CN104166783B - CUDA-based quick sequence distribution computing method for steady-state olefin copolymerization - Google Patents

Abstract

The invention discloses a CUDA-platform-based quick sequence distribution computing method applied to steady-state olefin copolymerization. For the steady-state process in an olefin reaction, the quick computing method for solving copolymer sequence distribution is provided under a CUDA platform according to the dynamics mechanism of a copolymerization reaction and on the basis of the Monte Carlo method, In the method, firstly, different probabilities required in the Monte Carlo method are provided according to the dynamics mechanism of the copolymerization reaction and the needed sequence distribution is finally obtained by executing the Monte Carlo method on the CUDA platform in a parallel mode. Due to the fact that the whole computing process is high in parallelism degree, the computing time is greatly shortened. Thus, the method is called as a quick sequence distribution computing technology.

Description

A kind of stable state olefin-copolymerization rapid serial distribution calculation method based on CUDA

Technical field

The present invention relates to based on the rapid serial Distributed Computing Technology in the polymer copolymerization steady-state process under CUDA platforms Method.

Background technology

Random number generator, the function that can generate random number for referring to or program module.In random variable of continuous type Distribution in, most simple and most basic distribution is that unit is uniformly distributed, and the Simple sample extracted by the distribution is referred to as random Number Sequence, each of which is individual to be referred to as random number.Independence, uniformity are two indispensable features of random number.It is special including covering In interior most of algorithms, Caro computational methods require that adopted random number sequence is obeyed and are uniformly distributed, i.e., in same scope Any one to count existing probability identical.

DSMC, also referred to as statistical simulation methods, are middle 1940s sending out due to science and technology Exhibition and electronic computer invention and be suggested it is a kind of with Probability Statistics Theory as instruct the very important numerical value of a class count Calculation method.The method solves many computational problems using random number (or more conventional pseudo random number), and corresponding with it is true Deterministic algorithm.DSMC is in chemical field it has been recognised that and application.In the case of given kinetics mechanism, root The probability of differential responses type is calculated according to each state value of co-polymeric systems stable state；Secondly, deposit in the copolymerization system of setting Strand number, and a series of random numbers for further being generated according to random number generator repeat judgement reaction In each bar chain response situation, till all chains in whole system are all terminated.

Unified calculation equipment framework (CUDA), is the computing platform of video card business men NVIDIA releases, is a kind of universal parallel Computing architecture.As it contains instruction set architecture and parallel computation engine, the calculating therefore, it is possible to solve many complexity is asked Topic, and significantly shorten the calculating time, computational efficiency is significantly improved.Sequence is distributed, and refers to variety classes monomer The one class distribution of the sequence of composition frequency of occurrences in strand.In chemical field, the performance indications of polymer include Common melt index, mean molecule quantity, molecular weight distribution, but these indexs completely can not be described in copolymerization system The performance of polymer, in addition to strict alternating copolymerization and block copolymerization, in same macromolecular, the arrangement of each monomer is not Rule, therefore there is the sequence distribution of segment.

The content of the invention

The purpose of the present invention is the application scenarios for Raolical polymerizable in stable state olefin-copolymerization system, there is provided a kind of Stable state olefin-copolymerization rapid serial distribution calculation method based on CUDA.

Technical scheme is as follows：

Comprised the steps based on the stable state olefin-copolymerization rapid serial distribution calculation method of CUDA：

A. the state value of stable state olefin-copolymerization system is read, it is normal including the dynamics of chain growth, chain tra nsfer, chain termination reaction Several and all kinds of monomers, chain-transferring agent, the concentration of chain terminating agent；

B. each probable value required for DSMC is calculated, chain occurs including the living chain ended up with all kinds of monomers The probability P of reaction of propagation_iAnd the probability P that the living chain ended up with all kinds of monomers increases to all kinds of monomer chains_ij, with all kinds of monomers The living chain of ending occur chain propagation reaction probability will the chain of all kinds of monomers endings increase chemical reaction rate and be multiplied by accordingly Adding with chain growth, chain tra nsfer divided by the ending of all kinds of monomers, chain termination chemical reaction rate are multiplied by phase after the concentration of monomer Answer it is after the concentration of monomer plus and, the probability that the living chain ended up with all kinds of monomers increases to all kinds of monomer chains will be to all kinds of Monomer chain increases the concentration that chemical reaction rate is multiplied by correspondence monomer, increases chemical reaction rate divided by the chain of all kinds of monomers ending Be multiplied by it is after the concentration of corresponding monomer plus and；Represented with formula：

Wherein, R_piThe living chain rate of chain growth ended up with monomer i in representing polymerisation；R_tiRepresent and ended up with monomer i Living chain chain tra nsfer speed；R_diRepresent the living chain chain termination speed ended up with monomer i；[j], [m] represent respectively monomer j, The concentration of monomer m；k_pij、k_pimRepresent anti-to the chemistry that monomer j, monomer m generation chain increases with the living chain of monomer i endings respectively Answer speed；

C. step b calculated probable value is delivered on CUDA platforms from CPU platforms；

D. memory space and number for records series information is opened up on CUDA platforms is equal to the total chain number of simulation Thread Count；

E. all threads of parallel execution, by the probability obtained in step b in each thread, sequentially judge corresponding Whether living chain there is chain growth；If it is not, the simulation for stopping the thread calculating and the sequence information for obtaining exists by thread number Stored in memory space；If so, then proceed to judge which kind of monomer to carry out chain to increases and record corresponding sequence Information；

F. repeat step e, until obtaining Stop message and exiting；

G. the sequence information of record is delivered on CPU platforms from CUDA platforms；

H. all of sequence information is counted, the sequence distribution required for obtaining.

The analog platform of the DSMC described in step b is CUDA.DSMC described in step b Analog form is the simulation process that each simulation thread only carries out a chain.The mould of the DSMC described in step b Plan order is the parallel multiple Monte Carlo simulation threads of execution.

Record information described in step e is all of sequence information in chain.

Based on the core concept of the rapid serial distribution calculation method in the stable state olefin-copolymerization of CUDA it is：Use each thread The simulation of every chain in copolyreaction is carried out, and these threads are run into realization under CUDA platforms, so as to realize quick calculating. Method is：First, setting needs the number and the parameter value of some systems of the chain of simulation calculating；Secondly, it is total to according to given Under poly- kinetic reaction mechanism and stable state, corresponding dynamic parameter value and system mode value, calculate with different copolymer species The living chain of type ending carries out the probability of various kinetic reactions and further anti-to differential responses species type on this basis Probability answered etc.；Then, parameter value above and the probability for calculating are passed on CUDA platforms, with chain number as Thread Count Repetitive operation is carried out, till meeting the number of chain of setting or maximum chain length；Finally, simulation on CUDA is calculated The information of every chain pass main program back, the not homotactic number required for counting, then these values are normalized whole Copolymer sequence distribution required for obtaining after reason.

Compared with the prior art, the invention has the advantages that：As the simulation calculating process of Monte Carlo is with multithreading Form distributes to the operation of CUDA platforms, therefore degree of parallelism is higher, the calculating time is greatly shortened, it is achieved thereby that rapid serial point Cloth computational methods.

Description of the drawings

Fig. 1 is the main program module flow chart of the stable state olefin-copolymerization rapid serial distribution calculation method based on CUDA；

Fig. 2 is the Monte Carlo simulation computing module flow chart in the present invention；

Fig. 3 is the sequence profile that the present invention is obtained.

Specific embodiment

By taking olefin-copolymerization reaction system as an example, technical scheme is further described.

1 example background introduction

In the present invention, with olefin-copolymerization reaction system as case study on implementation.Alkene due to its abundant raw materials and it is cheap, Be easily worked shaping, high comprehensive performance, be a class yield it is huge, using quite varied macromolecular material.In olefinic polymerization In system, as the kind of polymer can not only be expanded by copolymerization, and some can be allowed to be difficult to the monomer of homopolymerization Polymerisation is participated in, therefore the application of copolymerization system is than wide.

2 polymerization reaction mechanisms

In the present invention, by taking two-spot copolymerization as an example, it is considered to which in olefin-copolymerization reaction system, the chain with end effect increases anti- Should with chain transfer reaction, as shown in table 1.

1 olefin-copolymerization reaction mechanism of table

Wherein, A and B represents two kinds of monomer types of binary copolymerization reaction respectively；P_r ^ABe a length of r of chain and with A end up Living chain；P_r ^BIt is a length of r of chain the living chain ended up with B；D_rIt is the dead polymers chain of a length of r of chain；P₀It is sky active sites；H₂For hydrogen Gas；Al is co-catalyst；k_p,k_tIt is that chain increases the kinetic reaction speed constant with chain tra nsfer respectively.

3 main program modules

Main program module is mainly responsible for the preparation of simulation work and last data preparation work, as shown in Figure 1. Preparation has：Each parameter value required for carrying out Monte Carlo simulation is calculated according to given system mode value, and is opened Ward off the Thread Count equal with total chain number of setting.Data preparation work has：Count every chain that each thread simulation is calculated In each shared proportion of 8 kinds of sequences (AAA, AAB, ABA, ABB, BAA, BAB, BBA, BBB), count these proportion information and obtain Required sequence distribution.

4 Monte Carlo simulation computing modules

Monte Carlo simulation calculation flow chart under each thread is as shown in Fig. 2 comprise the following steps that：

Step one：Obtain from main program and be transmitted through next system parameter values (r_n,r_A,r_B,f_A,f_B,q_tA,q_tB,P_p,LS,P_pLS,A), Jump to step 2；

Step 2：By chain length (r) zero setting, (LS, SS, TS are that chain is last to the mark of last three monomers of every chain respectively The mark of one monomer, the mark of chain penultimate monomer, the mark of chain third last monomer) zero setting, the note of 8 kinds of sequences Record value (n_AAA,n_AAB,n_ABA,n_ABB,n_BAA,n_BAB,n_BBA,n_BBB) zero setting, jump to step 3；

Step 3：One is generated using random number generator, and (0,1) random number, according to the mark of last monomer of living chain Remember LS to judge that the random number for generating is compared with concrete which probable value, so as to judge that being carried out chain increases or chain turn Move；If chain increases, then step 4 is jumped to；If chain tra nsfer, then step 2 12 is jumped to；

Step 4：Perform r from add operation, and again generate one (0,1) random number, also according to living chain last Label L S of monomer is compared with concrete which probable value judging the random number for generating, so as to judge to be carried out monomer A chains Increase or monomer B chains increase；If monomer A chains increase, then step 5 is jumped to；If monomer B chains increase, then step is jumped to Rapid six；

Step 5：All of mark is updated, that is, SS is assigned to TS, LS is assigned to SS, LS is assigned to A, jump to step Seven；

Step 6：All of mark is updated, that is, SS is assigned to TS, LS is assigned to SS, LS is assigned to B, jump to step Seven；

Step 7：Judge whether the chain third last monomer is A according to the value of TS, if it is, jumping to step 8；If It is not then to jump to step 9；

Step 8：Judge whether the chain penultimate monomer is A according to the value of SS, if it is, jumping to step 10；If It is not then to jump to step 11；

Step 9：Judge whether the chain penultimate monomer is A according to the value of SS, if it is, jumping to step 12；Such as Fruit is not then to jump to step 13；

Step 10：Judge whether the chain last monomer is A according to the value of LS, if it is, jumping to step 14；If It is not then to jump to step 15；

Step 11：Judge whether the chain last monomer is A according to the value of LS, if it is, jumping to step 10 six；Such as Fruit is not then to jump to step 10 seven；

Step 12：Judge whether the chain last monomer is A according to the value of LS, if it is, jumping to step 10 eight；Such as Fruit is not then to jump to step 10 nine；

Step 13：Judge whether the chain last monomer is A according to the value of LS, if it is, jumping to step 2 ten；Such as Fruit is not then to jump to step 2 11；

Step 14：Perform n_AAAFrom add operation, step 3 is jumped to；

Step 15：Perform n_AABFrom add operation, step 3 is jumped to；

Step 10 six：Perform n_ABAFrom add operation, step 3 is jumped to；

Step 10 seven：Perform n_ABBFrom add operation, step 3 is jumped to；

Step 10 eight：Perform n_BAAFrom add operation, step 3 is jumped to；

Step 10 nine：Perform n_BABFrom add operation, step 3 is jumped to；

Step 2 ten：Perform n_BBAFrom add operation, step 3 is jumped to；

Step 2 11：Perform n_BBBFrom add operation, step 3 is jumped to；

Step 2 12：Information (n required for preserving_AAA,n_AAB,n_ABA,n_ABB,n_BAA,n_BAB,n_BBA,n_BBB), program operation Terminate.

5 contrast effects

In the present invention, setting value is as follows：

r_n=1000, r_A=5.0, r_B=0.2, f_A=0.6, f_B=0.4, q_tA=0.5, q_tA=0.5

P_p0=P_pAf_A+P_pBf_B,P_p0A=P_AAf_A+P_BAf_B

Wherein, r_nRepresent the equal chain length of number；r_ARepresent the reaction rate increased to A chains with the living chain that A ends up divided by tying with A The reaction rate that the living chain of tail increases to B chains；r_BRepresent the reaction rate increased to B chains with the living chain that B ends up divided by with B The reaction rate that the living chain of ending increases to A chains；f_ARepresent the concentration of monomer A divided by the concentration of concentration and the B of A plus and；f_B Represent the concentration of monomer B divided by the concentration of concentration and the B of A plus and；q_tARepresent anti-with the chain tra nsfer of A endings, chain termination chemistry Speed is answered to be multiplied by after the concentration of corresponding monomer plus and take advantage of divided by the chain tra nsfer, chain termination chemical reaction rate ended up with A and B After with the concentration of corresponding monomer plus and；q_tBRepresent that the chain tra nsfer ended up with B, chain termination chemical reaction rate are multiplied by corresponding list It is after the concentration of body plus and be multiplied by the concentration of corresponding monomer divided by the chain tra nsfer, chain termination chemical reaction rate ended up with A and B Afterwards plus and；Represent monomer A molar average in the copolymer point rates；Represent monomer B averagely rubbing in the copolymer You divide rate；P_pARepresent the probability that chain propagation reaction occurs with the living chain that A ends up；P_AARepresent with A end up living chain occur to The probability of A chain propagation reactions；P_pBRepresent the probability that chain propagation reaction occurs with the living chain that B ends up；P_BARepresent what is ended up with B There is the probability to A chain propagation reactions in living chain；P_p0With P_p0AIt is for carrying out judging which kind of list chain increases with specifically to respectively The probability that body chain increases.

According to these parameter values, it is inserted in module above, sequence distribution can be obtained and be illustrated in fig. 3 shown below：

Serial operation, the parallel running under CUDA platforms under CPU platforms respectively of whole program, each required time is as follows Shown in table 2：

2 Operational Timelines of table

Further, acceleration effect can be calculated：

Can see, the simulation calculating for carrying out Monte Carlo under CUDA platforms can significantly lift computational efficiency, So as to realize rapid serial Distributed Computing Technology.

Claims (4)

1. a kind of stable state olefin-copolymerization rapid serial distribution calculation method based on CUDA, it is characterised in that comprise the steps：

A. read stable state olefin-copolymerization system state value, including chain growth, chain tra nsfer, chain termination reaction kinetic constant with And the concentration of all kinds of monomers, chain-transferring agent, chain terminating agent；

B. each probable value required for DSMC is calculated, chain is occurred including the living chain ended up with all kinds of monomers and is increased The probability P of reaction_iAnd the probability P that the living chain ended up with all kinds of monomers increases to all kinds of monomer chains_ij：

$P_i=\frac{R_{pi}}{R_{pi}+R_{ti}+R_{di}}$

$P_{ij}=\frac{k_{pij}\[j\]}{\underset{m}{\Σ}{k}_{pim}\[m\]}$

Wherein, R_piThe living chain rate of chain growth ended up with monomer i in representing polymerisation；R_tiRepresent the work ended up with monomer i Property chain chain tra nsfer speed；R_diRepresent the living chain chain termination speed ended up with monomer i；[j], [m] represent monomer j, monomer m respectively Concentration；k_pij、k_pimRepresent respectively and the chemical reaction speed that chain increases occurs with the living chain that monomer i ends up to monomer j, monomer m Rate；

The analog form of described DSMC is the simulation process that each simulation thread only carries out a chain；

C. step b calculated probable value is delivered on CUDA platforms from CPU platforms；

D. the thread that memory space and number for records series information are equal to the total chain number of simulation is opened up on CUDA platforms Number；

E. all threads of parallel execution, by the probability obtained in step b in each thread, sequentially judge corresponding activity Whether chain there is chain growth；If it is not, the simulation for stopping the thread being calculated and is storing the sequence information for obtaining by thread number Stored in space；If so, then proceed to judge which kind of monomer to carry out chain to increases and record corresponding sequence information；

F. repeat step e, until obtaining Stop message and exiting；

G. the sequence information of record is delivered on CPU platforms from CUDA platforms；

H. all of sequence information is counted, the sequence distribution required for obtaining.

2. a kind of stable state olefin-copolymerization rapid serial distribution calculation method based on CUDA according to claim 1, which is special Levy be the analog platform of DSMC described in step b be CUDA.

3. a kind of stable state olefin-copolymerization rapid serial distribution calculation method based on CUDA according to claim 1, which is special Levy be the simulation order of DSMC described in step b be the multiple Monte Carlo simulation threads of parallel execution.

4. a kind of stable state olefin-copolymerization rapid serial distribution calculation method based on CUDA according to claim 1, which is special Levy be record information described in step e be all of sequence information in chain.