Performance optimization method and system for closed cooling tower

Abstract

The invention provides a performance optimization method and system for a closed cooling tower, and relates to the technical field of data processing.The method comprises the steps that input parameters describing the closed cooling tower are obtained; determining a cumulative distribution function of each input parameter; discretizing each input parameter to form a discretized simulation sample; performing computational fluid mechanics simulation on the closed cooling tower by utilizing the simulation samples, and determining system response of each simulation sample; performing principal component analysis on system response data through singular value decomposition; establishing an incidence relation between the input variable and the score matrix through Kriging interpolation, and forming a complete preliminary prediction model between the input variable and the system response; through a high-dimensional model representation technology, the high-order interaction effect of the preliminary prediction model is optimized, and a performance prediction model of the closed cooling tower is obtained; in order to improve the cooling efficiency and reduce the construction cost, the design parameters of the closed cooling tower are optimized through a butterfly optimization algorithm.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a method and system for optimizing the performance of a closed cooling tower. Background Technology

[0002] Optimizing the performance of closed-circuit cooling towers is crucial for improving energy efficiency, reducing operating costs, and enhancing system reliability. By optimizing the design and operating parameters of cooling towers, cooling performance can be significantly improved, while construction costs, energy consumption, and water waste can be reduced.

[0003] In existing technologies, fluid dynamics simulation is often used to simulate and optimize the performance of closed-circuit cooling towers. The fluid dynamics simulation process requires the mathematical description of the operation of the closed-circuit cooling tower using mass conservation, energy conservation, and the Navier-Stokes equations. Boundary conditions are set, a mesh is generated, and then the equations are solved using methods such as Runge-Kutta.

[0004] However, this kind of fluid dynamics simulation involves a very large amount of computation when solving the equations. In the process of optimizing the performance of a closed cooling tower, it is necessary to continuously adjust the design parameters and control parameters of the closed cooling tower. Each adjustment requires solving the equations again, which consumes a lot of computational resources and takes a long time. As a result, the performance optimization of the closed cooling tower is time-consuming and inefficient. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the purpose of this invention is to provide a method for optimizing the performance of a closed-loop cooling tower. This method can solve the technical problems of existing technologies, such as the large amount of computation required for solving equations in fluid dynamics simulations, the need to continuously adjust the design and control parameters of the closed-loop cooling tower during performance optimization, the need to solve the equations again for each adjustment, the high consumption of computational resources, and the long solution time, resulting in the time-consuming and inefficient performance optimization of closed-loop cooling towers.

[0006] A first aspect of this invention provides a method for optimizing the performance of a closed-loop cooling tower, comprising:

[0007] S1: Obtain input parameters describing the closed cooling tower, including deterministic parameters and uncertain parameters affected by seasonal climate, the deterministic parameters including design parameters and operating parameters;

[0008] S2: Determine the cumulative distribution function of each of the input parameters;

[0009] S3: Discretize each input parameter according to the cumulative distribution function of each input parameter to form a discretized simulation sample;

[0010] S4: Using the simulation samples, perform computational fluid dynamics simulation on the closed cooling tower to determine the system response for each simulation sample;

[0011] S5: Principal component analysis is performed on the system response data through singular value decomposition, and the system response data is characterized using the principal component matrix and the score matrix;

[0012] S6: By using Kriging interpolation, a correlation is established between the input variables and the score matrix to form a preliminary prediction model between the input variables and the system response;

[0013] S7: By using high-dimensional model representation technology, the higher-order interaction effect of the preliminary prediction model is optimized to obtain the performance prediction model of the closed cooling tower;

[0014] S8: Based on the performance prediction model, with the goal of improving cooling efficiency and reducing construction costs, the design parameters of the closed cooling tower are optimized using the butterfly optimization algorithm.

[0015] A second aspect of the present invention provides a performance optimization system for a closed-loop cooling tower, comprising: a processor and a memory;

[0016] The memory stores programs or instructions that can run on the processor, which, when executed by the processor, implement the steps of the performance optimization method for closed-loop cooling towers as described in the first aspect.

[0017] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following:

[0018] In this embodiment of the invention, a performance prediction model for a closed-loop cooling tower is constructed using principal component analysis, kriging interpolation, and high-dimensional model representation techniques. This enables accurate prediction of the response to complex fluid dynamics simulation systems, reducing computational resource consumption and optimization time while accurately predicting cooling tower performance. It avoids the need for tedious equation solving every time design and control parameters are adjusted, thus significantly improving optimization efficiency. Further optimization of design parameters using the butterfly optimization algorithm effectively improves cooling efficiency, reduces construction costs, and accelerates the design process. Attached Figure Description

[0019] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts. Obviously, the drawings described below are merely some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0020] Figure 1 This is a schematic flowchart of a method for optimizing the performance of a closed cooling tower provided in an embodiment of the present invention.

[0021] Figure 2 This is a schematic diagram of the structure of a performance optimization system for a closed cooling tower provided in an embodiment of the present invention. Detailed Implementation

[0022] To enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. It should be understood that these descriptions are merely exemplary and are not intended to limit the scope of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0023] The performance optimization method for closed cooling towers provided by the present invention will be described in detail below with reference to the accompanying drawings, through specific embodiments and application scenarios.

[0024] Reference manual attached Figure 1 The diagram shows a flow chart of a performance optimization method for a closed cooling tower provided by an embodiment of the present invention.

[0025] This invention provides a method for optimizing the performance of a closed-loop cooling tower, which may include the following steps:

[0026] S1: Obtain the input parameters describing the closed cooling tower.

[0027] It should be noted that all input parameters are related to the performance of the closed-circuit cooling tower.

[0028] The performance optimization method described in this application is applicable to the performance optimization of various types of closed cooling towers.

[0029] This section describes a classic closed-circuit cooling tower structure. Cooling water is pressurized by a circulating pump and delivered to the cooling coils inside the tower, where the water circulates continuously. Simultaneously, a pump draws water from a reservoir at the bottom of the tower to spray nozzles at the top, where it is evenly sprayed down, forming a water film covering the outer wall of the coils. Heat is first exchanged through convection between the cooling water and the inner wall of the coils, and then conducted through the inner wall to the outer wall, which is then covered by the sprayed water film. Finally, convection and evaporation between the water film and the air release the heat into the air, and a fan is responsible for exhausting this hot, humid air outside the tower.

[0030] The input parameters include deterministic parameters and uncertain parameters affected by seasonal climate.

[0031] Among them, deterministic parameters include design parameters and operational parameters.

[0032] Optionally, design parameters include: heat exchanger material, width, tube length, tube diameter, tube spacing coefficient, number of tube rows per pass, and number of passes.

[0033] Optionally, the operating parameters include: air velocity, spray water flow rate, spray water temperature, circulating water temperature, and circulating water flow rate.

[0034] Optionally, the uncertainty parameters include: dry-bulb temperature, wet-bulb temperature, and relative humidity.

[0035] S2: Determine the cumulative distribution function of each input parameter.

[0036] In one possible implementation, S2 specifically includes sub-steps S201 and S202:

[0037] S201: For deterministic parameters, use a normal distribution to describe the cumulative distribution function.

[0038] It should be noted that by assuming these parameters follow a normal distribution, parameter variations can be modeled simply and effectively, providing a reasonable parameter range for the optimization process. The normal distribution assumption is very common in many engineering applications, facilitating data processing and model construction.

[0039] S202: For the uncertainty parameter, the cumulative distribution function is described by Gaussian kernel density estimation:

[0040]

[0041] Among them, P s Let P represent the cumulative distribution function for the s-th seasonal group, z represent the independent variable (a certain input parameter), and P represent the cumulative distribution function for the s-th seasonal group. s (z) represents the probability that the input parameter value is less than or equal to z in the s-th seasonal group, β represents the smoothing factor, and n s σ represents the number of samples in the s-th seasonal group. s Let z represent the standard deviation of the s-th seasonal group, G represent the Gaussian kernel function, and z s (u) represents the data point of the u-th sample in the s-th seasonal group, exp represents the exponential function with the natural constant as the base, and v represents the integral variable.

[0042] It should be noted that the uncertainty parameter is easily affected by weather conditions. The uncertainty parameter depends on the actual weather conditions, which typically vary with temperature and humidity in different seasons. Therefore, it is difficult to use any standard parametric probability distribution model (such as the normal distribution) to describe the distribution of the uncertainty parameter. The sample can be divided into four groups according to the season, and then Gaussian kernel density estimation can be used to describe the cumulative distribution function of the uncertainty parameter.

[0043] In this embodiment of the invention, Gaussian kernel density estimation is used to describe the cumulative distribution function of the uncertainty parameter. This method does not rely on a preset standard probability distribution, but rather estimates the distribution of the uncertainty parameter based on actual data in a smooth manner. Using Gaussian kernel density estimation can accurately capture the actual changing trend of the uncertainty parameter and distinguish between different seasonal conditions (such as modeling through different seasonal groups), thereby enhancing the model's adaptability to environmental changes.

[0044] S3: Discretize each input parameter according to the cumulative distribution function of each input parameter to form a discretized simulation sample.

[0045] In one possible implementation, S3 specifically includes sub-steps S301 to S305:

[0046] S301: Based on the cumulative distribution function of each input parameter, discretization sampling is performed using the Hammersley sequence to form discretized simulation samples.

[0047] Hamersley sequences are used to generate uniformly distributed discrete sample sequences, commonly employed in numerical optimization and random sampling. Unlike traditional pseudo-random number generation methods, Hamersley sequences generate samples using a deterministic algorithm, ensuring a uniform distribution of sample points in multidimensional space and avoiding the clustering phenomenon that can occur with random samples.

[0048] Specifically, firstly, Hamersley sequences are used to generate uniformly distributed sample points, ensuring that the samples are uniformly distributed in the multidimensional input space. Then, using these uniformly distributed sample points as a basis, the inverse cumulative distribution function is used to map them onto the actual input parameter distribution, thereby obtaining discretized samples that conform to the actual statistical characteristics.

[0049] In this embodiment of the invention, using Hamersley sequences for discretization sampling ensures that samples are uniformly distributed in the multidimensional input space, thereby avoiding the sample clustering problem that may occur with traditional random sampling methods. A uniform sample distribution helps to more comprehensively represent the changes in the input space and improves the reliability of simulation results.

[0050] S302: Perform inverse cumulative distribution function operation on the dataset composed of discretized simulation samples to obtain the dataset after inverse transformation.

[0051] The inverse cumulative distribution function (CDF) is a mapping process from probability values ​​to random variable values, used to generate samples that conform to a given probability distribution. For a known cumulative distribution function (CDF), the inverse CDF can return a corresponding variable value with a specified probability.

[0052] It should be noted that transforming the discretized simulation samples from a uniform distribution to a true parameter distribution using the inverse cumulative distribution function can accurately reflect the uncertainties in the actual system. The dataset after the inverse transformation can better simulate parameter changes in actual operation, thereby improving the accuracy of the simulation results.

[0053] S303: Use the Pearson correlation coefficient to determine the correlation between various uncertainty parameters and form a correlation structure matrix.

[0054] The Pearson correlation coefficient is a statistic that measures the strength and direction of the linear relationship between two variables, with values ​​ranging from -1 to +1. +1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no linear relationship. By calculating the Pearson correlation coefficient, the degree of interdependence between input variables can be quantified, and the correlation structure between various variables can be established. In cooling tower performance optimization, the Pearson correlation coefficient can be used to analyze the correlation between different uncertain parameters (such as temperature and humidity), thereby more accurately describing the impact of these parameters on system performance.

[0055] S304: The correlation structure matrix is ​​decomposed into a lower triangular matrix using Cholesky decomposition.

[0056] Cholesky decomposition is a matrix decomposition technique that decomposes a symmetric positive definite matrix into the product of a lower triangular matrix and its transpose.

[0057] It should be noted that Cholesky decomposition transforms the correlation structure matrix into a lower triangular matrix. This step effectively handles the correlation between uncertain parameters, making subsequent calculations more efficient and stable. Cholesky decomposition simplifies matrix operations, making them more direct, especially for the optimization of large-scale systems, significantly reducing computation time.

[0058] S305: Multiply the inverse transformed dataset with the lower triangular matrix to obtain the correlation-corrected dataset.

[0059] It should be noted that the correlation-corrected dataset is obtained by multiplying with the lower triangular matrix. This operation corrects the correlation between input parameters, making the sampled data more consistent with reality. It can more realistically reflect the mutual influence between uncertain parameters during the optimization process, thereby improving the accuracy and reliability of the model.

[0060] In this embodiment of the invention, the input parameters are discretized according to the cumulative distribution function of each input parameter to form discretized simulation samples. This ensures that the samples uniformly cover the entire input space, thereby more accurately reflecting the parameter distribution in the actual system. This method not only improves the representativeness and accuracy of the samples and avoids the bias that may be caused by random sampling, but also effectively handles changes in uncertain parameters and enhances the robustness of the model.

[0061] S4: Using simulation samples, perform computational fluid dynamics simulations on the closed cooling tower to determine the system response for each simulation sample.

[0062] It should be noted that using fluid dynamics simulation to simulate closed-circuit cooling towers is a mature and existing technology. Simply put, the fluid dynamics simulation process requires using mass conservation, energy conservation, and the Navier-Stokes equations to mathematically describe the operation of the closed-circuit cooling tower, setting boundary conditions and meshing, and then using solution methods such as Runge-Kutta to solve the equations. This invention will not elaborate further.

[0063] This application aims to address the problem of high computational complexity in simulating closed-circuit cooling towers using fluid dynamics simulation. Step S4 might be misunderstood, leading some to believe that this application's solution also utilizes fluid dynamics simulation, adding another step and thus hindering optimization. Therefore, it needs clarification: this application employs a subsequent lightweight performance prediction model to simulate the system response results of the fluid dynamics simulation. This can be understood as first using fluid dynamics simulation to obtain system responses under certain parameters—this could be 10, 100 (or a finite number) of results—and then using these system responses to train the subsequent lightweight performance prediction model. When subsequently using the butterfly optimization algorithm to optimize the parameters of the closed-circuit cooling tower, it's necessary to solve the fluid dynamics simulation equations every time parameters are adjusted. Instead, the lightweight performance prediction model can directly determine the performance parameters for each parameter, thereby reducing computational resource consumption and optimization time, and improving optimization efficiency.

[0064] S5: Principal component analysis is performed on the system response data through singular value decomposition, and the system response data is characterized using the principal component matrix and the score matrix.

[0065] Singular Value Decomposition (SVD) is a matrix decomposition technique that solves a matrix of arbitrary shape into the product of three matrices. This is a very mature existing technology, and will not be elaborated upon in this invention.

[0066] Principal component analysis (PCA) is a statistical analysis method used to reduce the dimensionality of data while retaining the most important features.

[0067] In one possible implementation, S5 specifically includes sub-steps S501 to S503:

[0068] S501: Decompose the system response data using singular value decomposition:

[0069]

[0070] Where Z represents the system response output, and U represents the left singular vector. Let represent a diagonal matrix containing the singular values ​​on the diagonal. The magnitude of the singular values ​​reflects the importance of the corresponding principal components. V represents the right singular vector. T This indicates the matrix transpose.

[0071] S502: Extract the principal components with the most singular values ​​and construct the principal component matrix.

[0072] It should be noted that decomposing the system response data using Singular Value Decomposition (SVD) and extracting principal components with larger singular values ​​to construct the principal component matrix helps to effectively reduce the dimensionality and complexity of the data.

[0073] S503: Represent the system response data using the principal component matrix and the score matrix:

[0074]

[0075] Where Z represents the system response output, and δ represents the principal component matrix. This represents the score matrix.

[0076] In this embodiment of the invention, the principal component matrix and score matrix accurately characterize the system response output, retaining the most important feature information while ignoring smaller components that contribute less to the system response. This reduces computational load, improves computational efficiency, and avoids interference from redundant information when processing high-dimensional data, resulting in a simpler model with higher interpretability. Through principal component analysis, we can focus on key variables and interaction effects, optimizing data modeling and prediction accuracy.

[0077] Furthermore, for any input variable within the restricted range, the principal component matrix remains unchanged, while the score matrix changes. Therefore, as long as the correlation between the input variable and the score matrix is ​​established, a correlation can be established between the input variable and the system response.

[0078] S6: By using Kriging interpolation, a correlation is established between the input variables and the score matrix, forming a preliminary prediction model between the input variables and the system response.

[0079] Kriging interpolation is a statistical spatial interpolation method used to predict or interpolate between known data points. It assumes spatial correlation in the data and estimates the values ​​of unobserved points by building a model. Kriging interpolation utilizes a Gaussian process as a stochastic model based on the correlation and variability of known data points to obtain unbiased estimates with minimal variance.

[0080] It should be noted that Kriging interpolation establishes a correlation between the input variables and the score matrix.

[0081] In one possible implementation, S6 specifically includes sub-steps S601 and S602:

[0082] S601: Establishing a correlation between the input variables and the score matrix through Kriging interpolation:

[0083]

[0084] in, Let X represent the score matrix, pt represent the input parameters, rt represent the polynomial terms, and rt represent the residual terms. A stochastic Gaussian process is used.

[0085] S602: The optimal parameters of the Kriging interpolation model are determined by fitting the maximum likelihood estimation.

[0086] Among them, maximum likelihood estimation (MLE) is a parameter estimation method that estimates model parameters by maximizing the likelihood function of observed data. This is a very mature existing technology, and will not be elaborated upon in this invention.

[0087] In this embodiment of the invention, a correlation is established between the input variables and the score matrix through Kriging interpolation, and the optimal parameters of the fitted model are further effectively established by using maximum likelihood estimation. This allows for the efficient creation of a predictive model between the input parameters and the system response. By introducing polynomial terms and a stochastic Gaussian process, the Kriging interpolation method can capture the nonlinear relationship and random fluctuations between the input parameters and the system response, thereby providing more accurate predictions.

[0088] S7: By using high-dimensional model representation technology, the higher-order interaction effects of the preliminary prediction model are optimized to obtain the performance prediction model of the closed cooling tower.

[0089] High-dimensional model representation is a technique used for modeling and analyzing high-dimensional data. It simplifies the modeling process and improves computational efficiency by decomposing complex nonlinear relationships in a multidimensional input space into lower-dimensional function terms.

[0090] In one possible implementation, S7 specifically includes sub-steps S701 and S702:

[0091] S701: Obtain the system response prediction results of the preliminary prediction model.

[0092] S702: Based on the system response prediction results of the preliminary prediction model, higher-order interaction effects are introduced. Through polynomial expansion, the system response is characterized by higher-order interaction to obtain the performance prediction model of the closed cooling tower.

[0093]

[0094] Among them, y f This represents the system response prediction result of the preliminary prediction model, where f0 represents the constant term, and x... a Let x represent the a-th input variable. b This represents the b-th input variable, which consists of input parameters filtered through principal component analysis. This represents the first-order term, which is the first-order response value of the a-th input variable. This represents the second-order term, which is the second-order interaction response value between the a-th input variable and the b-th input variable. This represents an m-th order term, which is the m-th order interaction response value between m input variables, where m represents the total number of input variables.

[0095] In this embodiment of the invention, the preliminary prediction model is optimized using high-dimensional model representation techniques, and higher-order interaction effects are introduced, which helps to more accurately capture the complex nonlinear relationships and interactions between input variables. High-dimensional model representation techniques decompose complex relationships in a multi-dimensional input space into lower-dimensional function terms, simplifying the modeling process and improving computational efficiency. By introducing higher-order interaction effects (such as first-, second-, and higher-order interaction terms), the interactions between different input variables can be comprehensively described, improving the accuracy and flexibility of system response prediction.

[0096] S8: Based on a performance prediction model, with the goal of improving cooling efficiency and reducing construction costs, the design parameters of the closed cooling tower are optimized using the butterfly optimization algorithm.

[0097] The Butterfly Optimization Algorithm (BOA) is a nature-inspired optimization algorithm that simulates the foraging behavior of butterflies. This algorithm mimics the group cooperation and individual exploration mechanisms exhibited by butterflies in their food-finding process, combining the mutual influence between individual butterflies to achieve a balance between global and local search.

[0098] In one possible implementation, S8 specifically includes sub-steps S801 and S802:

[0099] S801: To improve the cooling efficiency and reduce the construction cost, determine the fitness function of the butterfly optimization algorithm:

[0100]

[0101] Where F represents the fitness function, Y represents the set of design parameters, F(Y) represents the fitness value of the closed cooling tower constructed with the set of design parameters Y, η represents the heat exchange efficiency, η(Y) represents the heat exchange efficiency of the closed cooling tower constructed with the set of design parameters Y, C represents the construction cost, C(Y) represents the construction cost of the closed cooling tower constructed with the set of design parameters Y, and λ represents the weighting coefficient of the heat exchange efficiency.

[0102] Those skilled in the art can set the weighting coefficient λ of heat exchange efficiency according to actual conditions; this invention does not impose any limitations.

[0103] In this embodiment of the invention, by setting a fitness function, it is possible to ensure that the performance of the cooling tower (increases heat exchange efficiency) is improved while controlling the construction cost during the optimization process, thereby obtaining a comprehensive optimized design scheme.

[0104] Optionally, by inputting a set of design parameters X into the performance prediction model, and given the setting of operating parameters and uncertainty parameters, various performance parameters under the set of design parameters X can be directly obtained.

[0105] Optionally, the heat exchange efficiency is calculated by dividing the temperature difference between the inlet and outlet water temperatures of the cooling tower by the temperature difference between the inlet water temperature and the ambient wet-bulb temperature.

[0106] Optionally, construction costs can be calculated and assessed based on the heat exchange area. Theoretically, the larger the heat exchange area, the more heat exchange materials (such as pipes and the surface area of ​​the heat exchanger) are required. Of course, more precise cost accounting methods can also be used, but this is not the focus of this application.

[0107] S802: Based on the fitness function, the design parameters of the closed cooling tower are optimized using the butterfly optimization algorithm.

[0108] Specifically, Sine chaotic mapping is used to initialize butterfly individuals. Each butterfly individual represents a feasible set of closed-loop cooling tower design parameters. Each butterfly individual consists of multiple dimensional components, and each component represents one:

[0109]

[0110]

[0111] Where, x i Let lb represent the initial position of the i-th butterfly individual. i Let ub represent the lower bound of the i-th feasible solution. i Let y denote the upper bound of the i-th feasible solution. i Let y represent the chaos number corresponding to the i-th butterfly individual. i-1 Let μ represent the chaos number corresponding to the (i-1)th butterfly individual, μ represent the chaos parameter, which is usually taken as 0.99, and sin represent the sine function.

[0112] In this embodiment of the invention, initializing butterfly individuals using a Sine chaotic map ensures a uniform distribution of initial solutions, avoiding the problems of sample concentration or uneven distribution that may occur in traditional random initialization methods. The chaotic map, by introducing nonlinear dynamic changes, can generate more diverse and widespread solutions, thus avoiding the predicament of getting trapped in local optima. Simultaneously, the setting of chaotic parameters makes the evolution process of solutions more exploratory and stable, increasing the global search capability. This initialization method provides more representative initial solutions for the butterfly optimization algorithm, making the algorithm more efficient in the search process and improving the accuracy and globality of the optimization results.

[0113] Generate a random number and determine if it is less than the adaptive transformation probability. If so, proceed to the global search phase. Otherwise, proceed to the local search phase.

[0114] Optionally, the adaptive transition probability is specifically:

[0115]

[0116] in, P represents the adaptive transition probability of the i-th butterfly individual in the t-th iteration. min P represents the minimum transition probability. max f represents the maximum transition probability. max This represents the fitness value of the globally optimal butterfly individual. Let represent the fitness value of the i-th butterfly individual, and log represent the logarithmic function.

[0117] In this embodiment of the invention, as iterations proceed, the fitness value of an individual affects the transition probability. Individuals with poor fitness tend to perform a global search, thus avoiding getting trapped in local optima, while individuals with good fitness tend to perform local searches for further refinement. Through this dynamic adjustment strategy, the algorithm can broadly explore the search space in the initial stage, and gradually focus on the local region of the optimal solution as the optimization process progresses, thereby improving search efficiency and accuracy, ensuring that the algorithm can both find the global optimum and converge quickly.

[0118] During the global search phase, based on the fragrance concentration value, the butterfly individual is guided to approach the globally optimal butterfly individual, and its position is updated accordingly.

[0119]

[0120] in, ω represents the position of the i-th butterfly in the (t+1)-th iteration. t This represents the nonlinear weighting factor at the t-th iteration. This represents the position of the i-th butterfly in the t-th iteration, where rand represents a random number between 0 and 1, and x best f represents the position of the globally optimal butterfly individual. i represents the fragrance concentration value of the i-th butterfly individual, and Cauchy represents the Cauchy variation factor.

[0121] In this embodiment of the invention, during the global search phase, the algorithm's global exploration capability is effectively enhanced by guiding individual butterflies closer to the globally optimal butterfly based on their fragrance concentration values ​​and updating their positions. The fragrance concentration value represents the "attractiveness" of an individual butterfly in the search space; individuals with high fragrance concentrations will guide other individuals toward the globally optimal solution, thereby accelerating the search for the global optimum. By using Cauchy mutation factors and nonlinear weighting factors, a certain degree of randomness and variability is introduced during the update process, allowing individual butterflies to escape local optima and avoid getting trapped in stable regions. This mechanism improves the algorithm's global search efficiency and diversity, helps the optimization process avoid premature convergence, and ultimately improves the accuracy and globality of the solution.

[0122] Optionally, the nonlinear weighting factor is specifically:

[0123]

[0124] Where t represents the current iteration number, T m ω represents the maximum number of iterations. max ω represents the maximum weighting factor. min denoted as the minimum weight factor, and cos represents the cosine function.

[0125] In this embodiment of the invention, a nonlinear weighting factor based on the number of iterations is introduced to dynamically adjust the balance between global and local searches. In the early stages of optimization, a larger weighting factor encourages individual butterflies to perform more global searches, exploring a wider solution space. As the number of iterations increases, the weighting factor gradually decreases, thereby enhancing local searches and refining the approximation of the global optimum. This dynamic adjustment helps avoid early entrapment in local optima and ensures that the search process is both extensive and precise, contributing to improved accuracy and efficiency of the final optimization results.

[0126] Optionally, the aroma concentration value is specifically:

[0127]

[0128] Among them, f i This represents the fragrance concentration value of the i-th individual butterfly. Let α represent the sensory factor coefficient of the i-th butterfly individual at the t-th iteration, where I represents the stimulus intensity and α represents the power exponent.

[0129] In this embodiment of the invention, as iterations proceed, changes in fragrance concentration reflect an individual's attraction to the global optimum, thereby influencing its exploration strategy in the search space. By introducing a power exponent, the influence of stimulus intensity on individual position updates can be adjusted, further enhancing the flexibility and diversity of the search process. This method helps to precisely control the search direction, allowing butterfly individuals to flexibly switch between global and local searches, improving the efficiency and accuracy of the optimization process.

[0130] Optionally, the perception factor coefficient is specifically:

[0131]

[0132] in, Let represent the sensory factor coefficient of the i-th butterfly individual at the t-th iteration, and d represent the fragrance concentration update control parameter, typically taken as 0.025. m This indicates the maximum number of iterations.

[0133] In this embodiment of the invention, as the iteration proceeds, the perception factor coefficient gradually changes, allowing the individual to continuously adjust its focus on the global optimum within the search space. This dynamic adjustment helps enhance global exploration capabilities in the early stages of optimization, while gradually enhancing the refined search for local solutions in the later stages, thereby effectively avoiding early convergence or getting trapped in local optima.

[0134] During the local search phase, based on the fragrance concentration value, two butterfly individuals are randomly selected to move closer together, and their positions are updated accordingly.

[0135]

[0136] in, This represents the position of the j-th butterfly in the t-th iteration. This represents the position of the k-th butterfly individual at the t-th iteration.

[0137] In this embodiment of the invention, during the local search phase, randomly selecting two butterfly individuals based on their fragrance concentration values ​​to approach each other and updating their positions helps to enhance the local refinement capability of the search. This method, by simulating the interaction between butterfly individuals, allows them to explore more effectively within local areas of the search space, avoiding the limitations of over-reliance on the global optimum. Randomly selecting two individuals to approach each other increases the diversity of the search, and the guidance of fragrance concentration values ​​allows individuals to focus more precisely on potential optimal solution regions, thereby accelerating the convergence process and improving the accuracy and efficiency of the optimization results.

[0138] Update the fitness values ​​of each individual butterfly and the global best individual.

[0139] Determine if the current iteration count has reached the maximum iteration count. If yes, output the set of design parameters represented by the butterfly individual with the highest fitness. Otherwise, return to continue iterating.

[0140] In this embodiment of the invention, by optimizing the design parameters of a closed-loop cooling tower based on a performance prediction model and employing the butterfly optimization algorithm, a balance can be achieved between improving cooling efficiency and reducing construction costs. The butterfly optimization algorithm possesses powerful global and local search capabilities, enabling it to efficiently explore optimal solutions in complex design spaces. By introducing adaptive search strategies and diverse exploration mechanisms, the algorithm avoids early convergence, ensuring the discovery of the globally optimal solution.

[0141] Furthermore, the optimal design parameter set determined by the butterfly optimization algorithm can be used to design and construct closed-loop cooling towers.

[0142] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following:

[0143] In this embodiment of the invention, a performance prediction model for a closed-loop cooling tower is constructed using principal component analysis, kriging interpolation, and high-dimensional model representation techniques. This enables accurate prediction of the response to complex fluid dynamics simulation systems, reducing computational resource consumption and optimization time while accurately predicting cooling tower performance. It avoids the need for tedious equation solving every time design and control parameters are adjusted, thus significantly improving optimization efficiency. Further optimization of design parameters using the butterfly optimization algorithm effectively improves cooling efficiency, reduces construction costs, and accelerates the design process.

[0144] Reference manual attached Figure 2The diagram shows a structural schematic of a performance optimization system for a closed cooling tower provided in an embodiment of the present invention.

[0145] This invention provides a performance optimization system 20 for a closed cooling tower, comprising: a processor 201 and a memory 202;

[0146] The memory 202 stores programs or instructions that can run on the processor 201. When the program or instructions are executed by the processor 201, they implement the steps of the above-described closed-loop cooling tower performance optimization method and achieve the same technical effect. To avoid repetition, the present invention will not elaborate further.

[0147] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the embodiments of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing the performance of a closed-loop cooling tower, characterized in that, include: S1: Obtain input parameters describing the closed cooling tower, including deterministic parameters and uncertain parameters affected by seasonal climate, the deterministic parameters including design parameters and operating parameters; S2: Determine the cumulative distribution function of each of the input parameters; S3: Discretize each input parameter according to the cumulative distribution function of each input parameter to form a discretized simulation sample; S4: Using the simulation samples, perform computational fluid dynamics simulation on the closed cooling tower to determine the system response for each simulation sample; S5: Principal component analysis is performed on the system response data through singular value decomposition, and the system response data is characterized using the principal component matrix and the score matrix; S6: By using Kriging interpolation, a correlation is established between the input variables and the score matrix to form a preliminary prediction model between the input variables and the system response; S7: By using high-dimensional model representation technology, the higher-order interaction effect of the preliminary prediction model is optimized to obtain the performance prediction model of the closed cooling tower; S8: Based on the performance prediction model, with the goal of improving cooling efficiency and reducing construction costs, the design parameters of the closed cooling tower are optimized using the butterfly optimization algorithm.

2. The performance optimization method for a closed-loop cooling tower according to claim 1, characterized in that, The design parameters include: heat exchanger material, width, tube length, tube diameter, tube spacing coefficient, number of tube rows per pass, and number of passes; The operating parameters include: air velocity, spray water flow rate, spray water temperature, circulating water temperature, and circulating water flow rate; The uncertain parameters include: dry-bulb temperature, wet-bulb temperature, and relative humidity.

3. The performance optimization method for a closed-loop cooling tower according to claim 1, characterized in that, S2 specifically includes: S201: For the deterministic parameters, a normal distribution is used to describe the cumulative distribution function; S202: For the uncertainty parameter, the cumulative distribution function is described by Gaussian kernel density estimation.

4. The performance optimization method for a closed-loop cooling tower according to claim 1, characterized in that, S3 specifically includes: S301: Based on the cumulative distribution function of each input parameter, discretization sampling is performed using the Hammersley sequence to form discretized simulation samples; S302: Perform inverse cumulative distribution function operation on the dataset composed of discretized simulation samples to obtain the dataset after inverse transformation; S303: Use the Pearson correlation coefficient to determine the correlation between the various uncertainty parameters and form a correlation structure matrix; S304: The correlation structure matrix is ​​decomposed into a lower triangular matrix by Cholesky decomposition; S305: Multiply the inverse transformed dataset with the lower triangular matrix to obtain the correlation-corrected dataset.

5. The performance optimization method for a closed-loop cooling tower according to claim 1, characterized in that, S5 specifically includes: S501: The system response data is decomposed through the singular value decomposition. S502: Extract the principal components with the highest singular values ​​and construct the principal component matrix; S503: The system response data is characterized using the principal component matrix and the score matrix.

6. The performance optimization method for a closed-loop cooling tower according to claim 1, characterized in that, S6 specifically includes: S601: Establish a correlation between the input variables and the score matrix through Kriging interpolation; S602: The optimal parameters of the Kriging interpolation model are determined by fitting the maximum likelihood estimation.

7. The performance optimization method for a closed-loop cooling tower according to claim 1, characterized in that, Specifically, S7 includes: S701: Obtain the system response prediction results of the preliminary prediction model; S702: Based on the system response prediction results of the preliminary prediction model, a higher-order interaction effect is introduced, and the system response is characterized by a higher-order interaction through polynomial expansion to obtain the performance prediction model of the closed cooling tower.

8. The performance optimization method for a closed-loop cooling tower according to claim 1, characterized in that, S8 specifically includes: S801: Determine the fitness function of the butterfly optimization algorithm with the goal of improving the cooling efficiency and reducing the construction cost; S802: Based on the fitness function, the design parameters of the closed cooling tower are optimized using the butterfly optimization algorithm.

9. The performance optimization method for a closed-loop cooling tower according to claim 8, characterized in that, The heat exchange efficiency is calculated by dividing the temperature difference between the inlet and outlet water temperatures of the cooling tower by the temperature difference between the inlet water temperature and the ambient wet-bulb temperature. The construction cost is calculated and evaluated based on the heat exchange area.

10. A performance optimization system for a closed-loop cooling tower, characterized in that, include: Processor and memory; The memory stores programs or instructions that can run on the processor, which, when executed by the processor, implement the steps of the performance optimization method for a closed cooling tower as described in any one of claims 1 to 9.

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