Robust optimization method and robust optimization device for pollutant emissions

Abstract

The application discloses a robust optimization method and device for pollutant emission. The robust optimization method comprises the following steps: obtaining sampling data of uncertain input variables of a cracking furnace; performing numerical simulation on the sampling data via a turbulent combustion coupling model to obtain a training data set; constructing a sparse chaotic polynomial model according to the uncertain input variables, and training the sparse chaotic polynomial model via the training data set to obtain a first uncertain quantification model; introducing deterministic optimization variables of the cracking furnace into the first uncertain quantification model, and obtaining a second uncertain quantification model dependent on the deterministic optimization variables based on a Legendre polynomial; and performing robust optimization on the deterministic optimization variables of the pollutant emission via the second uncertain quantification model. The application can solve the uncertain quantification precision and efficiency problem of a large-scale numerical model, establish a continuous robust optimization model, and greatly improve the optimization efficiency.

Description

Technical Field

[0001] This invention relates to the field of combustion numerical simulation, specifically to a robust optimization method for pollutant emissions, a robust optimization device for pollutant emissions, and a computer-readable storage medium. Background Technology

[0002] Flue gas from industrial pyrolysis units contains significant amounts of air pollutants, particularly nitrogen oxides (NOx). NOx emissions cause serious environmental problems, deplete the ozone layer, and harm human health. However, in the past, product yield and energy efficiency were the primary evaluation indicators in the design of industrial pyrolysis furnaces, with less consideration given to pollutant emissions. Currently, reducing NOx and CO emissions from industrial processes has become a key issue in controlling environmental pollution; therefore, controlling NOx and CO emissions from industrial pyrolysis furnaces is of great importance in preventing environmental pollution.

[0003] Traditional computational fluid dynamics (CFD) numerical simulations cannot account for the uncertainties in actual industrial production. As the main combustion device inside the pyrolysis furnace, the uncertainties in the structure and operating parameters of the burner in actual industrial processes will directly affect the combustion and emission characteristics of the industrial pyrolysis furnace, which will lead to unreliable predictions in the pyrolysis furnace and mislead the design optimization.

[0004] Uncertainty quantification (UQ) is a method for quantifying the impact of uncertainty on response characteristics, and it can quantify the influence of actual uncertainty on fluctuations in pollutant emissions. However, research on uncertainty analysis in combustion processes is still limited. Furthermore, classical UQ methods, such as Monte Carlo (MC), while capable of uncertainty quantification through simple sampling, have slow convergence speeds and require a large number of samples to achieve high-precision quantification, making them unsuitable for computationally intensive numerical simulations. Moreover, traditional polynomial chaos expansion (PCE) cannot compute large-scale models and can only perform discrete optimization by repeatedly calculating uncertainty quantification results under different operating conditions, failing to consider the continuity of design variables.

[0005] To address the aforementioned problems in existing technologies, there is an urgent need in this field for a robust optimization technique for pollutant emissions that can solve the problems of uncertainty quantification accuracy and efficiency in large-scale numerical models, establish a continuous robust optimization model, and significantly improve optimization efficiency. Summary of the Invention

[0006] The following provides a brief overview of one or more aspects to offer a basic understanding of them. This overview is not an exhaustive summary of all conceived aspects, nor is it intended to identify key or decisive elements of all aspects, nor to define the scope of any or all aspects. Its sole purpose is to present some concepts of one or more aspects in a simplified form as a prelude to the more detailed descriptions that follow.

[0007] To overcome the aforementioned deficiencies in the existing technology, this invention provides a robust optimization method for pollutant emissions, a robust optimization device for pollutant emissions, and a computer-readable storage medium, which can solve the problems of uncertainty quantification accuracy and efficiency in large-scale numerical models, establish a continuous robust optimization model, and significantly improve optimization efficiency.

[0008] Specifically, the robust optimization method for pollutant emissions provided by the first aspect of the present invention includes the following steps: acquiring sampled data of uncertain input variables of a pyrolysis furnace; performing numerical simulation on the sampled data via a turbulent combustion coupling model to obtain a training dataset; constructing a sparse chaotic polynomial model based on the uncertain input variables, and training the sparse chaotic polynomial model via the training dataset to obtain a first uncertainty quantization model; introducing deterministic optimization variables of the pyrolysis furnace into the first uncertainty quantization model, and obtaining a second uncertainty quantization model dependent on the deterministic optimization variables based on Legendre polynomials; and robustly optimizing the deterministic optimization variables of the pollutant emissions via the second uncertainty quantization model.

[0009] The robust optimization apparatus for pollutant emissions according to a second aspect of the present invention includes: a memory; and a processor connected to the memory and configured to implement the robust optimization method for pollutant emissions according to the first aspect.

[0010] Furthermore, according to a third aspect of the present invention, a computer-readable storage medium is provided having computer instructions stored thereon. When executed by a processor, these computer instructions implement the robust optimization method for pollutant emissions described above, as provided in the first aspect of the present invention. Attached Figure Description

[0011] The above-described features and advantages of the present invention will be better understood after reading the following detailed description of embodiments of the present disclosure in conjunction with the accompanying drawings. In the drawings, components are not necessarily drawn to scale, and components having similar related characteristics or features may have the same or similar reference numerals.

[0012] Figure 1 A flowchart illustrating a robust optimization method for pollutant emissions provided according to some embodiments of the present invention is shown.

[0013] Figure 2A A schematic diagram of a structural model of an ethylene cracking furnace according to some embodiments of the present invention is shown;

[0014] Figure 2B yes Figure 2A A schematic diagram of the mesh generation for the structural model of the ethylene cracking furnace shown;

[0015] Figure 3 This is a schematic diagram of the process for acquiring sampling data according to some embodiments of the present invention;

[0016] Figure 4 A schematic diagram of the sample set results after Latin hypercube sampling provided according to some embodiments of the present invention is shown;

[0017] Figure 5 This is a schematic diagram of the process for obtaining a training dataset according to some embodiments of the present invention;

[0018] Figure 6 This is a schematic diagram of the process for obtaining a second uncertainty quantification model according to some embodiments of the present invention;

[0019] Figure 7 This is a schematic diagram of robust optimization results according to an embodiment of the present invention; and

[0020] Figure 8 A structural block diagram of a robust optimization device for pollutant emissions provided according to other embodiments of the present invention is shown.

[0021] Figure label:

[0022] 200 Ethylene Cracking Furnace;

[0023] 210 multi-stage fuel burner;

[0024] 211 Air intake;

[0025] 212 Main fuel gas inlet;

[0026] 213 Secondary fuel gas inlet;

[0027] Robust optimization device for 800 pollutant emissions;

[0028] 810 memory;

[0029] 820 processor;

[0030] Steps S110~S150;

[0031] Steps S111~S112

[0032] Steps S121~S124; and

[0033] Steps S141~S144. Detailed Implementation

[0034] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Although the description of the present invention is presented in conjunction with preferred embodiments, this does not mean that the features of the invention are limited to these embodiments. On the contrary, the purpose of describing the invention in conjunction with embodiments is to cover other options or modifications that may be derived based on the claims of the present invention. To provide a thorough understanding of the invention, many specific details will be included in the following description. The invention may also be implemented without using these details. Furthermore, to avoid confusion or obscuring the focus of the invention, some specific details will be omitted in the description.

[0035] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0036] Furthermore, the terms "upper," "lower," "left," "right," "top," "bottom," "horizontal," and "vertical" used in the following description should be understood as the orientations shown in the relevant paragraphs and accompanying drawings. These relative terms are for illustrative purposes only and do not imply that the described apparatus must be manufactured or operated in a specific orientation, and therefore should not be construed as limiting the invention.

[0037] It is understood that although terms such as "first," "second," and "third" may be used herein to describe various components, regions, layers, and / or parts, these components, regions, layers, and / or parts should not be limited by these terms, and these terms are only used to distinguish different components, regions, layers, and / or parts. Therefore, the first components, regions, layers, and / or parts discussed below may be referred to as second components, regions, layers, and / or parts without departing from some embodiments of the present invention.

[0038] As mentioned above, uncertainty quantification is a method for quantifying the impact of uncertainty on response characteristics, and it can quantify the influence of actual uncertainty on fluctuations in pollutant emissions. However, research on uncertainty analysis in combustion processes is still limited, and classical UQ methods, such as Monte Carlo (MC), although capable of uncertainty quantification through simple sampling, have slow convergence speeds and require a large number of samples to achieve high-precision quantification. Therefore, this method is not suitable for computationally intensive numerical simulations. Moreover, traditional polynomial chaos expansion (PCE) cannot compute large-scale models and can only perform discrete optimization by repeatedly calculating uncertainty quantification results under different operating conditions, failing to consider the continuity of design variables.

[0039] To address the aforementioned problems in the prior art, this invention provides a robust optimization method for pollutant emissions, a robust optimization device for pollutant emissions, and a computer-readable storage medium. These methods can solve the problems of uncertainty quantification accuracy and efficiency in large-scale numerical models, establish continuous robust optimization models, and significantly improve optimization efficiency.

[0040] In some non-limiting embodiments, the robust optimization method for pollutant emissions provided in the first aspect of the present invention can be implemented by the robust optimization apparatus for pollutant emissions provided in the second aspect of the present invention.

[0041] First, please refer to Figure 1 , Figure 1 A flowchart illustrating a robust optimization method for pollutant emissions according to some embodiments of the present invention is shown. In this invention, the robust optimization method for pollutant emissions mainly includes the following steps:

[0042] S110: Obtain sampled data of uncertain input variables of the cracking furnace.

[0043] In some non-limiting embodiments, the object of the present invention can be an ethylene cracking furnace in an industrial cracking furnace, specifically an ethylene cracking furnace equipped with a multi-stage fuel burner. The present invention mainly studies the generation of pollutants during combustion, and can select emissions with NO and CO characteristics, which are the main components of pollutant emissions. The sampling point can be determined at the highest point in the center of the furnace bottom to obtain stable flue gas data.

[0044] Please refer to Figure 2A , Figure 2A A schematic diagram of the structural model of an ethylene cracking furnace provided according to some embodiments of the present invention is shown.

[0045] like Figure 2A As shown, in some optional embodiments, the overall dimensions of the ethylene cracking furnace 200 can be 24.83m (length) × 2.971m (width) × 11.621m (height). Specifically, as... Figure 2A As shown in the enlarged partial view I, 64 bottom multi-stage fuel burners 210 are installed near the side walls. Each bottom multi-stage fuel burner 210 may have one preheating air inlet 211, three main fuel gas inlets 212 for primary combustion, and three secondary fuel gas inlets 213 for auxiliary combustion. The flue gas outlet is located at the top of the furnace. As an important component of the ethylene cracking furnace 200, the bottom multi-stage fuel burner 210 is susceptible to uncontrollable fluctuations in flame and emission characteristics due to processing and operational errors during industrial production.

[0046] In some embodiments, multiple uncertain input variables in the bottom multistage fuel burner 210, such as preheated air temperature, primary fuel inlet flow rate, secondary fuel inlet flow rate, and operating pressure, can be selected to perform uncertainty quantification (UQ). These uncertain input variables are considered to be independent of each other.

[0047] Further, please see Figure 3 , Figure 3 This is a schematic diagram of the process for acquiring sampling data according to some embodiments of the present invention. Figure 3 As shown, step S110 may include steps S111 to S112.

[0048] S111: Define the uncertain input variables of the ethylene cracking furnace through the distribution assumption to obtain the distribution of uncertain variables.

[0049] In one embodiment, the probability distribution can be a commonly used Gaussian distribution. The measurement uncertainty of the bottom multi-stage fuel burner 210 is typically tested at 3%, therefore, in this embodiment, the fluctuation range of the uncertain input variable can be selected as 3%. If the i-th uncertain input variable can be characterized by its mean and standard deviation... If the distribution is Gaussian, then a 3% fluctuation under a Gaussian distribution can be roughly assumed to be 3σ. Therefore, the distributions of the various uncertain input variables in this embodiment are shown in Table 1 below:

[0050] Table 1

[0051]

[0052] Those skilled in the art will understand that the above-described scheme for defining the distribution of uncertain input variables based on Gaussian distribution is merely a non-limiting implementation provided by the present invention, intended to clearly demonstrate the main concept of the present invention and provide a specific scheme that is easy for the public to implement, rather than being used to limit the scope of protection of the present invention.

[0053] S112: The Latin hypercube method is used to sample data of uncertain input variables in order to obtain sampled data that fully represents the distribution of uncertain variables with a small number of sample points.

[0054] In some embodiments of the present invention, after defining the aforementioned uncertain input variables, the Latin hypercube method can be used to sample the data of the uncertain input variables. The Latin hypercube method can stably and uniformly represent the distribution of the input variables with a small number of sample points according to the definition requirements of the experimental input variables, greatly reducing the computational burden of subsequent numerical simulations.

[0055] For example, please see Figure 4 , Figure 4 A schematic diagram of the sample set results after Latin hypercube sampling, provided according to some embodiments of the present invention, is shown. Figure 4 In the example shown, the total number of samples selected is 400. Figure 4 The horizontal axis in the graph represents uncertain input variables. The vertical axis represents uncertain input variables. , , , , These represent the four uncertain input variables mentioned above: preheated air temperature, primary gas inlet flow rate, secondary gas inlet flow rate, and operating pressure. When i=j, it represents a sampled histogram of one uncertain input variable; when i≠j, it represents a two-dimensional sampled scatter plot of two variables. For example... Figure 4 As shown, whether from the sampling results of univariate variables or the scatter plots of multivariate variables, it can be seen that the overall trend of each uncertain input variable is highly consistent with the uncertain distribution defined by the input variables. This fully demonstrates the effectiveness of the Latin hypercube method under low sample conditions.

[0056] S120: Numerical simulation of the sampled data is performed using a turbulent combustion coupling model to obtain a training dataset.

[0057] The dataset obtained from the above sampling was used to perform high-precision numerical simulations to obtain pollution emission data for all samples. For details, please refer to... Figure 5 , Figure 5 This is a schematic diagram illustrating the process of obtaining a training dataset according to some embodiments of the present invention. Figure 5 As shown, step S120 may include steps S121 to S124.

[0058] S121: Determine the structural model of the ethylene cracking furnace and mesh it.

[0059] exist Figure 2AIn the schematic diagram of the ethylene cracking furnace structure shown, considering the symmetry of the structure and the simplification of calculations, the structural model of the ethylene cracking furnace can be meshed. Please refer to... Figure 2B , Figure 2B yes Figure 2A The diagram shows a mesh generation schematic of the structural model of an ethylene cracking furnace. Figure 2B As shown, in this embodiment, a 1 / 32 scale furnace structure of the original pyrolysis furnace can be used for simulation, and then a mesh is generated. The purpose of mesh generation is to divide the solution domain into discrete elements. The number and quality of the generated meshes largely determine the accuracy and solution stability of the subsequent simulation.

[0060] S122: Based on the structural model after mesh generation, determine the turbulence model, combustion model, and radiation heat transfer model in the ethylene cracking furnace cracking process.

[0061] In some preferred embodiments, the turbulence model can be the standard k-ε model, which has excellent performance in non-swirling flames, and its expression is as follows:

[0062]

[0063] in, Indicates the dependent variable. The generalized diffusion coefficient, This is a generalized source term.

[0064] The bottom-stage multi-stage fuel burner 210 employs non-premixed combustion where air and fuel gas enter the reaction zone from different inlets; therefore, a non-premixed combustion model can be selected. Optionally, the mixture fraction variance... The conservation equation is calculated using the following equation:

[0065]

[0066] In the above equation , , and This is an experimental constant.

[0067] In some preferred embodiments of the present invention, a probability density function (PDF) can be further used to calculate the average scalar characteristics of the non-adiabatic system in the ethylene cracking furnace, and a hypothetical probability density function in the Fluent computer program can be used. The value is obtained by integration during the generation of the equilibrium lookup table. The temperature- and density-weighted average mass fraction can be calculated as follows:

[0068]

[0069] in, It is the average enthalpy.

[0070] In ethylene cracking furnaces, the primary form of heat transfer is radiation. This radiation can be modeled using a discrete coordinate (DO) radiation model, the formula for which is as follows:

[0071]

[0072] in, Represents radiation intensity. Represents a position vector. Represents the direction vector. It is the scattering direction vector. Indicates the absorption coefficient. Indicates refractive index, This represents the scattering coefficient. Represents the phase function. The solid angle is represented by the gray band model. This model allows the use of gray band models to model non-gray radiation, and employs the Weighted-Sum-of-Gray-Gases Model (WSGGM) to calculate the absorption coefficient. This model divides the emissivity of the real gas into a weighted sum of several gray gases, resulting in high computational accuracy and efficiency.

[0073] S123: Based on the turbulence model, combustion model and radiation heat transfer model, establish a turbulence-combustion coupled model.

[0074] S124: Numerical simulation of the sampled data is performed using a turbulent combustion coupling model to obtain a training dataset.

[0075] By using the aforementioned turbulent combustion coupling model to numerically simulate the sampled data of uncertain input variables in the pyrolysis furnace, high-precision numerical simulation results can be obtained, thereby establishing a training dataset for the uncertainty quantification model. Numerical simulation is a fundamental data source for this invention. Subsequent construction of the quantification model, considering industrial uncertainties, is based on the aforementioned high-precision numerical simulation. Therefore, this invention employs the turbulent combustion coupling model to ensure the accuracy of the numerical simulation and to guarantee the effectiveness of the subsequent quantification model.

[0076] S130: Based on the uncertain input variables, construct a sparse chaotic polynomial model and train the sparse chaotic polynomial model through the training dataset to obtain the first uncertainty quantization model.

[0077] Currently, due to the highly nonlinear nature of the combustion emission process, a highly expanded chaotic polynomial expansion (PCE) model is required for accurate fitting. However, when the input variables are uncertain or the expansion order is large, the computational cost will also increase.

[0078] To further reduce CFD computation costs while ensuring sufficient accuracy, in some embodiments of this invention, based on the aforementioned uncertain variable distribution and determined training dataset, chaotic polynomial expansion (PCE) is introduced to efficiently quantify uncertainty. Chaotic polynomial expansion can quantify the impact of uncertain input variables on response characteristics using orthogonal polynomials.

[0079] Specifically, as shown in Table 1 above, after defining the uncertain input variables by probability distribution, a generalized chaotic polynomial model is established based on the orthogonal polynomial basis corresponding to each uncertain variable distribution. The generalized chaotic polynomial model can be expressed by the following formula:

[0080]

[0081] in, These are weighting coefficients. It is a set of multi-index multivariate polynomials , For uncertain input variables that need to be standardized and independent, n is the number of uncertain input variables. Multidimensional polynomials built from one-dimensional polynomials , where the coefficient The quantity is , For the total coefficient, Let be the total order of the generalized chaotic polynomial expansion.

[0082] As can be seen from the formula of the generalized chaotic polynomial model above, as the total order p increases, the total number of bases and the computational complexity increase significantly, and the increase in the total order p may even lead to the curse of dimensionality. The curse of dimensionality refers to the situation where, as the dimension increases, the volume of the space increases very rapidly (exponentially), causing the available data to become sparse. Typically, to obtain a statistically reliable result, the amount of data required to support the result often increases exponentially with the increase in dimension; this sparsity causes statistical difficulties. Therefore, in some preferred embodiments, a finite number of orders can be preserved through an appropriate degree truncation scheme.

[0083] Specifically, the degree of the above generalized chaotic polynomial model can be truncated to obtain a simplified generalized chaotic polynomial model of finite order, as shown in the following formula:

[0084]

[0085] in, The set of multivariate polynomials with multiple indices after adopting the degree truncation scheme. It is the sum of residuals generated after degree truncation. This is a set of observation data.

[0086] To accommodate the sparse PCE model, in some embodiments, the polynomial basis in the simplified generalized chaotic polynomial model can be reduced in dimensionality using the Least Angle Regression (LAR) algorithm to achieve sparsity and obtain a sparse chaotic polynomial model. The elements selected in the PCE model are the polynomial basis. The model response is composed of a polynomial basis and uncertain input variables. Sparse PCE reduces the number of unimportant polynomial bases. The number of coefficients is used to reduce the dimensionality of the unfolded array. The coefficient expressions obtained from the LAR calculation above are as follows:

[0087]

[0088] in, The term is a regularization term, which aims to construct a sparse chaotic polynomial expansion.

[0089] Furthermore, when the total degree of the polynomial is large, overfitting may occur. In some preferred embodiments, a cross-validation error can be introduced to address the overfitting problem. To train a sparse chaotic multinomial model, where the cross-validation error... It can be:

[0090]

[0091] in, For m response models to be built, single model training does not include the j-th experiment design used for validation. The mean of the response characteristics.

[0092] To ensure the accuracy of the trained model, in some preferred embodiments, an adaptive order strategy can be adopted. That is, based on the sparse strategy, the truncation degree of the chaotic polynomial expansion is adaptively adjusted to establish the PCE model with the highest accuracy. .

[0093] Specifically, in some embodiments, an initial cutoff value for the sparse chaotic polynomial model can be preset, for example, the initial cutoff value can be set to 2. Starting from the initial cutoff value, the cutoff value of the sparse chaotic polynomial model is increased, and the cross-validation error is compared during the increase. The value of . When the cross-validation error When the cutoff degree is increased twice consecutively, the current sparse chaotic polynomial model can be determined as the highest precision quantization model, i.e., the first uncertain quantization model, and the current order can be determined as the target order of the model.

[0094] In response to completing cross-validation error After the model is trained, when the coefficients are finally determined At that time, the first uncertainty quantization result can be output, which is the mean of the response characteristics. and variance , where the mean It can be expressed using polynomial coefficients as follows:

[0095]

[0096] variance It can be expressed using polynomial coefficients as follows:

[0097]

[0098] in, These are the coefficients of the constant term in the polynomial chaotic expansion. For the first The coefficients of the term polynomial.

[0099] S140: Introduce deterministic optimization variables of the pyrolysis furnace into the first uncertainty quantification model, and obtain a second uncertainty quantification model that depends on the deterministic optimization variables based on Legendre polynomials.

[0100] In traditional optimization processes, conventional chaotic polynomial quantization can only calculate the quantization result under one working condition at a time. However, the actual optimization process requires constantly finding a large number of new working conditions for evaluation. The calculation of expansion coefficients requires a system evaluation to be performed again each time. The computational cost of optimization is affected by the selection of the initial working condition point and the effectiveness of the specific optimization algorithm. In optimization work, conventional chaotic polynomial quantization can only perform inefficient discrete optimization. Therefore, this invention improves upon the conventional chaotic polynomial by introducing Legendre polynomials to establish the dependence of the chaotic polynomial on the optimization design variables.

[0101] Specifically, please refer to Figure 6 , Figure 6 This is a schematic diagram of the process for obtaining a second uncertainty quantification model according to some embodiments of the present invention. Figure 6 As shown, step S140 may include steps S141 to S144.

[0102] S141: Determine the deterministic optimization variables for the pyrolysis furnace.

[0103] The deterministic optimization variables for an ethylene cracking furnace may include theoretical parameters, such as the theoretical parameter for the excess air coefficient in the ethylene cracking furnace. In an optional embodiment, the excess air coefficient is selected as the deterministic optimization variable.

[0104] S142: Define deterministic optimization variables by uniform distribution to obtain the distribution of deterministic variables.

[0105] In some optional embodiments, a uniform distribution can be chosen from the distribution assumptions to define the aforementioned deterministic optimization variables. Those skilled in the art will understand that the above-described scheme for defining the distribution of deterministic optimization variables based on a uniform distribution is merely a non-limiting implementation provided by the present invention, intended to clearly demonstrate the main concept of the invention and provide a specific solution convenient for public implementation, rather than being intended to limit the scope of protection of the present invention.

[0106] S143: Based on the optimal orthogonal polynomial basis corresponding to the distribution of deterministic variables, determine the Legendre polynomials, and obtain the second uncertainty quantization model dependent on the deterministic optimization variables based on the first uncertainty quantization model.

[0107] As shown in Table 1 above, the optimal orthogonal polynomial corresponding to the distribution of deterministic variables is the Legendre polynomial. The upper and lower limits of the actual range of the excess air coefficient are set as uniformly distributed variables. After introducing the Legendre polynomial, based on the first uncertainty quantification model, the expression for the second uncertainty quantification model, which depends on the deterministic optimization variables, is obtained as follows:

[0108]

[0109] in, For the uncertain input variable, in this embodiment it can be a Gaussian distribution, using Hermite polynomials as its orthogonal polynomial base. For the deterministic optimization variable u, in this embodiment it can be a uniform distribution, using Legendre polynomials as its orthogonal polynomial base. For a multidimensional polynomial with uncertain input variables, To determine the multidimensional polynomial of the input variables.

[0110] S144: Based on the second uncertainty quantification model, obtain the expectation and variance of the deterministic optimization variables.

[0111] Specifically, the expressions for the expectation and variance of the deterministic optimization variables obtained from the second uncertainty quantification model described above are as follows:

[0112]

[0113]

[0114] S150: Robust optimization of the deterministic optimization variables of pollutant emissions is performed using the second uncertainty quantification model.

[0115] Specifically, in some embodiments, the expectation and variance are completely derived from deterministic optimization variables through the expression in the previous step. This is used to represent the multinomial moments and establish their dependencies on the deterministic optimization variables. Therefore, the expectation can be represented using the deterministic optimization variables. and variance The expression for the robust optimization model, which serves as the optimization objective, is as follows:

[0116]

[0117]

[0118] The above expression will expect and variance The weighted sum is the optimization objective of the robust optimization model. The optimization considers both the mean performance and the fluctuation represented by the variance, thereby improving the system's robustness. Simultaneously, the upper and lower limits of the deterministic optimization variable u in the actual process are defined. and As constraints in the optimization model, based on the aforementioned robust optimization model and combined with advanced optimization algorithms, a robust optimization method based on improved chaotic polynomials can be established to robustly optimize the deterministic optimization variables of pollutant emissions.

[0119] To further clarify the robust optimization method for pollutant emissions protected by the first aspect of the present invention, the following will use a complete specific embodiment to verify the effectiveness of the robust optimization method for pollutant emissions provided by the present invention.

[0120] The specific experimental design process is as described above and will not be repeated here. For details regarding the selection of deterministic optimization variables and uncertain input variables, please refer to Table 2 below.

[0121] Table 2

[0122]

[0123] In this embodiment, regarding the uncertainties of the ethylene cracking furnace, the main uncertain input variables can be selected as the preheating air coefficient, the main fuel inlet velocity, the secondary inlet velocity, and the outlet pressure. The deterministic optimization variable is selected as the excess air coefficient, and the emission performance parameter is selected as the CO emission.

[0124] After hypercubic Latin sampling, 400 sample points were obtained as the training sample set for the chaotic polynomial. The selection range of the deterministic optimization variable u is the excess air coefficient of 1.1~1.3, and other uncertain input variables can be quantified by 3% scalar fluctuation.

[0125] A chaotic polynomial was constructed using the aforementioned 400 samples. The coefficients of the chaotic polynomial were constructed using LAR (Layered Arithmetic Reduction) to obtain a sparse chaotic polynomial, thereby reducing the overall scale of the polynomial and preventing the "curse of dimensionality." Table 3 below shows the PCE uncertain quantization model results in this embodiment. As can be seen from Table 3, the overall truncation order was reduced to order 3 in this embodiment. Simultaneously, the number of expanded terms was further reduced by about half through a sparse algorithm. Furthermore, the quantization accuracy of the overall model was ensured through order adaptation while reducing the scale, resulting in a final model error accuracy of 4.1613e-04, maintaining a very small error.

[0126] Table 3

[0127]

[0128] Furthermore, after obtaining the corresponding first uncertainty quantification model, we can introduce the multi-order Legendre optimal polynomial corresponding to the excess air coefficient, which is assumed to be uniformly distributed, and its expression is as follows:

[0129]

[0130]

[0131] Combining the formulas for calculating the mean and variance based on the coefficients of chaotic polynomials, the mean and variance are expressed as expressions for u (excess air coefficient):

[0132]

[0133]

[0134] Traditional scalar optimization only considers minimizing the expectation and does not take into account fluctuations. Its optimization model is represented as follows:

[0135]

[0136]

[0137] In contrast, the robust optimization model in this invention can optimize using weights w, taking into account both expectation and variance, and finding a balanced optimization condition. The expression of the improved robust optimization model is as follows:

[0138]

[0139]

[0140] In this embodiment, w is chosen as 100 for trade-offs; the optimization results can be found in [reference needed]. Figure 7 , Figure 7This is a schematic diagram of robust optimization results according to an embodiment of the present invention. Figure 7 In the figure, the horizontal axis represents the excess air coefficient, and the vertical axis represents the objective function value of the improved robust optimization model. Figure 7 The weighted results of expectation and mean square error obtained through the improved robust optimization model are shown. The trend of the optimization evaluation index reveals that as the excess air increases, the index first decreases and then increases. Scalar optimization considering only the expectation deviates significantly from the final robust optimization result. Only robust optimization considering fluctuations can truly find the optimal point of the robust optimization index.

[0141] Further, please refer to Table 4 below, which lists a comparison between the robust optimization results and the scalar optimization results.

[0142] Table 4

[0143]

[0144] In combination with the above Figure 7 As shown in Table 4, compared with the traditional scalar optimization method, the robust optimization method for pollutant emissions provided by this invention, when considering the uncertain influence of CO emissions, significantly reduces the variance and coefficient of variation, representing uncertain fluctuations, thus improving the robustness of system emissions. This also verifies the effectiveness of the robust optimization method for pollutant emissions provided by this invention.

[0145] Although the methods described above are illustrated and depicted as a series of actions for the sake of simplicity, it should be understood and appreciated that these methods are not limited by the order of the actions, as some actions may occur in a different order and / or concurrently with other actions from the illustrations and descriptions herein or not illustrated and described herein but which may be understood by those skilled in the art, according to one or more embodiments.

[0146] This concludes the introduction of a robust optimization method for pollutant emissions provided by the first aspect of the present invention. The second aspect of the present invention also provides a robust optimization apparatus for pollutant emissions. Please refer to... Figure 8 , Figure 8 A structural block diagram of a robust optimization device for pollutant emissions provided according to other embodiments of the present invention is shown.

[0147] like Figure 8As shown, the robust optimization apparatus 800 for pollutant emissions may include a memory 810 and a processor 820. The memory 810 includes, but is not limited to, the computer-readable storage medium described in the third aspect of the present invention, on which computer instructions are stored. The processor 820 is connected to the memory 810 and configured to execute the computer instructions stored in the memory 810 to implement the robust optimization method for pollutant emissions described in the first aspect of the present invention.

[0148] Furthermore, those skilled in the art will understand that the embodiments of the robust optimization method for pollutant emissions described in the first aspect above are merely some non-limiting implementations provided by the present invention, intended to clearly demonstrate the main concept of the invention and provide some specific solutions that are easy for the public to implement, rather than being used to limit all operating modes or all functions of the robust optimization device 800 for pollutant emissions. Similarly, the robust optimization device 800 for pollutant emissions is also merely a non-limiting implementation provided by the present invention and does not constitute a limitation on the entities implementing each step in the robust optimization method for pollutant emissions described above.

[0149] In summary, this invention provides a robust optimization method for pollutant emissions, a robust optimization device for pollutant emissions, and a computer-readable storage medium, which can solve the problems of uncertainty quantification accuracy and efficiency in large-scale numerical models, establish a continuous robust optimization model, and significantly improve optimization efficiency.

[0150] The prior description of this disclosure is provided to enable any person skilled in the art to make or use this disclosure. Various modifications to this disclosure will be apparent to those skilled in the art, and the general principles defined herein may be applied to other variations without departing from the spirit or scope of this disclosure. Therefore, this disclosure is not intended to be limited to the examples and designs described herein, but should be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A robust optimization method for pollutant emissions, characterized in that, Includes the following steps: Obtain sampled data of uncertain input variables of the cracking furnace; The sampled data were numerically simulated using a turbulent combustion coupling model to obtain a training dataset. Based on the uncertain input variables, a sparse chaotic polynomial model is constructed, and the sparse chaotic polynomial model is trained via the training dataset to obtain a first uncertain quantization model. A deterministic optimization variable for the pyrolysis furnace is introduced into the first uncertainty quantification model, and a second uncertainty quantification model dependent on the deterministic optimization variable is obtained based on Legendre polynomials; and Robust optimization of the deterministic optimization variables of the pollutant emissions is performed using the second uncertainty quantification model.

2. The robust optimization method as described in claim 1, characterized in that, The cracking furnace includes an ethylene cracking furnace, and the step of obtaining sampled data of the uncertain input variables of the cracking furnace includes: The uncertain input variables of the ethylene cracking furnace are defined by a distributional assumption to obtain the distribution of uncertain variables; and The uncertain input variable is sampled using the Latin hypercube method to obtain sampled data that fully represents the distribution of the uncertain variable using a small number of sample points.

3. The robust optimization method as described in claim 2, characterized in that, The step of performing numerical simulation on the sampled data using a turbulent combustion coupling model to obtain a training dataset includes: The structural model of the ethylene cracking furnace was determined, and its mesh was generated. Based on the structural model after mesh generation, the turbulence model, combustion model, and radiation heat transfer model of the ethylene cracking furnace cracking process are determined. The turbulence model adopts the standard k-ε model, the combustion model is a non-premixed combustion model, and the radiation heat transfer model adopts the discrete coordinate radiation model. Based on the turbulence model, the combustion model, and the radiation heat transfer model, a turbulence-combustion coupling model is established; and The training dataset is obtained by numerically simulating the sampled data using the turbulent combustion coupling model.

4. The robust optimization method as described in claim 3, characterized in that, The step of constructing a sparse chaotic polynomial model based on the uncertain input variables includes: Based on the orthogonal polynomial basis corresponding to the distribution of the uncertain variables, a generalized chaotic polynomial model is established, wherein the generalized chaotic polynomial model is expressed by the following formula: in, These are weighting coefficients. It is a set of multi-index multivariate polynomials , For uncertain input variables that need to be standardized and independent, n is the number of such uncertain input variables. Multidimensional polynomials built from one-dimensional polynomials , where the coefficient The quantity is , For the total coefficient, The total order of the expansion of the generalized chaotic polynomial; The degree of the generalized chaotic polynomial model is truncated to obtain a simplified generalized chaotic polynomial model of finite order: in, The set of the multivariate polynomials with multiple indices. It is the sum of residuals generated after degree truncation. A set of observational data; and The simplified generalized chaotic polynomial model is dimensionality-reduced using the minimum angle regression algorithm to obtain the sparse chaotic polynomial model. The coefficient expressions obtained by the minimum angle regression algorithm are as follows: in, This is a regularization term.

5. The robust optimization method as described in claim 4, characterized in that, The step of training the sparse chaotic multinomial model using the training dataset to obtain the first uncertainty quantization model includes: In response to overfitting of the sparse chaotic polynomial model, cross-validation error is introduced. To train the sparse chaotic polynomial model, wherein the cross-validation error for in, For m response models that need to be built, The mean of the response characteristics; In response to completing the cross-validation error After training, the mean of the response features is obtained. and variance , wherein the mean Expressed using polynomial coefficients: The variance Expressed using polynomial coefficients: in, These are the coefficients of the constant term in the polynomial chaotic expansion. For the first The coefficients of the term polynomial.

6. The robust optimization method as described in claim 5, characterized in that, The response to overfitting of the sparse chaotic polynomial model introduces cross-validation error. The steps for training the sparse chaotic polynomial model include: The initial cutoff value of the sparse chaotic polynomial model is preset; Starting from the initial cutoff, the cutoff of the sparse chaotic polynomial model is increased, and the cross-validation error is compared. The value; and In response to the cross-validation error The cutoff degree is increased twice consecutively to determine the current sparse chaotic polynomial model as the first uncertain quantization model, and the current order is determined as the target order of the model.

7. The robust optimization method as described in claim 4, characterized in that, The step of introducing the deterministic optimization variable of the pyrolysis furnace into the first uncertainty quantification model and obtaining a second uncertainty quantification model dependent on the deterministic optimization variable based on Legendre polynomials includes: Determine the deterministic optimization variables for the pyrolysis furnace; The deterministic optimization variables are defined by a uniform distribution to obtain the deterministic variable distribution; Based on the optimal orthogonal polynomial basis corresponding to the distribution of the deterministic variables, the Legendre polynomial is determined, and based on the first uncertainty quantification model, a second uncertainty quantification model dependent on the deterministic optimization variables is obtained. in, Let u be the uncertain input variable, and let u be the deterministic optimization variable. For the multidimensional polynomial of the uncertain input variables, The multidimensional polynomial that determines the input variables; Based on the second uncertainty quantification model, the expected value of the deterministic optimization variable is obtained. and variance , wherein the expectation and the variance Let be the optimization objective of the second uncertainty quantification model, and express it as follows: 。 8. The robust optimization method as described in claim 7, characterized in that, The step of robustly optimizing the deterministic optimization variables of pollutant emissions via the second uncertainty quantification model includes: Based on the aforementioned expectations and the variance Establish a robust optimization model: Wherein, the expectation and the variance The sum of the weights is the optimization objective of the robust optimization model. and These are the upper and lower bounds of the deterministic optimization variables, respectively; and Based on the robust optimization model, robust optimization is performed on the deterministic optimization variables of the pollutant emissions.

9. A robust optimization device for pollutant emissions, characterized in that, include: Memory; as well as A processor, connected to the memory, and configured to implement a robust optimization method for pollutant emissions as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing computer instructions thereon, characterized in that, When the computer instructions are executed by the processor, a robust optimization method for pollutant emissions as described in any one of claims 1 to 8 is implemented.

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