CN106599431A - FDY (fully drawn yarn) spinning technology for optimizing multi-model method based on mixture Gaussian weighting function - Google Patents

Abstract

The invention discloses an FDY (fully drawn yarn) spinning technology for optimizing a multi-model method based on a mixture Gaussian weighting function. The relation models between the breaking strength and orientation degree of a FDY as well as between the crystalline degree and the fiber elongation rate of the FDY are firstly established, meanwhile the relation function between the temperatures and speeds of GR1 and GR2 and the orientation degree and the crystalline degree of the FDY is established, then a database is established, finally the temperatures and speeds of the GR1 and GR2 are calculated according to the relation function by selecting the breaking strength, and the spinning technology is adjusted. The establishment of the relation model comprises the following steps: 1) determining the number of local models; 2) determining the structures of the local models; 3) determining the mixture Gaussian weighting function; 4) estimating unknown parameters in the local models and the mixture Gaussian weighting function; and 5) obtaining the relation model. The model established in the invention has the characteristics of high accuracy and high reliability, and the spinning technology in the invention is beneficial for preparing fibers with excellent mechanical property.

Description

The FDY that a kind of multi-model process based on mixed Gaussian weighting function is optimized is washed Synthetic fibre continuous yarn spinning technique

Technical field

The invention belongs to FDY polyester filament spinning techniques field, is related to a kind of multimode based on mixed Gaussian weighting function The FDY polyester filament spinning techniques that type method is optimized.

Background technology

Existing FDY polyester filaments model can set up the structure of fiber and the model of fibrous fracture intensity, but cannot The change of fibre property is directly reflected by technique adjustment.Based on actual demand, FDY polyester filament spinning technique structures are set up The quantitative relationship of performance, i.e. fibrous fracture intensity and the degree of orientation, degree of crystallinity, the relational model of elongate fiber rate, by known Technological parameter prediction fibrous fracture intensity while, also can by model reversely be used for normal productive process process optimization, be New technology, the exploitation of new product lay the foundation, and to lift fiber quality guidance is provided.

In general, the operation that fiber production process will not be random in operating area, and always according to certain operation Strategy operation, such operation strategy is interrelated with the dynamic characteristic of system, obtains different by different operation strategies Product.Operation strategy is usually to be made up of a series of operating points set in advance, and such work point variable is scheduling variable.Adjust Degree variable is a physical descriptor that decide system operating mode, itself is slowly varying.It is many due to scheduling variable Working characteristicses so that for mixing cistern system modeling problem and can apply multi-model process with scheduling variable.

Existing multi-model Modeling Method mainly has two assumed conditions：(1) it is in small distance between operated adjacent point；(2) The process dynamics of operating point near zone can be expressed by partial model.However, work as in larger distance between operated adjacent point, Traditional Gauss weighting function is then not enough to express transient data.In addition, each partial model is for each operating point Affect perhaps the presence of periodicity, that is to say, that for single operating point, weighting function has Gaussian characteristics；And for whole Operating point, weighting function has non-Gaussian feature, or mixed Gaussian characteristic.

The content of the invention

The purpose of the present invention is, for FDY polyester filament spinning technique optimization problems, to set up FDY polyester filament fibrous fractures Intensity and the degree of orientation, degree of crystallinity, the relational model of elongate fiber rate, there is provided a kind of multi-model modeling of mixed Gaussian weighting function Method.

To reach above-mentioned purpose, the technical solution used in the present invention is：

The FDY polyester filament spinning techniques that a kind of multi-model process based on mixed Gaussian weighting function is optimized, FDY Polyester filament spinning technique flow process is：Melt conveying-spinning manifold-measuring pump-component spinneret-quenching-oils- Hot-rolling drawing-off-high-speed winding-inspection-packaging, step is as follows：

1) first FDY polyester filaments fracture strength and the degree of orientation, degree of crystallinity and fibre are set up by mixed Gaussian weighting function Relational model between dimension elongation, while setting up the temperature of GR1 in hot-rolling drafting link (the first hot-rolling) and GR2 (the second hot-rolling) Degree and the relation function between speed and the FDY polyester filaments degree of orientation and degree of crystallinity；The relation function is as follows：

V₁=6.3*10⁴-10⁵u1+10⁵u2；

T₁=911-1639u1+1639u2；

V₂ ²=2.4*10⁷-4.7*10⁶u1-3.14*10⁸u2；

T₂ ²=-7.25*10⁷+2.5*10⁴u1+3.37*10⁸u2；

In formula, u1 is the degree of orientation, and u2 is degree of crystallinity, V₁For GR1 speed, T₁For GR1 temperature, V₂For GR2 speed, T₂For GR2 Temperature, the unit of the degree of orientation for °, the unit of degree of crystallinity is %, the unit of temperature for DEG C, the unit of speed is m/min；

2) a series of degree of orientation of FDY polyester filaments of stochastic inputs, degree of crystallinity and elongate fiber rate, by the relational model Output fracture strength, sets up the database of FDY polyester filament fracture strengths, the degree of orientation, degree of crystallinity and elongate fiber rate；

3) fracture strength in selected data storehouse is the FDY polyester filament fracture strengths that expection is obtained, in database Search the corresponding degree of orientation of the fracture strength and degree of crystallinity；

4) degree of orientation and degree of crystallinity for being obtained by lookup according to the relation function calculates the temperature and speed of GR1 and GR2 Degree, and the temperature and speed of the GR1 in FDY polyester filament spinning techniques and GR2 be adjusted accordingly；

The establishment step of the relational model is as follows：

(1) determine partial model number, collect fracture strength, the degree of orientation, degree of crystallinity and the elongate fiber of FDY polyester filaments Rate data constitute historical data base as historical data, and the FDY polyester filaments are in same process flow, different technical parameters Under the conditions of obtained fiber, the different technical parameters refer to that GR1 is different with speed with the temperature of GR2, the historical data Length is N, and selection output variable y is fibrous fracture intensity, and input variable u1 is the degree of orientation, and input variable u2 is degree of crystallinity, is adjusted Degree variable w is elongate fiber rate, and scheduling variable w is a physical descriptor that decide system operating mode, itself is have one Individual stable operating point is transitioned into another stable operating point in slope form, and the unit of fibrous fracture intensity is cN/dtex, The unit of elongate fiber rate is %, chooses elongate fiber rate when elongate fiber in N number of elongate fiber rate reaches stable state and makees For operating point T, T={ T₁,T₂,…,T_M, number M of operating point T is number M of partial model, T_iFor i-th partial model Operating point, i=1,2 ..., M, C_obsFor all data acquisition systems for observing, i.e. fibrous fracture intensity, the degree of orientation, degree of crystallinity, Elongate fiber rate and operating point, C_obs={ y_1:N,u1_1:N,u2_1:N,w_1:N,T_1:M, wherein, y₁,y₂,…,y_NSimplification is designated as y_1:N, u1₁,u1₂,...,u1_NSimplification is designated as u1_1:N, u2₁,u2₂,...,u2_NSimplification is designated as u2_1:N, w₁,w₂,...,w_NSimplification is designated as w_1:N, T₁,T₂,...,T_MSimplification is designated as T_1:M；

(2) determine partial model structure, estimating system is come as partial model using the autoregression model of the additional input of band Local dynamic station, it is specific as follows：

y_k=θ_ix_k+e_k；

In formula, sampling instant k=1,2 ..., N, y_kFor the corresponding fibrous fracture intensity of sampling instant k, x_kFor regressor, u1_kAnd u2_kFor the corresponding degrees of orientation of sampling instant k and degree of crystallinity, n_aAnd n_bThe order for respectively exporting and being input into, θ_iFor i-th The parameter sets of partial model, e_kIt is that 0, variance is σ for average²White Gaussian noise, i.e. e_k～N (0, σ²)；

Unknown parameter is θ in partial model structure_iAnd σ, the set of unknown parameter is M partial model parameter sets

(3) mixed Gaussian weighting function, mixed Gaussian weighting function α are determined_k,iFormula be：

In formula,For not normalized mixed Gaussian weighting function, π_i,jExist for mixed weight-value, i.e. mixed weight-value matrix π The element of the i-th row jth row, o_i,jFor the effective width in jth operating point of i-th partial model, w_kFor sampling instant k correspondences Elongate fiber rate, T_iFor i-th operating point, i=1,2 ..., M, j=1,2 ..., M；

Unknown parameter is π in mixed Gaussian weighting function_i,jAnd o_i,j, the set of unknown parameter is in weighting function Parameter setsParameter sets Θ of world model are the parameter of partial model and the parameter of weighting function Set, i.e. Θ={ Θ_m,Θ_w}；

(4) parameter unknown in partial model and mixed Gaussian weighting function is estimated；

(5) according to the ginseng estimated in partial model number, partial model structure, mixed Gaussian weighting function and step (4) Number, obtains the relational model between FDY polyester filaments fracture strength and the degree of orientation, degree of crystallinity and elongate fiber rate, specific as follows：

In formula,Prediction for FDY polyester filament fracture strengths is exported, α_k,iFor mixed Gaussian weighting function,It is The prediction output of the partial model at i operating point；

It is described to estimate comprising the following steps that for parameter unknown in partial model and mixed Gaussian weighting function：

1) mixed weight-value π is selected_i,j, mixed weight-value π_i,jThere are 3 kinds of selections, the Ith kind need not estimate parameter, calculate simple, the II kind of need estimate that parameter is more, but amount of calculation is placed in the middle, the IIIth kind of number of parameters between the Ith kind and the IIth kind, but due to It is non-linear, estimate parameter complexity highest, to see according to computational accuracy, the IIIth kind of precision is higher than the IIth kind, and the IIth kind is higher than the Ith Kind, it is specific as follows：

I. mixed weight-value π_i,jFor determination value, χ is calculated first_i,jMixed weight-value matrix χ is obtained, χ is normalized by row vector Mixed weight-value matrix π is obtained, mixed weight-value π is obtained by mixed weight-value matrix π_i,j, χ_i,jComputing formula it is as follows：

In formula, χ_i,jFor the element of the i-th row jth row in mixed weight-value matrix χ, T_jFor j-th operating point；

II. mixed weight-value π_i,jIt is unknown, first by estimating χ_i,jMixed weight-value matrix χ is obtained, χ is normalized by row vector Mixed weight-value matrix π is obtained, mixed weight-value π is obtained by mixed weight-value matrix π_i,j, the expression formula of mixed weight-value matrix χ is：

Wherein, as i=j, χ_ijThe diagonal element of=1, matrix χ is 1, i.e. χ₁₁=1, χ₂₂=1 ..., χ_MM=1；As i ≠ j When, 0<χ_ij<1；As i≤j<During l, χ_ij>χ_il, M × (M-1)/2 parameter is had in mixed weight-value matrix χ to be needed to estimate；

III. mixed weight-value π_i,jWith Gaussian Profile, mixed weight-value π_i,jComputing formula is as follows：

In formula, τ_iFor parameter to be estimated；

2) set initial parameter Θ ', i.e. Θ_mAnd Θ_wInitial value, set Θ_mMiddle θ_iWith the initial value of σ, Θ is set_wJust During initial value, as mixed weight-value π_i,jFor determination value when,Now set o_i,jInitial value, work as mixed weight-value π_i,jWhen unknown,Now set π_i,jAnd o_i,jInitial value, as mixed weight-value π_i,jWith Gaussian Profile When,Now set τ_iAnd o_i,jInitial value；

3) calculate Q- functions, according to known parameters Θ ', i.e. Θ_mAnd Θ_wInitial value, calculate Q- functions, Q- function formulas It is as follows：

In formula, C₂It is the constant unrelated with parameter；

4) Q- functions are maximized to obtain parameter sets Θ of renewal, then：

By θ_iAnd σ²The Θ of optimum is obtained_m；

Due to parameter Θ of mixed Gaussian weighting function_wIt is difficult to obtain its analytic solutions, is solved using nonlinear optimization algorithm, Its mathematic(al) representation is as follows：

Above formula is maximized, to ask for the Θ of optimum_w；

By optimum Θ_mWith optimum Θ_wParameter sets Θ for updating can be obtained；

5) repeat step 3) and 4) until the variable quantity of Θ is less than the threshold epsilon of setting, that is, repeat to make step 4) obtain more New parameter sets Θ=Θ ', and Θ is substituted into into Q- functions, the local that parameter sets Θ for obtaining are estimated is updated for the last time Unknown parameter in model and mixed Gaussian weighting function.

As preferred technical scheme：

The FDY polyester filaments that a kind of multi-model process based on mixed Gaussian weighting function as above is optimized spin Silk technique, the specification of the FDY polyester filaments is 83dtex/72f.

The FDY polyester filaments that a kind of multi-model process based on mixed Gaussian weighting function as above is optimized spin Silk technique, mixed weight-value π_i,jWith adjacent work dot spacing from relevant, π_i,jWith following restrictive condition：

(a)

(b)0≤π_i,j≤1；

(c)π_i,j>π_i,v, wherein | T_i-T_j|<|T_i-T_v|。

The FDY polyester filaments that a kind of multi-model process based on mixed Gaussian weighting function as above is optimized spin Silk technique, initial parameter Θ ' span be [0,1].

The FDY polyester filaments that a kind of multi-model process based on mixed Gaussian weighting function as above is optimized spin Silk technique, the threshold epsilon value is 10e-5.

The present invention relates to the FDY polyester filaments that a kind of multi-model process based on mixed Gaussian weighting function is optimized spin Silk technique.The fracture strength of FDY polyester filaments reflects fiber and produces extension directly in the axial force for gradually being increased Into the overall process of final fracture, the dependence of load and elongation can obtain the machinery of fiber by stress-strain diagram Performance indications, this is critically important for the textile process of fiber and the performance of product.The present invention passes through mixed Gaussian weighting function The relational model set up between FDY polyester filaments fracture strength and the degree of orientation, degree of crystallinity and elongate fiber rate of multi-model process, By partial model and its world model of the combination constructing system of weighting function, and under the framework of expectation-maximization algorithm, The parameter of partial model and mixed Gaussian weighting function is estimated simultaneously, is obtained fibrous fracture intensity and is taken with fiber in technological parameter After world model between Xiang Du, degree of crystallinity, elongate fiber rate, you can estimate fibrous fracture according to known technological parameter strong Degree, while fracture strength, the degree of orientation, degree of crystallinity and fiber that can be to set up FDY polyester filaments according to the relational model set up Elongation rate data storehouse, selectes fracture strength and searches the corresponding degree of orientation and degree of crystallinity, according to the degree of orientation and crystallization in database Relation pair spinning technique between degree and spinning technology parameter is optimized, and prepares the fiber of good mechanical performance.

Beneficial effect：

1) present invention sets up FDY polyester filaments fracture strength and the pass between the degree of orientation, degree of crystallinity and elongate fiber rate It is that model reversely can require adjustment according to already known processes parameter forward prediction fibrous fracture intensity by its fracture strength Optimizing Process Parameters；

2) the mixed Gaussian weighting function that the present invention is adopted can break through the assumed condition of Gauss weighting function, improve many The autgmentability and reliability of model modelling approach；

3) multi-model process of mixed Gaussian weighting function of the invention is more more general than traditional Gauss weighting function method Property, more meet FDY polyester filament spinning technique optimization characteristics.

Description of the drawings

Fig. 1 is the relational model set up between FDY polyester filaments fracture strength and the degree of orientation, degree of crystallinity and elongate fiber rate Flow chart；

Fig. 2 is the prediction comparative result of FDY polyester filaments fracture strength and simulation time.

Specific embodiment

With reference to specific embodiment, the present invention is expanded on further.It should be understood that these embodiments are merely to illustrate this Bright rather than restriction the scope of the present invention.In addition, it is to be understood that after the content for having read instruction of the present invention, art technology Personnel can make various changes or modifications to the present invention, and these equivalent form of values equally fall within the application appended claims and limited Fixed scope.

The FDY polyester filament spinning techniques that a kind of multi-model process based on mixed Gaussian weighting function is optimized, FDY The specification of polyester filament is 83dtex/72f, and FDY polyester filament spinning technique flow processs are：Melt conveying-spinning manifold-metering Pump-component spinneret-quenching-oils-hot-rolling drawing-off-high-speed winding-inspection-packaging, and step is as follows：

1) first FDY polyester filaments fracture strength and the degree of orientation, degree of crystallinity and fibre are set up by mixed Gaussian weighting function Relational model between dimension elongation, while it is long with FDY terylene to set up the temperature and speed of GR1 and GR2 in hot-rolling drafting link Relation function between the silk degree of orientation and degree of crystallinity；Relation function is as follows：

V₁=6.3*10⁴-10⁵u1+10⁵u2；

T₁=911-1639u1+1639u2；

V₂ ²=2.4*10⁷-4.7*10⁶u1-3.14*10⁸u2；

T₂ ²=-7.25*10⁷+2.5*10⁴u1+3.37*10⁸u2；

In formula, u1 is the degree of orientation, and u2 is degree of crystallinity, V₁For GR1 speed, T₁For GR1 temperature, V₂For GR2 speed, T₂For GR2 Temperature, the unit of the degree of orientation for °, the unit of degree of crystallinity is %, the unit of temperature for DEG C, the unit of speed is m/min；

2) a series of degree of orientation of FDY polyester filaments of stochastic inputs, degree of crystallinity and elongate fiber rate, are exported by relational model Fracture strength, sets up the database of FDY polyester filament fracture strengths, the degree of orientation, degree of crystallinity and elongate fiber rate；

3) fracture strength in selected data storehouse is the FDY polyester filament fracture strengths that expection is obtained, in database Search the corresponding degree of orientation of the fracture strength and degree of crystallinity；

4) degree of orientation and degree of crystallinity for being obtained by lookup according to relation function calculates the temperature and speed of GR1 and GR2, and The temperature and speed of the GR1 in FDY polyester filament spinning techniques and GR2 are adjusted accordingly；

As shown in figure 1, the establishment step of relational model is as follows：

(1) determine partial model number, collect fracture strength, the degree of orientation, degree of crystallinity and the elongate fiber of FDY polyester filaments Rate data constitute historical data base as historical data, and FDY polyester filaments are in same process flow, different technical parameters condition Lower obtained fiber, different technical parameters refer to that GR1 is different with speed with the temperature of GR2, length N=1000 of historical data, Selection output variable y is fibrous fracture intensity, and input variable u1 is the degree of orientation, and input variable u2 is degree of crystallinity, and scheduling variable w is Elongate fiber rate, scheduling variable w is a physical descriptor that decide system operating mode, itself is have a stable work Make point and be transitioned into another stable operating point in slope form, the unit of fibrous fracture intensity is cN/dtex, elongate fiber rate Unit be %, choose elongate fiber rate when elongate fiber in N number of elongate fiber rate reaches stable state as operating point T, T ={ 0.1,0.3,0.8 }, the number of operating point T is the number 3, C of partial model_obsFor all data acquisition systems for observing, i.e., Fibrous fracture intensity, the degree of orientation, degree of crystallinity, elongate fiber rate and operating point, C_obs={ y_1:1000,u_1:1000,w_1:1000,T_1:3}；

(2) determine partial model structure, estimating system is come as partial model using the autoregression model of the additional input of band Local dynamic station, it is specific as follows：

y_k=θ_ix_k+e_k；

In formula, sampling instant k=1,2 ... 1000, y_kFor the corresponding fibrous fracture intensity of sampling instant k, x_kFor regressor, u1_kAnd u2_kFor the corresponding degrees of orientation of sampling instant k and degree of crystallinity, n_a=2 and n_b=2 orders for respectively exporting and being input into, θ_iFor The parameter sets of i-th partial model, i=1,2,3, e_k～N (0, σ²) it is e_k～N (0,2)；

3 partial model parameter sets

(3) mixed Gaussian weighting function, mixed Gaussian weighting function α are determined_k,iFormula be：

In formula,For not normalized mixed Gaussian weighting function, π_i,jExist for mixed weight-value, i.e. mixed weight-value matrix π The element of the i-th row jth row, o_i,jFor the effective width in jth operating point of i-th partial model, w_kFor sampling instant k correspondences Elongate fiber rate, T_iFor i-th operating point, i=1,2,3, j=1,2,3；

Mixed weight-value π_i,jWith adjacent work dot spacing from relevant, π_i,jWith following restrictive condition：

(a)

(b)0≤π_i,j≤1；

(c)π_i,j>π_i,v, wherein | T_i-T_j|<|T_i-T_v|；

Parameter sets in weighting functionParameter sets Θ of world model are The parameter of partial model and the parameter sets of weighting function, i.e. Θ={ Θ_m,Θ_w}；

(4) parameter unknown in partial model and mixed Gaussian weighting function is estimated；

(5) according to the ginseng estimated in partial model number, partial model structure, mixed Gaussian weighting function and step (4) Number, obtains the relational model between FDY polyester filaments fracture strength and the degree of orientation, degree of crystallinity and elongate fiber rate, specific as follows：

In formula,Prediction for FDY polyester filament fracture strengths is exported, α_k,iFor mixed Gaussian weighting function,It is The prediction output of the partial model at i operating point；

As shown in figure 1, estimating comprising the following steps that for unknown parameter in partial model and mixed Gaussian weighting function：

1) mixed weight-value π is selected_i,j, mixed weight-value π_i,jThere are 3 kinds of selections, the Ith kind need not estimate parameter, calculate simple, the II kind of need estimate that parameter is more, but amount of calculation is placed in the middle, the IIIth kind of number of parameters between the Ith kind and the IIth kind, but due to It is non-linear, estimate parameter complexity highest, to see according to computational accuracy, the IIIth kind of precision is higher than the IIth kind, and the IIth kind is higher than the Ith Kind, it is specific as follows：

I. mixed weight-value π_i,jFor determination value, χ is calculated first_i,jMixed weight-value matrix χ is obtained, χ is normalized by row vector Mixed weight-value matrix π is obtained, mixed weight-value π is obtained by mixed weight-value matrix π_i,j, χ_i,jComputing formula it is as follows：

In formula, χ_i,jFor the element of the i-th row jth row in mixed weight-value matrix χ, T_jFor j-th operating point；

II. mixed weight-value π_i,jIt is unknown, first by estimating χ_i,jMixed weight-value matrix χ is obtained, χ is normalized by row vector Mixed weight-value matrix π is obtained, mixed weight-value π is obtained by mixed weight-value matrix π_i,j, the expression formula of mixed weight-value matrix χ is：

Wherein, as i=j, χ_ijThe diagonal element of=1, matrix χ is 1, i.e. χ₁₁=1, χ₂₂=1 ..., χ_MM=1；As i ≠ j When, 0<χ_ij<1；As i≤j<During l, χ_ij>χ_il, 3 parameters are had in mixed weight-value matrix χ to be needed to estimate；

III. mixed weight-value π_i,jWith Gaussian Profile, mixed weight-value π_i,jComputing formula is as follows：

In formula, τ_iFor parameter to be estimated；

2) set initial parameter Θ ', the span of Θ ' is [0,1], i.e. Θ_mAnd Θ_wInitial value, set Θ_mMiddle θ_i With the initial value of σ, Θ is set_wInitial value when, as mixed weight-value π_i,jFor determination value when,Now set o_i,jInitial value, as mixed weight-value π_i,jWhen unknown,Now set π_i,jAnd o_i,jInitial value, when Mixed weight-value π_i,jDuring with Gaussian Profile,Now set τ_iAnd o_i,jInitial value；

3) calculate Q- functions, according to known parameters Θ ', i.e. Θ_mAnd Θ_wInitial value, calculate Q- functions, Q- function formulas It is as follows：

In formula, C₂It is the constant unrelated with parameter；

4) Q- functions are maximized to obtain parameter sets Θ of renewal, then：

By θ_iAnd σ²The Θ of optimum is obtained_m；

Due to parameter Θ of mixed Gaussian weighting function_wIt is difficult to obtain its analytic solutions, is solved using nonlinear optimization algorithm, Its mathematic(al) representation is as follows：

Above formula is maximized, to ask for the Θ of optimum_w；

By optimum Θ_mWith optimum Θ_wParameter sets Θ for updating can be obtained；

5) repeat step 3) and 4) until the variable quantity of Θ is less than the threshold epsilon for setting, threshold epsilon value is 10e-5, that is, repeat Make step 4) the parameter sets Θ=Θ ' of renewal that obtains, and Θ is substituted into into Q- functions, the parameter set for obtaining is updated for the last time Close parameter unknown in the partial models estimated of Θ and mixed Gaussian weighting function.

FDY polyester filaments fracture strength and the pass between the degree of orientation, degree of crystallinity and elongate fiber rate using above-mentioned foundation It is that model measures FDY polyester filaments fracture strength obtained in different simulation times, and is compared with real fracture strength, ties The fracture strength that fruit is estimated as shown in Fig. 2 as can be seen from Figure under identical simulation time, using the model with it is real Fracture strength difference is less, illustrates that the relational model of present invention foundation can accurately, effectively to the mechanical property of FDY polyester filaments Can be estimated, and then FDY polyester filament spinning techniques are reasonably regulated and controled.

Claims (5)

1. a kind of FDY polyester filament spinning techniques that multi-model process based on mixed Gaussian weighting function is optimized, FDY is washed Synthetic fibre continuous yarn spinning technological process is：Melt conveying-spinning manifold-measuring pump-component spinneret-quenching-oils-heat Roller drawing-off-high-speed winding-inspection-packaging, is characterized in that, step is as follows：

1) set up FDY polyester filaments fracture strength by mixed Gaussian weighting function first to stretch with the degree of orientation, degree of crystallinity and fiber Relational model between long rate, while set up the temperature and speed of GR1 and GR2 in hot-rolling drafting link taking with FDY polyester filaments To the relation function between degree and degree of crystallinity；The relation function is as follows：

V₁=6.3*10⁴-10⁵u1+10⁵u2；

T₁=911-1639u1+1639u2；

V₂ ²=2.4*10⁷-4.7*10⁶u1-3.14*10⁸u2；

T₂ ²=-7.25*10⁷+2.5*10⁴u1+3.37*10⁸u2；

In formula, u1 is the degree of orientation, and u2 is degree of crystallinity, V₁For GR1 speed, T₁For GR1 temperature, V₂For GR2 speed, T₂For GR2 temperature, The unit of the degree of orientation for °, the unit of degree of crystallinity is %, the unit of temperature for DEG C, the unit of speed is m/min；

2) a series of degree of orientation of FDY polyester filaments of stochastic inputs, degree of crystallinity and elongate fiber rate, are exported by the relational model Fracture strength, sets up the database of FDY polyester filament fracture strengths, the degree of orientation, degree of crystallinity and elongate fiber rate；

3) fracture strength in selected data storehouse is the FDY polyester filament fracture strengths that expection is obtained, and is searched in database The corresponding degree of orientation of the fracture strength and degree of crystallinity；

4) degree of orientation and degree of crystallinity for being obtained by lookup according to the relation function calculates the temperature and speed of GR1 and GR2, and The temperature and speed of the GR1 in FDY polyester filament spinning techniques and GR2 are adjusted accordingly；

The establishment step of the relational model is as follows：

(1) determine partial model number, collect fracture strength, the degree of orientation, degree of crystallinity and the elongate fiber rate number of FDY polyester filaments Historical data base is constituted according to as historical data, the FDY polyester filaments are in same process flow, different technical parameters condition Lower obtained fiber, the different technical parameters refer to that GR1 is different with speed with the temperature of GR2, the length of the historical data For N, selection output variable y is fibrous fracture intensity, and input variable u1 is the degree of orientation, and input variable u2 is degree of crystallinity, and scheduling becomes Amount w is elongate fiber rate, and the unit of fibrous fracture intensity is cN/dtex, and the unit of elongate fiber rate is %, chooses N number of fiber Elongate fiber rate when elongate fiber reaches stable state in elongation is used as operating point T, T={ T₁,T₂,…,T_M, operating point T Number M be number M of partial model, T_iFor the operating point of i-th partial model, i=1,2 ..., M, C_obsFor all sights The data acquisition system for measuring, i.e. fibrous fracture intensity, the degree of orientation, degree of crystallinity, elongate fiber rate and operating point, C_obs={ y_1:N, u1_1:N,u2_1:N,w_1:N,T_1:M, wherein, y₁,y₂,…,y_NSimplification is designated as y_1:N, u1₁,u1₂,...,u1_NSimplification is designated as u1_1:N, u2₁, u2₂,...,u2_NSimplification is designated as u2_1:N, w₁,w₂,...,w_NSimplification is designated as w_1:N, T₁,T₂,...,T_MSimplification is designated as T_1:M；

(2) determine partial model structure, the local of estimating system is come as partial model using the autoregression model of the additional input of band Dynamic, it is specific as follows：

y_k=θ_ix_k+e_k；

$x_k=[y_{k-1},...,y_{k-n_a},{u1}_{k-1},...,{u1}_{k-n_b},{u2}_{k-1},...,{u2}_{k-n_b}];$

In formula, sampling instant k=1,2 ..., N, y_kFor the corresponding fibrous fracture intensity of sampling instant k, x_kFor regressor, u1_kWith u2_kFor the corresponding degrees of orientation of sampling instant k and degree of crystallinity, n_aAnd n_bThe order for respectively exporting and being input into, θ_iFor i-th local The parameter sets of model, e_kIt is that 0, variance is σ for average²White Gaussian noise, i.e. e_k～N (0, σ²)；

Unknown parameter is θ in partial model structure_iAnd σ, the set of unknown parameter is M partial model parameter sets

(3) mixed Gaussian weighting function, mixed Gaussian weighting function α are determined_k,iFormula be：

In formula,For not normalized mixed Gaussian weighting function, π_i,jFor mixed weight-value, i.e., mixed weight-value matrix π is in the i-th row The element of jth row, o_i,jFor the effective width in jth operating point of i-th partial model, w_kFor the corresponding fibers of sampling instant k Elongation, T_iFor i-th operating point, i=1,2 ..., M, j=1,2 ..., M；

Unknown parameter is π in mixed Gaussian weighting function_i,jAnd o_i,j, the set of unknown parameter is the parameter in weighting function SetParameter sets Θ of world model are the parameter of partial model and the parameter set of weighting function Close, i.e. Θ={ Θ_m,Θ_w}；

(4) parameter unknown in partial model and mixed Gaussian weighting function is estimated；

(5) according to the parameter estimated in partial model number, partial model structure, mixed Gaussian weighting function and step (4), obtain Relational model between FDY polyester filaments fracture strength and the degree of orientation, degree of crystallinity and elongate fiber rate, it is specific as follows：

${\hat{y}}_k=\underset{i=1}{\overset{M}{\&Sigma;}}{\mathrm{\&alpha;}}_{k,i}{\hat{y}}_k^i;$

In formula,Prediction for FDY polyester filament fracture strengths is exported, α_k,iFor mixed Gaussian weighting function,It is in i-th work Make the prediction output of the partial model at point；

Unknown parameter comprises the following steps that in the estimation partial model and mixed Gaussian weighting function：

1) mixed weight-value π is selected_i,j, mixed weight-value π_i,jThere are 3 kinds of selections, it is specific as follows：

I. mixed weight-value π_i,jFor determination value, χ is calculated first_i,jMixed weight-value matrix χ is obtained, χ is obtained by row vector normalization Mixed weight-value matrix π, by mixed weight-value matrix π mixed weight-value π is obtained_i,j, χ_i,jComputing formula it is as follows：

${\mathrm{\&chi;}}_{i,j}=\left\{\begin{array}{cc}1,& T_i=T_j\\ \frac{1}{2^{T_i-T_j}},& T_i>T_j\\ \frac{1}{2^{T_j-T_i}},& T_i<T_j\end{array}\right.;$

In formula, χ_i,jFor the element of the i-th row jth row in mixed weight-value matrix χ, T_jFor j-th operating point；

II. mixed weight-value π_i,jIt is unknown, first by estimating χ_i,jMixed weight-value matrix χ is obtained, χ is obtained by row vector normalization Mixed weight-value matrix π, by mixed weight-value matrix π mixed weight-value π is obtained_i,j, the expression formula of mixed weight-value matrix χ is：

Wherein, as i=j, χ_ijThe diagonal element of=1, matrix χ is 1, i.e. χ₁₁=1, χ₂₂=1 ..., χ_MM=1；As i ≠ j, 0 <χ_ij<1；As i≤j<During l, χ_ij>χ_il, M × (M-1)/2 parameter is had in mixed weight-value matrix χ to be needed to estimate；

III. mixed weight-value π_i,jWith Gaussian Profile, mixed weight-value π_i,jComputing formula is as follows：

${\mathrm{\&pi;}}_{i,j}=\frac{\exp (-\frac{{(T_i-T_j)}^2}{2{\left({\mathrm{\&tau;}}_i\right)}^2})}{\underset{i=1}{\overset{M}{\&Sigma;}}\exp (-\frac{{(T_i-T_j)}^2}{2{\left({\mathrm{\&tau;}}_i\right)}^2})};$

In formula, τ_iFor parameter to be estimated；

2) set initial parameter Θ ', i.e. Θ_mAnd Θ_wInitial value, set Θ_mMiddle θ_iWith the initial value of σ, Θ is set_wInitial value When, as mixed weight-value π_i,jFor determination value when,Now set o_i,jInitial value, as mixed weight-value π_i,jNot When knowing,Now set π_i,jAnd o_i,jInitial value, as mixed weight-value π_i,jDuring with Gaussian Profile,Now set τ_iAnd o_i,jInitial value；

3) calculate Q- functions, according to known parameters Θ ', i.e. Θ_mAnd Θ_wInitial value, calculate Q- functions, Q- function formulas are as follows：

$\begin{array}{c}Q\left(\mathrm{\&Theta;}|{\mathrm{\&Theta;}}^{\&prime;}\right)\\ =\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\log p\left(y_k|x_k,{\mathrm{\&Theta;}}_m\right)p\left(i|w_k,C_{obs},{\mathrm{\&Theta;}}^{\&prime;}\right)\\ +\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\log p\left(i|w_k,T_{1:M},{\mathrm{\&Theta;}}_w\right)p\left(i|w_k,C_{obs},{\mathrm{\&Theta;}}^{\&prime;}\right)+C_2\end{array};$

In formula, C₂It is the constant unrelated with parameter；

4) Q- functions are maximized to obtain parameter sets Θ of renewal, then：

${\mathrm{\&theta;}}_i=\frac{\underset{k=1}{\overset{N}{\&Sigma;}}p\left(i\right|w_k,C_{obs},{\mathrm{\&Theta;}}^{\&prime;})x_k^T{y}_k}{\underset{k=1}{\overset{N}{\&Sigma;}}p\left(i\right|w_k,C_{obs},{\mathrm{\&Theta;}}^{\&prime;})x_k^T{x}_k};$

${\mathrm{\&sigma;}}^2=\frac{\underset{k=1}{\overset{N}{\&Sigma;}}\underset{i=1}{\overset{M}{\&Sigma;}}p\left(i\right|w_k,C_{obs},{\mathrm{\&Theta;}}^{\&prime;}){(y_k-{{\mathrm{\&theta;}}_i}^T{x}_k)}^T(y_k-{{\mathrm{\&theta;}}_i}^T{x}_k)}{\underset{k=1}{\overset{N}{\&Sigma;}}\underset{i=1}{\overset{M}{\&Sigma;}}p\left(i\right|w_k,C_{obs},{\mathrm{\&Theta;}}^{\&prime;})};$

By θ_iAnd σ²The Θ of optimum is obtained_m；

Due to parameter Θ of mixed Gaussian weighting function_wIt is difficult to obtain its analytic solutions, is solved using nonlinear optimization algorithm, its number Learn expression formula as follows：

$max\underset{k=1}{\overset{N}{\&Sigma;}}\underset{i=1}{\overset{M}{\&Sigma;}}\log p\left(i\right|w_k,T_{1:M},{\mathrm{\&Theta;}}_w)p\left(i\right|w_k,C_{obs},{\mathrm{\&Theta;}}^{\&prime;});$

Above formula is maximized, to ask for the Θ of optimum_w；

By optimum Θ_mWith optimum Θ_wParameter sets Θ for updating can be obtained；

5) repeat step 3) and 4) until the variable quantity of Θ is less than the threshold epsilon of setting, that is, repeat to make step 4) renewal that obtains Parameter sets Θ=Θ ', and Θ is substituted into into Q- functions, the partial model that parameter sets Θ for obtaining are estimated is updated for the last time With parameter unknown in mixed Gaussian weighting function.

2. the FDY that a kind of multi-model process based on mixed Gaussian weighting function according to claim 1 is optimized is washed Synthetic fibre continuous yarn spinning technique, it is characterised in that the specification of the FDY polyester filaments is 83dtex/72f.

3. the FDY that a kind of multi-model process based on mixed Gaussian weighting function according to claim 1 is optimized is washed Synthetic fibre continuous yarn spinning technique, it is characterised in that mixed weight-value π_i,jWith adjacent work dot spacing from relevant, π_i,jBar is limited with following Part：

(a)

(b)0≤π_i,j≤1；

(c)π_i,j>π_i,v, wherein | T_i-T_j|<|T_i-T_v|。

4. the FDY that a kind of multi-model process based on mixed Gaussian weighting function according to claim 1 is optimized is washed Synthetic fibre continuous yarn spinning technique, it is characterised in that initial parameter Θ ' span be [0,1].

5. the FDY that a kind of multi-model process based on mixed Gaussian weighting function according to claim 1 is optimized is washed Synthetic fibre continuous yarn spinning technique, it is characterised in that the threshold epsilon value is 10e-5.