Renewable energy data clustering method and system based on optical quantum computer

Abstract

The invention discloses a renewable energy source data clustering method and system based on an optical quantum computer, and the method comprises the steps: building a renewable energy source data clustering optimization problem based on a quadratic unconstrained binary optimization (QUBO) model based on a discrete optimization objective function, carrying out the matrix of the objective function, carrying out the clustering optimization of the objective function through a kernel method, and carrying out the clustering optimization of the objective function. The method comprises the following steps of: establishing a target function item, converting the target function item into a matrix form, constructing a matrix of a new clustering model, finally solving a new QUBO optimization problem by using CIM, and converting the new QUBO optimization problem into an optimal clustering result. According to the method, data similarity measurement is improved by constructing the QUBO model and combining a kernel method, and a renewable energy source data clustering problem is converted into a form suitable for CIM solution, so that the calculation bottleneck of a classical calculation method in high-dimensional data processing is avoided. According to the method, the nonlinear characteristic of the data can be kept, efficient clustering optimization calculation can be realized, and the calculation efficiency and the clustering precision are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of data clustering and quantum computing, and mainly relates to a renewable energy data clustering method and system based on an optical quantum computer. Background Art

[0002] Clustering technology is a basic tool for power system data analysis and aggregation control, and the clustering analysis of renewable energy data is a key step in its pattern recognition and feature extraction. However, clustering technology is usually formulated as a combinatorial optimization problem, and faces the problem of excessively high computational complexity when dealing with large-scale and high-dimensional data. Especially when solving on a classical computer based on integrated circuits, it is easily restricted by the curse of dimensionality.

[0003] When the data dimension is high, the computational complexity of traditional clustering methods increases significantly, and the calculation time rises sharply, making it difficult to meet the real-time requirements. To solve this problem, researchers have proposed various clustering methods based on classical computers, such as K-means and K-medoids, etc. Although these methods perform well on small-scale data, when dealing with large-scale data, the computational complexity increases rapidly, making it difficult to cope with the challenges of NP-hard problems. Summary of the Invention

[0004] In view of the problems that the prior art is difficult to process large-scale data and has low processing efficiency, the present invention proposes a renewable energy data clustering method and system based on an optical quantum computer. First, based on a discrete optimization objective function, a renewable energy data clustering optimization problem based on a quadratic unconstrained binary optimization (QUBO) model is constructed. Then, the objective function is matrixized, and through the kernel method, the clustering optimization objective function terms are optimized, and the objective function terms are converted into matrix form to construct the matrixization of the new clustering model. Finally, the CI M is used to solve the new QUBO optimization problem and convert it into the optimal clustering result. The method of the present invention improves the data similarity measurement by constructing a QUBO model and combining the kernel method, and converts the renewable energy data clustering problem into a form suitable for CI M solution, thereby avoiding the computational bottleneck of classical computing methods in high-dimensional data processing. This method can not only maintain the nonlinear characteristics of the data, but also achieve efficient clustering optimization calculation, significantly improving the computational efficiency and clustering accuracy.

[0005] To achieve the above object, the technical solution adopted by the present invention is: a renewable energy data clustering method based on an optical quantum computer, including the following steps:

[0006] S1. Based on a discrete optimization objective function, construct a renewable energy data clustering optimization problem based on a quadratic unconstrained binary optimization (QUBO) model, and the clustering optimization problem is specifically:

[0007]

[0008] Among them, g ∈ {1, 2,..., G} is the clustering index, and G is the number of clusters; i, j ∈ {1, 2,..., N}, and N is the number of samples; d i,j represents the Euclidean distance between sample i and sample j; is a binary decision variable, indicating that sample i is assigned to the g-th cluster;

[0009] S2. Matrixize the objective function in step S1 to be applicable to the calculation of an optical coherence Ising machine (CIM);

[0010] S3. Through the kernel method, optimize the objective function terms of clustering and convert the objective function terms into matrix form to construct the matrixization of a new clustering model;

[0011] S4. Use CIM to solve the new QUBO optimization problem constructed in step S3 and convert it into the optimal clustering result.

[0012] As an improvement of the present invention, the discrete optimization objective function in step S1 is specifically:

[0013]

[0014] Augment the constraint condition into a penalty term H cons , and the optimization objective function is reconstructed into a quadratic unconstrained binary optimization (QUBO) form, specifically:

[0015]

[0016] where λ i is the penalty coefficient.

[0017] As another improvement of the present invention, the penalty coefficient λ i in step S1 satisfies:

[0018]

[0019] where is the maximum value of the Euclidean distance d i,j between all sample pairs.

[0020] As another improvement of the present invention, the matrixization of the objective function in step S2 specifically includes the following steps:

[0021] S21. Perform matrixization conversion on the objective function term H obj :

[0022]

[0023] Among them, is a binary decision variable vector; is the upper triangular part of matrix D, where the elements are d i,j ; is the identity matrix; represents the Kronecker product;

[0024] After S22, ignoring the constant term, the constraint term H cons is subjected to matrix transformation:

[0025]

[0026] Among them, is a diagonal matrix, and its diagonal elements are the penalty coefficients λ i ; is an upper triangular matrix, the main diagonal elements are 0, and the remaining upper triangular elements are all 1;

[0027] S23. Combining the objective function term in step S21 and the constraint term in step S22, the matrix form of the objective function is specifically:

[0028]

[0029] As another improvement of the present invention, the objective function term optimized by the kernel method clustering in step S2 is specifically:

[0030]

[0031] Among them, g i,j is the non-linear kernel similarity index;

[0032] Convert the objective function term of the kernel method into matrix form:

[0033]

[0034] Among them, is a diagonal matrix containing only the diagonal elements of G; the matrix its elements are g i,j , including all similarity information for clustering; is the upper triangular matrix of G, its main diagonal elements are 0, and the remaining upper triangular elements are the same as G.

[0035] As another improvement of the present invention, step S4 specifically includes the following steps:

[0036] S41. The QUBO objective function is transformed into an equivalent quadratic optimization problem, and its mathematical form is as follows:

[0037] f QUBO f(x) = x T Qx

[0038] where Q is a symmetric weight matrix;

[0039] S42. Through variable substitution, convert the QUBO problem into the Ising Hamiltonian form. According to the QUBO matrix output in steps S2 and S3, construct the coupling coefficient J i,j and the bias term h i ;

[0040] S43. The CIM physically realizes the spin state through a degenerate optical parametric oscillator. During the iteration process, the CIM adjusts the variable state according to the principle of minimizing the system energy, so that the system reaches a steady-state solution, and finally outputs the spin configuration s i ∈{-1, +1}, which is the optimal solution and corresponds to the optimal value of the QUBO variable;

[0041] S44. Map each optimal spin configuration s i ∈{-1, +1} output by the CIM back to the original binary decision variable Map the optimal solution calculated by the CIM back to the clustering label to achieve the optimal classification of the data.

[0042] To achieve the above object, the technical solution adopted by the present invention is also: a renewable energy data clustering system based on an optical quantum computer, including a computer program, and when the computer program is executed by a processor, it implements the steps of any one of the above methods.

[0043] Compared with the prior art, the beneficial effects of the present invention are: by revealing the connection between the QUBO model and the CIM, the present invention proposes a renewable energy data clustering method and system based on an optical quantum computer. This method effectively overcomes the computational complexity problem of classical computers when dealing with large-scale data, thus significantly reducing the computational burden; in addition, by introducing the kernel method, the present invention further improves the clustering accuracy, can better capture the non-linear structure of the data, and overcomes the limitations of traditional methods when dealing with non-linear data. The method of the present invention can not only maintain the non-linear characteristics of the data, but also achieve efficient clustering optimization calculation, significantly improving the computational efficiency and clustering accuracy. Description of the Drawings

[0044] Figure 1 is the flowchart of the steps of the renewable energy data clustering method based on an optical quantum computer of the present invention;

[0045] Figure 2 is the comparison chart of the clustering results of different algorithms of classical computers and CIMs with different numbers of variables in the test example of the present invention. Detailed implementation manners

[0046] The present invention will be further illustrated below in conjunction with the accompanying drawings and specific implementation manners. It should be understood that the following specific implementation manners are only used to illustrate the present invention and not to limit the scope of the present invention.

[0047] Embodiment 1

[0048] A renewable energy data clustering method based on an optical quantum computer, as Figure 1 shown, includes the following steps:

[0049] Step S1, construct a renewable energy data clustering optimization problem based on a quadratic unconstrained binary optimization (QUBO) model.

[0050] In this embodiment, for the clustering optimization problem of renewable energy power output data, the photovoltaic (PV) time series power output data is taken as the research object. Suppose there are N sets of output characteristic data (i.e., N samples), which need to be divided into G clusters. Define a discrete optimization objective function H obj , which is used to minimize the distance between data points within the same cluster, and its expression is as follows:

[0051]

[0052] where g ∈ {1, 2,..., G} is the cluster index; y i , y j ∈ {1, 2,.., G} (i, j ∈ {1, 2,..., N}) is an integer variable, representing the cluster number to which sample i belongs. If y i = y j , it means that sample i and sample j are assigned to the same cluster; d i,j represents the Euclidean distance between sample i and sample j, which is used to quantify the similarity between data.

[0053] Since the feasible solution space of the optimization objective function is highly non-convex, it is difficult for traditional methods to obtain its optimal solution. To overcome this problem, the integer variable y i is usually converted into G binary variables, that is:

[0054]

[0055] where is a binary decision variable, represents that sample i is assigned to the g-th cluster. In addition, since each sample can only belong to one cluster, the constraint needs to be satisfied:

[0056]

[0057] Then the clustering problem can be transformed into the following form:

[0058]

[0059] Taking the constraint as a penalty term, the optimization objective function is reconstructed into the form of quadratic unconstrained binary optimization (QUBO):

[0060]

[0061] where λ i is the penalty coefficient.

[0062] To ensure the effectiveness of the constraint, λ i should satisfy:

[0063]

[0064] where is the maximum value of the Euclidean distance d i,j between all sample pairs.

[0065] Step S2. Matrixize the QUBO objective function to be applicable to the calculation of the optical coherence Ising machine (CIM).

[0066] S21. Perform the following matrix transformation on the objective function term H obj :

[0067]

[0068] where is the binary decision variable vector; is the upper triangular part of the matrix D, and its elements are d i,j ; is the identity matrix; represents the Kronecker product;

[0069] S22. After ignoring the constant term, perform the following matrix transformation on the constraint term H cons :

[0070]

[0071] where is a diagonal matrix, and its diagonal elements are the penalty coefficients λ i ; is an upper triangular matrix, the main diagonal elements are 0, and the remaining upper triangular elements are all 1;

[0072] S23. Combining the objective function term and the constraint term, the matrix form of the QUBO objective function is as follows:

[0073]

[0074] Step S3. Combine the kernel method to improve the clustering accuracy and construct the matrix form of a new clustering model.

[0075] S31. Adopt the non - linear kernel similarity index g i,j to replace the original Euclidean distance d i,j as follows:

[0076]

[0077] where c ∈ {1, 2,..., N} is the column index and r ∈ {1, 2,..., N} is the row index, represents the non - linear Gaussian kernel function;

[0078] Define the matrix whose elements are g i,j , containing all the similarity information for clustering; Based on this, the clustering optimization objective function term of the kernel method can be expressed as follows:

[0079]

[0080] S32. Further transform the objective function term of the kernel method into the matrix form as follows:

[0081]

[0082] where, is a diagonal matrix containing only the diagonal elements of G; is the upper triangular matrix of G, whose main diagonal elements are 0 and the remaining upper triangular elements are the same as those of G;

[0083] The constraint term remains unchanged. Therefore, the QUBO objective function based on the kernel method is expressed as follows:

[0084]

[0085] This formula is in the QUBO form that can be solved by the optical quantum computer (CIM).

[0086] Step S4. Use CIM to solve the QUBO optimization problem and transform it into the optimal clustering result.

[0087] The present invention is based on the optical coherent Ising machine to solve the QUBO objective function and obtain the optimal clustering result. CIM uses the Ising model for calculation, and its goal is to minimize the total energy of the system:

[0088]

[0089] where s i∈{-1, +1} represents the spin variable, corresponding to the QUBO variable x i 's binary mapping; J i,j is the interaction coupling coefficient, which defines the influence relationship between variables; h i is the external field effect, which adjusts the bias value of each variable.

[0090] Since the QUBO objective function can be transformed into an equivalent quadratic optimization problem, its mathematical form is as follows:

[0091] f QUBO (x) = x T Qx

[0092] where Q is a symmetric weight matrix, and this matrix corresponds to the part of the QUBO objective function term based on the kernel method in S32.

[0093] Through variable substitution, the QUBO problem is transformed into the Ising Hamiltonian form, making it applicable to CIM. The QUBO matrix output by steps S2 and S3 is used to construct the coupling coefficient J i,j and the bias term h i .

[0094] CIM physically realizes the spin state through a degenerate optical parametric oscillator. During the iteration process, CIM continuously adjusts the variable state according to the principle of minimizing the system energy, so that the system reaches a steady-state solution. The finally output spin configuration is the optimal solution, corresponding to the optimal value of the QUBO variable.

[0095] Since CIM outputs s i ∈{-1, +1}, it is necessary to perform variable mapping back to the original binary decision variable Map the optimal solution calculated by CIM back to the clustering label to achieve the optimal classification of the data. Finally, the clustering effect can also be evaluated according to the calculated silhouette coefficient to ensure that the classification quality meets the application requirements.

[0096] Test example

[0097] This test example is to test the proposed method on a 400-bit CIM provided by QBoson. The photovoltaic output data comes from the Yulara solar system. The data is collected at 5-minute intervals and the hourly average value is taken for analysis.

[0098] This test example compares different clustering algorithms, including K-means (MATLAB), K-medoids (MATLAB), and simulated quantum annealing (SQA, OpenJij) running on a classical computer (i5-13400F 2.5GHz, 32G RAM). Four different scales of test cases are set in the experiment, that is, dividing 50 / 60 / 70 / 80 photovoltaic output data into 2 / 3 / 4 / 5 clusters, corresponding to 100 / 180 / 280 / 400 binary variables respectively. The silhouette coefficient proposed by Rousseeuw is used to evaluate the clustering effect.

[0099] According to the steps of the renewable energy data clustering method based on an optical quantum computer of the present invention, in order to verify the ability of CIM to overcome the curse of dimensionality and compare the computational efficiency of different methods, the clustering results of the classical computer and different algorithms of CIM with different numbers of variables in this test example are compared as Figure 2 shown.

[0100] The computational times of different clustering algorithms with different variable scales are as Figure 2 (a) shown. Figure 2 As can be seen from (a), the computational time of CIM is hardly affected by the scale of input variables, while for all other methods running on a classical computer, their computational times show a significant upward trend as the variable scale increases. This phenomenon clearly shows that classical computers are vulnerable to the curse of dimensionality when solving NP-hard clustering problems, while CIM is hardly affected. In all test cases of this test example, the computational time of CIM is basically stable at about 3ms, and the maximum does not exceed 3.105ms.

[0101] The silhouette coefficients of different clustering algorithms with different variable scales are as Figure 2 (b) shown. Figure 2 As can be seen from (b), the clustering effect of this method is comparable to that of the K-medoids and K-means methods, indicating that this method can ensure the effectiveness and accuracy of clustering, thus verifying its applicability in renewable energy data analysis.

[0102] From the above test comparison, it can be seen that this method performs excellently in terms of computational efficiency and clustering effect, proving its feasibility in large-scale quantum computing applications.

[0103] Therefore, the present method proposes a renewable energy data clustering framework based on an optical quantum computer, which uses QUBO modeling and CIM calculation to achieve efficient clustering analysis. The method of the present invention constructs a clustering model combined with a kernel method, improves the data similarity measure through matrixization, and adapts to CIM for calculation, overcoming the computational complexity problem encountered by traditional calculation methods in high-dimensional data processing through optical quantum computing. In addition, the proposed QUBO modeling scheme provides valuable guidance for the application of CIM in combinatorial optimization problems, helping to further expand the application of optical quantum computing in large-scale renewable energy data analysis.

[0104] It should be noted that the above content only illustrates the technical idea of the present invention and cannot be used to limit the protection scope of the present invention. For those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements all fall within the protection scope of the claims of the present invention.

Claims

1. A renewable energy data clustering method based on an optical quantum computer, characterized in that: The steps include: S1. Based on the discrete optimization objective function, a renewable energy data clustering optimization problem based on the quadratic unconstrained binary optimization (QUBO) model is constructed. The clustering optimization problem is specifically: Where g∈{1,2,...,G} is the cluster index, G is the number of clusters; i,j∈{1,2,...,N}, N is the number of samples; d i,j represents the Euclidean distance between sample i and sample j; is a binary decision variable, Indicates that sample i is assigned to the gth cluster; S2, matrixing the objective function in step S1 to be suitable for calculation of optical coherent Ising machine (CIM); S3. Clustering optimizes the objective function terms through the kernel method, and converts the objective function terms into a matrix form to construct a matrix of a new clustering model; S4. Use CIM to solve the new QUBO optimization problem constructed in step S3 and convert it into the optimal clustering result.

2. The renewable energy data clustering method based on optical quantum computer according to claim 1, characterized in that: The discrete optimization objective function in step S1 is specifically: The constraints Augmented with penalty term H cons , the optimization objective function is reconstructed into the quadratic unconstrained binary optimization (QUBO) form, specifically: Among them, λ i is the penalty coefficient.

3. The renewable energy data clustering method based on optical quantum computer according to claim 2, characterized in that: The penalty coefficient λ in step S1 i satisfy: in, is the Euclidean distance d between all sample pairs i,j The maximum value of .

4. The renewable energy data clustering method based on optical quantum computer according to claim 2, characterized in that: The step S2 specifically includes the following steps for matrixing the objective function: S21, for the objective function term H obj Perform matrix transformation: in, is a vector of binary decision variables; is the upper triangular part of the matrix D, where the elements are d i,j ; is the identity matrix; represents the Kronecker product; S22, after ignoring the constant term, for the constraint term H cons Perform matrix transformation: in, is a diagonal matrix whose diagonal elements are penalty coefficients λ i ; It is an upper triangular matrix, the main diagonal elements are 0, and the other upper triangular elements are 1; S23, combining the objective function term of step S21 and the constraint term of step S22, the matrix form of the objective function is specifically:

5. The renewable energy data clustering method based on optical quantum computer according to claim 2, characterized in that: The objective function term optimized by kernel clustering in step S2 is specifically: Among them, g i,j is the nonlinear kernel similarity index; Convert the objective function term of the kernel method into matrix form: in, is a diagonal matrix containing only the diagonal elements of G; the matrix Its element is g i,j , contains all similarity information used for clustering; is the upper triangular matrix of G, whose main diagonal elements are 0 and the remaining upper triangular elements are the same as G.

6. The renewable energy data clustering method based on optical quantum computer according to claim 5, characterized in that: The step S4 specifically includes the following steps: S41, QUBO objective function is transformed into an equivalent quadratic optimization problem, and its mathematical form is as follows: f QUBO (x)=x T Qx Among them, Q is a symmetric weight matrix; S42, by variable substitution, the QUBO problem is converted into the Ising Hamiltonian form, and the coupling coefficient J in CIM is constructed according to the QUBO matrix output in steps S2 and S3 i,j and the bias term h i ; S43, CIM physically realizes the spin state through a degenerate optical parametric oscillator. In the iterative process, CIM adjusts the variable state according to the principle of system energy minimization to make the system reach a steady-state solution. The final output spin configuration is the optimal solution, corresponding to the optimal value of the QUBO variable; S44, optimal spin configuration for each bit of CIM output i ∈{-1,+1} to map the variables back to the original binary decision variables The optimal solution calculated by CIM is mapped back to the clustering label to achieve optimal classification of the data.

7. A renewable energy data clustering system based on an optical quantum computer, comprising a computer program, characterized in that: When the computer program is executed by a processor, the steps of any of the above methods are implemented.

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