Electric precipitation inlet flue gas flow deviation reason analysis and optimization decision-making method

Abstract

The invention relates to the technical field of flue gas treatment equipment, and discloses an electric precipitation inlet flue gas flow deviation reason analysis and optimization decision-making method which comprises the following steps: establishing a three-dimensional flow field calculation model and defining a continuous operation working condition space; generating a flow guiding device parameterized model driven by the design variable; constructing a response surface agent model for predicting flow deviation and total pressure drop according to working conditions and design variables; performing multi-target robust optimization based on the proxy model to obtain a Pareto optimal leading edge; selecting a final design scheme according to the Pareto optimal leading edge; after commissioning, actual work KPI and flow deviation are collected in real time, and a model prediction residual error is calculated; and when the predicted residual error exceeds a threshold value, the response surface agent model is updated online by using the actually measured data. According to the method, through multi-target robust optimization and online adaptive correction, the high performance of the flow guide device under all working conditions and the adaptive capacity of the flow guide device in the whole life cycle are achieved, and the design robustness is improved.

Description

Technical Field

[0001] This invention relates to the field of flue gas treatment equipment technology, specifically to a method for analyzing the causes of flue gas flow deviation at the inlet of an electrostatic precipitator and making optimization decisions. Background Technology

[0002] In industrial sectors such as thermal power generation, electrostatic precipitators (ESPs) are core equipment for purifying flue gas and controlling particulate matter emissions. Their operating efficiency is directly related to the uniformity of the inlet flue gas velocity distribution. Significant flow deviations can lead to problems such as excessively high flue gas velocity in localized areas, secondary dust generation, and uneven electric field distribution, severely restricting their overall dust removal performance. Therefore, designing and installing effective flow guiding devices within the ESP inlet flue to optimize flue gas flow has become a key technical measure to ensure the efficient operation of ESPs and meet increasingly stringent environmental standards.

[0003] Currently, the design of inlet flow guiding devices for electrostatic precipitators mainly relies on a combination of engineering experience and computational fluid dynamics (CFD) simulation. The typical process is as follows: engineers first create a 3D model of the inlet flue based on design drawings. Using their professional knowledge and understanding of fluid mechanics, they manually pre-determine the initial layout and shape of the flow guide plates within the model. Subsequently, CFD software is used to perform numerical simulations under several pre-defined, representative unit operating conditions (such as 100% rated load and 75% load). The effectiveness of the design scheme is evaluated by analyzing the simulation results, and repeated manual adjustments and recalculations are performed until a scheme that meets the design requirements is obtained.

[0004] While existing technologies can improve inlet flow distribution to some extent, several shortcomings remain: First, the robustness and adaptability of the design across all operating conditions are insufficient. This is because design optimization is essentially based on a few discrete, static operating points, while the actual load of a generator set fluctuates continuously and dynamically over a wide range. The enormous computational cost of CFD simulation makes it impractical to perform calculations for all possible operating conditions. This results in a scheme optimized for rated operating conditions potentially experiencing significantly reduced flow guiding performance when the unit operates at low or variable loads, due to fundamental changes in the flow field characteristics. Second, the design process heavily relies on engineers' subjective experience, representing a repetitive, manual trial-and-error process. This not only leads to lengthy and inefficient development cycles but, more importantly, confines the merits of design solutions within the engineer's existing cognitive framework, making it difficult to systematically explore the entire design space to discover unconventional globally optimal configurations. Most critically, existing designs are one-off, static solutions that cannot adapt to changes in the physical state of the equipment throughout its operational lifecycle. The initial design was based on an idealized clean flue model. However, during long-term operation, phenomena such as dust accumulation, wear, and blockage will continuously change the internal geometry and flow resistance characteristics of the flue. The existing technical framework lacks an online monitoring feedback and model correction mechanism, and cannot detect this performance degradation or provide adaptive adjustments. Ultimately, the gap between the actual operating effect and the initial design expectations gradually widens over time. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for analyzing the causes of flue gas flow deviation at the inlet of electrostatic precipitators and making optimization decisions. This method solves the problems of existing flow guiding device designs being limited to discrete operating conditions, relying on subjective experience, and unable to perform online adaptive correction, resulting in poor robustness under all operating conditions and long-term performance degradation.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for analyzing and optimizing the deviation of flue gas flow at the inlet of an electrostatic precipitator, comprising the following steps: S1. Establish a three-dimensional flow field calculation model of the inlet flue of the electrostatic precipitator and define a continuous operating condition parameter space. S2. Generate a parametric model of the flow guide device driven by a set of design variables; S3. Construct a response surface proxy model, which is used to predict the flow deviation coefficient and the total system pressure drop based on the operating condition parameter space and the design variables. S4. Based on the response surface surrogate model, solve a multi-objective robust optimization problem to determine the optimal solution set of the design variables, thereby obtaining the Pareto optimal frontier; S5. Based on the Pareto optimal frontier, select the final flow guiding device design scheme; S6. After the diversion device is put into operation, the actual operating condition parameters and the measured flow deviation coefficient are collected in real time, and the prediction residual between the measured flow deviation coefficient and the predicted value of the response surface surrogate model is calculated. S7. When the predicted residual continues to exceed the preset threshold, the response surface proxy model is updated online using the collected data including the actual operating condition parameters and the measured flow deviation coefficient.

[0007] Preferably, the step of generating the parameterized model of the flow guiding device includes: In the three-dimensional flow field calculation model, a design domain is defined, and a topology optimization algorithm is used to generate the initial configuration of the flow guiding device. Based on the initial configuration, key geometric features are extracted and associated with the design variables to establish the parametric model.

[0008] Preferably, the response surface proxy model is a Kriging model; The steps for constructing the response surface proxy model include: using the optimal Latin hypercube sampling method to generate sample point combinations in the joint parameter space formed by the operating condition parameter space and the design variable space composed of the design variables; using computational fluid dynamics to batch calculate and obtain the flow deviation coefficient and total system pressure drop corresponding to each sample point combination, and using the calculation results to train and generate the Kriging model.

[0009] Preferably, the optimization objectives of the multi-objective robust optimization problem include: Minimize the mathematical expectation of the flow deviation coefficient within the operating condition parameter space; Minimize the mathematical variance of the flow deviation coefficient within the operating condition parameter space; Minimize the mathematical expectation of the total system pressure drop within the operating condition parameter space.

[0010] Preferably, the steps for solving a multi-objective robust optimization problem include: The non-dominated sorting genetic algorithm II is used to solve the multi-objective robust optimization problem to obtain the Pareto optimal front.

[0011] Preferably, the step of selecting the final flow guiding device design includes: Assign weight coefficients to each optimization objective of the multi-objective robust optimization problem to construct a unified utility function; The utility function is used to comprehensively score all solutions on the Pareto optimal frontier, and the solution with the best utility value is selected as the final flow guiding device design scheme.

[0012] Preferably, the flow deviation coefficient is calculated by: calculating the standard deviation of the flue gas flow rate of all inlet channels of the electrostatic precipitator, and dividing the standard deviation by the average flow rate of the flue gas flow rate of all inlet channels.

[0013] Preferably, the online update step includes: The data points containing the actual operating condition parameters and the measured flow deviation coefficient are used as new training samples and incorporated into the original sample dataset to form an enhanced dataset. The response surface proxy model is retrained using the enhanced dataset.

[0014] Preferably, after the response surface proxy model is updated online, the following step S8 model adaptive correction is further included: Dynamic decision support is provided based on the updated response surface proxy model, which includes predictive early warning based on future forecasts or performance benchmarking based on current real-time conditions.

[0015] Preferably, the optimization objective of the topology optimization algorithm is a weighted combination of flow distribution uniformity and flow pressure drop.

[0016] This invention provides a method for analyzing the causes of deviations in the flue gas flow rate at the inlet of an electrostatic precipitator and for making optimization decisions. It has the following beneficial effects: 1. This invention constructs a continuous operating condition parameter space and employs a multi-objective robust optimization method. It not only pursues the optimal average performance (minimization of mathematical expectation) of the flow deviation coefficient across the entire operating range but also takes performance fluctuation (minimization of mathematical variance) as the core optimization objective. This overcomes the limitations of traditional design methods that optimize only a few discrete operating points, ensuring that the final design scheme maintains efficient and stable flow guiding performance under actual operating conditions such as unit load fluctuations.

[0017] 2. This invention utilizes topology optimization algorithms to automatically generate unconventional initial configurations based on first principles, overcoming the limitations of engineer-driven design experience. By combining parametric modeling and response surface surrogate models, it replaces time-consuming high-fidelity CFD simulation calculations with instantaneous prediction, achieving automated and rapid optimization of massive design schemes, thereby improving design efficiency and the performance ceiling of the final solution.

[0018] 3. This invention calculates the residual between the model's predicted values ​​and the measured values ​​in real time through an online monitoring module. This invention can accurately identify model inaccuracies caused by factors such as dust accumulation and wear. Once the residual exceeds a threshold, the model's adaptive correction mechanism uses new measured data to update the response surface model online, ensuring that the digital model and the physical entity remain consistent. This provides a high-fidelity model foundation for predictive early warning and other dynamic decision support functions. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the method for analyzing and optimizing the deviation of flue gas flow at the inlet of the electrostatic precipitator according to the present invention. Figure 2 This is a schematic diagram illustrating the spatial definition of the three-dimensional flow field calculation model and operating condition parameters of this invention. Figure 3 This is a schematic diagram of the initial configuration topology optimization generation process of the flow guiding device of the present invention; Figure 4 This is a schematic diagram of the parametric modeling process of the flow guiding device of the present invention; Figure 5 This is a schematic diagram of the response surface proxy model construction process of the present invention; Figure 6 This is a schematic diagram illustrating the multi-objective robust optimization and Pareto optimal front generation of this invention; Figure 7 This is a schematic diagram illustrating the quantitative decision-making and engineering implementation process of this invention; Figure 8 This is a schematic diagram of the online monitoring and model verification process of the present invention; Figure 9 This is a schematic diagram of the adaptive correction and dynamic decision support process of the model in this invention. Detailed Implementation

[0020] The technical solutions in the embodiments 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, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] Please see the appendix Figure 1 , Figure 1 This is a flowchart illustrating a method for analyzing and optimizing the flow rate deviation of flue gas at the inlet of an electrostatic precipitator according to an embodiment of the present invention. The present invention provides a method for analyzing and optimizing the flow rate deviation of flue gas at the inlet of an electrostatic precipitator, which may include: Step S1: Establish a three-dimensional flow field calculation model of the inlet flue of the electrostatic precipitator, and based on historical operating data, define a continuous operating condition parameter space consisting of multiple key operating parameters such as unit load and pressure difference on both sides of the air preheater.

[0022] Step S2: Define the design domain of the flow guiding device in the three-dimensional flow field calculation model, and use the topology optimization algorithm to generate the initial configuration of the flow guiding device. The optimization objective of this algorithm is a weighted combination of flow distribution uniformity and flow pressure drop, in order to seek the comprehensive optimality of the two.

[0023] Step S3: Analyze the initial configuration generated in step S2, extract the key geometric features that play a decisive role in the flow guiding performance, and establish a parametric model driven by multiple design variables.

[0024] Step S4 involves constructing a response surface surrogate model capable of rapidly predicting flow deviation and system pressure drop. This step S4 selects sample points using experimental design methods, employs CFD batch calculations to obtain the flow deviation coefficient and total system pressure drop corresponding to each sample point, and uses this sample data to train and generate the surrogate model. The flow deviation coefficient is used to quantify the uniformity of flow distribution among the inlet channels.

[0025] Step S5: Based on the response surface surrogate model, construct and solve a multi-objective robust optimization problem. The optimization objectives of this problem include: minimizing the mathematical expectation of the flow deviation coefficient across the entire operating range to pursue optimal average performance; minimizing the mathematical variance of the flow deviation coefficient to ensure the robustness of the scheme to operating condition fluctuations; and minimizing the mathematical expectation of the total system pressure drop to improve economic efficiency. Solving this problem yields a Pareto optimal front containing a series of optimal trade-offs.

[0026] Step S6: Based on the specific needs and constraints of the project, make quantitative decisions on the Pareto optimal frontier, select the final flow diversion device design scheme, and carry out engineering implementation.

[0027] Step S7: After the diversion device is put into operation, the actual operating parameters and flow distribution data of the power plant are collected in real time. The measured flow deviation coefficient is compared with the predicted value of the response surface proxy model, and the prediction residual between the two is calculated.

[0028] Step S8: When the predicted residuals continuously exceed a preset threshold, the model adaptive correction mechanism is triggered. This mechanism uses new measured data to update the response surface surrogate model online and provides dynamic decision support to operators based on the updated model.

[0029] This invention also provides a system for analyzing and optimizing the causes of deviations in the flue gas flow rate at the inlet of an electrostatic precipitator. This system is used to execute the above method and may include: The system modeling and spatial definition module is used to execute step S1, establish a three-dimensional flow field calculation model, and define the operating condition parameter space.

[0030] The initial configuration generation module is used to execute step S2, which uses a topology optimization algorithm to generate the initial configuration of the flow guiding device.

[0031] The parametric modeling module is used to execute step S3, which analyzes the initial configuration and establishes a parametric model.

[0032] The response surface surrogate model building module is used to execute step S4, which constructs the response surface surrogate model through experimental design, CFD calculation and model training.

[0033] The multi-objective robust optimization module is used to execute step S5, construct and solve the multi-objective robust optimization problem, and generate the Pareto optimal front.

[0034] The quantitative decision-making module is used to execute step S6, providing a visual interface to assist users in selecting the final design scheme on the Pareto optimal frontier.

[0035] The online monitoring and verification module is used to execute step S7, collect running data in real time, compare it with the model prediction value, and calculate the prediction residual.

[0036] The adaptive correction and support module is used to perform step S8, which updates the response surface model online when the triggering conditions are met, and provides dynamic decision support.

[0037] Please see the appendix Figure 2 , Figure 2 This is a schematic diagram of the spatial definition of a three-dimensional flow field calculation model and operating condition parameters according to an embodiment of the present invention.

[0038] Step S1 of the method of the present invention aims to establish an accurate digital physical model and define clear analytical boundaries for subsequent analysis and optimization. Step S1 may include sub-steps S101 and S102.

[0039] In sub-step S101, a three-dimensional flow field calculation model is established. Based on the design drawings, equipment ledgers, and on-site survey data of the electrostatic precipitator and its connected flue system, a high-fidelity three-dimensional geometric model is established using computer-aided design (CAD) software. The geometric range of this model covers the entire area that has a significant impact on the inlet flow distribution. Its starting boundary is the air preheater outlet flue, and its ending boundary is a straight section of flue after the inlet bell mouth of each chamber of the electrostatic precipitator, including all bends, merging sections, branching sections, and diameter changing sections.

[0040] After the geometric model is constructed, it is spatially discretized, i.e., meshed. To balance computational accuracy and efficiency, polyhedral meshes or hybrid meshing techniques with hexahedral cores can be used. During meshing, local mesh refinement is performed in areas with drastic changes in physical quantity gradients, such as the inner side of elbows, the pre-installed area of ​​guide vanes, and areas where the flue cross-section changes rapidly.

[0041] Simultaneously, to accurately solve the flow near the wall region, boundary layer meshes are generated near all solid walls to ensure that the dimensionless distance y+ from the wall meets the requirements of the selected turbulence model. After mesh generation, a quality check is required to ensure that key indicators such as mesh orthogonality, aspect ratio, and skewness are within reasonable ranges.

[0042] This computational model solves the Reynolds-averaged Navier-Stokes (RANS) equations to describe the turbulent flow of flue gas. The equations include the continuity equation and the momentum equation: ; In the formula, and For speed in and Component of direction; and The coordinate direction; It is static pressure; The density of the flue gas; The dynamic viscosity of the flue gas; This is the time-averaged product of the velocity fluctuation components, representing the Reynolds stress term; For the momentum equation in The generalized source term in the direction. The Reynolds stress term is closed by choosing an appropriate turbulence model, such as the Realizable k-ε model or the Shear Stress Transport (SST) k-ω model.

[0043] In sub-step S102, the operating condition parameter space is defined. The goal of this sub-step S102 is to construct a continuous parameter space that can comprehensively characterize all possible states of the unit in actual operation, in order to replace the limitation of traditional methods that only analyze a few discrete operating points.

[0044] To achieve this goal, historical data from at least one complete operating cycle (e.g., one year) of the power plant's distributed control system (DCS) is first retrieved and analyzed. Through mechanistic analysis and data correlation analysis, independent key operating parameters that significantly influence the inlet flue gas flow distribution are identified. Examples of these parameters include, but are not limited to, unit load. Total air pressure or pressure difference on both sides of air preheater A or B and primary air-fuel ratio .

[0045] After identifying key operating parameters, based on historical operating data, the actual operating range of each parameter is calculated, that is, its minimum and maximum values ​​are determined throughout the entire statistical period. These parameters and their respective value ranges together constitute a multi-dimensional, continuous operating condition parameter space. This space can be mathematically represented as a vector, where each component represents a key operational parameter: ; In the formula, This is a vector space for operating condition parameters; For unit load; The pressure difference across the air preheater; This is the mass ratio of primary air to pulverized coal, i.e., the primary air-to-pulverized coal ratio. The ellipsis represents other key operating parameters that affect the flow field; The transpose symbol indicates This is a column vector. The establishment of this parameter space provides a foundation for subsequent response surface modeling and robustness optimization across the entire operating range.

[0046] Please see the appendix Figure 3 , Figure 3 This is a schematic diagram of the initial configuration topology optimization generation process of a flow guiding device according to an embodiment of the present invention.

[0047] Step S2 of the method of the present invention aims to creatively generate the initial form of the flow guiding device in a data-driven, non-empirical manner. This step breaks through the limitations of traditional methods that rely on engineers' experience to pre-determine the shape and layout of the flow guiding plate, and automatically finds the optimal flow guiding structure based on first principles of physics. Step S2 may include sub-steps S201, S202, and S203.

[0048] In sub-step S201, the mathematical construction of the topology optimization problem is performed. In the three-dimensional flow field calculation model established in step S1, based on the preliminary flow field analysis results or engineering experience, one or more closed three-dimensional spaces are delineated as design domains at key locations inside the flue. These locations are usually the main areas that cause uneven flow distribution, such as large-angle bends in the flue, T-shaped or Y-shaped bifurcations, and areas where the cross-section expands sharply.

[0049] Subsequently, the Solid Isotropic Material with Penalization (SIMP) method was employed to transform the structural design problem of the flow guiding device into a material distribution optimization problem. In this method, the design domain is discretized into a large number of finite elements, each with a relative material density... It is defined as a design variable, and its value ranges from 0 to 1. A value close to 0 indicates the element is a fluid, and a value close to 1 indicates it is a solid. The goal of the optimization problem is to find an optimal set of material density distributions. This allows specific flow field performance indicators to reach their optimal levels.

[0050] The optimization problem is constructed as a multi-objective optimization problem, with its joint optimization objective function being... The goal is to simultaneously maximize the uniformity of flow distribution and minimize the flow pressure drop. This objective function can be expressed as: ; In the formula, This is the joint objective function for topology optimization; the smaller its value, the better the overall performance of the design scheme. For the design domain The relative material density of each finite element is the design variable for this optimization problem; Weighting coefficients for the flow uniformity objective; The weighting coefficient for the target flow pressure drop; The objective function characterizing flow uniformity can be expressed as the root mean square deviation or standard deviation of the flow rate at each inlet channel of the electrostatic precipitator. The value of this function depends on the material density distribution. ; The objective function characterizing flow resistance can be specifically represented as the total pressure drop of the flue gas flowing through the design domain. The value of this function also depends on the material density distribution. .

[0051] This optimization problem is constrained by the amount of material used, meaning the volume of the generated flow guiding device cannot exceed a preset upper limit. This constraint is expressed as: ; In the formula, The total number of finite elements within the design domain; For the design domain The relative material density of each finite element is the design variable for this optimization problem; For the first The volume of a finite element; The maximum allowable material volume fraction is a dimensionless parameter with a value range of (0,1). Let be the total volume of the entire design domain. Simultaneously, the entire optimization process must satisfy the governing equations for fluid flow, namely the Navier-Stokes equations.

[0052] In sub-step S202, the topology optimization problem is solved. Gradient-based optimization algorithms, such as the Method of Moving Asymptotes (MMA) or Sequential Quadratic Programming (SQP), are used to iteratively solve the constructed optimization problem. In each iteration step, the flow field control equations are first solved to obtain the flow field distribution under the current structure. Then, the adjoint sensitivities of the objective function and constraint functions to the design variables are calculated. Finally, the design variables are updated based on the sensitivity information. This process is repeated until the objective function converges or the preset number of iterations is reached.

[0053] In sub-step S203, configuration extraction and smoothing are performed. The final result of the topology optimization solution is a relative material density distribution cloud map of each element within the design domain. To transform this into a solid model suitable for engineering manufacturing, a density threshold is first set (e.g., =0.5). All units with a relative material density greater than this threshold are considered solid components, and those with a density less than this threshold are considered fluid components. By extracting the isosurfaces formed by these solid units, a preliminary solid configuration with a jagged or irregular surface can be generated.

[0054] Subsequently, the preliminary configuration is imported into computer-aided design (CAD) software, where it is smoothed and refined using reverse engineering techniques or surface reconstruction capabilities. This process aims to eliminate numerical artifacts caused by mesh dependency, generating a smooth, hydrodynamically sound, and easily manufactured initial 3D configuration of the flow guiding device. This initial 3D configuration forms the basis for subsequent parametric fine-tuning.

[0055] Please see the appendix Figure 4 , Figure 4 This is a schematic diagram of the parametric modeling process of a flow guiding device according to an embodiment of the present invention.

[0056] Step S3 of the method of this invention aims to transform the relatively complex initial configuration generated in step S2 into a finite number of design variables that can be described and controlled using mathematical language. This step serves as a bridge connecting innovative structural design and automated numerical optimization, enabling efficient exploration of a large number of design variants through parametric modeling. Step S3 may include sub-steps S301 and S302.

[0057] In sub-step S301, key geometric features of the flow guiding device are identified and extracted. The initial configuration of the flow guiding device obtained after smoothing in step S2 is subjected to geometric and flow field mechanism analysis to identify the key geometric features that determine its overall flow guiding performance. These features are typically core structural elements that influence the mainstream direction, the separation vortex region, and the intensity of the secondary flow.

[0058] The identified key geometric features may include, but are not limited to, the following categories: Main structural parameters: For example, for structures similar to guide vanes or airfoils, the reference position coordinates (X,Y,Z) of their installation, the installation angle (e.g., angle of attack, tilt angle) relative to the flue wall or centerline, the blade chord length, the blade thickness distribution pattern, etc.

[0059] Surface morphology parameters: For a flow guide structure with a complex surface, the radius of curvature of its key cross-section line, the coordinates of the control points of the spline curve that controls the surface morphology, etc.

[0060] Relative relationship parameters: If the initial configuration contains multiple separate flow guide components, then the relative distance and relative angle between each component are included.

[0061] Local detailed parameters: such as the fillet radius of the front and rear edges of the flow guide structure, the size and position of the openings or channels, etc.

[0062] In sub-step S302, a parametric model is established. Computer-aided design (CAD) software supporting parametric modeling is selected, and each key geometric feature identified in sub-step S301 is associated with an independent, continuously varying mathematical variable; these variables are the design variables. By establishing geometric constraints and mathematical relationships, the entire three-dimensional model of the flow guiding device is driven entirely by this set of design variables.

[0063] All identified and defined design variables together constitute a multidimensional design variable vector. This vector fully describes the specific design scheme of the flow guiding device: ; in, The design variable vector represents a specific design scheme for the flow guiding device; For the first Each design variable corresponds to a specific key geometric feature parameter; This represents the total number of design variables. This can represent the installation angle of attack of the main flow blades. It can represent its chord length. It can represent its position coordinates on the cross-section of the flue, etc.

[0064] For each design variable Set a reasonable range of values. The determination of this range is based on engineering experience, manufacturing process constraints, and preliminary simulation analysis to ensure that the geometric models generated in subsequent optimization processes are physically feasible and practically meaningful.

[0065] After completing parametric modeling, the design variable vector is modified. By analyzing the values ​​of one or more components, CAD software can automatically and instantly update and generate a new, differently shaped 3D model of the flow guiding device. This fully parametric model forms the basis for subsequent automated, large-scale simulation optimization, transforming the design process, which originally required repeated manual model modifications, into a purely mathematical vector optimization problem.

[0066] Please see the appendix Figure 5 , Figure 5 This is a schematic diagram of the response surface proxy model construction process according to an embodiment of the present invention.

[0067] Step S4 of the method of this invention aims to establish a mathematical surrogate model with extremely low computational cost to replace time-consuming CFD simulation for performance prediction, thereby laying the foundation for subsequent large-scale automated optimization. Step S4 may include sub-steps S401, S402, and S403.

[0068] In sub-step S401, experimental design and sample point generation are performed. To ensure that the constructed surrogate model accurately reflects the system performance across the entire parameter space, a Design of Experiments (DoE) method with good space-filling properties is used to select training sample points. In a preferred embodiment, the Optimal Latin Hypercube Sampling method is used within the operating condition parameter space defined by step S1. The design variable space established in step S3 Within the resulting joint parameter space, a suitable number of sample point combinations (e.g., 200 to 500) are generated. Each sample point... This represents the state of a specific flow guiding device design under specific operating conditions, where, For the first A vector of operating condition parameters for each sample point, which contains multiple parameter values ​​describing a specific operating condition; For the first A vector of design variables for each sample point, which contains multiple parameter values ​​describing the geometry of a specific flow guide device; For a single sample point pair, the state of a specific flow guiding device design scheme under specific operating conditions is fully defined; The index of the sample point; This represents the total number of sample points.

[0069] In sub-step S402, batch calculations of the performance of the sample points are performed. To efficiently obtain the performance response values ​​of all sample points, an automated script is written to achieve unattended batch execution of the simulation calculation process. For each sample point... The script automatically performs the following operations: based on the design variable vector The value is used to update the 3D geometric model of the flow guide device using parametric CAD software; the updated model is then automatically re-meshed; and the operating condition parameter vector is... The values ​​in the parameters are set as boundary conditions for the CFD calculation; the CFD solver is started to perform numerical simulation until the calculation converges; after the calculation is completed, the post-processing program is automatically executed to extract and record the two key performance indicators corresponding to the sample point: flow deviation coefficient. and total system voltage drop .

[0070] Flow deviation coefficient The calculation formula is: ; In the formula, , is the flow deviation coefficient, a dimensionless parameter used to quantify the degree of unevenness in flow distribution among all inlet channels of an electrostatic precipitator; This represents the total number of inlet channels for the electrostatic precipitator, and is an integer. For the inflow of the first The flue gas mass flow rate or volumetric flow rate for each channel is expressed in kg / s or m³. 3 / s; For all Average traffic of each channel; This is the index number for the inlet channel. Total system voltage drop. This is the mass-weighted average total pressure difference of the flue gas from the inlet section to the outlet section of the selected computational domain.

[0071] In sub-step S403, the surrogate model is selected and trained. This invention preferably uses a Kriging model as the response surface surrogate model. The Kriging model is an interpolation method based on Gaussian process regression, which not only provides high-precision predictions but also assesses the uncertainty of the prediction results, facilitating the analysis of the model's global and local accuracy.

[0072] Using all the sample data calculated in sub-step S402, i.e., input and output data pairs Two independent Kriging models were trained. The first model was used to fit the flow deviation coefficient, and the second model was used to fit the total system pressure drop. The training process aimed to determine the optimal hyperparameters (e.g., the type and parameters of the correlation function) in the Kriging models. After training, two response surface functions were obtained that could accurately and instantaneously predict the system performance under arbitrary parameter combinations. and : ; These two well-trained response surface proxy models will replace direct CFD calculations in subsequent multi-objective optimization steps, thereby reducing the time required for a single performance evaluation from hours to milliseconds.

[0073] Please see the appendix Figure 6 , Figure 6 This is a schematic diagram of multi-objective robust optimization and Pareto optimal front generation according to an embodiment of the present invention.

[0074] Step S5 of the method of this invention aims to systematically and automatically find a set of robust design schemes that can perform optimally and stably across the entire operating range from a vast number of possible design schemes. This step transforms the design problem into a multi-objective robust optimization problem and solves it using an advanced intelligent optimization algorithm. Step S5 may include sub-steps S501 and S502.

[0075] In sub-step S501, the robustness optimization objective function is defined. To ensure that the design scheme not only has excellent average performance but is also insensitive to changes in operating conditions, this invention constructs the optimization problem as a mathematical problem that simultaneously optimizes three conflicting objectives. The optimization object is the flow guide device design variable vector defined in step S3. .

[0076] The three optimization objectives are as follows: Minimize performance expectations: This objective aims to optimize the flow guiding device across the entire operating parameter space. The average performance within the range reaches its optimal level. Its mathematical expression is the flow deviation coefficient. Mathematical expectation Minimize: ; In the formula, To optimize the operator, it indicates that the objective function is about the design variable vector. The minimization problem; The performance index is the flow deviation coefficient. Throughout the entire operating condition parameter space The mathematical expectation within the range characterizes the average performance level of the design scheme; For constructing a flow deviation coefficient Response surface proxy model function; It is a vector representing a specific operating condition, whose components are the unit load. Pressure difference across the air preheater Key operating parameters; Let be a vector representing a specific design scheme for a flow guiding device, whose components are all the design variables dkdk of that scheme; The joint probability density function of the operating condition parameters characterizes different operating conditions. The probability or frequency of occurrence in actual operation.

[0077] Minimizing performance variance: This objective is central to robust design, aiming to minimize the fluctuation in the performance of the flow guide device as operating conditions change, ensuring stable high performance under various conditions. Its mathematical expression is the flow deviation coefficient. variance Minimize: ; In the formula, To optimize the operator, it indicates that the objective function is about the design variable vector. The minimization problem; The performance index is the flow deviation coefficient. Throughout the entire operating condition parameter space The variance within the design scheme characterizes the stability and robustness of the design scheme's performance; the smaller the variance, the better the robustness. For constructing a flow deviation coefficient Response surface proxy model function; This is the mathematical expectation of the flow deviation coefficient, which has been defined in the above formula; A vector representing a specific operating condition; A vector representing a specific design scheme for a flow guiding device; This is the joint probability density function of the operating condition parameters.

[0078] Minimizing variance means that the selected design is insensitive to changes in operating conditions.

[0079] Minimizing economic efficiency: This objective aims to control the additional operating energy consumption introduced by the addition of diversion devices. Its mathematical expression is the total system pressure drop. Mathematical expectation Minimize: ; In the formula, To optimize the operator, it indicates that the objective function is about the design variable vector. The minimization problem; Total pressure drop of the economic indicator system Throughout the entire operating condition parameter space The mathematical expectation within the range characterizes the average operating energy consumption level of the design scheme; To construct a system for predicting total voltage drop. Response surface proxy model function; A vector representing a specific operating condition; A vector representing a specific design scheme for a flow guiding device; This is the joint probability density function of the operating condition parameters.

[0080] In actual calculations, the above integrals are approximated using numerical methods such as Monte Carlo integration or Gaussian integration.

[0081] In sub-step S502, the optimization algorithm is selected and solved. Since the three objective functions mentioned above are often conflicting (for example, pursuing extremely low flow deviation often increases system pressure drop), there is no single solution that can simultaneously optimize all objectives. Therefore, this invention employs a multi-objective optimization algorithm for solving the problem.

[0082] In a preferred embodiment, the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is used as the solver. This algorithm is a heuristic global optimization algorithm that simulates the biological evolution process and is particularly suitable for handling complex multi-objective optimization problems. The specific execution flow of the algorithm is as follows: First, a vector of multiple different design variables is randomly generated. An initial population is formed. Subsequently, the algorithm enters an iterative loop. In each generation, by calling the response surface surrogate model trained in step S4, the algorithm quickly calculates the three objective function values ​​corresponding to each individual in the population (i.e., each design scheme). Based on these objective function values, the algorithm evaluates and ranks the individuals in the population through non-dominated sorting and crowding calculation, and performs genetic operations such as selection, crossover, and mutation accordingly to generate a new offspring population.

[0083] This iterative process continues until the population converges or reaches the preset maximum number of generations. The final output of the algorithm is not a single optimal solution, but a set of solutions known as the Pareto optimal front. Each solution on this front represents a specific flow guide device design, and these designs share a common characteristic: for any solution on the front, it is impossible to find another solution that is better or equal to all objectives without sacrificing at least one objective performance. This Pareto optimal front provides a series of optimal trade-off alternatives for the final engineering decision.

[0084] Please see the appendix Figure 7 , Figure 7 This is a schematic diagram of a quantitative decision-making and engineering implementation process according to an embodiment of the present invention.

[0085] Step S6 of the present invention aims to transform the Pareto optimal front, the mathematical solution set generated in step S5, into a definite final design scheme suitable for engineering manufacturing and installation. This step provides designers and decision-makers with a systematic, data-driven decision-making process, ensuring that the selected scheme best meets the comprehensive requirements of the project. Step S6 may include sub-steps S601, S602, and S603.

[0086] In sub-step S601, the Pareto optimal frontier is visualized. To intuitively show decision-makers the performance trade-offs between the various optimal alternatives, the Pareto optimal frontier output in step S5 is visualized as a two-dimensional or three-dimensional scatter plot. In a preferred embodiment, a two-dimensional scatter plot is used, where the horizontal axis represents the expected performance. The vertical axis represents the performance variance. The third objective is economic expectation. This is represented by the color or size of the scatter points. Each point on the graph corresponds to a specific, non-dominated design scheme and its design variable vector. .

[0087] In sub-step S602, a quantitative decision is made to select the final solution. To avoid subjectivity in decision-making, this invention provides various quantitative decision-making methods to objectively select a final solution from the Pareto optimal frontier.

[0088] One decision-making approach is a constraint-based screening method. Decision-makers set thresholds for one or more objective functions based on the project's rigid constraints (e.g., regulatory emission stability limits, maximum permissible pressure drop increments determined by turbine margins). For example, setting... and By eliminating all solutions that do not satisfy these constraints from the Pareto optimal frontier, decision-makers only need to choose from the remaining smaller subset that satisfies all rigid constraints.

[0089] Another decision-making approach is the utility function method based on multi-attribute decision theory. This method constructs a unified utility function. We will then comprehensively score each solution on the Pareto optimal frontier. First, we normalize the values ​​of the three objective functions. Then, based on the specific preferences of the project, we assign weight coefficients to the performance expectation, performance variance, and economic expectation. , , (in + + =1). Utility function It can be defined as: ; In the formula, For a specific design scheme (consisting of a vector of design variables) The comprehensive utility value calculated (as defined) is used to quantify and rank different schemes on the Pareto optimal frontier; To design a variable vector; Preset weighting coefficients for the performance target; Preset weighting coefficients for the performance variance objective; Preset weighting coefficients for the expected economic goals; The expected performance value for the Pareto optimal frontier solution set The value obtained after normalization; The performance variance value of the Pareto optimal frontier solution set The value obtained after normalization; The economic expectation value for the Pareto optimal frontier solution set The value obtained after normalization.

[0090] Calculating the utility function values ​​of all solutions on the Pareto optimal front will yield the optimal (minimum in this case) value. The solution with the best value is taken as the final design scheme.

[0091] In sub-step S603, the finalization of the solution and engineering implementation are carried out. After selecting a final optimal solution through sub-step S602, the system retrieves the specific design variable vector corresponding to the solution from the database. . This vector The values ​​of each component in the model are substituted into the parametric CAD model established in step S3. Based on the input design variable values, the parametric model automatically generates a precise three-dimensional solid model of the final flow guiding device. Based on this three-dimensional model, two-dimensional engineering drawings, material lists, and installation coordinate data can be directly generated to guide production and on-site installation.

[0092] Please see the appendix Figure 8 , Figure 8 This is a schematic diagram of an online monitoring and model verification process according to an embodiment of the present invention.

[0093] Step S7 of the method of this invention aims to correlate the digital model established in the offline design phase with the actual operating state of the equipment. Through continuous online monitoring and data comparison, the long-term effectiveness and accuracy of the response surface proxy model are verified and monitored in real time and quantitatively. This step is a prerequisite for achieving adaptive optimization throughout the system's entire lifecycle. Step S7 may include sub-steps S701, S702, and S703.

[0094] In sub-step S701, real-time acquisition of operational data is performed. After the diversion device is installed and put into operation according to the scheme in step S6, a stable data link is established between the system of this invention and the power plant's distributed control system (DCS) or related real-time or historical database by deploying a data interface module. This data interface module is configured to periodically (e.g., every minute) or in real-time read actual operating condition parameters corresponding to the key operating parameters defined in step S1 from the DCS, forming a real-time operating condition parameter vector. Simultaneously, the module acquires actual flow distribution data from flow monitoring devices (such as Pitot tube arrays, ultrasonic flow meters, etc.) installed in each inlet channel of the electrostatic precipitator, and calculates the real-time flow deviation coefficient as the true value according to the formula in step S4. .

[0095] In sub-step S702, online model prediction is performed. The system uses the real-time operating condition parameter vector collected in sub-step S701. And the design variable vector of the diversion device that has been determined and solidified during the engineering implementation phase. As input, the response surface proxy model that has been trained and deployed in step S4 is substituted into it. Based on these inputs, the model instantly calculates the theoretically expected flow deviation coefficient under the current actual operating conditions; this value is recorded as the model prediction value. The calculation process can be expressed as follows: ; In the formula, The flow deviation coefficient predicted by the model is the theoretically calculated value output by the response surface proxy model based on real-time operating conditions and implemented design schemes; This is a trained response surface surrogate model function used to predict the flow deviation coefficient, which establishes a nonlinear mapping relationship between operating condition parameters and design variables and the flow deviation coefficient. This is a vector of actual operating condition parameters collected in real time from the power plant's distributed control system (DCS) via a data interface. Its components are the current values ​​of key operating parameters such as unit load and air preheater differential pressure. This is the design variable vector corresponding to the flow guiding device scheme that has been completed and installed in the flue. During equipment operation, this vector has a fixed value.

[0096] In sub-step S703, the prediction residuals are calculated and monitored. The system will then display the model prediction values. Compared with the true value obtained through actual measurements via sensor networks Continuous comparisons are performed to evaluate the online prediction accuracy of the model. The deviation between the two is quantified as the prediction residual. In a preferred embodiment, the predicted residuals are... The result is obtained by calculating the absolute difference between the two: ; In the formula, To predict residuals, it is used to quantify the accuracy of the model's predictions. Its value directly reflects the degree of agreement between the digital model and the physical entity in the current state. The true flow deviation coefficient is calculated after the actual flow distribution is measured by a sensor network installed in each inlet channel of the electrostatic precipitator. This is the flow deviation coefficient obtained by the model based on real-time operating conditions prediction.

[0097] This prediction residual As a key performance indicator, it is continuously recorded and monitored by the system. It directly reflects the degree of consistency between the digital model and physical reality. A consistently small residual value indicates that the model is currently accurate; while a consistently increasing residual value or one that exceeds the normal fluctuation range indicates that the physical characteristics of the equipment may have changed in ways not considered in the initial modeling, such as dust accumulation, wear, or blockage, thus providing a trigger for the adaptive correction mechanism in step S8.

[0098] Please see the appendix Figure 9 , Figure 9 This is a schematic diagram of a model adaptive calibration and dynamic decision support process according to an embodiment of the present invention.

[0099] Step S8 of the method of this invention is a key step in realizing intelligent operation throughout the entire lifecycle of the system. This step endows the system with self-learning and self-adaptive capabilities, enabling it to compensate for model inaccuracies caused by changes in physical conditions such as dust accumulation and wear, and continuously provide high-value, data-driven decision support for power plant operation. Step S8 may include sub-steps S801 and S802.

[0100] In sub-step S801, adaptive correction of the model is performed. The system integrates a residual monitoring and alarm module, which continuously tracks the predicted residuals calculated in step S7. To avoid misjudgments caused by instantaneous measurement noise or drastic fluctuations in operating conditions, the residual monitoring and alarm module performs statistical analysis on the residual values ​​within a preset time window (e.g., 24 hours). When the residual... The moving average or duration within this time window exceeds a preset threshold. When the system determines that the model has become significantly inaccurate, it automatically triggers an adaptive correction mechanism.

[0101] Once the correction mechanism is triggered, the system will call upon the set of real operational data points collected during the period when the residuals exceeded the limit, which have undergone data cleaning and verification. These new data points, reflecting the true physical characteristics of the current device, are used as new training samples and incorporated into the original sample dataset from step S4, forming an enhanced dataset. Subsequently, the system uses this enhanced dataset to train the Kriging surrogate model established in step S4. and Online retraining is performed. Retraining can be done through online incremental learning, which involves fine-tuning the parameters of the existing model; or through full retraining, which involves rebuilding the entire model based on the augmented dataset. After retraining, the system generates a calibrated response surface surrogate model that more accurately reflects the current device status, denoted as... and .

[0102] In sub-step S802, dynamic decision support is provided. Based on the corrected, high-fidelity state-of-the-art response surface surrogate model from sub-step S801, the system can provide two types of dynamic and quantitative decision support for the daily operation and long-term planning of the power plant.

[0103] One type of decision support is predictive early warning. The system can interface with a power plant's generation planning system to obtain future unit load curves. This is achieved by forecasting future operating conditions. Input to the corrected model The system can predict the evolution trend of the flue gas flow deviation coefficient over a future period (e.g., the next 4 hours). If the deviation is predicted to exceed environmental or performance requirements, the system can issue an early warning to operators, providing them with a time window to take preventative adjustment measures (e.g., adjusting the air preheater supply balance).

[0104] Another form of decision support is performance benchmarking. The system can benchmark against current real-time operating conditions. Using the corrected model, the current installed diversion device scheme can be calculated instantaneously. The system calculates various performance indicators (expected performance, variance, and economy). Simultaneously, it dynamically and highlightes this performance point on the original Pareto optimal frontier generated in step S5. This allows operators to intuitively see the relative performance position of the existing equipment among all theoretically optimal solutions under current operating conditions. This enables a quantitative assessment of the potential and direction of operational adjustments, providing a data-driven and scientific basis for future equipment upgrades or technological transformations.

[0105] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for analyzing the causes of deviations in flue gas flow rate at the inlet of an electrostatic precipitator and for making optimization decisions, characterized in that... Includes the following steps: S1. Establish a three-dimensional flow field calculation model of the inlet flue of the electrostatic precipitator and define a continuous operating condition parameter space. S2. Generate a parametric model of the flow guide device driven by a set of design variables; S3. Construct a response surface proxy model, which is used to predict the flow deviation coefficient and the total system pressure drop based on the operating condition parameter space and the design variables. S4. Based on the response surface surrogate model, solve a multi-objective robust optimization problem to determine the optimal solution set of the design variables, thereby obtaining the Pareto optimal frontier; S5. Based on the Pareto optimal frontier, select the final flow guiding device design scheme; S6. After the diversion device is put into operation, the actual operating condition parameters and the measured flow deviation coefficient are collected in real time, and the prediction residual between the measured flow deviation coefficient and the predicted value of the response surface surrogate model is calculated. S7. When the predicted residual continues to exceed the preset threshold, the response surface proxy model is updated online using the collected data including the actual operating condition parameters and the measured flow deviation coefficient.

2. The method for analyzing and optimizing the deviation of flue gas flow rate at the inlet of the electrostatic precipitator according to claim 1, characterized in that, The steps for generating the parameterized model of the flow guiding device include: In the three-dimensional flow field calculation model, a design domain is defined, and a topology optimization algorithm is used to generate the initial configuration of the flow guiding device. Based on the initial configuration, key geometric features are extracted and associated with the design variables to establish the parametric model.

3. The method for analyzing and optimizing the deviation of flue gas flow rate at the inlet of the electrostatic precipitator according to claim 1, characterized in that, The response surface proxy model is the Kriging model; The steps for constructing the response surface proxy model include: using the optimal Latin hypercube sampling method to generate sample point combinations in the joint parameter space formed by the operating condition parameter space and the design variable space composed of the design variables; using computational fluid dynamics to batch calculate and obtain the flow deviation coefficient and total system pressure drop corresponding to each sample point combination, and using the calculation results to train and generate the Kriging model.

4. The method for analyzing and optimizing the deviation of flue gas flow rate at the inlet of the electrostatic precipitator according to claim 1, characterized in that, The optimization objectives of the multi-objective robust optimization problem include: Minimize the mathematical expectation of the flow deviation coefficient within the operating condition parameter space; Minimize the mathematical variance of the flow deviation coefficient within the operating condition parameter space; Minimize the mathematical expectation of the total system pressure drop within the operating condition parameter space.

5. The method for analyzing and optimizing the deviation of flue gas flow rate at the inlet of the electrostatic precipitator according to claim 4, characterized in that, The steps for solving a multi-objective robust optimization problem include: The non-dominated sorting genetic algorithm II is used to solve the multi-objective robust optimization problem to obtain the Pareto optimal front.

6. The method for analyzing and optimizing the deviation of flue gas flow rate at the inlet of the electrostatic precipitator according to claim 1, characterized in that, The steps for selecting the final flow guiding device design include: Assign weight coefficients to each optimization objective of the multi-objective robust optimization problem to construct a unified utility function; The utility function is used to comprehensively score all solutions on the Pareto optimal frontier, and the solution with the best utility value is selected as the final flow guiding device design scheme.

7. The method for analyzing and optimizing the deviation of flue gas flow rate at the inlet of the electrostatic precipitator according to claim 1, characterized in that, The flow deviation coefficient is calculated by calculating the standard deviation of the flue gas flow rate of all inlet channels of the electrostatic precipitator and dividing the standard deviation by the average flow rate of the flue gas flow rate of all inlet channels.

8. The method for analyzing and optimizing the deviation of flue gas flow rate at the inlet of the electrostatic precipitator according to claim 1, characterized in that, The online update steps include: The data points containing the actual operating condition parameters and the measured flow deviation coefficient are used as new training samples and incorporated into the original sample dataset to form an enhanced dataset. The response surface proxy model is retrained using the enhanced dataset.

9. The method for analyzing and optimizing the deviation of flue gas flow rate at the inlet of the electrostatic precipitator according to claim 1, characterized in that, After the response surface proxy model is updated online, step S8, model adaptive correction, is also included. The model adaptive correction includes the following steps: Dynamic decision support is provided based on the updated response surface proxy model, which includes predictive early warning based on future forecast operating conditions or performance benchmarking based on current real-time operating conditions.

10. The method for analyzing and optimizing the deviation of flue gas flow rate at the inlet of the electrostatic precipitator according to claim 2, characterized in that, The optimization objective of the topology optimization algorithm is a weighted combination of flow distribution uniformity and flow pressure drop.

Images