CN106599431B - FDY polyester filament spinning process optimized by multi-model method based on mixed Gaussian weight function - Google Patents

FDY polyester filament spinning process optimized by multi-model method based on mixed Gaussian weight function Download PDF

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CN106599431B
CN106599431B CN201611113654.0A CN201611113654A CN106599431B CN 106599431 B CN106599431 B CN 106599431B CN 201611113654 A CN201611113654 A CN 201611113654A CN 106599431 B CN106599431 B CN 106599431B
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crystallinity
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CN106599431A (en
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陈磊
丁永生
任立红
郝矿荣
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Donghua University
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Abstract

The invention relates to an FDY polyester filament spinning process optimized by a multi-model method based on a mixed Gaussian weight function, which comprises the steps of firstly establishing a relation model between the breaking strength and the orientation degree of FDY polyester filaments, between the crystallinity and the fiber elongation, simultaneously establishing a relation function between the temperature and the speed of GR1 and GR2 and between the orientation degree and the crystallinity of FDY polyester filaments, then establishing a database, finally selecting the breaking strength, calculating the temperature and the speed of GR1 and GR2 according to the relation function, and adjusting the spinning process, wherein the establishment of the relation model comprises the following steps: 1) determining the number of local models, 2) determining a local model structure, 3) determining a Gaussian mixture weight function, 4) estimating unknown parameters in the local models and the Gaussian mixture weight function, and 5) obtaining a relation model. The model established by the invention has the characteristics of high accuracy and strong reliability, and the spinning process disclosed by the invention is beneficial to preparing the fiber with excellent mechanical property.

Description

FDY polyester filament spinning process optimized by multi-model method based on mixed Gaussian weight function
Technical Field
The invention belongs to the field of FDY polyester filament spinning processes, and relates to an FDY polyester filament spinning process optimized by a multi-model method based on a mixed Gaussian weight function.
Background
The existing FDY polyester filament model can establish a model of the structure and the breaking strength of the fiber, but the change of the fiber performance can not be directly reflected through process adjustment. Based on actual requirements, a quantitative relation of structural properties of the FDY polyester filament spinning process is established, namely a relation model of fiber breaking strength, orientation degree, crystallinity and fiber elongation is established, the model can be reversely used for process optimization in a normal production process while the fiber breaking strength is predicted through known process parameters, a foundation is laid for development of new technologies and new products, and guidance is provided for improving the fiber quality.
generally, the fiber production process does not run randomly within the operating area, but always runs according to a certain operating strategy, such operating strategy being interrelated to the dynamic characteristics of the system, different products being obtained by different operating strategies. An operation strategy generally consists of a series of preset operating points, and such operating point variables are scheduling variables. The scheduling variable is a physical variable that determines the mode of operation of the system and is itself slowly changing. Due to the multi-working condition characteristic of the scheduling variable, a multi-model method can be applied to the modeling problem of the hybrid water tank system with the scheduling variable.
The existing multi-model modeling method mainly has two assumed conditions: (1) the distance between adjacent working points is small; (2) the process dynamics of the region around the operating point can be expressed by means of a local model. However, when the distance between adjacent operating points is large, the conventional gaussian weighting function is not sufficient to express the transient process data. In addition, the influence of each local model on each operating point may be periodic, that is, for a single operating point, the weighting function has a gaussian characteristic; while the weighting function has a non-gaussian, or gaussian mixture, characteristic for all operating points.
disclosure of Invention
the invention aims to establish a relation model of fiber breaking strength, orientation degree, crystallinity and fiber elongation of FDY polyester filaments aiming at the optimization problem of the FDY polyester filament spinning process, and provides a multi-model modeling method of a mixed Gaussian weight function.
In order to achieve the purpose, the invention adopts the technical scheme that:
An FDY polyester filament spinning process optimized by a multi-model method based on a mixed Gaussian weight function comprises the following process flows: melt conveying, spinning box body, metering pump, component spinning, air blowing cooling, oiling, hot roller drafting, high-speed winding, inspection and packaging, and the method comprises the following steps:
1) Firstly, establishing a relation model between the breaking strength and the orientation degree of the FDY polyester filament, between the crystallinity and the fiber elongation by a mixed Gaussian weight function, and simultaneously establishing a relation function between the temperature and the speed of GR1 (a first hot roller) and GR2 (a second hot roller) in a hot roller drafting link and the orientation degree and the crystallinity of the FDY polyester filament; the relationship 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；
Wherein u1 represents orientation degree, u2 represents crystallinity degree, and V represents1GR1 speed, T1At GR1 temperature, V2GR2 speed, T2Is the GR2 temperature, the units of orientation, the units of crystallinity, the units of temperature, and the units of speed are m/min;
2) Randomly inputting the orientation degree, the crystallinity and the fiber elongation of a series of FDY polyester filaments, outputting the breaking strength by the relation model, and establishing a database of the breaking strength, the orientation degree, the crystallinity and the fiber elongation of the FDY polyester filaments;
3) selecting one breaking strength in a database as the expected breaking strength of the FDY polyester filament, and searching the orientation degree and the crystallinity corresponding to the breaking strength in the database;
4) Calculating the temperature and the speed of GR1 and GR2 according to the relation function and the orientation degree and the crystallinity degree obtained by searching, and adjusting the temperature and the speed of GR1 and GR2 in the FDY polyester filament spinning process according to the temperature and the speed;
The establishment steps of the relation model are as follows:
(1) determining the number of local models, and collecting data of breaking strength, orientation degree, crystallinity and fiber elongation of FDY polyester filaments as historical data to form a historical database, wherein the FDY polyester filaments are fibers prepared under the conditions of the same process flow and different process parameters, the different process parameters mean that the temperatures and the speeds of GR1 and GR2 are different, the length of the historical data is N, an output variable y is selected as the fiber breaking strength, an input variable u1 is the orientation degree, an input variable u2 is the crystallinity, a scheduling variable w is the fiber elongation, the scheduling variable w is a physical variable determining the working mode of a system, and the scheduling variable w has a stable working pointThe fiber elongation is selected as the working point T when the fiber elongation reaches the steady state in N fiber elongations, and T is { T ═ T { (T }1，T2，…，TMThe number M of the working points T is the number M of the local models, TiIs the operating point of the ith local model, i is 1,2, …, M, Cobsfor all observed data sets, i.e. fiber breaking strength, degree of orientation, degree of crystallinity, fiber elongation and working point, Cobs＝{y1:N,u11:N,u21:N,w1:N,T1:MIn which y1，y2，…，yNsimplified notation as y1:N，u11,u12,...,u1NSimplified notation u11:N，u21,u22,...,u2NSimplified notation u21:N，w1,w2,...,wNSimplified notation by w1:N，T1,T2,...,TMsimplified notation as T1:M；
(2) Determining a local model structure, and estimating the local dynamics of the system by taking an autoregressive model with an out-of-band addition input as a local model, wherein the method specifically comprises the following steps:
yk＝θi xk+ek；
In the formula, the sampling time k is 1,2, L, N, ykFor the fiber breaking strength, x, corresponding to the sampling time kkAs a regressive quantity, u1kAnd u2kDegree of orientation and degree of crystallinity, n, for a sampling time kaAnd nborder of output and input, respectively, thetaiIs the parameter set of the ith local model, ekIs a mean value of 0 and a variance of σ2White Gaussian noise of (i.e. e)k～N(0,σ2)；
The unknown parameter in the local model structure is thetaiand σ, unknownset of parameters, i.e. M sets of local model parameters
(3) Determining a Gaussian mixture weight function, a Gaussian mixture weight function alphak,iThe formula of (1) is:
in the formula (I), the compound is shown in the specification,As a function of the unnormalised mixed Gaussian weight, pii,jIs a mixed weight, i.e. the element of the mixed weight matrix pi in the ith row and jth column, oi,jIs the effective width, w, of the ith local model at the jth operating pointkFor the fibre elongation corresponding to the sampling instant k, TiThe ith operating point is 1,2, …, M, j is 1,2, …, M;
the unknown parameter in the Gaussian mixture weight function is pii,jand oi,jSets of unknown parameters, i.e. parameter sets in weighting functionsThe parameter set Θ of the global model is a parameter set of the local model and the weighting function, that is, Θ ═ Θm,Θw}；
(4) Estimating unknown parameters in the local model and the Gaussian mixture weight function;
(5) obtaining a relation model between the breaking strength and the orientation degree of the FDY polyester filament yarn, the crystallinity and the fiber elongation according to the number of the local models, the structure of the local models, the mixed Gaussian weight function and the parameters estimated in the step (4), wherein the relation model comprises the following specific steps:
In the formula (I), the compound is shown in the specification,Is the predicted output of the breaking strength of the FDY polyester filament yarn, alphak,iIs a function of the weight of the mixture of gaussians,a predicted output for the local model at the ith operating point;
The specific steps for estimating the unknown parameters in the local model and the Gaussian mixture weight function are as follows:
1) selecting a mixing weight value pii,jMixed weight pii,jThere are 3 kinds of selection, the parameter need not to be estimated to the first kind, and the calculation is simple, and the second kind needs to be estimated the parameter more, but the calculated amount is middle, and III number of parameters is between the first kind and II kind, but because nonlinearity, estimates the parameter complexity the highest, according to calculation accuracy, III kind precision is higher than II kind, and II kind is higher than I kind, specifically as follows:
I. mixed weight pii,jTo determine the value, first χ is calculatedi,jobtaining a mixed weight matrix x, normalizing the x according to the row vector to obtain a mixed weight matrix pi, and obtaining a mixed weight pi from the mixed weight matrix pii,j，χi,jthe calculation formula of (a) is as follows:
In the formula, xi,jIs the element of the ith row and the jth column in the mixed weight matrix chi, TjIs the jth working point;
II, mixing weight pii,junknown, first by estimating χi,jObtaining a mixed weight matrix x, normalizing the x according to the row vector to obtain a mixed weight matrix pi, and obtaining a mixed weight pi from the mixed weight matrix pii,jThe expression of the mixed weight matrix χ is:
wherein, when i ═ j, χij1, the diagonal element of the matrix χ is 1, χ11＝1，χ22＝1，…，χMM1 is ═ 1; when i ≠ j, 0 < χijless than 1; when i is less than or equal to j and less than l, xij＞χilThe mixed weight matrix chi has M x (M-1)/2 parameters to be estimated;
III. mixing weight pii,jWith Gaussian distribution, mixed weight pii,jThe calculation formula is as follows:
In the formula, τiis a parameter to be estimated;
2) setting an initial parameter theta', namely thetamAnd Θwsetting theta as an initial value ofmMiddle thetaiAnd σ, setting ΘwWhen the initial value of (2) is greater, when the weight of mixing is pii,jIn order to determine the value of the value,At this time, set to oi,jwhen the mixing weight is pii,jWhen the time is not known, the user can select the target,At this time, pi is seti,jAnd oi,jwhen the mixing weight is pii,jin the case of a distribution of the gaussian components,at this time, τ is setiAnd oi,jan initial value of (1);
3) calculating the Q function according to the known parameter theta', namely thetamand Θwcalculates the Q function, which is formulated as follows:
in the formula, C2is a constant independent of the parameter;
4) Maximizing the Q function to obtain an updated set of parameters Θ, then:
By thetaiAnd σ2The optimal theta can be obtainedm；
Due to the parameter theta of the Gaussian mixture weight functionwThe analytical solution is difficult to obtain, the non-linear optimization algorithm is adopted for solving, and the mathematical expression is as follows:
maximize the above formula to find the optimal thetaw；
From the optimum thetamAnd an optimal Θwobtaining an updated parameter set theta;
5) And repeating the steps 3) and 4) until the variation of the theta is smaller than the set threshold epsilon, namely repeatedly enabling the updated parameter set theta obtained in the step 4) to be theta', substituting the theta into the Q function, and finally updating the obtained parameter set theta, namely the unknown parameters in the estimated local model and the Gaussian mixture weight function.
As a preferred technical scheme:
The FDY polyester filament spinning process is optimized by the multi-model method based on the mixed Gaussian weight function, and the specification of the FDY polyester filament is 83dtex/72 f.
the FDY polyester filament spinning process optimized by the multi-model method based on the mixed Gaussian weight function has the mixed weight pii,jin relation to the distance between adjacent working points, pii,jwith the following limitations:
(a)
(b)0≤πi,j≤1；
(c)πi,j＞πi,vWherein | Ti-Tj|＜|Ti-Tv|。
according to the FDY polyester filament spinning process optimized by the multi-model method based on the mixed Gaussian weight function, the value range of the initial parameter theta' is [0,1 ].
According to the FDY polyester filament spinning process optimized by the multi-model method based on the mixed Gaussian weight function, the value of the threshold epsilon is 10 e-5.
The invention relates to an FDY polyester filament spinning process optimized by a multi-model method based on a mixed Gaussian weight function. The breaking strength of the FDY polyester filament reflects the dependency relationship between load and elongation in the whole process of extending the fiber to the final breaking under the action of gradually increased axial acting force, and the mechanical property index of the fiber can be obtained through a stress-strain curve, which is important for the textile processing of the fiber and the performance of products. The invention establishes a relation model between the breaking strength and the orientation degree, the crystallinity and the fiber elongation of the FDY polyester filament by a multi-model method of a mixed Gaussian weight function, constructs a global model of a system by combining a local model and a weight function thereof, simultaneously estimates parameters of the local model and the mixed Gaussian weight function under the frame of an expectation-maximization algorithm, obtains the global model between the breaking strength and the fiber orientation degree, the crystallinity and the fiber elongation in process parameters, estimates the fiber breaking strength according to known process parameters, simultaneously establishes a breaking strength, orientation degree, crystallinity and fiber elongation database of the FDY polyester filament according to the established relation model, selects the breaking strength in the database to search the corresponding orientation degree and crystallinity, optimizes the spinning process according to the relation between the orientation degree, the crystallinity and the spinning process parameters, preparing the fiber with excellent mechanical property.
has the advantages that:
1) The relationship model between the breaking strength of the FDY polyester filament yarn and the orientation degree, the crystallinity and the fiber elongation can be used for predicting the breaking strength of the fiber in the forward direction according to the known process parameters, and the optimized process parameters can be adjusted according to the breaking strength requirement in the backward direction;
2) The mixed Gaussian weight function adopted by the invention can break through the assumed condition of the Gaussian weight function, and the expansibility and reliability of the multi-model modeling method are improved;
3) Compared with the traditional Gaussian weight function method, the multi-model method of the mixed Gaussian weight function has higher universality and better accords with the optimized characteristic of the FDY polyester filament spinning process.
drawings
FIG. 1 is a flow chart for establishing a model of the relationship between the breaking strength of FDY polyester filaments and the degree of orientation, crystallinity and fiber elongation.
Detailed Description
The invention will be further illustrated with reference to specific embodiments. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and such equivalents may fall within the scope of the present invention as defined in the appended claims.
an FDY polyester filament spinning process optimized by a multi-model method based on a mixed Gaussian weight function is provided, the specification of the FDY polyester filament is 83dtex/72f, and the FDY polyester filament spinning process flow is as follows: melt conveying, spinning box body, metering pump, component spinning, air blowing cooling, oiling, hot roller drafting, high-speed winding, inspection and packaging, and the method comprises the following steps:
1) Firstly, establishing a relation model between the breaking strength and the orientation degree of the FDY polyester filament, between the crystallinity and the fiber elongation by a mixed Gaussian weight function, and simultaneously establishing a relation function between the temperature and the speed of GR1 and GR2 in a hot roller drafting link and the orientation degree and the crystallinity of the FDY polyester filament; the relationship 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；
wherein u1 represents orientation degree, u2 represents crystallinity degree, and V represents1GR1 speed, T1At GR1 temperature, V2GR2 speed, T2Is the GR2 temperature, the units of orientation, the units of crystallinity, the units of temperature, and the units of speed are m/min;
2) Randomly inputting a series of orientation degree, crystallinity and fiber elongation of the FDY polyester filament yarns, outputting breaking strength by a relation model, and establishing a database of the breaking strength, the orientation degree, the crystallinity and the fiber elongation of the FDY polyester filament yarns;
3) Selecting one breaking strength in a database as the expected breaking strength of the FDY polyester filament, and searching the orientation degree and the crystallinity corresponding to the breaking strength in the database;
4) Calculating the temperature and the speed of GR1 and GR2 according to the orientation degree and the crystallinity degree obtained by searching according to the relation function, and adjusting the temperature and the speed of GR1 and GR2 in the FDY polyester filament spinning process according to the temperature and the speed;
as shown in fig. 1, the relationship model is established as follows:
(1) Determining the number of local models, collecting the breaking strength, orientation degree, crystallinity and fiber elongation data of FDY polyester filament as historical data to form a historical database, wherein the FDY polyester filament is fiber prepared under the conditions of the same process flow and different process parameters, the different process parameters mean that the temperatures and the speeds of GR1 and GR2 are different, the length N of the historical data is 1000, selecting an output variable y as the fiber breaking strength, an input variable u1 as the orientation degree, an input variable u2 as the crystallinity, a scheduling variable w as the fiber elongation, and a scheduling variable w as a physical variable determining the working mode of the systemThe method is characterized in that a stable working point is transited to another stable working point in a slope mode, the unit of the breaking strength of the fiber is cN/dtex, the unit of the elongation of the fiber is percent, the elongation of the fiber when the elongation of the fiber reaches the stable state in N fiber elongations is selected as the working point T, T is {0.1,0.3,0.8}, the number of the working points T is 3 of the local models, and C is the number of the local modelsobsFor all observed data sets, i.e. fiber breaking strength, degree of orientation, degree of crystallinity, fiber elongation and working point, Cobs＝{y1:1000,u1:1000,w1:1000,T1:3}；
(2) Determining a local model structure, and estimating the local dynamics of the system by taking an autoregressive model with an out-of-band addition input as a local model, wherein the method specifically comprises the following steps:
yk＝θi xk+ek；
In the formula, the sampling time k is 1,2, … 1000, ykFor the fiber breaking strength, x, corresponding to the sampling time kkas a regressive quantity, u1kAnd u2kdegree of orientation and degree of crystallinity, n, for a sampling time ka2 and nb2 is the order of the output and input, respectively, θiIs the parameter set of the ith local model, i is 1,2,3, ek～N(0,σ2) I.e. ek～N(0,2)；
3 sets of local model parameters
(3) Determining a Gaussian mixture weight function, a Gaussian mixture weight function alphak,iThe formula of (1) is:
in the formula (I), the compound is shown in the specification,As a function of the unnormalised mixed Gaussian weight, pii,jIs a mixed weight, i.e. the element of the mixed weight matrix pi in the ith row and jth column, oi,jIs the effective width, w, of the ith local model at the jth operating pointkFor the fibre elongation corresponding to the sampling instant k, TiI is 1,2,3, j is 1,2, 3;
Mixed weight pii,jin relation to the distance between adjacent working points, pii,jWith the following limitations:
(a)
(b)0≤πi,j≤1；
(c)πi,j＞πi,vwherein | Ti-Tj|＜|Ti-Tv|；
Parameter set in weighting functionThe parameter set Θ of the global model is a parameter set of the local model and the weighting function, that is, Θ ═ Θm,Θw}；
(4) Estimating unknown parameters in the local model and the Gaussian mixture weight function;
(5) Obtaining a relation model between the breaking strength and the orientation degree of the FDY polyester filament yarn, the crystallinity and the fiber elongation according to the number of the local models, the structure of the local models, the mixed Gaussian weight function and the parameters estimated in the step (4), wherein the relation model comprises the following specific steps:
In the formula (I), the compound is shown in the specification,Is the predicted output of the breaking strength of the FDY polyester filament yarn, alphak,iIs a function of the weight of the mixture of gaussians,a predicted output for the local model at the ith operating point;
As shown in fig. 1, the specific steps of estimating the unknown parameters in the local model and the gaussian mixture weight function are as follows:
1) selecting a mixing weight value pii,jmixed weight pii,jThere are 3 kinds of selection, the parameter need not to be estimated to the first kind, and the calculation is simple, and the second kind needs to be estimated the parameter more, but the calculated amount is middle, and III number of parameters is between the first kind and II kind, but because nonlinearity, estimates the parameter complexity the highest, according to calculation accuracy, III kind precision is higher than II kind, and II kind is higher than I kind, specifically as follows:
I. mixed weight pii,jTo determine the value, first χ is calculatedi,jObtaining a mixed weight matrix x, normalizing the x according to the row vector to obtain a mixed weight matrix pi, and obtaining a mixed weight pi from the mixed weight matrix pii,j，χi,jThe calculation formula of (a) is as follows:
In the formula, xi,jIs the element of the ith row and the jth column in the mixed weight matrix chi, TjIs the jth working point;
II, mixing weight pii,jUnknown, first by estimating χi,jObtaining a mixed weight matrix x, normalizing the x according to the row vector to obtain a mixed weight matrix pi, and obtaining a mixed weight pi from the mixed weight matrix pii,jThe expression of the mixed weight matrix χ is:
wherein, when i ═ j, χij1, the diagonal element of the matrix χ is 1, χ11＝1，χ22＝1，…，χMM1 is ═ 1; when i ≠ j, 0 < χijless than 1; when i is less than or equal to j and less than l, xij＞χilThe total 3 parameters of the mixing weight matrix chi need to be estimated;
III. mixing weight pii,jWith Gaussian distribution, mixed weight pii,jThe calculation formula is as follows:
In the formula, τiis a parameter to be estimated;
2) Setting the initial parameter theta' to be in the value range of [0,1]I.e. thetamAnd ΘwSetting theta as an initial value ofmMiddle thetaiAnd σ, setting ΘwWhen the initial value of (2) is greater, when the weight of mixing is pii,jin order to determine the value of the value,At this time, set to oi,jWhen the mixing weight is pii,jWhen the time is not known, the user can select the target,At this time, pi is seti,jAnd oi,jWhen the mixing weight is pii,jin the case of a distribution of the gaussian components,At this time, τ is setiAnd oi,jan initial value of (1);
3) Calculating the Q function according to the known parameter theta', namely thetamAnd ΘwCalculates the Q function, which is formulated as follows:
In the formula, C2Is a constant independent of the parameter;
4) Maximizing the Q function to obtain an updated set of parameters Θ, then:
By thetaiAnd σ2The optimal theta can be obtainedm；
due to the parameter theta of the Gaussian mixture weight functionwThe analytical solution is difficult to obtain, the non-linear optimization algorithm is adopted for solving, and the mathematical expression is as follows:
Maximize the above formula to find the optimal thetaw；
From the optimum thetamAnd an optimal ΘwObtaining an updated parameter set theta;
5) and repeating the steps 3) and 4) until the variation of theta is smaller than a set threshold epsilon, wherein the value of the threshold epsilon is 10e-5, namely repeatedly making the updated parameter set theta obtained in the step 4) equal to theta', substituting theta into the Q function, and finally updating the obtained parameter set theta, namely the unknown parameters in the estimated local model and the Gaussian mixture weight function.
The established relation model between the breaking strength of the FDY polyester filament yarn and the orientation degree, the crystallinity and the fiber elongation is used for measuring the breaking strength of the FDY polyester filament yarn prepared in different simulation time, and the breaking strength is compared with the real breaking strength, and the result shows that the difference between the breaking strength estimated by the model and the real breaking strength is smaller under the same simulation time.

Claims (5)

1. a mixed Gaussian weight function-based multi-model method is used for optimizing an FDY polyester filament spinning process, and the FDY polyester filament spinning process flow is as follows: melt conveying, spinning box body, metering pump, component spinning, air blowing cooling, oiling, hot roller drafting, high-speed winding, inspection and packaging, and is characterized by comprising the following steps:
1) Firstly, establishing a relation model between the breaking strength and the orientation degree of the FDY polyester filament, between the crystallinity and the fiber elongation by a mixed Gaussian weight function, and simultaneously establishing a relation function between the temperature and the speed of a first hot roller GR1 and a second hot roller GR2 in a hot roller drafting link and the orientation degree and the crystallinity of the FDY polyester filament; the relationship 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；
Wherein u1 represents orientation degree, u2 represents crystallinity degree, and V represents1GR1 speed, T1At GR1 temperature, V2GR2 speed, T2Is the GR2 temperature, the units of orientation, the units of crystallinity, the units of temperature, and the units of speed are m/min;
2) Randomly inputting the orientation degree, the crystallinity and the fiber elongation of a series of FDY polyester filaments, outputting the breaking strength by the relation model, and establishing a database of the breaking strength, the orientation degree, the crystallinity and the fiber elongation of the FDY polyester filaments;
3) selecting one breaking strength in a database as the expected breaking strength of the FDY polyester filament, and searching the orientation degree and the crystallinity corresponding to the breaking strength in the database;
4) Calculating the temperature and the speed of GR1 and GR2 according to the relation function and the orientation degree and the crystallinity degree obtained by searching, and adjusting the temperature and the speed of GR1 and GR2 in the FDY polyester filament spinning process according to the temperature and the speed;
The establishment steps of the relation model are as follows:
(1) determining the number of local models, collecting breaking strength, orientation degree, crystallinity and fiber elongation data of FDY polyester filaments as historical data to form a historical database, wherein the FDY polyester filaments are fibers prepared under the conditions of the same process flow and different process parameters, the different process parameters mean that the temperatures and the speeds of GR1 and GR2 are different, the length of the historical data is N, an output variable y is selected as the fiber breaking strength, an input variable u1 is the orientation degree, an input variable u2 is the crystallinity, a scheduling variable w is the fiber elongation, the unit of the fiber breaking strength is cN/dtex, the unit of the fiber elongation is selected, the fiber elongation when the fiber elongation reaches a stable state in N fiber elongations is selected as a working point T, and T is { T ═ T { (T) } when the fiber elongation reaches a stable state1，T2，…，TMthe number M of the working points T is the number M of the local models, TiIs the operating point of the ith local model, i is 1,2, …, M, CobsFor all observed data sets, i.e. fiber breaking strength, degree of orientation, degree of crystallinity, fiber elongation and working point, Cobs＝{y1:N,u11:N,u21:N,w1:N,T1:MIn which y1，y2，…，yNSimplified notation as y1:N，u11,u12,...,u1Nsimplified notation u11:N，u21,u22,...,u2NSimplified notation u21:N，w1,w2,...,wNSimplified notation by w1:N，T1,T2,...,TMSimplified notation as T1:M；
(2) Determining a local model structure, and estimating the local dynamics of the system by taking an autoregressive model with an out-of-band addition input as a local model, wherein the method specifically comprises the following steps:
yk＝θixk+ek；
in the formula, the sampling time k is 1,2, …, N, ykFor the fiber breaking strength, x, corresponding to the sampling time kkAs a regressive quantity, u1kAnd u2kDegree of orientation and degree of crystallinity, n, for a sampling time kaAnd nbOrder of output and input, respectively, thetaiis the parameter set of the ith local model, ekIs a mean value of 0 and a variance of σ2white Gaussian noise of (i.e. e)k～N(0,σ2)；
the unknown parameter in the local model structure is thetaiand σ, a set of unknown parameters, i.e., M sets of local model parameters
(3) Determining a Gaussian mixture weight function, a Gaussian mixture weight function alphak,iThe formula of (1) is:
In the formula (I), the compound is shown in the specification,As a function of the unnormalised mixed Gaussian weight, pii,jis a mixed weight, i.e. the element of the mixed weight matrix pi in the ith row and jth column, oi,jIs the effective width, w, of the ith local model at the jth operating pointkFor the fibre elongation corresponding to the sampling instant k, TiThe ith operating point is 1,2, …, M, j is 1,2, …, M;
the unknown parameter in the Gaussian mixture weight function is pii,jAnd oi,jSets of unknown parameters, i.e. parameter sets in weighting functionsthe parameter set theta of the global model isThe parameters of the local model and the parameter set of the weighting function, i.e. Θ ═ Θm,Θw}；
(4) Estimating unknown parameters in the local model and the Gaussian mixture weight function;
(5) Obtaining a relation model between the breaking strength and the orientation degree of the FDY polyester filament yarn, the crystallinity and the fiber elongation according to the number of the local models, the structure of the local models, the mixed Gaussian weight function and the parameters estimated in the step (4), wherein the relation model comprises the following specific steps:
in the formula (I), the compound is shown in the specification,is the predicted output of the breaking strength of the FDY polyester filament yarn, alphak,iIs a function of the weight of the mixture of gaussians,A predicted output for the local model at the ith operating point;
The specific steps for estimating the unknown parameters in the local model and the Gaussian mixture weight function are as follows:
1) Selecting a mixing weight value pii,jmixed weight pii,jThere are 3 options, specifically as follows:
I. mixed weight pii,jto determine the value, first χ is calculatedi,jobtaining a mixed weight matrix x, normalizing the x according to the row vector to obtain a mixed weight matrix pi, and obtaining a mixed weight pi from the mixed weight matrix pii,j，χi,jThe calculation formula of (a) is as follows:
In the formula, xi,jis the element of the ith row and the jth column in the mixed weight matrix chi, Tjis the jth working point;
II, mixing weight pii,jUnknown, first by estimating χi,jObtaining a mixed weight matrix x, normalizing the x according to the row vector to obtain a mixed weight matrix pi, and obtaining a mixed weight pi from the mixed weight matrix pii,jthe expression of the mixed weight matrix χ is:
Wherein, when i ═ j, χij1, the diagonal element of the matrix χ is 1, χ11＝1，χ22＝1，…，χMM1 is ═ 1; when i ≠ j, 0 < χijLess than 1; when i is less than or equal to j and less than l, xij＞χilThe mixed weight matrix chi has M x (M-1)/2 parameters to be estimated;
III. mixing weight pii,jWith Gaussian distribution, mixed weight pii,jthe calculation formula is as follows:
in the formula, τiIs a parameter to be estimated;
2) Setting an initial parameter theta', namely thetamand Θwsetting theta as an initial value ofmMiddle thetaiAnd σ, setting ΘwWhen the initial value of (2) is greater, when the weight of mixing is pii,jIn order to determine the value of the value,At this time, set to oi,jwhen the mixing weight is pii,jwhen the time is not known, the user can select the target,At this time, pi is seti,jAnd oi,jWhen the mixing weight is pii,jIn the case of a distribution of the gaussian components,at this time settingτiand oi,jAn initial value of (1);
3) calculating the Q function according to the known parameter theta', namely thetamAnd ΘwCalculates the Q function, which is formulated as follows:
In the formula, C2Is a constant independent of the parameter;
4) Maximizing the Q function to obtain an updated set of parameters Θ, then:
By thetaiAnd σ2The optimal theta can be obtainedm；
Due to the parameter theta of the Gaussian mixture weight functionwThe analytical solution is difficult to obtain, the non-linear optimization algorithm is adopted for solving, and the mathematical expression is as follows:
Maximize the above formula to find the optimal thetaw；
From the optimum thetamand an optimal ΘwObtaining an updated parameter set theta;
5) and repeating the steps 3) and 4) until the variation of the theta is smaller than the set threshold epsilon, namely repeatedly enabling the updated parameter set theta obtained in the step 4) to be theta', substituting the theta into the Q function, and finally updating the obtained parameter set theta, namely the unknown parameters in the estimated local model and the Gaussian mixture weight function.
2. the multi-model method based on the Gaussian mixture weight function of claim 1, used for optimizing the FDY polyester filament spinning process, wherein the FDY polyester filament has a specification of 83dtex/72 f.
3. The multi-model method based on Gaussian mixture weight function for optimizing FDY polyester filament spinning process according to claim 1, wherein the weight value of mixture is pii,jIn relation to the distance between adjacent working points, pii,jwith the following limitations:
(a)
(b)0≤πi,j≤1；
(c)πi,j＞πi,vwherein | Ti-Tj|＜|Ti-Tv|。
4. The multi-model method based on the Gaussian mixture weight function according to claim 1, which is used for optimizing an FDY polyester filament spinning process, and is characterized in that the value range of the initial parameter theta' is [0,1 ].
5. The mixed Gaussian weight function-based multi-model method for optimizing the FDY polyester filament spinning process according to claim 1, wherein the value of the threshold epsilon is 10 e-5.
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