CN114334030A - Method for evaluating high molecular polymerization reaction product based on quantum support vector machine - Google Patents
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Abstract
The invention provides a method for evaluating a high molecular polymerization reaction product based on a quantum support vector machine, which comprises the steps of carrying out original data acquisition and data preprocessing on reaction variables such as different reaction monomer usage, initiator proportion and the like involved in the polymerization reaction process of an adsorption type high molecular material and absorbance data of a solution after adsorption, and carrying out data set amplification by adopting a quantum genetic optimization algorithm; a high-molecular polymerization reaction product evaluation model is constructed based on a quantum support vector machine, and the model is trained, tested and evaluated by using the amplified data set, so that the aim of efficiently and accurately evaluating the adsorption performance of the polymerization reaction product is fulfilled.
Description
Technical Field
The invention relates to a method for evaluating a high molecular polymerization reaction product, in particular to a method for evaluating a high molecular polymerization reaction product based on a quantum support vector machine.
Background
The polymer chemical polymerization reaction process is complex, and has a plurality of influencing factors, including different reaction monomer concentrations and interaction relations, the proportion of the initiator in the monomer, the reaction temperature, the reaction time, the stirring speed, the drying time, the drying temperature and the like. The traditional research method is based on a large number of test process comparison and observation, direct or implicit complex interrelation exists between variable factors and data, certain influence is brought to analysis and optimization of test results, and the problems of long analysis period, complex test process, manual operation errors, chemical consumption, environmental pollution and the like exist.
The machine learning algorithm is utilized to evaluate the performance of the high molecular polymerization reaction product, the direct or indirect interaction relation among data variables can be fully considered, the influence of interference factors such as operation errors on the result is reduced to a certain extent, and the evaluation efficiency of the related test of the polymerization reaction product is improved.
Different from the traditional research method, the application of the machine learning algorithm to the performance evaluation of the high-molecular polymerization reaction product is a novel fast and efficient research mode. The mechanism process of the high-molecular polymerization reaction is clear, and the product performance is closely related to factors such as monomer concentration ratio, reaction temperature, time and the like, so the theoretical basis is solid.
In machine learning algorithms, the use of a support vector machine for property prediction is one of the actual scenarios, such as rice taste quality analysis, water source type determination, water quality chemical composition or gas concentration analysis, and sewage COD value prediction, but the application of a quantum support vector machine to the performance evaluation of high molecular polymerization reaction products has not been realized.
In order to solve the above problems, people are always seeking an ideal technical solution.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a method for evaluating a high-molecular polymerization reaction product based on a quantum support vector machine.
In order to achieve the purpose, the invention adopts the technical scheme that: a method for evaluating a high molecular polymerization reaction product based on a quantum support vector machine comprises the following steps:
setting different reaction conditions, preparing different reaction products by utilizing a high-molecular polymerization reaction, classifying and numbering the reaction products, treating the reaction products to be white powder, performing static adsorption capacity test by taking simulated saline as a solvent and quartz sand as an adsorption medium under the same solubility, temperature and time, taking solution samples before and after adsorption corresponding to different numbers, performing absorbance test by utilizing an ultraviolet spectrophotometer, calculating a concentration value according to a standard curve, and finally outputting the static adsorption capacity of the product;
wherein the different reaction conditions comprise monomer dosage, initiator proportion, reaction temperature, reaction time, drying temperature, drying time and fine granularity;
using the monomer amount, the initiator proportion, the reaction temperature, the reaction time, the drying temperature, the drying time and the fine granularity as model input vectors, and using the static adsorption capacity as a model output vector to form a high-molecular polymerization reaction product evaluation original data set;
sequentially carrying out standardization treatment on the original data sets for evaluating the high molecular polymerization reaction products to obtain a pre-amplification data set;
generating an optimal artificial data set in a sample space by adopting a quantum genetic optimization algorithm based on the pre-amplification data set;
repeating the steps for multiple times to generate a plurality of groups of different optimal artificial data sets, and combining the optimal artificial data sets with the pre-amplification data sets to generate a new high-molecular polymerization reaction product evaluation original data set;
dividing the new manual sample data set into a training sample set and a testing sample set according to 80/20%;
step 4, verifying the correctness of the high molecular polymerization reaction product evaluation model based on the high molecular polymerization reaction product evaluation model trained in the step 3 and the test sample set in the step 2;
and 5, predicting and comprehensively analyzing the experimental results under more different types of reaction process variables by using the polymer polymerization reaction product evaluation model passing the test in a real polymer polymerization reaction experimental environment, and correcting the evaluation model according to the feedback deviation condition.
The invention provides a high molecular polymerization reaction product evaluation system based on a quantum support vector machine, and a data acquisition module configured to acquire an original data set related to a high molecular polymerization reaction process
Setting different reaction conditions, preparing different reaction products by utilizing a high-molecular polymerization reaction, classifying and numbering the reaction products, treating the reaction products to be white powder, performing static adsorption capacity test by taking simulated saline as a solvent and quartz sand as an adsorption medium under the same solubility, temperature and time, taking solution samples before and after adsorption corresponding to different numbers, performing absorbance test by utilizing an ultraviolet spectrophotometer, calculating a concentration value according to a standard curve, and finally outputting the static adsorption capacity of the product;
wherein the different reaction conditions comprise monomer dosage, initiator proportion, reaction temperature, reaction time, drying temperature, drying time and fine granularity;
using the monomer amount, the initiator proportion, the reaction temperature, the reaction time, the drying temperature, the drying time and the fine granularity as model input vectors, and using the static adsorption capacity as a model output vector to form a high-molecular polymerization reaction product evaluation original data set;
the system comprises an original data set processing and classifying module, a pre-amplification data set and a pre-amplification data set, wherein the original data set processing and classifying module is configured to sequentially carry out standardization processing on a high molecular polymerization reaction product evaluation original data set to obtain a pre-amplification data set; generating an optimal artificial data set in a sample space by adopting a quantum genetic optimization algorithm based on the pre-amplification data set; repeating the steps for multiple times to generate a plurality of groups of different optimal artificial data sets, and combining the optimal artificial data sets with the pre-amplification data sets to generate a new high-molecular polymerization reaction product evaluation original data set; dividing the new manual sample data set into a training sample set and a testing sample set according to 80/20%;
the polymer polymerization reaction product evaluation model training module is configured to construct a polymer polymerization reaction product evaluation model based on a quantum support vector machine, and obtain the polymer polymerization reaction product evaluation model according to the constructed training sample set;
the model testing module is configured to verify the correctness of the high polymer polymerization reaction product evaluation model based on the trained high polymer polymerization reaction product evaluation model and the testing sample set;
and the prediction and correction module is configured to predict and comprehensively analyze the experimental results under more different types of reaction process variables by using the polymer polymerization reaction product evaluation model passing the test in a real polymer polymerization reaction experimental environment, and correct the evaluation model according to the feedback deviation condition.
Based on the above, generating an optimal artificial dataset in a sample space by using a quantum genetic optimization algorithm based on the pre-amplification dataset includes:
setting population scale, maximum genetic iteration times and chromosome length, wherein each population individual in the population corresponds to a model input vector, and the chromosome length is the total length of binary strings of all elements in the model input vector;
initializing a population, and randomly generating chromosomes with a certain quantity of quantum bit codes;
measuring the population individuals in sequence to obtain a determined state, namely binary codes;
performing decimal conversion on the binary array obtained by measurement according to the set variable range of each reaction, substituting the decimal conversion into a support vector machine model, and realizing fitness evaluation aiming at the measurement result, wherein the root mean square error is used as a fitness value function;
recording original optimal individuals and corresponding optimal fitness values;
measuring the population individuals in sequence to obtain a determined state, namely binary codes;
carrying out fitness evaluation on the measurement result;
updating the optimal fitness and the related index information;
updating the probability amplitude of the quantum bit by using a quantum revolving gate to realize individual genetic variation of the population and obtain new population individuals;
adding 1 to the iteration times, returning to execute and recording the original optimal individual and the corresponding optimal fitness value until all iterations are finished;
and finally outputting all the recorded optimal individuals and the optimal fitness value as an optimal artificial data set.
Compared with the prior art, the method has outstanding substantive characteristics and remarkable progress, and particularly, the method carries out original data acquisition and data pretreatment on reaction variables such as different reaction monomer usage, initiator proportion and the like involved in the polymerization reaction process of the adsorption type high polymer material and absorbance data of the solution after adsorption, and trains, tests and evaluates a model by utilizing the pretreated polymerization reaction data based on a quantum support vector machine algorithm so as to realize the purpose of efficiently and accurately evaluating the adsorption performance of the polymerization reaction product; aiming at the defects that a small sample data set is loose in data structure and discrete in distribution, information intervals exist among sample points, effective information cannot be obtained and the like, an optimal artificial data set meeting requirements is generated in a sample space based on the small sample data set by adopting a quantum genetic optimization algorithm, effective amplification of the data set is realized, and then the training and testing requirements of a subsequent evaluation model are met.
Drawings
FIG. 1 is a flow chart of the method for evaluating a polymer polymerization product of the present invention.
FIG. 2 is a diagram of a SWAP-test quantum wire.
FIG. 3 is a quantum circuit diagram for the HHL algorithm to solve the linear system of equations.
Detailed Description
The technical solution of the present invention is further described in detail by the following embodiments.
As shown in fig. 1, a method for evaluating a high molecular polymerization reaction product based on a quantum support vector machine comprises the following steps:
the step of collecting the original test data is the key content of the invention, and the quality of the test data is about the training and testing of the subsequent model, so that the invention has important significance;
setting different reaction conditions aiming at the polymerization reaction process of a high polymer material, preparing different reaction products by utilizing high polymer polymerization reaction, classifying and numbering the reaction products, processing the reaction products into white powder, performing static adsorption quantity test by using simulated saline as a solvent and quartz sand as an adsorption medium under the same solubility, temperature and time, taking solution samples before and after adsorption corresponding to different numbers, performing absorbance test by utilizing an ultraviolet spectrophotometer under the wavelength of 590nm, calculating a concentration value of the solution sample according to a standard curve, and finally outputting the static adsorption quantity of the product; the whole data acquisition process constructs original data influencing the performance of the polymerization reaction product comprehensively, and can be effectively used for training and testing a polymerization reaction product performance evaluation model;
wherein, the static adsorption capacity calculation formula is as follows: Γ ═ V (c)o-ce)/msWherein gamma is the static adsorption capacity, V is the volume of the test solution, msIs the mass of the quartz sand, coAnd ceRespectively showing the effective concentration of the solution before and after static adsorption;
wherein the different reaction conditions comprise monomer dosage, initiator proportion, reaction temperature, reaction time, drying temperature, drying time and fine granularity;
using the monomer amount, the initiator proportion, the reaction temperature, the reaction time, the drying temperature, the drying time and the fine granularity as model input vectors, and using the static adsorption capacity as a model output vector to form a high-molecular polymerization reaction product evaluation original data set;
based on the problems of different dimensions, large dimension and the like of the related original data of the high molecular polymerization reaction process obtained in the step 1, the calculation speed is low, the calculation precision is low, and the subsequent training and testing of a support vector machine model are not facilitated, so that the evaluation original data set of the high molecular polymerization reaction product obtained in the step 1 needs to be sequentially subjected to standardization processing to obtain a pre-amplification data set;
in addition, due to the limitation of test conditions, the number of samples in the original polymer polymerization reaction product evaluation data set obtained in the step 1 is small, small sample data sets often have the defects of loose data structure, discrete distribution, information intervals among sample points, unavailable effective information and the like, so that a prediction model constructed based on the small sample data sets is often difficult to meet the precision requirement or has poor learning generalization capability, and an overfitting phenomenon is easy to occur;
therefore, after the pre-amplification data set is obtained, effective amplification of data is performed by using a quantum genetic optimization algorithm in a set condition, and an optimal individual and an optimal fitness value are finally output, wherein the optimal individual comprises an optimal monomer dosage, an initiator proportion, a reaction temperature, a reaction time, a drying temperature, a drying time and a fine granularity required by a model;
repeating the steps for multiple times to generate a plurality of groups of different optimal artificial data sets, combining the optimal artificial data sets with the pre-amplification data sets to generate a new high-molecular polymerization reaction product evaluation original data set, realizing effective amplification of the data sets and further meeting the training and testing requirements of a subsequent evaluation model;
dividing a new high-molecular polymerization reaction product evaluation original data set into a training sample set and a testing sample set according to the proportion of 80/20%;
step 4, verifying the correctness of the high molecular polymerization reaction product evaluation model based on the high molecular polymerization reaction product evaluation model trained in the step 3 and the test sample set in the step 2;
specifically, a static adsorption quantity value obtained by predicting a high molecular polymerization reaction product evaluation model and a static adsorption quantity value measured in an original test are calculated, a root mean square error evaluation index is solved, and the calculation formula is as follows:
wherein XtAnd XoRespectively obtaining a predicted value and a real test value of a static adsorption capacity model of the polymerization reaction product, wherein N is the number of test samples so as to verify the accuracy of a high molecular polymerization reaction product evaluation model of the trained high molecular polymerization reaction product; if the root mean square error of the predicted value and the true value of the trained model is extremely small, the difference between the predicted value and the true value is small, and the stability of the evaluation model is good;
and 5, predicting and comprehensively analyzing the experimental results under more different types of reaction process variables by using the polymer polymerization reaction product evaluation model passing the test in a real polymer polymerization reaction experimental environment, correcting the evaluation model according to the feedback deviation condition, and exploring the influence of different influence factors on the evaluation results to form a mature and stable polymer polymerization reaction product evaluation model.
Aiming at the problem that the evaluation original data set of the high molecular polymerization reaction product has less data, the method further introduces a quantum genetic optimization algorithm, generates new high molecular polymerization reaction test data in a reasonable range based on the evaluation original data set of the high molecular polymerization reaction product, and realizes effective amplification of the data set so as to avoid the defects of poor prediction precision or insufficient learning generalization capability of the constructed model caused by too small number of samples of the data set. Through the data processing operation process, on the basis of retaining data authenticity to the maximum extent, the influence of different dimensional variables and small sample data is considered, and an original data set is converted into a new high-molecular polymerization reaction data set.
Specifically, the final objective is to minimize the difference between the artificially generated data set and the actual test data set, so that the root mean square error is used as a fitness value function of the quantum genetic optimization algorithm to generate the optimal artificial data set, and a new artificial sample data set is obtained in a set condition frame, and the method specifically comprises the following steps:
setting parameters such as population scale, maximum genetic iteration times, chromosome length and the like;
initializing a population, and randomly generating chromosomes with a certain quantity of quantum bit codes;
measuring the population individuals in sequence to obtain a determined state, namely binary codes;
performing decimal conversion on the binary array obtained by measurement according to the set variable range of each reaction, and substituting the decimal array into a support vector machine model to realize fitness evaluation aiming at the measurement result; wherein, the fitness value function for fitness evaluation is root mean square error;
recording original optimal individuals and corresponding optimal fitness values;
measuring the population individuals in sequence to obtain a determined state, namely binary codes;
carrying out fitness evaluation on the measurement result;
updating the optimal fitness and the related index information;
updating the probability amplitude of the quantum bit by using a quantum revolving gate to realize individual genetic variation of the population and obtain new population individuals;
adding 1 to the iteration times, returning to execute and recording the original optimal individual and the corresponding optimal fitness value until all iterations are finished;
and finally outputting all the recorded optimal individuals and the optimal fitness value as an optimal artificial data set.
The quantum genetic optimization algorithm can find an optimal solution in a shorter time based on a small sample data set, the sample data size is small, the algorithm performance is not influenced, the individual diversity in a population can be kept, and in addition, the method has the advantages of higher search efficiency, good global search capability, strong adaptability and the like, and is very suitable for the amplification treatment of the small sample data set related to the polymerization reaction test.
Further, the specific steps of step 3 are as follows:
set training sample set as
Wherein
A jth model input vector composed of jth training samples; y isjOutputting a vector for a jth model formed by a jth training sample; n is the dimension of the model input vector and
m is the number of model input vectors and corresponds to the total number of training samples;
the goal is to find the optimal classification line
Ensuring maximum separation of the sample points, wherein
Is a weight vector, b is a bias constant, and the maximum classification interval is expressed as
Namely, it is
The classification problem will therefore translate into the following optimization problem:
introducing an error variable ejUsed to indicate the amount of deviation of the allowed data points, the objective function is transformed into
Wherein gamma is a penalty coefficient;
the limiting conditions are constrained by an inequality constraint conversion equation:
introducing lagrange function multipliers
Constructing a Lagrangian function:
wherein alpha isjNot less than 0 is corresponding to
The lagrange multiplier of (a) is,
is [ alpha ]1,α2,…,αj,…,αM]，
Is an error vector;
obtaining linear equation set by solving partial derivatives of Lagrange function based on KKT condition
Wherein, I ═ 1,1, …,1]，
And
j, k ═ 1,2, …, M for the jth and kth model input vectors, respectively;
based on the training sample set, adopting HHL quantum algorithm to pair linear equation set
Solving is carried out to obtain the parameters of the optimal hyperplane
Wherein
Is alphajFinally obtaining a maximum interval hyperplane, and realizing the construction of a polymer polymerization reaction product evaluation model, wherein the function mathematical expression is as follows:
in specific implementation, SWAP-test is adopted to calculate kernel function k (x)j,xk) As shown in fig. 2:
the above formula is expressed by dirac notation,
and
are respectively as
And
corresponding quantum state, |0>And |1>Are all auxiliary qubit states;
is composed of
|0>,|1>The corresponding tensor product;<0|1>,<0|0>,
are respectively as
|0>,|1>Corresponding inner product of wherein
Is the final target;
H1finger-to-first quantum state Hadamard gate conversion, Swap2，3Means that the second quantum state and the third quantum state are exchanged using a Swap gate; measure (Measure)1Refers to measuring the first quantum state.
In specific implementation, the specific steps of the HHL quantum algorithm circuit are shown in fig. 3, and include:
preparation of input Quantum states
Wherein
Is input in a quantum state, and is set
ujAre auxiliary variables.
Transforming a matrix F into unitary operation
The unitary matrix after conversion should meet the unitary requirement of quantum computation on quantum gate, if the matrix is
Being s-sparse matrix, unitary matrix
The simulation time of (d) is O (log (N));
applying quantum phase estimation to clock registers and input registers, decomposition on eigenvector basis
The phase estimation module comprises a Hadamard gate, unitary operation and inverse quantum Fourier transform; after this operation, the clock register and the input register respectively obtain the matrix
(equivalent to e)iFt) Characteristic value of (1) | λj>And feature vectors
When the phase estimation is accurate, entanglement will occur between the two registers, and the value will become
The clock register is used as a control quantum bit to rotate the auxiliary quantum bit and convert the auxiliary quantum bit into |0>And |1>The superposition state of (1); controlled rotation operation from ground state | λj>In each caseExtraction of lambdajTo a probability amplitude
And
wherein
Three register values will become
In practical operation, the auxiliary qubit extraction ratio directly clocks the eigenvalues | λ in the register and the input registerj>And feature vectors
Restoring | λ using inverse phase estimationi>(i.e. | λ)i>→|0>) The inverse phase estimation includes a quantum Fourier transform, unitary operation, Hadamard gate, and then Amplitude Amplification (Amplitude Amplification) to increase the Amplitude to |1>；
Measuring the auxiliary register to obtain a result of |1>Then the result of the input register will be AND
Proportional calculation results;
after all the above processes are finished, the input register will be started
Become into
Wherein
Thereby realizing the solution of the linear equation system, and the calculation complexity of the process is O (M)2) Becomes O (log (M)) on an optimum basis
Are respectively obtained
And finally constructing a maximum interval hyperplane.
In the step, a quantum support vector machine QSVM algorithm is introduced to train a high-molecular polymerization reaction product evaluation model, two aspects of inner product kernel function calculation and linear equation system solving are emphasized, and the calculation complexity is represented by O (log (epsilon)-1) poly (N, M)) to O (log (N, M)), where M, N are the number of samples in the training set and the feature vector dimension, respectively; meanwhile, the influence of various complex variable factors such as reaction monomer ratio, initiator ratio, reaction temperature, reaction time and the like on the performance of an experimental product can be fully considered, the advantages of a quantum algorithm in a complex environment are exerted, the calculation complexity is reduced, and the prediction efficiency is improved.
The second aspect of the present invention provides a system for evaluating a polymer polymerization reaction product based on a quantum support vector machine, comprising:
a data acquisition module configured to acquire a raw data set related to a polymerization reaction process of a polymer
Setting different reaction conditions, preparing different reaction products by utilizing a high-molecular polymerization reaction, classifying and numbering the reaction products, treating the reaction products to be white powder, performing static adsorption capacity test by taking simulated saline as a solvent and quartz sand as an adsorption medium under the same solubility, temperature and time, taking solution samples before and after adsorption corresponding to different numbers, performing absorbance test by utilizing an ultraviolet spectrophotometer, calculating a concentration value according to a standard curve, and finally outputting the static adsorption capacity of the product;
wherein the different reaction conditions comprise monomer dosage, initiator proportion, reaction temperature, reaction time, drying temperature, drying time and fine granularity;
using the monomer amount, the initiator proportion, the reaction temperature, the reaction time, the drying temperature, the drying time and the fine granularity as model input vectors, and using the static adsorption capacity as a model output vector to form a high-molecular polymerization reaction product evaluation original data set;
the system comprises an original data set processing and classifying module, a pre-amplification data set and a pre-amplification data set, wherein the original data set processing and classifying module is configured to sequentially carry out standardization processing on a high molecular polymerization reaction product evaluation original data set to obtain a pre-amplification data set; generating an optimal artificial data set in a sample space by adopting a quantum genetic optimization algorithm based on the pre-amplification data set; repeating the steps for multiple times to generate a plurality of groups of different optimal artificial data sets, and combining the optimal artificial data sets with the pre-amplification data sets to generate a new high-molecular polymerization reaction product evaluation original data set; dividing the new manual sample data set into a training sample set and a testing sample set according to 80/20%;
the polymer polymerization reaction product evaluation model training module is configured to construct a polymer polymerization reaction product evaluation model based on a quantum support vector machine, and obtain the polymer polymerization reaction product evaluation model according to the constructed training sample set;
the model testing module is configured to verify the correctness of the high polymer polymerization reaction product evaluation model based on the trained high polymer polymerization reaction product evaluation model and the testing sample set;
and the prediction and correction module is configured to predict and comprehensively analyze the experimental results under more different types of reaction process variables by using the polymer polymerization reaction product evaluation model passing the test in a real polymer polymerization reaction experimental environment, and correct the evaluation model according to the feedback deviation condition.
In specific implementation, generating an optimal artificial dataset in a sample space by using a quantum genetic optimization algorithm based on the pre-amplification dataset comprises:
setting population scale, maximum genetic iteration times and chromosome length, wherein each population individual in the population corresponds to a model input vector, and the chromosome length is the total length of binary strings of all elements in the model input vector;
initializing a population, and randomly generating chromosomes with a certain quantity of quantum bit codes;
measuring the population individuals in sequence to obtain a determined state, namely binary codes;
performing decimal conversion on the binary array obtained by measurement according to the set variable range of each reaction, substituting the decimal conversion into a support vector machine model, and realizing fitness evaluation aiming at the measurement result, wherein the root mean square error is used as a fitness value function;
recording original optimal individuals and corresponding optimal fitness values;
measuring the population individuals in sequence to obtain a determined state, namely binary codes;
carrying out fitness evaluation on the measurement result;
updating the optimal fitness and the related index information;
updating the probability amplitude of the quantum bit by using a quantum revolving gate to realize individual genetic variation of the population and obtain new population individuals;
adding 1 to the iteration times, returning to execute and recording the original optimal individual and the corresponding optimal fitness value until all iterations are finished;
and finally outputting all the recorded optimal individuals and the optimal fitness value as an optimal artificial data set.
Further, a polymer polymerization product evaluation model is constructed based on a quantum support vector machine, and the polymer polymerization product evaluation model is obtained according to the constructed training sample set by the following specific steps:
set training sample set as
Wherein
A jth model input vector composed of jth training samples; y isjOutputting a vector for a jth model formed by a jth training sample; n is the model input directionDimension of quantity and
m is the number of model input vectors and corresponds to the total number of training samples;
the goal is to find the optimal classification line
Ensuring maximum separation of the sample points, wherein
Is a weight vector, b is a bias constant, and the maximum classification interval is expressed as
Namely, it is
The classification problem will therefore translate into the following optimization problem:
introducing an error variable ejUsed to indicate the amount of deviation of the allowed data points, the objective function is transformed into
Wherein gamma is a penalty coefficient;
the limiting conditions are constrained by an inequality constraint conversion equation:
introducing lagrange function multipliers
Constructing a Lagrangian function:
wherein alpha isjNot less than 0 is corresponding to
The lagrange multiplier of (a) is,
is [ alpha ]1,α2,…,αj,…,αM]，
Is an error vector;
obtaining linear equation set by solving partial derivatives of Lagrange function based on KKT condition
Wherein, I ═ 1,1, …,1]，
And
j, k ═ 1,2, …, M for the jth and kth model input vectors, respectively;
based on the training sample set, adopting HHL quantum algorithm to pair linear equation set
Solving is carried out to obtain the parameters of the optimal hyperplane
Wherein
Is alphajFinally obtaining a maximum interval hyperplane, and realizing the construction of a polymer polymerization reaction product evaluation model, wherein the function mathematical expression is as follows:
finally, it should be noted that the above examples are only used to illustrate the technical solutions of the present invention and not to limit the same; although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art will understand that: modifications to the specific embodiments of the invention or equivalent substitutions for parts of the technical features may be made; without departing from the spirit of the present invention, it is intended to cover all aspects of the invention as defined by the appended claims.
Claims (8)
1. A method for evaluating a high molecular polymerization reaction product based on a quantum support vector machine is characterized by comprising the following steps:
step 1, obtaining a related original data set of a high molecular polymerization reaction process;
setting different reaction conditions, preparing different reaction products by utilizing a high-molecular polymerization reaction, classifying and numbering the reaction products, treating the reaction products to be white powder, performing static adsorption capacity test by taking simulated saline as a solvent and quartz sand as an adsorption medium under the same solubility, temperature and time, taking solution samples before and after adsorption corresponding to different numbers, performing absorbance test by utilizing an ultraviolet spectrophotometer, calculating a concentration value according to a standard curve, and finally outputting the static adsorption capacity of the product;
wherein the different reaction conditions comprise monomer dosage, initiator proportion, reaction temperature, reaction time, drying temperature, drying time and fine granularity;
using the monomer amount, the initiator proportion, the reaction temperature, the reaction time, the drying temperature, the drying time and the fine granularity as model input vectors, and using the static adsorption capacity as a model output vector to form a high-molecular polymerization reaction product evaluation original data set;
step 2, preprocessing and amplifying the original data set of the evaluation of the high molecular polymerization reaction product;
sequentially carrying out standardization treatment on the original data sets for evaluating the high molecular polymerization reaction products to obtain a pre-amplification data set;
generating an optimal artificial data set in a sample space by adopting a quantum genetic optimization algorithm based on the pre-amplification data set;
repeating the steps for multiple times to generate a plurality of groups of different optimal artificial data sets, and combining the optimal artificial data sets with the pre-amplification data sets to generate a new high-molecular polymerization reaction product evaluation original data set;
dividing the new manual sample data set into a training sample set and a testing sample set according to 80/20%;
step 3, constructing a high molecular polymerization reaction product evaluation model based on a quantum support vector machine, and obtaining the high molecular polymerization reaction product evaluation model according to the constructed training sample set;
step 4, verifying the correctness of the high molecular polymerization reaction product evaluation model based on the high molecular polymerization reaction product evaluation model trained in the step 3 and the test sample set in the step 2;
and 5, predicting and comprehensively analyzing the experimental results under more different types of reaction process variables by using the polymer polymerization reaction product evaluation model passing the test in a real polymer polymerization reaction experimental environment, and correcting the evaluation model according to the feedback deviation condition.
2. The method for evaluating a high molecular polymerization reaction product based on a quantum support vector machine according to claim 1, wherein the specific steps of step 3 comprise:
set training sample set as
Wherein
A jth model input vector composed of jth training samples; y isjOutputting a vector for a jth model formed by a jth training sample; n is the dimension of the model input vector and
m is the number of model input vectors and corresponds to the total number of training samples;
the goal is to find the optimal classification line
Ensuring maximum separation of the sample points, wherein
Is a weight vector, b is a bias constant, and the maximum classification interval is expressed as
Namely, it is
The classification problem will therefore translate into the following optimization problem:
introducing an error variable ejUsed to indicate the amount of deviation of the allowed data points, the objective function is transformed into
Wherein gamma is a penalty coefficient;
subject the restriction condition toThe equality constraint converts the equality constraint:
introducing lagrange function multipliers
Constructing a Lagrangian function:
wherein alpha isjNot less than 0 is corresponding to
The lagrange multiplier of (a) is,
is [ alpha ]1,α2,…,αj,…,αM]，
Is an error vector;
obtaining linear equation set by solving partial derivatives of Lagrange function based on KKT condition
Wherein,
and
j, k ═ 1,2, …, M for the jth and kth model input vectors, respectively;
based on the training sample set, adopting HHL quantum algorithm to pair linear equation set
Solving is carried out to obtain the parameters of the optimal hyperplane
Wherein
Is alphajFinally obtaining a maximum interval hyperplane, and realizing the construction of a polymer polymerization reaction product evaluation model, wherein the function mathematical expression is as follows:
3. the method for evaluating a high molecular weight polymerization reaction product based on a quantum support vector machine according to claim 2, wherein the SWAP-test is used to calculate a kernel function k (x)j,xk)：
The above formula is expressed by dirac notation,
and
are respectively as
And
corresponding quantum state, |0>And |1>Are all auxiliary qubit states;
is composed of
The corresponding tensor product;
are respectively as
Corresponding inner product of wherein
Is the final target;
H1finger-to-first quantum state Hadamard gate conversion, Swap2，3Means that the second quantum state and the third quantum state are exchanged using a Swap gate; measure (Measure)1Refers to measuring the first quantum state.
4. The method for evaluating a high molecular polymerization reaction product based on a quantum support vector machine according to claim 1, wherein the generating an optimal artificial data set in a sample space by using a quantum genetic optimization algorithm based on the pre-amplification data set comprises:
setting population scale, maximum genetic iteration times and chromosome length, wherein each population individual in the population corresponds to a model input vector, and the chromosome length is the total length of binary strings of all elements in the model input vector;
initializing a population, and randomly generating chromosomes with a certain quantity of quantum bit codes;
measuring the population individuals in sequence to obtain a determined state, namely binary codes;
performing decimal conversion on the binary array obtained by measurement according to the set variable range of each reaction, substituting the decimal conversion into a support vector machine model, and realizing fitness evaluation aiming at the measurement result, wherein the root mean square error is used as a fitness value function;
recording original optimal individuals and corresponding optimal fitness values;
measuring the population individuals in sequence to obtain a determined state, namely binary codes;
carrying out fitness evaluation on the measurement result;
updating the optimal fitness and the related index information;
updating the probability amplitude of the quantum bit by using a quantum revolving gate to realize individual genetic variation of the population and obtain new population individuals;
adding 1 to the iteration times, returning to execute and recording the original optimal individual and the corresponding optimal fitness value until all iterations are finished;
and finally outputting all the recorded optimal individuals and the optimal fitness value as an optimal artificial data set.
5. A high molecular polymerization reaction product evaluation system based on a quantum support vector machine is characterized by comprising:
a data acquisition module configured to acquire a raw data set related to a polymerization reaction process of a polymer
Setting different reaction conditions, preparing different reaction products by utilizing a high-molecular polymerization reaction, classifying and numbering the reaction products, treating the reaction products to be white powder, performing static adsorption capacity test by taking simulated saline as a solvent and quartz sand as an adsorption medium under the same solubility, temperature and time, taking solution samples before and after adsorption corresponding to different numbers, performing absorbance test by utilizing an ultraviolet spectrophotometer, calculating a concentration value according to a standard curve, and finally outputting the static adsorption capacity of the product;
wherein the different reaction conditions comprise monomer dosage, initiator proportion, reaction temperature, reaction time, drying temperature, drying time and fine granularity;
using the monomer amount, the initiator proportion, the reaction temperature, the reaction time, the drying temperature, the drying time and the fine granularity as model input vectors, and using the static adsorption capacity as a model output vector to form a high-molecular polymerization reaction product evaluation original data set;
the system comprises an original data set processing and classifying module, a pre-amplification data set and a pre-amplification data set, wherein the original data set processing and classifying module is configured to sequentially carry out standardization processing on a high molecular polymerization reaction product evaluation original data set to obtain a pre-amplification data set; generating an optimal artificial data set in a sample space by adopting a quantum genetic optimization algorithm based on the pre-amplification data set; repeating the steps for multiple times to generate a plurality of groups of different optimal artificial data sets, and combining the optimal artificial data sets with the pre-amplification data sets to generate a new high-molecular polymerization reaction product evaluation original data set; dividing the new manual sample data set into a training sample set and a testing sample set according to 80/20%;
the polymer polymerization reaction product evaluation model training module is configured to construct a polymer polymerization reaction product evaluation model based on a quantum support vector machine, and obtain the polymer polymerization reaction product evaluation model according to the constructed training sample set;
the model testing module is configured to verify the correctness of the high polymer polymerization reaction product evaluation model based on the trained high polymer polymerization reaction product evaluation model and the testing sample set;
and the prediction and correction module is configured to predict and comprehensively analyze the experimental results under more different types of reaction process variables by using the polymer polymerization reaction product evaluation model passing the test in a real polymer polymerization reaction experimental environment, and correct the evaluation model according to the feedback deviation condition.
6. The system for evaluating a high molecular polymerization reaction product based on a quantum support vector machine according to claim 5, wherein the generating an optimal artificial data set in a sample space by using a quantum genetic optimization algorithm based on the pre-amplification data set comprises:
setting population scale, maximum genetic iteration times and chromosome length, wherein each population individual in the population corresponds to a model input vector, and the chromosome length is the total length of binary strings of all elements in the model input vector;
initializing a population, and randomly generating chromosomes with a certain quantity of quantum bit codes;
measuring the population individuals in sequence to obtain a determined state, namely binary codes;
performing decimal conversion on the binary array obtained by measurement according to the set variable range of each reaction, substituting the decimal conversion into a support vector machine model, and realizing fitness evaluation aiming at the measurement result, wherein the root mean square error is used as a fitness value function;
recording original optimal individuals and corresponding optimal fitness values;
measuring the population individuals in sequence to obtain a determined state, namely binary codes;
carrying out fitness evaluation on the measurement result;
updating the optimal fitness and the related index information;
updating the probability amplitude of the quantum bit by using a quantum revolving gate to realize individual genetic variation of the population and obtain new population individuals;
adding 1 to the iteration times, returning to execute and recording the original optimal individual and the corresponding optimal fitness value until all iterations are finished;
and finally outputting all the recorded optimal individuals and the optimal fitness value as an optimal artificial data set.
7. The system for evaluating a polymer polymerization reaction product based on a quantum support vector machine according to claim 5, wherein the polymer polymerization reaction product evaluation model training module builds a polymer polymerization reaction product evaluation model based on the quantum support vector machine, and the specific steps of obtaining the polymer polymerization reaction product evaluation model according to the built training sample set include:
set training sample set as
Wherein
A jth model input vector composed of jth training samples; y isjOutputting a vector for a jth model formed by a jth training sample; n is the dimension of the model input vector and
m is the number of model input vectors and corresponds to the total number of training samples;
the goal is to find the optimal classification line
Ensuring maximum separation of the sample points, wherein
Is a weight vector, b is a bias constant, and the maximum classification interval is expressed as
Namely, it is
The classification problem will therefore translate into the following optimization problem:
introducing an error variable ejUsed to indicate the amount of deviation of the allowed data points, the objective function is transformed into
Wherein gamma is a penalty coefficient;
the limiting conditions are constrained by an inequality constraint conversion equation:
introducing lagrange function multipliers
Constructing a Lagrangian function:
wherein alpha isjNot less than 0 is corresponding to
The lagrange multiplier of (a) is,
is [ alpha ]1,α2,…,αj,…,αM]，
Is an error vector;
obtaining linear equation set by solving partial derivatives of Lagrange function based on KKT condition
Wherein, I ═ 1,1, …,1]，
And
j, k ═ 1,2, …, M for the jth and kth model input vectors, respectively;
based on the training sample set, adopting HHL quantum algorithm to pair linear equation set
Solving is carried out to obtain the parameters of the optimal hyperplane
Wherein
Is alphajFinally obtaining a maximum interval hyperplane, and realizing the construction of a polymer polymerization reaction product evaluation model, wherein the function mathematical expression is as follows:
8. the quantum-based support vector of claim 7The system for evaluating the high-molecular polymerization reaction product is characterized in that a SWAP-test is adopted to calculate a kernel function k (x)i,xj)：
The above formula is expressed by dirac notation,
and
are respectively as
And
corresponding quantum state, |0>And |1>Are all auxiliary qubit states;
is composed of
The corresponding tensor product;
are respectively as
Corresponding inner product of wherein
Is the final target;
H1finger-to-first quantum state Hadamard gate conversion, Swap2，3Means that the second quantum state and the third quantum state are exchanged using a Swap gate; measure (Measure)1Refers to measuring the first quantum state.
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