CN109145346A - Solidification thermal process space-time modeling method based on dual least square method supporting vector machine - Google Patents
Solidification thermal process space-time modeling method based on dual least square method supporting vector machine Download PDFInfo
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Abstract
The invention discloses the solidification thermal process space-time modeling methods based on dual least square method supporting vector machine, step 1, build chip curing oven temperature control platform, step 2, obtain the space-time data that Temperature Distribution of the chip curing oven in the case where solidifying working condition changes over time, step 3, host computer learn the space basic function of one group of characterization Space Nonlinear feature by PCA algorithm (i.e. Principal Component Analysis Algorithm).Thermal process for on-line prediction and control chip curing oven, it include the distributed parameter system of two intrinsic coupling nonlinears using two least square method supporting vector machines (LS-SVM) dual LS-SVM modeling in series, it is more effective in terms of the performance approximation of two coupling nonlinears, and model accuracy is high.
Description
Technical field
The present invention relates to solidification thermal process to model field, more particularly to the solidification based on dual least square method supporting vector machine
Thermal process space-time modeling method.
Background technique
In the process of chip packaging, solidification process is one of one process of most important one.Chip solidifies the good of quality
It is bad, directly affect the quality and service life of final finished.And equipment used in solidification process is chip curing oven.Gu
There is the heating module of an arch in the inside for changing furnace, its effect is so that the temperature field in furnace chamber is consistent.Furnace chamber lower end
There is a cooling device, its effect in this way may be used so that the temperature in furnace chamber forms a temperature gradient in the up-down direction
To meet the requirement of chip different temperatures needed for different cure stages.Due to the boundary condition of solidification process it is extremely complex with
And the influence of internal unknown disturbance, the accurate partial differential equation description of solidification process are difficult to obtain.Curing oven belongs to distributed ginseng
Number system (DPS), although can substantially obtain the partial differential equation structure of curing oven according to Heat transfer law, still have perhaps
Multimode shape parameter can not obtain.Due to chip, the space-time based on data very high to the Spreading requirements of temperature that solidifies quality
Distributed model has very important significance for the temperature management of solidification process.
Summary of the invention
It is an object of the invention to propose the solidification thermal process space-time modeling side based on dual least square method supporting vector machine
Method establishes chip solidification thermal process model, realizes the On-line Estimation of chip curing oven on-line temperature monitoring and Temperature Distribution, and
Modeling accuracy is high.
To achieve this purpose, the present invention adopts the following technical scheme:
A kind of solidification thermal process space-time modeling method based on dual least square method supporting vector machine:
Step 1 builds chip curing oven temperature control platform, installs lead frame in the furnace cavity bottom of chip curing oven,
Multiple thermocouple sensors are evenly arranged in the upper surface of lead frame, and acquire the temperature of all thermocouple sensors by host computer
Degree evidence is also evenly arranged multiple heaters above lead frame, and each heater is by a pulse-width signal and one
A power amplifier provides input signalChip curing oven is set to carry out solidification work；
Step 2, host computer count the temperature data of all thermocouple sensors, obtain chip curing oven in solidification work
The space-time data that Temperature Distribution under state changes over time, and by the space-time data is defined as:
T (x, y, z, t) | x=1 ..., nx, y=1 ..., ny, z=1 ..., nz, t=1 ..., L }
Wherein, nxIndicate data point number of the space-time data in the direction x, nyIndicate space-time data in the data point in the direction y
Number, nzSpace-time data is indicated in the data point number in the direction z, L is time span；
Step 3, host computer learn one group of characterization Space Nonlinear feature by PCA algorithm (i.e. Principal Component Analysis Algorithm)
Space basic functionTo which the collected space-time data T (x, y, z, t) of step 2 be decoupled are as follows:
Wherein, aiIt (t) is the ordinary differential equations model of space-time data T (x, y, z, t), n is the rank of ordinary differential equations model
Number；
Step 4, host computer use the golden method of gal the Liao Dynasty by ordinary differential equations model ai(t) resolve into two it is independent non-thread
Property module gi() and hi(): ai(t)=gi(ai(t-1))+hi(u(t-1))；
Step 5, host computer use two least square method supporting vector machines (LS-SVM) dual LS-SVM model in series
To approach nonlinear block gi() and hi(), and nonlinear block g is recognized by LS-SVM algorithmi() and hi(·)
Parameter；
Step 6, host computer are obtained by integrating the space basic function and the ordinary differential equations model, space-time synthesis
Temperature Temporal And Spatial Distribution Model of the chip curing oven 1 in the case where solidifying working condition.
Preferably, in the step 3, host computer learns the space of one group of characterization Space Nonlinear feature by PCA algorithm
Basic functionSpecifically:
Firstly, the assembly average for defining space-time data T (x, y, z, t) is
Define h1(x) and h2It (x) is (h in the inner product of spatial domain Ω1(x), h2(x))=∫Ωh1(x)h2(x)dx；
Then, the inner product of space-time data T (x, y, z, t) and space basic function is maximized:
subject to(φi(), φi())=1, φi(·)∈L2(Ω), i=1 ..., n；
Construct Lagrangian:
Wherein, X is coordinate (x, y, z), and the necessary condition of extreme value is functional derivative for all changesIt is zero:
And condition is simplified using arbitrary function Ψ (X) are as follows:
Wherein, R (X, ξ)=<T (X, t) T (ξ, t)>is symmetrical and positive definite space two point correlation function,To convert following characteristics value problem for condition:
Cδi=λiδi,
Wherein, CtkIt is two dot matrix of time:
δi=[δ1i, δ2i..., δLi]TIt is ith feature vector；
Then, by solving C δi=λiδiGenerate feature vector δ1, δ2..., δLAnd its corresponding eigenvalue λ1, λ2...,
λL, and pass throughObtain space basic function；
Finally, characteristic value is arranged according to sequence from big to small: λ1> λ2> ... > λL, wherein preceding n maximum feature
It is worth the accounting of sum are as follows:
Choose order of the corresponding value n in ratio >=0.99 as space basic function.
Preferably, the step 4 specifically:
Firstly, defining the equation residual error of space-time data T (x, y, z, t) are as follows:
Wherein, c is specific heat coefficient (J/kg DEG C), and Q=Q (x, y, z, t) is heat source,It is La Pu
Laplacian operater, k1=k0/ρoC is constant, k0And ρ0It is the nominal value around operating point；
Equation residual error is minimized using gal the Liao Dynasty golden method, makes (R, φi)=0；To obtain:
Wherein,
The range in the domain Ω is (0≤x≤x0, 0≤y≤y0, 0≤z≤z0),
Ignore the coupling effect between ordinary differential equations model, above formula simplifies are as follows:
WhereinΔ t is the sampling interval of discretization；
Then, nonlinear function is defined:
Thus by ordinary differential equations model ai(t) two independent nonlinear block g are resolved intoi() and hi(): ai
(t)=gi(ai(t-1))+hi(u(t-1))。
Preferably, dual LS-SVM model approaches nonlinear block gi() and hi() specifically:
Firstly, orthogonal project operator P is defined, to obtain time coefficient in exporting from space-time:
Wherein, φ=[φ1..., φn]T；
Due to space basic function φi(i=1 ..., ∞) is that unit is orthogonal, therefore time coefficient are as follows:
A (t)=[a1(t) ... ai(t) ..., an(t)]T；
Then, host computer approaches nonlinear block g using a least square method supporting vector machinei(), while using another
One least square method supporting vector machine approaches nonlinear block hi(), it may be assumed that
To ordinary differential equations model ai(t) are as follows:
Wherein,WithIt is mapping function,WithIt is mapping function respectivelyWithPower
Weight,WithIt is corresponding bias term.
Preferably, nonlinear block g is recognized by LS-SVM algorithmi() and hiThe mapping function of ()And
Its weight and bias term:
Firstly, least square method supporting vector machine principle is based on, to ordinary differential equations model ai(t) optimize are as follows:
Wherein, C is the iotazation constant traded off between approximation quality and model complexity, and the constraint condition of optimization is:
Then, Lagrangian is constructed:
Optimize the condition of Lagrangian are as follows:
It eliminatesAfter e (t), the condition for optimizing Lagrangian is converted into following matrix:
Wherein,
1L-1=[1 ..., 1]T, ai=[ai(2) ..., ai(L)]T；
According to Mercer theorem, inner productWithKernel function K (v can be used1, v2)
It defines, wherein v1And v2It is two aleatory variables, kernel function K (v1, v2) select Radial basis kernel function:Wherein σ indicates core width,
As kernel function K (v1, v2) it is given after, dual LS-SVM model becomes:
Unknown parameter thereinβi, γi,By optimization Lagrangian
Conditional matrix obtain.
Preferably, the temperature Temporal And Spatial Distribution Model of the step 6 are as follows:
Preferably, further includes: step 7 measures the temperature Temporal And Spatial Distribution Model using Rademacher complexity
The upper bound of anticipation error,
IfMeet loss functionSo
For arbitrary δ ∈ (0,1), all make in the presence of the probability of at least 1- δ allAll meet:
Wherein:It indicatesUsing the calculated risk of loss function l,
It indicatesUsing the empiric risk of loss function l,
It is loss function set related with H and l,
Be aboutRademacher complexity, m be test sample quantity；
IfSo Rademacher complexity circle of pattern function collection H
It is limited to:
If toMeet loss function
||βi||≤pi, then all making in the presence of the probability of at least 1- δ all for arbitrary δ ∈ (0,1)It is all full
Foot:
The solidification thermal process space-time modeling method based on dual least square method supporting vector machine, for on-line prediction and
The thermal process for controlling chip curing oven, uses two least square method supporting vector machines (LS-SVM) dual LS-SVM mould in series
Type will be designed exclusively for the DPS comprising two intrinsic coupling nonlinears, more be had in terms of the performance approximation of two coupling nonlinears
Effect, and model accuracy is high.
Detailed description of the invention
The present invention will be further described for attached drawing, but the content in attached drawing does not constitute any limitation of the invention.
Fig. 1 is the chip curing oven structural schematic diagram of the one of embodiment of the present invention；
Fig. 2 is the thermocouple sensor distribution map of the one of embodiment of the present invention；
Fig. 3 is the modeling procedure figure based on dual LS-SVM of the one of embodiment of the present invention；
Fig. 4 is the control input signal figure of second heater h2 of the one of embodiment of the present invention；
Fig. 5 is first orthogonal mapping function schematic diagram that the slave PCA method of the one of embodiment of the present invention obtains；
Fig. 6 is second orthogonal mapping function schematic diagram that the slave PCA method of the one of embodiment of the present invention obtains；
Fig. 7 is performance map of the PCA modeling method of the one of embodiment of the present invention at thermocouple sensor s6；
Fig. 8 is performance map of the PCA modeling method of the one of embodiment of the present invention at thermocouple sensor s11；
Fig. 9 is the temperature profile of the last sampling instant of the prediction of the one of embodiment of the present invention；
Figure 10 is that the ARE at the thermocouple sensor s6 of the one of embodiment of the present invention compares figure；
Figure 11 is that the ARE at the thermocouple sensor s11 of the one of embodiment of the present invention compares figure.
Wherein: chip curing oven 1；Lead frame 2；Thermocouple sensor 3, s1, s2, s3, s4, s5, s6, s7, s8, s9,
s10,s11,s12,s13,s14,s15,s16；Heater 4, h1, h2, h3, h4.
Specific embodiment
To further illustrate the technical scheme of the present invention below with reference to the accompanying drawings and specific embodiments.
Embodiment one
The solidification thermal process space-time modeling method based on dual least square method supporting vector machine of the present embodiment:
Step 1 builds chip curing oven temperature control platform, as shown in Figure 1 and Figure 2, at the furnace chamber bottom of chip curing oven 1
Lead frame 2 is installed in portion, is evenly arranged multiple thermocouple sensors 3 in the upper surface of lead frame 2, and acquire institute by host computer
There is the temperature data of thermocouple sensor 3, is also evenly arranged multiple heaters 4, each heater 4 in the top of lead frame 2
Input signal is provided by a pulse-width signal and a power amplifierSolidify chip curing oven 1
Work；
Step 2 obtains chip curing oven as shown in figure 3, host computer counts the temperature data of all thermocouple sensors 3
The space-time data that 1 Temperature Distribution in the case where solidifying working condition changes over time, and by the space-time data is defined as:
T (x, y, z, t) | x=1 ..., nx, y=1 ..., ny, z=1 ..., nz, t=1 ..., L }
Wherein, nxIndicate data point number of the space-time data in the direction x, nyIndicate space-time data in the data point in the direction y
Number, nzSpace-time data is indicated in the data point number in the direction z, L is time span；
Step 3, host computer learn one group of characterization Space Nonlinear feature by PCA algorithm (i.e. Principal Component Analysis Algorithm)
Space basic functionTo which the collected space-time data T (x, y, z, t) of step 2 be decoupled are as follows:
Wherein, aiIt (t) is the ordinary differential equations model of space-time data T (x, y, z, t), n is the rank of ordinary differential equations model
Number；
Step 4, host computer use the golden method of gal the Liao Dynasty by ordinary differential equations model ai(t) resolve into two it is independent non-thread
Property module gi() and hi(): ai(t)=gi(ai(t-1))+hi(u(t-1))；
Step 5, host computer use two least square method supporting vector machines (LS-SVM) dual LS-SVM model in series
To approach nonlinear block gi() and hi(), and nonlinear block g is recognized by LS-SVM algorithmi() and hi(·)
Parameter；
Step 6, host computer are obtained by integrating the space basic function and the ordinary differential equations model, space-time synthesis
Temperature Temporal And Spatial Distribution Model of the chip curing oven 1 in the case where solidifying working condition.
According to the HEAT TRANSFER LAW of chip curing oven 1, the thermal process general expression of chip curing oven 1 be can be described as:
Wherein (x, y, z) is space coordinate, and T (x, y, z, t) indicates the temperature at time t and position S=(x, y, z)
(unit DEG C), (x, y, z), x ∈ [0, x0], y ∈ [0, y0] and z ∈ [0, z0] it is space coordinate, c is specific heat coefficient (unit J/kg
DEG C), fc(T) and frIt (T) is respectively unknown convection current and radiation nonlinear effect.Q=Q (x, y, z, t) is heat source, ρ andkRespectively
It is density (units/kg/m3) and thermal conductivity (W/m DEG C of unit).
Thermal conductivitykWith density p depending on temperature, and can indicate are as follows:
Wherein, k0And ρ0It is the nominal value around operating point,WithIt is the function of T (x, y, z, t).
Therefore, following form can be switched to:
Wherein,It is Laplace operator, k1=k0/ρoC is constant；
It is the unknown nonlinear function about T.It is obvious that there are two nonlinear function F () and Q (), wherein Q ()
It is the nonlinear function about u (t).The partial differential equation of the thermal process description of chip curing oven 1 have the feature wirelessly tieed up, institute
Cannot be directly used in on-line prediction and control.Therefore for practical application, the ODE for establishing a finite dimension is retouched
The model stated is extremely important.
In order to simulate this system, PCA algorithm (i.e. Principal Component Analysis Algorithm) be will be first for infinite dimension model conversion
For finite dimension model；Then, a new double model structure is connected using two least square method supporting vector machines (LS-SVM)
Constituting dual LS-SVM model will be exclusively for comprising two intrinsic coupling nonlinear ai(t)=gi(ai(t-1))+hi(u(t-1))
DPS design.
Due to above two coupling nonlinear, two LS-SVM models will be constructed preferably to approach master mould, it is each
A nonlinear block can distinguish approximation using the existing model of least square method supporting vector machine (LS-SVM).Although one
LS-SVM can approach any nonlinear function, still, property of than one LS-SVM of two LS-SVM in two coupling nonlinears
The approximate aspect of energy is more effective.
Preferably, in the step 3, host computer learns the space of one group of characterization Space Nonlinear feature by PCA algorithm
Basic functionSpecifically:
Firstly, the assembly average for defining space-time data T (x, y, z, t) is
Define h1(x) and h2It (x) is (h in the inner product of spatial domain Ω1(x), h2(x))=∫Ωh1(x)h2(x)dx；
Then, the inner product of space-time data T (x, y, z, t) and space basic function is maximized:
subject to(φi(), φi())=1, φi(·)∈L2(Ω), i=1 ..., n；
PCA method is to learn in one group of space-time data to space basic functionWherein constrain
(φi(), φi())=it 1 is uniqueness in order to guarantee space basic function；
Construct Lagrangian:
Wherein, X is coordinate (x, y, z), and the necessary condition of extreme value is functional derivative for all changesIt is that zero, R indicates real number field:
And condition is simplified using arbitrary function Ψ (X) are as follows:
Wherein, R (X, ξ)=<T (X, t) T (ξ, t)>is symmetrical and positive definite space two point correlation function,To convert following characteristics value problem for condition:
Cδi=λiδi,
Wherein, CtkIt is two dot matrix of time:
δi=[δ1i, δ2i..., δLi]TIt is ith feature vector；
Then, by solving C δi=λiδiGenerate feature vector δ1, δ2..., δLAnd its corresponding eigenvalue λ1, λ2...,
λL, and pass throughObtain space basic function；
Finally, characteristic value is arranged according to sequence from big to small: λ1> λ2> ... > λL, wherein preceding n maximum feature
It is worth the accounting of sum are as follows:
Choose order of the corresponding value n in ratio >=0.99 as space basic function.
PCA algorithm (i.e. Principal Component Analysis Algorithm) is to the mechanism process of real system without knowing, it is only necessary to experimental data
It can obtain the mathematical model of original system.Therefore this method is widely applied in DPS modelling application.This method
Idea about modeling mainly first carries out dimension-reduction treatment to testing collected space-time data, by ask characteristic value feature vector problem come
Obtain the space basic function of finite number.Then traditional concentration modeling method, such as neural network (NN), supporting vector are used
Machine (SVM), the methods of fuzzy model determine low order temporal model.Finally by the reconstruction of time and space, original system can be obtained
DPS model based on data.
Preferably, the step 4 specifically:
Firstly, defining the equation residual error of space-time data T (x, y, z, t) are as follows:
Wherein, c is specific heat coefficient (J/kg DEG C), and Q=Q (x, y, z, t) is heat source,It is La Pu
Laplacian operater, k1=k0/ρoC is constant, k0And ρ0It is the nominal value around operating point；
Equation residual error is minimized using gal the Liao Dynasty golden method, makes (R, φi)=0；To obtain:
Wherein,
The range in the domain Ω is (0≤x≤x0, 0≤y≤y0, 0≤z≤z0),
Ignore the coupling effect between ordinary differential equations model, above formula simplifies are as follows:
WhereinΔ t is the sampling interval of discretization；
Then, nonlinear function is defined:
Thus by ordinary differential equations model ai(t) two independent nonlinear block g are resolved intoi() and hi(): ai
(t)=gi(ai(t-1))+hi(u(t-1))。
By the partial differential equation of 1 thermal process of chip curing oven, Temporal-Spatial Variables separation is carried out and using the golden method pair of gal the Liao Dynasty
It is truncated, and the low order nominal plant model finally obtained can be similar to two independent nonlinear block gi() and hi(·)。
If weighting functionIt is selected as space basic functionSo this method
It is properly termed as the golden method of gal the Liao Dynasty.The advantages of gal the Liao Dynasty golden method be residual error with each space basic function be it is orthogonal, therefore, most
Excellent solution is n space basic functionSince this method finally need to only determine space basic function,
So having the characteristics that simple and effective.
Preferably, dual LS-SVM model approaches nonlinear block gi() and hi() specifically:
Firstly, since the data measured are spatial and temporal distributions data, so first handling spatial and temporal distributions data, to obtain
Lower-order model output data could further recognize lower-order model parameter in this way, orthogonal project operator P be defined, with defeated from space-time
Time coefficient is obtained in out:
Wherein, φ=[φ1..., φn]T；
Due to space basic function φi(i=1 ..., ∞) is that unit is orthogonal, therefore time coefficient are as follows:
A (t)=[a1(t) ... ai(t) ..., an(t)]T；
Then, LS-SVM method is the feature sky for sample data being projected to by a nonlinear mapping function more higher-dimension
Between, so that a nonlinear problem is converted to the linear solution problem of high-dimensional feature space, host computer uses a minimum two
Multiply support vector machines and approaches nonlinear block gi(), while nonlinear model is approached using another least square method supporting vector machine
Block hi(), it may be assumed that
To ordinary differential equations model ai(t) are as follows:
Wherein,WithIt is mapping function,WithIt is mapping function respectivelyWithPower
Weight,WithIt is corresponding bias term.Ordinary differential equations model ai(t) all mapping functions and corresponding weight all need in
It recognizes to obtain.
Preferably, nonlinear block g is recognized by LS-SVM algorithmi() and hiThe mapping function of ()And
Its weight and bias term:
Firstly, least square method supporting vector machine principle is based on, to ordinary differential equations model ai(t) optimize are as follows:
Wherein, C is the iotazation constant traded off between approximation quality and model complexity, and the constraint condition of optimization is:
Other than traditional LS-SVM is to the constraint of system, two constraint conditions in the constraint condition of the optimization are most
The approximate error of each nonlinear block of smallization；
Then, Lagrangian is constructed:
Optimize the condition of Lagrangian are as follows:
It eliminatesAfter e (t), the condition for optimizing Lagrangian is converted into following matrix:
Wherein,
1L-1=[1 ..., 1]T, ai=[ai(2) ..., ai(L)]T；
According to Mercer theorem, inner productWithKernel function K (v can be used1, v2)
It defines, wherein v1And v2It is two aleatory variables, kernel function K (v1, v2) select Radial basis kernel function:Wherein σ indicates core width,
As kernel function K (v1, v2) it is given after, dual LS-SVM model becomes:
Unknown parameter thereinβi, γi,By optimization Lagrangian
Conditional matrix obtain.Mercer theorem is that any positive semi-definite function all can serve as kernel function.
Preferably, the temperature Temporal And Spatial Distribution Model of step 6 are as follows:
After the acquisition of low order temporal model, it can reconstruct to obtain a Temporal And Spatial Distribution Model.
Preferably, further includes: step 7 measures the temperature Temporal And Spatial Distribution Model using Rademacher complexity
The upper bound of anticipation error,
IfMeet loss functionSo
For arbitrary δ ∈ (0,1), all make in the presence of the probability of at least 1- δ allAll meet:
Wherein:It indicatesUsing the calculated risk of loss function l,
It indicatesUsing the empiric risk of loss function l,
It is loss function set related with H and l,
Be aboutRademacher complexity, m be test sample quantity；
IfSo Rademacher complexity circle of pattern function collection H
It is limited to:
If toMeet loss function
||βi||≤pi, then all making in the presence of the probability of at least 1- δ all for arbitrary δ ∈ (0,1)It is all full
Foot:
Rademacher (ladd Mach) complexity is used to measure the rich of a kind of real-valued function, and arrive according to the observation
The anticipation error of training sample error limitation learner.With the Vapnik-Chervonenkis dimension for being only used for binary function
Difference, the complexity of Rademacher can also be used for analyzing other learning algorithms, such as based on the algorithm of kernel.Step 7 it is specific
Process are as follows: by using the concept of Rademacher complexity, following theorem can be exported:
Theorem 1 assumes that the calculated risk of this method is less than the summation of empiric risk and constant, then it is contemplated that risk will be had
Boundary.So the method proposed is convergent.
Theorem 1 is proved in order to use the concept of Rademacher complexity, needs following lemma.
Lemma 1 is assumedLoss function is all met for any δ ∈ (0,1)For
H meets allThe sample for being m for length, probability are at least 1- δ；
Wherein:It indicatesUse the calculated risk of loss function l.
It indicatesUse the empiric risk of loss function l.
It is loss function set related with H and l,
Be aboutRademacher complexity.
Lemma 2 is assumedSo pattern function collection H's
Rademacher complexity boundary are as follows:
In learning process, it is as follows to define loss function:
Assuming thatQuadratic loss functionIt is to have
Constant D=2 (A+ | | T | |∞) Lipschitz function (Lipchitz function).So loss function collectionRademacher
Complexity can be expressed as follows:
According to lemma 1, for any δ ∈ (0,1), length is the test sample of m, and probability is at least 1- δ, in H
It is allMeet:
In summary:
Last two on the right of above formula are equal to a constant.
Embodiment two
The present embodiment verifies proposed modeling method by carrying out experiment in real time.Firstly, building chip solidification furnace temperature
Control platform is spent, as shown in Figure 1, the furnace cavity bottom in chip curing oven 1 installs lead frame 2, in the upper surface of lead frame 2
It is evenly arranged the thermocouple sensor 3 of 16 same sizes, the detailed position of thermocouple sensor 3 is as shown in Figure 2.Drawing
The top of wire frame 2 is evenly arranged the heater 4 of four same sizes, and the power of each heater 4 is 700w, thermocouple sensing
Device 3 is uniformly arranged in the same level of 4 lower section 5mm of heater.Each heater 4 is by a pulse-width signal and one
A power amplifier provides input signalChip curing oven 1 is set to carry out solidification work；Wherein second heater
The control input signal of h2As shown in Figure 4.
The temperature data of all thermocouple sensors 3 is acquired by host computer.Sampling interval is Δ t=10s, each thermocouple
Sensor 3 all acquires 2100 groups of temperature datas.The temperature data of wherein thermocouple sensor s1-s5, s7-s10, s12-s16
For determining that model, the temperature data of thermocouple sensor s6 and s11 are used to test the model and are not training the performance at position
Performance.
Then, the learning algorithm based on PCA is applied to these temperature datas, and constructs 3 using PCA algorithm and orthogonal reflects
Penetrate function.Wherein low-dimensional embedded space γikFirst and second orthogonal mapping function such as Fig. 5 of middle individual features value size, 6 institutes
Show.Fig. 7 and Fig. 8 shows that the performance of selected location (s6 and s11) compares, wherein the very close practical system of estimation performance (real number)
It unites (dotted line).Obviously, the model proposed can be used to simulate the dynamic change of unbred position in furnace chamber.For space
The performance in domain, the comparison of the last one sample (the 2100th) as shown in figure 9, the model wherein developed room and time domain all
With good model performance.
Under identical experiment condition, single LS-SVM, dual LS-SVM is used to establish corresponding low order timing mould respectively
Type, and synthesized with the space basic function space-time based on PCA, obtain respective Temporal And Spatial Distribution Model.
Next compare the model performance of two methods, following standard is for assessing:
1. spatial normalization absolute error (SNAE):
2. time normalization absolute error (TNAE):
3. root-mean-square error (RMSE):
The performance indicator TNAE (X) of test is as shown in table 1:
Table 1
In order to further disclose the superiority of the dual LS-SVM model of the present embodiment, the comparison of selected location (s6 and s11)
Index A RE is as shown in Figure 10, Figure 11, and R-square is as shown in table 2.
Table 2
The Temporal And Spatial Distribution Model precision of prediction based on dual LS-SVM for illustrating that the present embodiment proposes is high.
The technical principle of the invention is described above in combination with a specific embodiment.These descriptions are intended merely to explain of the invention
Principle, and shall not be construed in any way as a limitation of the scope of protection of the invention.Based on the explanation herein, the technology of this field
Personnel can associate with other specific embodiments of the invention without creative labor, these modes are fallen within
Within protection scope of the present invention.
Claims (7)
1. a kind of solidification thermal process space-time modeling method based on dual least square method supporting vector machine, it is characterised in that:
Step 1 builds chip curing oven temperature control platform, installs lead frame in the furnace cavity bottom of chip curing oven, is drawing
The upper surface of wire frame is evenly arranged multiple thermocouple sensors, and the temperature number of all thermocouple sensors is acquired by host computer
According to being also evenly arranged multiple heaters above lead frame, each heater is by a pulse-width signal and a function
Rate amplifier provides input signalChip curing oven is set to carry out solidification work；
Step 2, host computer count the temperature data of all thermocouple sensors, obtain chip curing oven in solidification working condition
Under the space-time data that changes over time of Temperature Distribution, and by the space-time data is defined as:
T (x, y, z, t) | x=1 ..., nx, y=1 ..., ny, z=1 ..., nz, t=1 ..., L }
Wherein, nxIndicate data point number of the space-time data in the direction x, nyIndicate space-time data the direction y data point number,
nzSpace-time data is indicated in the data point number in the direction z, L is time span；
Step 3, host computer learn the sky of one group of characterization Space Nonlinear feature by PCA algorithm (i.e. Principal Component Analysis Algorithm)
Between basic functionTo which the collected space-time data T (x, y, z, t) of step 2 be decoupled are as follows:
Wherein, aiIt (t) is the ordinary differential equations model of space-time data T (x, y, z, t), n is the order of ordinary differential equations model；
Step 4, host computer use the golden method of gal the Liao Dynasty by ordinary differential equations model ai(t) two independent nonlinear blocks are resolved into
gi() and hi(): ai(t)=gi(ai(t-1))+hi(u(t-1))；
Step 5, host computer are forced using two least square method supporting vector machines (LS-SVM) dual LS-SVM model in series
Nearly nonlinear block gi() and hi(), and nonlinear block g is recognized by LS-SVM algorithmi() and hiThe ginseng of ()
Number；
Step 6, host computer obtain chip by integrating the space basic function and the ordinary differential equations model, space-time synthesis
Temperature Temporal And Spatial Distribution Model of the curing oven in the case where solidifying working condition.
2. the solidification thermal process space-time modeling method according to claim 1 based on dual least square method supporting vector machine,
It is characterized in that, host computer learns the space base letter of one group of characterization Space Nonlinear feature by PCA algorithm in the step 3
NumberSpecifically:
Firstly, the assembly average for defining space-time data T (x, y, z, t) isDefine h1
(x) and h2It (x) is (h in the inner product of spatial domain Ω1(x),h2(x))=∫Ωh1(x)h2(x)dx；
Then, the inner product of space-time data T (x, y, z, t) and space basic function is maximized:
subject to(φi(·),φi())=1, φi(·)∈L2(Ω), i=1 ..., n；
Construct Lagrangian:
Wherein, X is coordinate (x, y, z), and the necessary condition of extreme value is functional derivative for all changesη ∈ R is zero:
And condition is simplified using arbitrary function ψ (X) are as follows:
Wherein, R (X, ξ)=<T (X, t) T (ξ, t)>is symmetrical and positive definite space two point correlation function,To convert following characteristics value problem for condition:
Cδi=λiδi,
Wherein, CtkIt is two dot matrix of time:
δi=[δ1i,δ2i,...,δLi]TIt is ith feature vector；
Then, by solving C δi=λiδiGenerate feature vector δ1,δ2,...,δLAnd its corresponding eigenvalue λ1,λ2,...,λL,
With pass throughObtain space basic function；
Finally, characteristic value is arranged according to sequence from big to small: λ1> λ2> ... > λL, wherein preceding n maximum eigenvalue sum
Accounting are as follows:
Choose order of the corresponding value n in ratio >=0.99 as space basic function.
3. the solidification thermal process space-time modeling method according to claim 2 based on dual least square method supporting vector machine,
It is characterized in that, the step 4 specifically:
Firstly, defining the equation residual error of space-time data T (x, y, z, t) are as follows:
Wherein, c is specific heat coefficient (J/kg DEG C), and Q=Q (x, y, z, t) is heat source,It is Laplce
Operator, k1=k0/ρoC is constant, k0And ρ0It is the nominal value around operating point；
Equation residual error is minimized using gal the Liao Dynasty golden method, makes (R, φi)=0；To obtain:
Wherein,
The range in the domain Ω is (0≤x≤x0,0≤y≤y0,0≤z≤z0),
Ignore the coupling effect between ordinary differential equations model, above formula simplifies are as follows:
WhereinΔ t is the sampling interval of discretization；
Then, nonlinear function is defined:
Thus by ordinary differential equations model ai(t) two independent nonlinear block g are resolved intoi() and hi(): ai(t)=gi
(ai(t-1))+hi(u(t-1))。
4. the solidification thermal process space-time modeling method according to claim 3 based on dual least square method supporting vector machine,
It is characterized in that, dual LS-SVM model approaches nonlinear block gi() and hi() specifically: firstly, definition is just traded
Shadow operator P, to obtain time coefficient in exporting from space-time:
Wherein, φ=[φ1,...,φn]T；
Due to space basic function φi(i=1 ..., ∞) is that unit is orthogonal, therefore time coefficient are as follows:
A (t)=[a1(t),...ai(t),...,an(t)]T；
Then, host computer approaches nonlinear block g using a least square method supporting vector machinei(), while most using another
Small two, which multiply support vector machines, approaches nonlinear block hi(), it may be assumed that
To ordinary differential equations model ai(t) are as follows:
Wherein,WithIt is mapping function,WithIt is mapping function respectivelyWithWeight,WithIt is corresponding bias term.
5. the solidification thermal process space-time modeling method according to claim 4 based on dual least square method supporting vector machine,
It is characterized in that, recognizing nonlinear block g by LS-SVM algorithmi() and hiThe mapping function of ()And its power
Weight and bias term:
Firstly, least square method supporting vector machine principle is based on, to ordinary differential equations model ai(t) optimize are as follows:
Wherein, C is the iotazation constant traded off between approximation quality and model complexity, and the constraint condition of optimization is:
Then, Lagrangian is constructed:
Optimize the condition of Lagrangian are as follows:
It eliminatesAfter e (t), the condition for optimizing Lagrangian is converted into following matrix:
Wherein,
1L-1=[1 ..., 1]T,ai=[ai(2),...,ai(L)]T；
According to Mercer theorem, inner productWithKernel function K (v can be used1,v2) determine
Justice, wherein v1And v2It is two aleatory variables, kernel function K (v1,v2) select Radial basis kernel function:Wherein σ indicates core width,
As kernel function K (v1,v2) it is given after, dual LS-SVM model becomes:
Unknown parameter thereinβi, γi,By the item of optimization Lagrangian
Part matrix obtains.
6. the solidification thermal process space-time modeling method according to claim 5 based on dual least square method supporting vector machine,
It is characterized in that, the temperature Temporal And Spatial Distribution Model of the step 6 are as follows:
7. the solidification thermal process space-time modeling method according to claim 6 based on dual least square method supporting vector machine,
It is characterized by further comprising:
Step 7 measures the upper bound of the anticipation error of the temperature Temporal And Spatial Distribution Model using Rademacher complexity,
IfMeet loss functionSo for
Arbitrary δ ∈ (0,1) makes in the presence of the probability of at least 1- δ allAll meet:
Wherein:It indicatesUsing the calculated risk of loss function l,
It indicatesUsing the empiric risk of loss function l,
It is loss function set related with H and l,
Be aboutRademacher complexity, m be test sample quantity；
IfThe Rademacher complexity boundary of so pattern function collection H are as follows:
If toMeet loss function||βi
||≤pi, then all making in the presence of the probability of at least 1- δ all for arbitrary δ ∈ (0,1)All meet:
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| CN113486597A (en) * | 2021-07-27 | 2021-10-08 | 中南大学 | Low-order space-time modeling method for temperature field |
| CN113568309A (en) * | 2021-07-27 | 2021-10-29 | 中南大学 | Online space-time control method for temperature field |
| CN113486597B (en) * | 2021-07-27 | 2022-10-11 | 中南大学 | Low-order space-time modeling method for temperature field |
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