storage at present, can obtain the comprehensive and accurate information of the grain temperature field, and provides the comprehensive and accurate information for monitoring the grain quality.
Fig. 1 is a flow chart of a method for estimating a temperature field of stored three-dimensional grains based on transfer learning according to the present invention. Taking a reserve grain depot of a certain country in China as an example, taking three grain depots with similar attributes in the grain depot as research objects, and establishing an estimation model of a three-dimensional grain temperature field in the storage process. The geographical location, specifications, types of stored grains, and external environments of the three barns are the same, so that the temperature field changes of the three barns have similar characteristics. In the embodiment, the grain temperature ranges of the three temperature fields are set to be (-50 ℃ and 50 ℃), and the grain temperature sensor data are acquired by a temperature sensor and recorded as observation data Ym(S, T), S ∈ S, T ∈ T, where m denotes the number of the grain bin, that is, m is 1,2,3, S denotes the range of the spatial independent variable S of the observed data, and T denotes the range of the temporal independent variable T of the observed data. In this example, S is defined as follows: the specifications of the three grain temperature fields are all 26m 46m 6m, and the sensors are allThe layout of (1) is such that the distance between adjacent sensors in the longitudinal and width directions is 5m and the distance between adjacent sensors in the height direction is 1.8 m. T is defined as follows: the sampling time of the grain temperature data is from 7/2/2012 to 3/4/2013, and a group of sensor data is acquired every 7 days, wherein 47 groups of data are acquired.
Establishing a storage three-dimensional grain temperature field estimation model based on transfer learning as follows:
1) establishing a mixed effect model framework
If the estimation of a certain grain temperature field is defined as one task, there are 3 tasks in total. For task m (m ═ 1,2,3), the temperature values of the grain temperature field are composed of an average function term representing the global temperature variation, a local variation term representing the local temperature variation, and a random noise term. Suppose ym(s, t) represents the temperature value of the three-dimensional temperature field at a space-time point (s, t), s and t represent independent variables of space and time respectively, and the framework of the mixed effect model is as follows:
ym(s,t)＝um(s,t)+bm(s,t)+εm(s, t) (formula 1)
Wherein u ism(s, t) represents a mean function term of the task m at a space-time point (s, t) and is used for describing the global temperature change condition of the temperature field; bm(s, t) represents a local variation item of the task m at a space-time point (s, t) and is used for describing the local temperature variation condition of the temperature field; epsilonm(s, t) represents a random noise term at the point in time space (s, t) for task m to characterize temperature variations due to random or uncontrollable factors. It is generally assumed that ∈1(s,t),…,,…,εM(s, t) } are mutually independent in the time dimension, taking into account only their spatial correlation, i.e. assuming εm(s, t) (M1, …, M) obeys a normal distribution at any time Denotes the time epsilon at tm(s,t)(m＝1, …, M) is subject to a variance of the normal distribution. In the following, the mean function term μ (s, t) and the local variation term w (s, t) will be modeled separately.
2) Mean function term mum(s, t) modeling and solving
Fully considering the influence of environmental factors and applying a mean function term um(s, t) establishing a three-dimensional unsteady Fourier heat transfer model:
in the formula 2, um(x, y, Z, t) represents the mean function term of task m in a cartesian coordinate system, where the spatial coordinates s ═ x, y, Z, and x, y, and Z represent the coordinates in X, Y and Z directions, respectively; rho represents the density of the grain, c represents the specific heat capacity of the grain, and lambdax，λyAnd λzWhich respectively represent the thermal conductivity of a substance in x, y and z directions 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，λzBoth are 2000J/(kg. K). For each grain temperature field, the initial grain temperature and the boundary grain temperature are given, and the finite difference method is adopted to solve the formula 2, so that the global temperature change condition of the temperature field is obtained.
3) Local variation term bmModeling and parameter estimation of (s, t)
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 an autocorrelation time series model and a multi-task learning model. For task m (m ═ 1,2,3), the following model was established:
in equation 3, the local variation term b of the task m at the space-time point (s, t)m(s, t) is represented byAn autocorrelation time series model is adopted to depict the time correlation of the local variation item at the time t and the local variation item in the L time before the time t,a correlation parameter representing the local variation item at the t moment and the local variation item at the t-l moment;representing the change produced by the local change term at time t compared to the previous t-L, assumingIs a Gaussian process with the mean value of zero, and adopts a multi-task learning model to describe the relation between a task M and other M-1 tasksThe spatial correlation of (a).
C1. Depicting using multi-task learning models
For task m (m ═ 1,2,3), the limited sensor data does not enable accurate temperature field estimation. In order to estimate the temperature fields more accurately, the invention considers 3 temperature fields with similar attributes, utilizes temperature sensing data in 3 tasks as observation data, and simultaneously realizes accurate estimation of 3 grain temperature fields. At time t (t ═ 0, …,46), assume thatWith similar model structure, parameters of their correlation are drawn instantlyObey the sameGaussian process with mean vector of μtThe covariance matrix is Ct. Suppose μtAnd CtObey the inverse weixate distribution:
in formula 4, μtHas a prior mean vector of 0 and a covariance matrix ofPi represents the precision of the function; ctHas a prior scale matrix of κ-1The precision is τ. The multi-task learning model comprises the following steps:
step one, generating mu from formula 4tAnd CtAn initial value of (1);
step two, for all tasks m (m is 1,2,3), parameters
Step three, giving an arbitrary space position s,wherein κ(s)iS) represents the sum of position siAnd s-related kernel functions.
The spatial correlation between two different locations in the temperature field is described using the following kernel functions:
in formula 5, s and s' represent two different spatial positions, δ2Representing a parameter related to spatial distance.
The present technique estimates a multi-task learning model using a maximum Expectation (EM) algorithmParameter (2) ofAndfirst, mu is obtained by using formula 4tAnd CtOf the initial prior value, mutAnd CtThe posterior estimate of (a) is obtained by the following two steps:
the step of (E) is desirably: based on phitEstimates the current estimated value of each task m (m is 1,2,3)And
wherein κmA spatial location kernel function matrix representing task m;indicating the observation data corresponding to the task m at the time t.
Maximum (M) step: updating mu based on the result of step Et、CtAndposterior estimates of (a):
in equation 9, κ denotes a kernel function matrix of all spatial location points included in 3 tasks, and tr (-) denotes a trace of the matrix. The two steps of the EM algorithm are repeated until the parameters sought converge. Using estimated values of parametersAnddepicting
C2. Parameter estimation for multi-task learning techniques and autocorrelation time series models
The multitask learning technology and the autocorrelation time series model comprise three parameters: a priori parameter Ψ ═ { π, τ, δ }, parameter Φ for multitask learningt＝{μt,Ct,σt0, …,46 and parameters of the autocorrelation time series model The training data is defined as the difference between the temperature sensor data and the mean function term corresponding to its temporal, spatial position, i.e.The prior parameter psi can be determined through engineering experience, namely the smaller pi and tau, the higher the temperature field estimation precision, the invention sets pi to 1 and tau to 0, sigmatRepresenting the distance between the two points that are farthest apart in the barn. The invention adopts an iterative algorithm to estimate parametersAnd βm. The process of the parameter iterative estimation algorithm is shown in fig. 2, and the initial values of the two types of parameters are set to be zero, that is, when the iteration number k is equal to 1,filling missing data of the positions of some sensors in the training data by using a simple interpolation method to form a new training data setThe parameter iterative estimation algorithm comprises two steps:
step one, estimating parameters of an autocorrelation time series model
First, based on the existing parameter values, the values are obtained using equation 11Is estimated value ofThen calculating a training data setAnddifference of (2)
Data is obtained about an autocorrelation time series model. I.e. the expression of the autocorrelation time series model is The data isObtaining estimates of parameters from a correlation time series model using a least squares method
Step two, estimating the parameters of the multi-task learning model
Estimation of parameters based on time series modelObtaining data on a multitask learning model, i.e.
Obtaining parameter estimation values of a multi-task learning model by using the maximum expectation algorithm introduced in C1And
when both types of parameters are estimated, the iteration number k is updated to k + 1. The current parameter estimated value is brought into a multi-task learning technology and an autocorrelation time sequence model to fill in missing data of the positions of some sensors in a training data set to form a new training data set
And repeating the first step and the second step until the algorithm converges. Is defined asThe algorithm terminates with e representing a positive number approaching zero.
4) The space-time temperature field estimation method comprises the following steps:
after the parameter estimation, for task m (m is 1,2,3), the estimation of the temperature value at time t and space s in the grain temperature field is implemented by equation 15:
wherein,andand respectively representing the parameter estimation values of the autocorrelation time series model and the multitask learning model. Fig. 3 is an example of the temperature variation curves of some positions of three grain temperature fields estimated by the present invention. 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. Fig. 4 is an example of three grain temperature fields estimated by the present invention, and fig. 4 shows that the grain temperature fields are dynamically varied with time and space, and the three grain temperature fields have similar variation characteristics.
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 (5)
1. A method for estimating a three-dimensional storage grain temperature field based on transfer learning realizes accurate estimation of the three-dimensional storage grain temperature field, so that the storage grain temperature is obtained; the method comprises the following steps:
1) establishing a mixed effect model, and measuring the temperature value y of the three-dimensional grain temperature field at a space-time point (s, t)m(s, t) is expressed as the sum of a global temperature variation term of the temperature field, a local temperature variation term of the temperature field, and a noise term caused by random or uncontrollable factors;
for a task M, M is 1, …, M is estimated, M tasks are total, a temperature value of a three-dimensional grain temperature field is composed of a mean function term representing global temperature change, a local change term representing local temperature change and a random noise term, and an established mixed effect model is expressed as formula 1:
ym(s,t)＝um(s,t)+bm(s,t)+εm(s, t) (formula 1)
Wherein, ym(s, t) represents the temperature value of the three-dimensional grain temperature field at the space-time point (s, t); s and t represent the independent variables of space and time, respectively; u. ofm(s, t) is a mean function term of the task m at the space-time point (s, t), and represents the global temperature change condition of the temperature field; bm(s, t) is a local variation term of the task m at the space-time point (s, t), and represents the local temperature variation condition of the temperature field; epsilonm(s, t) is a random noise term at the time-space point (s, t) for task m, representing temperature variations due to random or uncontrollable factors; let εm(s, t) obeys a normal distribution at any time Denotes the time epsilon at tm(s, t) (M ═ 1, …, M) obeyed a variance of the normal distribution;
2) global temperature variation term mu for temperature fieldm(s, t) modeling, performing the following operations:
in a Cartesian coordinate system, for um(s, t) establishing a three-dimensional unsteady Fourier heat transfer model, which is expressed by the following formula 2:
in the formula 2, um(x, y, Z, t) represents the mean function term of task m in a cartesian coordinate system, where the spatial coordinates s ═ x, y, Z, and x, y, and Z represent the coordinates in X, Y and Z directions, respectively; rho represents the density of the grain, c represents the specific heat capacity of the grain, and lambdax，λyAnd λzRespectively expressed in three-dimensional cartesianThermal conductivity of grains in x, y and z directions under a molar coordinate system; giving initial grain temperature and boundary conditions, and solving the formula 2 by adopting a finite difference method;
3) local temperature variation term b for temperature fieldm(s, t) modeling, expressed as equation 3:
in equation 3, the local variation term b of the task m at the space-time point (s, t)m(s, t) is represented byAdopting an autocorrelation time series model to represent the time correlation of the local variation item at the time t and the local variation item in the L time before the local variation item;a correlation parameter representing the local variation item at the t moment and the local variation item at the t-l moment;representing the change of the local change item at the time t compared with the change generated at the previous time t-L; suppose thatIs a Gaussian process with the mean value of zero, and adopts a multi-task learning model to represent the relation between the task M and other M-1 tasksEstimating parameters of a multi-task learning model and an autocorrelation time series model;
4) estimating a space-time temperature field:
for task m, estimating the temperature value of the grain temperature field at time t and space s by equation 15:
wherein,andrespectively representing the parameter estimation values of the autocorrelation time series model and the multitask learning model;
thereby obtaining a grain temperature value with space-time properties.
2. The method of claim 1, wherein in the step 2) modeling of the local temperature variation term, setting is performedIs a Gaussian process with a mean value of zero and is based on a multi-task learning method pairModeling, and estimating to obtain parameters of a multi-task learning and autocorrelation time series model; the following operations are specifically executed:
C1. obtained by a multitask learning method
For task m, assume representationParameters of correlationSubject to the same gaussian process,having a similar model structure at time t, Gaussian processMean vector of μtThe covariance matrix is Ct(ii) a Let utAnd CtThe prior distribution of (a) follows a normal-inverse weixate distribution, represented by equation 4:
in formula 4, μtHas a prior mean vector of 0 and a covariance matrix ofPi represents the precision of the function; ctHas a prior scale matrix of κ-1Precision is tau; calculated through multi-task learningThe steps include S1-S3:
s1, generating mu from the formula 4tAnd CtAn initial value of (1);
s2, for all tasks m, parametersEstimating the derived parametersAnd
s3, given an arbitrary spatial position S, using the estimated values of the parametersAndto represent
Wherein κ(s)iS) represents the sum of position siAnd s-related kernel functions.
C2. Obtaining parameters of a space-time temperature field migration learning model through an estimation method, wherein the parameters comprise: prior parameter Ψ ═ { pi, τ, δ }, parameter for multitask learningAnd parameters of an autocorrelation time series model
3. The method of claim 2, wherein the calculation is performed by multi-task learningThe kernel function in step S3 specifically represents the spatial correlation κ between two different positions in the grain temperature field by using formula 5:
in formula 5, s and s' represent two different spatial positions, δ2Representing a parameter related to spatial distance.
4. The method of claim 2, wherein the parameters in the multi-task learning model are estimated using a maximum expectation algorithm EMAndthe following operations are specifically executed:
first, mu is obtained by using formula 4tAnd CtAn initial prior value of;
obtaining mu through the expectation step E and the maximum step MtAnd CtPosterior estimates of (a):
the expected step E: based on phitThe current estimated value of (c) is estimated for each task M (M is 1, …, M) according to equations 6 and 7And
wherein, κmA spatial location kernel function matrix representing task m;representing observation data corresponding to the task m at the time t;
maximum step M: based on the results obtained in the expected step E, μ is updated according to equation 8t、CtAndposterior estimates of (a):
in formula 9, κ represents a kernel function matrix of spatial location points included in the M tasks; tr (-) denotes the trace of the matrix;
the expectation step E and the maximum step M are repeated until the convergence of the parameters sought.
5. The method as claimed in claim 2, wherein the parameters are estimated in step C2 by using an iterative estimation algorithmAnd βmSpecifically, the following operations are performed:
c21, setting parametersAnd βmAll of which are zero, i.e. when the number of iterations k is 1,
c22, training data areFilling up missing data of the sensor by interpolation to form a new training data set
C23, estimating parameters of the autocorrelation time series model:
first, the compound is obtained by equation 11Is estimated value of
Then, a training data set is obtained by calculation using equation 12Andthe difference value of (a) obtains data on an autocorrelation time series model:
then obtaining the estimated value of the parameter obtained from the correlation time series model by adopting a least square method
C24, estimating parameters of the multitask learning model:
estimation of parameters based on time series modelData is obtained for a multitask learning model, represented as equation 13:
obtaining parameter estimation values of a multi-task learning model by adopting a maximum expectation algorithmAnd
c25, when both the parameters are estimated, updating the iteration number k to k + 1;
c26, substituting the current parameter estimated value into the multi-task learning model and the autocorrelation time sequence model to obtain the missing data of the sensor in the training data set, and forming a new training data setExpressed as formula 14:
c27, repeating the steps C23 to C26 until the algorithm converges; is defined asThe algorithm terminates with e representing a positive number approaching zero.
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