Intelligent optimization system and method for laser cladding process parameters of water turbine

Abstract

The invention relates to the technical field of laser surface modification, and discloses a water turbine laser cladding process parameter intelligent optimization system and method, and the system comprises a data preparation and preprocessing module which is used for obtaining and preprocessing water turbine laser cladding process parameters and corresponding cladding layer quality index data; a physical information guided multi-task prediction network construction and training module; a causal inference analysis module; and a causal perception multi-objective optimization algorithm module. By constructing a multi-task prediction network guided by physical information, the internal physical law of the laser cladding process is fused into a deep learning model, and the accuracy and reliability of predicting a plurality of key quality indexes of the laser cladding layer of the water turbine are remarkably improved. Compared with a traditional pure data driving model, the method can generate a prediction result more conforming to an actual cladding mechanism by means of guidance of physical constraints even under the condition of limited experimental data, and lays a solid data foundation for subsequent process optimization.

Description

Technical Field

[0001] The present invention relates to the technical field of laser surface modification, and particularly to an intelligent optimization system and method for laser cladding process parameters of a hydraulic turbine. Background Technique

[0002] As the core equipment for hydropower generation, key components of hydraulic turbines such as blades, guide vanes, and main shafts are subject to long-term erosion by high-speed water flow, wear by sediment, and cavitation damage during operation, resulting in deterioration of their surface properties and seriously affecting the safe and stable operation and service life of the hydraulic turbine unit. As an advanced surface modification and repair technology, laser cladding technology can significantly improve the service performance and life of key components of hydraulic turbines by cladding an alloy coating with specific properties (such as high hardness, wear resistance, corrosion resistance, and cavitation resistance) on the substrate surface. Therefore, it has received increasing attention and application in the hydropower industry. The laser cladding process is a complex dynamic process involving the coupling of multiple physical fields (such as thermal field, flow field, phase change, etc.). The final quality of the cladding layer, including macroscopic morphology, microstructure, mechanical properties (such as hardness, bonding strength), and defect control (such as cracks, pores, lack of fusion), is comprehensively affected by numerous process parameters (such as laser power, scanning speed, powder feeding rate, spot diameter, preheating temperature, overlapping rate, etc.). There are often complex non-linear interaction effects between these process parameters, making it a key challenge in the application of laser cladding technology to accurately regulate them to obtain a cladding layer with ideal comprehensive properties.

[0003] In the prior art, the optimization of laser cladding process parameters mainly relies on empirical trial-and-error methods, orthogonal experimental design, and traditional statistical methods such as response surface methodology (RSM). Empirical trial-and-error methods are not only time-consuming and laborious, but also costly, and it is difficult to ensure obtaining a globally optimal combination of process parameters, and they are highly dependent on the experience of operators. Although statistical methods such as orthogonal experiments can reduce the number of experiments to a certain extent and analyze the main effects of parameters, they are usually based on simplified linear or low-order polynomial models, which are difficult to accurately capture the complex non-linear relationships in the laser cladding process, and their ability to explore high-dimensional parameter spaces is limited.

[0004] In addition, laser cladding of hydraulic turbines usually needs to meet multiple quality index requirements simultaneously. For example, it is required that the cladding layer has high hardness, good toughness, low dilution rate, and no cracks. There are often coupled or even conflicting relationships among these goals, constituting a typical multi-objective optimization problem. When dealing with such multi-objective problems, existing optimization methods either simplify them into single-objective problems or use optimization algorithms that are difficult to fully explore the entire Pareto front, resulting in the obtained optimization solutions may not be globally optimal or cannot provide a sufficient variety of choices to meet specific requirements under different working conditions. At the same time, the existing optimization process also rarely considers the causal logic behind parameter adjustment, making the selection of the optimization path and the interpretation of the final solution lack depth. Summary of the Invention

[0005] Aiming at the deficiencies of the existing technology, the present invention provides an intelligent optimization system and method for the process parameters of laser cladding of hydraulic turbines, which solves the problems of the existing optimization methods for the process parameters of laser cladding of hydraulic turbines, such as limited experimental data, difficulty in fully utilizing physical mechanism knowledge, lack of understanding of the deep causal relationship between parameters, and insufficient efficiency and robustness in multi-objective collaborative optimization.

[0006] To achieve the above objectives, the present invention is realized through the following technical solutions: An intelligent optimization system for the process parameters of laser cladding of hydraulic turbines, comprising:

[0007] A data preparation and preprocessing module, configured to obtain and preprocess the process parameters of laser cladding of hydraulic turbines and the corresponding quality index data of the cladding layer;

[0008] A physical information-guided multi-task prediction network construction and training module, configured to construct and train a multi-task neural network model based on the preprocessed process parameters and a preset physical control equation of laser cladding to predict the quality index of the cladding layer;

[0009] A causal inference analysis module, configured to analyze the causal effect of the process parameters on the quality index of the cladding layer based on the prediction results output by the physical information-guided multi-task prediction network construction and training module or the preprocessed process parameters;

[0010] A causal perception-based multi-objective optimization algorithm module, configured to use the multi-task neural network model trained by the physical information-guided multi-task prediction network construction and training module as a surrogate model, and combine the causal effect analysis results output by the causal inference analysis module to perform multi-objective optimization to obtain optimized process parameters.

[0011] Preferably, when training the multi-task neural network model, the physical information-guided multi-task prediction network construction and training module adopts a loss function including a data fitting loss term and a physical residual loss term, and the physical residual loss term is determined according to the deviation between the prediction result of the multi-task neural network model and the preset physical control equation of laser cladding.

[0012] Preferably, the multi-task neural network model includes a shared feature extraction layer and task-specific output layers for different cladding layer quality indicators, and the shared feature extraction layer is used to learn the common features among different cladding layer quality indicator prediction tasks.

[0013] Preferably, the data fitting loss term is used to measure the difference between the cladding layer quality indicators predicted by the multi-task neural network model and the actually observed cladding layer quality indicators obtained through the data preparation and preprocessing module.

[0014] Preferably, the causal inference analysis module is further configured to use the multi-task neural network model trained by the physical information-guided multi-task prediction network construction and training module to generate virtual sample data in the process parameter space and perform the causal effect analysis based on the virtual sample data.

[0015] Preferably, the causal effect analysis result output by the causal inference analysis module includes the average causal effect estimation value of each process parameter on each cladding layer quality indicator and the identified key process parameters that have a significant causal impact on the cladding layer quality indicators.

[0016] Preferably, the causality-aware multi-objective optimization algorithm module adopts a multi-objective evolutionary algorithm and uses the multiple cladding layer quality indicators predicted by the multi-task neural network model as the fitness function of the multi-objective evolutionary algorithm.

[0017] Preferably, the causality-aware multi-objective optimization algorithm module uses the causal effect analysis result to guide the search process of the multi-objective evolutionary algorithm, and the guidance includes at least one of the following: key parameter guidance for population initialization based on causal effects, adaptive adjustment of evolutionary operators according to the causal sensitivity of parameters, or interpretation of the trade-off relationship in the Pareto optimal solution set based on causal paths.

[0018] Preferably, the system further includes a system integration and human-computer interaction module for integrating the data preparation and preprocessing module, the physical information-guided multi-task prediction network construction and training module, the causal inference analysis module, and the causality-aware multi-objective optimization algorithm module, and providing a user interface to allow users to configure optimization tasks, monitor the optimization process, and visually display the optimization results including the Pareto optimal solution set and the corresponding causal explanations.

[0019] An intelligent optimization method for the process parameters of laser cladding of a water turbine, comprising the following steps:

[0020] Step 1: Obtain and preprocess the process parameters of laser cladding of the water turbine and the corresponding quality index data of the cladding layer;

[0021] Step 2: Based on the preprocessed process parameters and a preset physical control equation for laser cladding, construct and train a physics-informed multi-task neural network model to predict the quality index of the cladding layer;

[0022] Step 3: Based on the output prediction result of the physics-informed multi-task neural network model or the preprocessed data, analyze the causal effect of the process parameters on the quality index of the cladding layer;

[0023] Step 4: Use the physics-informed multi-task neural network model as a surrogate model, and combine the causal effect analysis result to perform multi-objective optimization to obtain optimized process parameters.

[0024] The present invention provides an intelligent optimization system and method for the process parameters of laser cladding of a water turbine. It has the following beneficial effects:

[0025] 1. By constructing a physics-informed multi-task prediction network, the present invention integrates the internal physical laws of the laser cladding process into the deep learning model, significantly improving the accuracy and reliability of predicting multiple key quality indexes of the laser cladding layer of the water turbine. Compared with traditional pure data-driven models, even in the case of limited experimental data, the present invention can generate prediction results that are more in line with the actual cladding mechanism under the guidance of physical constraints, laying a solid data foundation for subsequent process optimization.

[0026] 2. The present invention introduces a causal inference analysis module, which can identify the causal relationships with real driving effects from the complex relationships between process parameters and the quality indexes of the cladding layer, rather than just the surface statistical correlations. This enables technicians to deeply understand the real influence mechanism of each process parameter on the final performance of the cladding layer during the laser cladding process of the water turbine, thereby accurately locking the core process parameters that are most critical for improving specific quality indexes and avoiding blind adjustment and trial and error.

[0027] 3. The causal perception multi-objective optimization algorithm proposed by the present invention cleverly combines the parameter influence mechanism revealed by causal analysis with the multi-objective evolutionary algorithm, and uses the trained efficient physics-informed prediction network as a surrogate model. This combination makes the search process of the optimization algorithm more targeted, and can converge more quickly to the preferred process parameter combination region that can simultaneously meet multiple or even conflicting quality requirements of the cladding layer, significantly improving the efficiency and effect of optimizing the process parameters of laser cladding of the water turbine.

[0028] 4. By embedding physical laws and considering causal relationships, the present invention enhances the robustness and generalization ability of the optimized process parameter scheme. Since the optimization decision not only depends on the observed data, but more on the understanding of the internal physical mechanism of the laser cladding process and the grasp of the causal effects between parameters, the obtained process scheme can still maintain good performance when facing the minor fluctuations or incompletely covered working conditions that may exist in actual production, reducing the risk from laboratory to actual application. Brief Description of the Drawings

[0029] Figure 1 It is the overall system architecture and main flow chart of the present invention;

[0030] Figure 2 It is a schematic diagram of the training of the physics-informed prediction model of the present invention;

[0031] Figure 3 It is a schematic diagram of the causality-aware guided multi-objective optimization of the present invention. Detailed Embodiments

[0032] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0033] The following will further describe the present invention in detail in conjunction with the attached Figures 1-3 drawings.

[0034] The present invention provides an intelligent optimization system for the process parameters of laser cladding of a water turbine. By constructing a physics-informed multi-task prediction network and integrating the internal physical laws of the laser cladding process into the deep learning model, the accuracy and reliability of predicting multiple key quality indicators of the laser cladding layer of the water turbine are significantly improved. Compared with the traditional pure data-driven model, the present invention can generate more prediction results that conform to the actual cladding mechanism by virtue of the guidance of physical constraints even when the experimental data is limited, laying a solid data foundation for subsequent process optimization.

[0035] The intelligent optimization system for the process parameters of laser cladding of a water turbine may include:

[0036] A data preparation and preprocessing module, configured to obtain and preprocess the process parameters of laser cladding of a water turbine and the corresponding data of the quality indicators of the cladding layer;

[0037] The physical information-guided multi-task prediction network construction and training module is configured to construct and train a multi-task neural network model based on the preprocessed process parameters and the preset physical control equations of laser cladding to predict the quality indicators of the cladding layer;

[0038] The causal inference analysis module is configured to analyze the causal effect of the process parameters on the quality indicators of the cladding layer based on the prediction results output by the physical information-guided multi-task prediction network construction and training module or the preprocessed data;

[0039] The causality-aware multi-objective optimization algorithm module is configured to use the multi-task neural network model trained by the physical information-guided multi-task prediction network construction and training module as a surrogate model, and combine the causal effect analysis results output by the causal inference analysis module to perform multi-objective optimization to obtain optimized process parameters.

[0040] In this embodiment, the data preparation and preprocessing module, as the initial link of a hydroturbine laser cladding process parameter intelligent optimization system and method, its core purpose is to systematically acquire, organize, and standardize various types of data related to the hydroturbine laser cladding process, laying a solid and reliable data foundation for the subsequent construction of a high-precision physical information-guided multi-task prediction network model. The effective execution of this module plays a crucial role in ensuring the accuracy and robustness of the subsequent analysis and optimization results.

[0041] Specifically, the operation of this data preparation and preprocessing module includes the following aspects:

[0042] Data collection stage:

[0043] This stage is dedicated to comprehensively collecting various types of information that affect the laser cladding process and the final quality of the cladding layer.

[0044] Obtaining process parameters:

[0045] The system first records and collects in detail all the process parameters set and adopted during the hydroturbine laser cladding experiment or production process. These parameters are the input variables that directly control the cladding process.

[0046] These process parameters are organized into a process parameter vector, denoted as , where represents the total dimension of the process parameters. For example, typical process parameters may include, but are not limited to: laser power (whose unit is usually watt, W), which directly determines the energy density input to the cladding area; scanning speed (whose unit is usually millimeter per second, mm / s), which affects the interaction time between the laser beam and the material; powder feeding rate (Its unit is usually grams per minute, g / min), which determines the supply rate of the cladding material; the spot diameter (Its unit is usually millimeters, mm), which affects the distribution area of the laser energy; the preheating temperature (Its unit is usually degrees Celsius, °C), which can improve the wettability of the material and reduce the thermal stress; and the overlapping rate (Usually expressed as a percentage, %), which affects the geometric morphology and metallurgical bonding during multi-pass cladding. Therefore, the process parameter vector can be specifically expressed as . The purpose of collecting these parameters is to establish the mapping relationship between them and the quality indexes of the cladding layer.

[0047] Obtaining the quality indexes of the cladding layer:

[0048] Corresponding to each specific set of process parameters above, the system needs to accurately measure and record the key quality indexes of the cladding layer formed after the cladding experiment. These quality indexes are the output variables for evaluating the cladding effect and also the goals for the subsequent optimization process.

[0049] These quality indexes are organized into a quality index vector, denoted as , where represents the total dimension of the quality indexes. For example, typical quality indexes of the cladding layer may include but are not limited to: the macro-hardness of the cladding layer (Its unit is usually Vickers hardness, HV), which reflects the wear resistance of the cladding layer; the dilution rate (Usually expressed as a percentage, %), which characterizes the dilution degree of the substrate to the composition of the cladding layer and affects the performance of the cladding layer; the cladding depth (Its unit is usually millimeters, mm), which is related to the bonding strength between the cladding layer and the substrate; the cladding width (Its unit is usually millimeters, mm), which affects the cladding efficiency and morphology; the residual stress in the key area (Its unit is usually megapascals, MPa), and excessive residual stress may lead to cracking; the crack sensitivity index , for example, evaluated by quantifying the number or total length of cracks per unit area or length; and the bonding strength between the cladding layer and the substrate (Its unit is usually megapascals, MPa). Therefore, the quality index vector can be specifically expressed as:

[0050] ;

[0051] Through systematic experimental design (such as using orthogonal experimental design, uniform experimental design or response surface method, etc.) or accumulating from historical production data, this module aims to obtain sets of complete experimental data pairs 。These paired data are the basis for training subsequent prediction models.

[0052] Collection of physical properties of materials:

[0053] To support the construction of subsequent physics-informed neural network models, this module also needs to collect detailed physical property parameters of the substrate materials (such as martensitic stainless steel, austenitic stainless steel, etc. commonly used in turbine components) and the selected cladding powders (such as iron-based alloy powders, nickel-based alloy powders, or cobalt-based wear-resistant and corrosion-resistant alloy powders) involved in the laser cladding process.

[0054] These physical property parameters are crucial for accurately describing the thermophysical phenomena during the cladding process. For example, the density of the material , which may vary with temperature , is denoted as ; the specific heat capacity of the material , which may also vary with temperature , is denoted as The thermal conductivity of the material , which may also vary with temperature , is denoted as ; the solidus temperature of the material and the liquidus temperature The latent heat of phase change during melting and solidification of the material ; and the absorptivity of the material surface to laser beams of a specific wavelength (such as the commonly used wavelength of lasers) The purpose of collecting these parameters is to provide the necessary coefficients and material property data for the physical control equations (such as the heat conduction equation) embedded in the subsequent models.

[0055] Data preprocessing stage:

[0056] After completing the preliminary data collection, in order to improve the efficiency, stability of subsequent model training and the prediction performance of the final model, a series of preprocessing operations need to be performed on the collected raw data.

[0057] Data cleaning:

[0058] Original experimental data or production data often may have incomplete or inaccurate situations, and data cleaning aims to address these issues.

[0059] For missing values in the data, this module can adopt various strategies for filling. For example, for numerical data, the mean or median of the feature column can be used for filling; for parameters related to time series, the previous valid observation or the next valid observation can be considered for filling, or more complex model-based imputation methods (such as K-nearest neighbor imputation, regression imputation, etc.) can be adopted. The choice of filling method depends on the characteristics of the data and the mechanism of missing. The purpose of this step is to ensure the integrity of the dataset and avoid sample loss or model bias caused by data missing.

[0060] For outliers or extreme points in the data, that is, those observations that significantly deviate from the main distribution of the data, this module can adopt statistical methods (such as the 3-sigma principle or the interquartile range method based on box plots) for identification. Once the outliers are identified, the sample can be selected for removal according to the possible reasons for its generation, or a method similar to that for handling missing values can be adopted for correction. The purpose of this step is to reduce the possible negative impact of abnormal data on subsequent model training and improve the robustness of the model.

[0061] Data normalization or standardization:

[0062] Since the different process parameters and quality indicators collected often have different physical units and numerical magnitudes (for example, the laser power may be in the range of several hundred to several kilowatts, while the scanning speed may be in the range of several millimeters per second to dozens of millimeters per second), if this difference is directly input into models such as neural networks, it may cause some parameters to dominate in model training, or make the optimization algorithm converge slowly or even difficult to converge. Therefore, data normalization or standardization processing is required.

[0063] In this embodiment, the physical information-guided multi-task prediction network construction and training module (hereinafter referred to as the PINN-MTL module) is the core component of an intelligent optimization system and method for the water turbine laser cladding process parameters of the present invention. This module aims to construct and train a deep neural network model, which can not only learn the complex non-linear mapping relationship between process parameters and multiple cladding layer quality indicators from the limited experimental data provided by the "data preparation and preprocessing module", but more importantly, it incorporates the physical laws of the laser cladding process as prior knowledge into the model learning process. This guidance of physical information helps to improve the prediction accuracy and generalization ability of the model in the data-sparse region and ensure the rationality of its prediction results at the physical level.

[0064] Specifically, the implementation of the PINN-MTL module involves the following key aspects:

[0065] Network structure design:

[0066] To simultaneously predict multiple cladding layer quality indicators and effectively utilize the potential correlations between them, this module adopts a neural network architecture of multi-task learning (MTL).

[0067] Input layer:

[0068] The input layer of this network receives the preprocessed process parameter vector output from the "Data Preparation and Preprocessing Module". . This vector contains key process parameters that affect the cladding process, such as laser power, scanning speed, powder feeding rate, etc.

[0069] Shared feature extraction layer (Shared Layers): Immediately following the input layer, a series of fully connected hidden layers are set up, which constitute the shared feature extraction part of the network. These shared layers are composed of several neurons and use non-linear activation functions. Preferred activation functions may include Rectified Linear Unit (ReLU), Hyperbolic Tangent (Tanh), or adaptive activation functions such as Gaussian Error Linear Unit (GELU) or SiLU (Sigmoid Linear Unit), etc., to enhance the non-linear expression ability of the network.

[0070] The parameters of the shared layer, denoted as , are shared among all prediction tasks. Its design purpose is to learn and extract deeper, abstract common feature representations from the input process parameters that are beneficial to the prediction of all or most cladding layer quality indicators. Through this parameter sharing mechanism, different tasks can learn from and transfer information to each other. Especially when the training samples of some tasks are few, the knowledge of other related tasks can be used to improve the learning effect, thereby improving the data utilization efficiency and the overall generalization performance of the model.

[0071] Task-specific output layer (Task-specific Layers): Above the output of the shared feature extraction layer, for different cladding layer quality indicators to be predicted (such as hardness, dilution rate, melt depth, etc.), independent output sub-networks are constructed respectively, which are also called task-specific layers. Each task-specific sub-network usually also contains one or more fully connected layers, and its parameters are denoted as (for the th quality indicator )。These sub-networks receive the features extracted by the shared layer as input and further learn the personalized mapping relationships for specific quality metrics. The last layer of each task-specific sub-network usually contains a neuron (for scalar quality metric prediction), and the choice of activation function depends on the value range and characteristics of the corresponding quality metric. For example, for metrics with an unbounded value range (such as hardness), a linear activation function can be used; for metrics with values in a specific interval (such as dilution rate, usually between 0 and 100%), after normalization, a Sigmoid activation function (output range 0 to 1) or Tanh activation function (output range -1 to 1) can be used in combination with subsequent scaling transformations. Therefore, the predicted value of the network for the th quality metric is denoted as , where represents all the trainable weight and bias parameters in the entire PINN-MTL network. The overall predicted output of the network is a vector containing all predicted quality metrics: .

[0072] Physical information embedding mechanism:

[0073] This mechanism is the key innovation of the PINN-MTL module compared to traditional pure data-driven models. It explicitly encodes domain knowledge (i.e., the physical principles of the laser cladding process) into the training objective of the neural network.

[0074] Select physical control equations: First, it is necessary to select physical control equations closely related to the laser cladding process and the formation mechanism of the cladding layer quality metrics of interest. A core example is the heat conduction equation in the laser cladding process, which describes the temperature field inside the material (where are spatial coordinates, is time) as it changes over time and space: ;

[0075] where, , , are the material density, specific heat capacity, and thermal conductivity that vary with temperature obtained from the "Data Preparation and Preprocessing Module" respectively. represents the laser heat source term, and its specific form depends on the input process parameters (such as laser power , scanning speed , spot diameter ) and the laser energy distribution model adopted (for example, Gaussian surface heat source model, Gaussian volume heat source model, double ellipsoid heat source model, etc.). Represents the latent heat of phase change term absorbed or released during the melting and solidification of the material. This physical governing equation (partial differential equation, PDE) is transformed into a physical residual function in the form of. For example, for the above heat conduction equation, its physical residual can be defined as:

[0076] ;

[0077] where is the temperature field predicted or indirectly derived by the PINN-MTL network (or a part of it). If the network does not directly predict the complete temperature field but predicts mass metrics related to temperature (such as the melt depth, which is defined as the maximum depth reaching the melting point temperature), then a mathematical relationship between these mass metrics and the temperature field needs to be established, and the automatic differentiation (AD) function of the neural network is used to calculate with respect to the spatial coordinates and time for the necessary partial derivatives (such as the gradient and the time derivative ), and substitute these derivatives into the physical residual expression. Automatic differentiation is a core function of modern deep learning frameworks (such as TensorFlow, PyTorch), which can accurately calculate the derivatives of complex functions (such as neural networks) without manual derivation or symbolic differentiation. In addition to the heat conduction equation, other related physical laws, such as melt pool hydrodynamics (e.g., a simplified form of the Navier-Stokes equation, considering the Marangoni effect, etc.), phase change kinetics during solidification (e.g., a simplified model describing grain growth or the formation of a specific phase), if their mathematical forms are known or can be reasonably approximated and are related to the mass metrics of interest, can also be similarly transformed into corresponding physical residual terms .

[0078] Construction of the multi-task joint loss function:

[0079] To simultaneously optimize the data fitting degree and physical consistency, the PINN-MTL module adopts a carefully designed joint loss function to guide the learning of the network parameters . This loss function is mainly composed of the following two parts:

[0080] Data fitting loss : This term is used to measure the multiple cladding layer quality metrics predicted by the neural network and the actual observed experimental data provided by the "Data Preparation and Preprocessing Module" Consistency among them. Its mathematical expression is usually the weighted sum of the losses of each task:

[0081] ;

[0082] where is the single-point loss function of the th prediction task (corresponding to the th quality indicator). Preferably, for the prediction of quality indicators with a regression nature, the mean squared error (Mean Squared Error, MSE), i.e., , or the mean absolute error (Mean Absolute Error, MAE) can be used. is the weight coefficient of the data loss term of the th task. These weights can be manually set according to the importance of different quality indicators in actual applications, or more advanced dynamic weighting strategies (e.g., weighting methods based on task uncertainty, or gradient normalization methods such as GradNorm) can be used to automatically adjust during the training process to balance the learning progress and contributions of different tasks.

[0083] Physical residual loss : This term is used to penalize the deviation of the prediction result of the neural network from the preset physical control equation, thereby guiding the network to learn physically meaningful solutions. To calculate this loss, a set of collocation points need to be selected within the domain where the physical equation is defined. These collocation points are usually sampled within the process parameter space and the spatio-temporal domain where physical phenomena occur, such as using uniform grid sampling, random sampling, or residual-based adaptive sampling strategies. is the total number of collocation points, which is usually much larger than the number of experimental data points to ensure that the physical constraints are satisfied throughout the domain of interest. The physical residual loss is usually defined as the mean of the norms (e.g., L2 norm) of the physical residuals calculated at these collocation points:

[0084] ;

[0085] where is the number of independent physical constraints introduced (i.e., the physical residual term ). is the weight coefficient of the th physical constraint term, which is used to balance the importance or numerical scale of different physical laws. (or other related physical quantities) is the output of the network at the th collocation point, from the input (and possibly The explicit or implicit predictions generated, the symbol represents the square of the L2 norm and is used to quantify the magnitude of the physical residual vector.

[0086] Total loss function:

[0087] The final total loss function is a weighted sum of the data fitting loss and the physical residual loss: ;

[0088] where is a crucial balancing hyperparameter used to regulate the contribution of the physical constraint term relative to the data fitting term in the total loss. The value of has a significant impact on the training effect of the model, and its selection usually requires cross-validation, empirical adjustment, or the adoption of an adaptive adjustment strategy (e.g., gradually increasing the value of

[0089] during the training process, i.e., the idea of curriculum learning).

[0090] Through the above construction and training process, this PINN-MTL module can finally generate a multi-output prediction model that can not only accurately fit the existing experimental data but also comply with relevant physical laws. This model can quickly predict the corresponding multiple clad layer quality indicators for any given combination of process parameters, providing an efficient and reliable surrogate model for subsequent causal inference analysis and multi-objective optimization. The incorporation of this physical information enables the model to make more reasonable extrapolations and interpolations even in the case of insufficient experimental data, enhancing the robustness and interpretability of the model.

[0091] Specifically, the operation of this causal inference analysis module involves the following core aspects:

[0092] Construction of the data basis for causal analysis:

[0093] To conduct robust and effective causal inference, sufficient and representative data are required. This module can construct a dataset for causal analysis using one or both of the following methods:

[0094] Generating virtual sample data using the physics-informed multi-task prediction network (PINN-MTL): Considering that in actual industrial scenarios, it is often costly and time-consuming to obtain a large amount of real experimental data covering all regions of the process parameter space. Therefore, a preferred approach is to utilize the PINN-MTL model trained in the aforementioned "Construction and Training Module of Physics-Informed Multi-Task Prediction Network", which has good prediction accuracy and physical consistency. . This PINN-MTL model can be regarded as a high-quality digital twin or surrogate model. By systematically sampling within a predefined and reasonable process parameter space (for example, Latin Hypercube Sampling (LHS) can be used to ensure uniform distribution of samples in each dimension, or denser uniform grid sampling can be adopted), the PINN-MTL model can be driven to generate a large number of virtual (or synthetic) sample data pairs , where ;

[0095] Since the PINN-MTL model has incorporated the physical constraints of the laser cladding process during training, the virtual sample data it generates can better reflect the potential data generation mechanism and the true response of the physical process compared to statistical interpolation or extrapolation based solely on sparse observational data. This high-quality virtual dataset provides a richer and more reliable data basis for subsequent causal structure learning and causal effect quantification, especially helping to overcome the problem of insufficient real experimental data.

[0096] Utilizing the preprocessed actual observational data:

[0097] In another case, if the "Data Preparation and Preprocessing Module" can already provide a sufficient quantity, high quality, and good coverage of actual observational experimental data , then these real data that have been cleaned and preprocessed can also be directly used as the input for causal inference analysis.

[0098] Causal structure learning (an optional but recommended step):

[0099] In many actual application scenarios, the complete causal relationship network between process parameters and quality indicators is not fully known a priori. Therefore, this module can include a sub-step of causal structure learning (also known as causal discovery), which aims to learn the causal dependence relationships between variables from the data and usually represents them as a Directed Acyclic Graph (DAG).

[0100] Selection and Application of Causal Discovery Algorithms: Based on the characteristics of the data (e.g., whether it is continuous, whether there are latent variables, the amount of data, etc.), appropriate causal discovery algorithms can be selected. For example, constraint-based methods such as the PC (Peter-Clark) algorithm or its improved versions can be adopted. These algorithms gradually determine whether there is an edge between variables and the direction of the edge through a series of conditional independence tests. Or, scoring-based methods such as the GES (Greedy Equivalence Search) algorithm can be used. This method searches for the DAG structure that can best fit the data in the space of equivalent classes. For scenarios assuming linear non-Gaussian relationships, LiNGAM (Linear Non-Gaussian Acyclic Model) and its variants (such as DirectLiNGAM) can provide effective causal ordering and structure identification. If there are suspected unobserved confounding factors (i.e., unmeasured variables that simultaneously affect a certain process parameter and a certain quality indicator), algorithms such as FCI (Fast Causal Inference) can be considered. This algorithm can identify causal relationships that may involve latent variables. The learned causal graph can not only help visualize the direct and indirect influence paths between parameters and indicators, but more importantly, it provides key structural information for subsequent accurate causal effect estimation, such as identifying the set of confounding variables that need to be adjusted.

[0101] Identification of Key Causal Parameters and Interpretation of Effects:

[0102] Based on the average causal effect estimates of each process parameter on each cladding layer quality indicator obtained from the above quantification, this module will conduct further analysis and interpretation.

[0103] Identification of Key Parameters:

[0104] By comparing the absolute values of the ACEs of different process parameters on the same quality indicator, the key process parameters that have the most significant causal impact on this quality indicator can be identified. At the same time, the sign (positive or negative) of the ACE also reveals the directional impact (promotion or inhibition) of the adjustment of this parameter.

[0105] Confidence intervals can be calculated for each ACE estimate or hypothesis tests can be conducted to evaluate its statistical significance, so as to more reliably judge whether the causal effect of a parameter truly exists rather than being random fluctuations.

[0106] Comprehensive Analysis of Causal Effects:

[0107] In addition to the effects of individual parameters on individual indicators, this module can also analyze more complex causal relationship patterns. For example:

[0108] Identify “pleiotropic” parameters that have positive (or negative) causal effects on multiple desired quality indicators.

[0109] Analyze the possible interactive causal effects between process parameters, that is, the size or direction of the causal effect of one parameter on a certain indicator may depend on the value level of another parameter.

[0110] Identifying parameters that have conflicting causal effects on different quality metrics (e.g., a parameter that significantly improves hardness but also significantly increases residual stress) is crucial for trade-off decisions in subsequent multi-objective optimization.

[0111] The causal effect analysis results obtained, including the average causal effect estimate of each process parameter on each cladding layer quality index, as well as the list of key process parameters identified to have significant causal influence on the cladding layer quality index and the relationship between them, will be input as important knowledge into the subsequent "causal-aware multi-objective optimization algorithm module".

[0112] Through the above steps, the causal inference analysis module can provide deep insights beyond traditional statistical models for the optimization of turbine laser cladding process parameters. It not only indicates which parameter adjustments are most likely to bring about the desired quality improvement, but also helps understand the causal mechanisms behind these improvements, making the optimization process more targeted, efficient and explainable.

[0113] In this embodiment, the causal-aware multi-objective optimization algorithm module is the core execution unit for realizing the final process parameter decision in the intelligent optimization system and method for process parameters of water turbine laser cladding of the present invention. This module aims to utilize the efficient proxy model trained by the aforementioned "physical information-guided multi-task prediction network construction and training module", and deeply integrate the causal relationship insight between process parameters and cladding layer quality indicators revealed by the "causal inference analysis module", and use advanced multi-objective optimization algorithms to search for the optimal process parameter combination that can simultaneously meet multiple, even conflicting cladding layer quality indicator requirements of water turbine laser cladding in a systematic and intelligent manner. The core is to improve the efficiency of the optimization process, the quality of the solution, and the interpretability of the final decision through the guidance of causal knowledge.

[0114] Specifically, the implementation of the causal-aware multi-objective optimization algorithm module involves the following key links:

[0115] Formal definition of multi-objective optimization problem:

[0116] Firstly, the optimization of process parameters for hydraulic turbine laser cladding is accurately formalized as a multi-objective optimization problem.

[0117] Establishment of the objective function:

[0118] Suppose there exist objectives that need to be optimized simultaneously. Each objective function ,for ,is a function of the process parameter vector . These objective functions directly or indirectly originate from the cladding layer quality index vector predicted by the "Physics-Informed Multi-Task Prediction Network Construction and Training Module". For example, the objectives may include: minimizing the dilution rate ,i.e., ; maximizing the hardness of the cladding layer ,i.e., (since optimization algorithms typically solve minimization problems); minimizing the residual stress ,i.e., controlling the melt depth near a specific target value ,i.e.:

[0119] o;

[0120] Therefore, the optimization objective can be expressed as minimizing a vector-valued function: ;

[0121] Definition of decision variables: The decision variables for optimization are the process parameter vector defined in the "Data Preparation and Preprocessing Module";

[0122] Setting of constraint conditions:

[0123] The optimization process needs to be carried out under the premise of meeting certain constraint conditions. These constraints mainly include: Physical boundary constraints of process parameters: Each process parameter has its allowable value range, i.e., ,where and are the lower and upper limits of the th parameter respectively. Performance constraints (optional): May also include specific requirements for certain predicted quality indicators. For example, requiring that the dilution rate does not exceed a certain maximum value, or the bonding strength must be higher than a certain minimum value. These can be expressed as inequality constraints or equality constraints .

[0124] Selection and basic framework of the multi-objective evolutionary algorithm (MOEA):

[0125] Due to the complexity, non-linearity of the relationship between laser cladding process parameters and cladding layer quality indicators, and the characteristic that there is usually no single optimal solution for multi-objective optimization problems, this embodiment preferably adopts a multi-objective optimization algorithm based on evolutionary computation (Multi-Objective Evolutionary Algorithm, MOEA). MOEAs have been widely applied because of their robustness and global search ability when dealing with such complex optimization problems.

[0126] Selection of representative MOEA:

[0127] MOEAs that can be selected include but are not limited to: NSGA-II, which is famous for its efficient non-dominated sorting and crowding degree calculation; NSGA-III, which is particularly suitable for dealing with high-dimensional objective space optimization problems with three or more objectives, and maintains population diversity by introducing reference points; MOEA / D, which decomposes the original multi-objective problem into a series of single-objective sub-problems and optimizes them collaboratively. The choice of which MOEA can be determined according to the number of objectives, characteristics of the specific problem, and computing resources.

[0128] Basic operation process of MOEA:

[0129] MOEA usually iteratively improves the candidate solution set by simulating the "survival of the fittest" principle in biological evolution. Its general process includes.

[0130] i. Population initialization: Randomly generate or generate an initial population containing several candidate process parameter combinations (individuals) according to prior knowledge.

[0131] ii. Fitness evaluation: For each individual in the population (i.e., a set of process parameters ), calculate the corresponding multiple objective function values .

[0132] iii. Selection: Select a part of the individuals to enter the next generation or participate in reproduction as parents according to the superiority of the individuals in the objective space (e.g., based on non-dominated sorting and crowding degree).

[0133] iv. Crossover (recombination): Imitating the biological reproduction process, select parent individuals and generate new offspring individuals by exchanging some of their "genes" (i.e., process parameter values).

[0134] v. Mutation: Make small random perturbations to some "genes" of the offspring individuals to introduce new genetic material, increase population diversity, and help jump out of local optima.

[0135] vi. Population Update / Environmental Selection: Combine the parent generation and the offspring generation, and select a specified number of excellent individuals from them to form a new generation of population. The above steps will be iteratively executed until a preset termination condition is met, such as reaching the maximum number of evolutionary generations, the solution set converges, or there is no significant improvement within a predetermined time. The final output of the MOEA is usually an approximate Pareto optimal solution set, where each solution represents a trade-off between different objectives.

[0136] Implementation of the Causal Knowledge-Guided MOEA Search Strategy:

[0137] The core innovation of this module lies in integrating the causal knowledge obtained from the "Causal Inference Analysis Module" into the operation mechanism of the MOEA, thereby achieving "causality-aware" optimization.

[0138] PINN-MTL as an Efficient Surrogate Model / Fitness Function Evaluator: In the fitness evaluation stage of the MOEA, for each candidate process parameter individual in the population , there is no longer a need to conduct time-consuming physical experiments or high-precision numerical simulations to obtain its corresponding clad layer quality index. Instead, the PINN-MTL model trained in the "Physics-Informed Multi-Task Prediction Network Construction and Training Module" is used to quickly and accurately predict these quality indices. Subsequently, based on these predicted quality indices the values of multiple objective functions of this individual are calculated . Since the prediction process of the PINN-MTL model is usually very fast (millisecond level or lower), as a surrogate model, it greatly accelerates the fitness evaluation process of the MOEA, enabling the algorithm to explore a wider parameter space within a limited time, thus having a greater chance of finding high-quality Pareto optimal solutions.

[0139] Key Parameter Guidance for Population Initialization Based on Causal Effects: The population initialization of traditional MOEAs usually generates individuals randomly within the feasible region of parameters. In this embodiment, the average causal effect (ACE) estimates of each process parameter on each objective quality index output by the "Causal Inference Analysis Module" can be used to guide the generation of the initial population. Specifically, for those key process parameters that are identified by causal analysis as having a significant positive causal effect on one or more desired objectives (e.g., hardness that is desired to be maximized, dilution rate that is desired to be minimized), when generating initial population individuals, their values can be consciously biased towards the "favorable" intervals of these parameters. For example, if increasing the laser power is found to significantly increase the hardness , then the individuals in the initial population Values can be sampled more from the higher value region within their allowable range. This biased initialization strategy aims to enable the MOEA to start the search from a more promising starting point, thereby potentially accelerating the convergence to the region of high-quality solutions.

[0140] Adaptively adjust the evolutionary operators according to the causal sensitivity of the parameters:

[0141] The design of the evolutionary operators (mainly crossover and mutation) is crucial for the search performance of the MOEA. This module can dynamically adjust the behavior of these operators according to the causal sensitivity of the parameters.

[0142] For example, in the mutation operation, for those process parameters that are confirmed by causal analysis to have a large causal impact on the objectives that have not been well optimized yet, the probability of mutating them can be moderately increased, or the mutation step size (perturbation amplitude) can be increased. This is done to encourage the algorithm to explore the neighborhoods of these key parameters more actively.

[0143] Conversely, for those parameters with weak causal effects or whose adjustment has little impact on the trade-off between multiple objectives, the mutation frequency or amplitude can be reduced.

[0144] Similarly, in the crossover operation, strategies can also be designed to make the parameter segments with strong causal effects more likely to be exchanged and recombined between parents.

[0145] This adaptive adjustment aims to allocate more computational resources and search efforts to the parameter dimensions that are more potential for improving the solution quality.

[0146] Explain the trade-off relationships in the Pareto optimal solution set based on the causal path: The result of multi-objective optimization is a Pareto optimal solution set, which shows the inherent trade-offs existing between different objectives. For example, a set of process parameters may result in a very high hardness of the clad layer, but also a relatively high dilution rate; another set of parameters may have a very low dilution rate, but at the expense of hardness. This module can utilize the causal structure diagram or the quantified causal effect path learned by the "causal inference analysis module" to help users understand and explain how these trade-off relationships are formed. For a specific solution on the Pareto front (i.e., a set of optimized process parameters and their corresponding predicted performance , it is possible to trace which process parameters mainly contributed to its performance on each objective through which direct or indirect causal paths. For example, it can be analyzed that parameter A significantly improved objective 1 through path P1, but at the same time had a negative impact on objective 2 through path P2, and the adjustment of parameter B compensated for this negative impact to a certain extent. This causal-based explanation not only enhances users' trust in the optimization results but also helps users make more informed final choices from the Pareto solution set based on their preferences for different causal mechanisms and considerations of different objective priorities.

[0147] Output of optimization results and subsequent suggestions:

[0148] After the optimization process iteration ends, this module will output the obtained Pareto optimal solution set. Each solution contains a set of recommended process parameter combinations and the corresponding cladding layer quality indicators predicted by the PINN-MTL model. These solutions can be presented to users in various visualization ways such as tables, parallel coordinate plots, and scatter plot matrices.

[0149] Preferably, the system will recommend that users select several representative or particularly interesting process parameter combinations from the Pareto solution set for actual laser cladding experiment verification to confirm the prediction accuracy of the model and the effectiveness of the optimization scheme in practical applications. The results of the experimental verification can also be fed back to the "Data Preparation and Preprocessing Module" for future model iteration updates and performance improvement.

[0150] Through the above-mentioned causal-aware multi-objective optimization strategy, this module can not only efficiently find a series of excellent and diverse solutions in the complex problem of optimizing the process parameters of hydroturbine laser cladding but also provide explanations based on causal mechanisms, thus significantly improving the intelligent level and practical value of the optimization process.

[0151] The device of an intelligent optimization method for hydroturbine laser cladding process parameters described below can be mutually referenced with the intelligent optimization system for hydroturbine laser cladding process parameters described above.

[0152] The present invention also provides an intelligent optimization system for hydroturbine laser cladding process parameters, including the following steps:

[0153] Step 1: Obtain and preprocess the process parameters of hydroturbine laser cladding and the corresponding cladding layer quality index data;

[0154] Step 2: Based on the preprocessed process parameters and the preset physical control equations of laser cladding, construct and train a physics-informed multi-task neural network model to predict the cladding layer quality index;

[0155] Step 3. Analyze the causal effect of the process parameters on the quality index of the cladding layer based on the output prediction result of the multi-task neural network model guided by the physical information or the preprocessed data;

[0156] Step 4. Use the multi-task neural network model guided by the physical information as a surrogate model, and combine the causal effect analysis result to perform multi-objective optimization to obtain the optimized process parameters.

[0157] The method of this embodiment can be used to implement the above method embodiment, and its principle and technical effect are similar, so details are not described herein again.

[0158] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principle and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. An intelligent optimization system for the process parameters of laser cladding of a water turbine, characterized in that, Comprising: A data preparation and preprocessing module, configured to obtain and preprocess the process parameters of the laser cladding of the water turbine and the corresponding data of the cladding layer quality indicators; A physical-information-guided multi-task prediction network construction and training module, configured to construct and train a multi-task neural network model based on the preprocessed process parameters and the preset physical control equations of the laser cladding to predict the cladding layer quality indicators; A causal inference analysis module, configured to analyze the causal effect of the process parameters on the cladding layer quality indicators based on the prediction results output by the physical-information-guided multi-task prediction network construction and training module or the preprocessed process parameters; A causality-aware multi-objective optimization algorithm module, configured to use the multi-task neural network model trained by the physical-information-guided multi-task prediction network construction and training module as a surrogate model, and combine the causal effect analysis results output by the causal inference analysis module to perform multi-objective optimization to obtain optimized process parameters.

2. The intelligent optimization system for the process parameters of laser cladding of a hydraulic turbine according to claim 1, characterized in that, When training the multi-task neural network model, the loss function adopted by the physical-information-guided multi-task prediction network construction and training module includes a data fitting loss term and a physical residual loss term, and the physical residual loss term is determined according to the deviation between the prediction result of the multi-task neural network model and the preset physical control equations of the laser cladding.

3. An intelligent optimization system for the process parameters of laser cladding of a water turbine according to claim 1, characterized in that, The multi-task neural network model includes a shared feature extraction layer and task-specific output layers for different cladding layer quality indicators, and the shared feature extraction layer is used to learn the common features among different cladding layer quality indicator prediction tasks.

4. An intelligent optimization system for the process parameters of laser cladding of a water turbine according to claim 2, characterized in that, The data fitting loss term is used to measure the difference between the cladding layer quality indicators predicted by the multi-task neural network model and the actually observed cladding layer quality indicators obtained through the data preparation and preprocessing module.

5. An intelligent optimization system for the process parameters of laser cladding of a water turbine according to claim 1, characterized in that, The causal inference analysis module is further configured to generate virtual sample data in the process parameter space by using the multi-task neural network model trained by the physical-information-guided multi-task prediction network construction and training module, and perform the causal effect analysis based on the virtual sample data.

6. The intelligent optimization system for the laser cladding process parameters of a hydraulic turbine according to claim 1, characterized in that, The causal effect analysis results output by the causal inference analysis module include the average causal effect estimation values of the process parameters on the cladding layer quality indicators, and the identified key process parameters that have a significant causal impact on the cladding layer quality indicators.

7. An intelligent optimization system for the process parameters of laser cladding of a hydraulic turbine according to claim 1, characterized in that, The causality-aware multi-objective optimization algorithm module adopts a multi-objective evolutionary algorithm, and uses the multiple cladding layer quality indicators predicted by the multi-task neural network model as the fitness function of the multi-objective evolutionary algorithm.

8. An intelligent optimization system for the process parameters of laser cladding of a water turbine, as described in claim 1, characterized in that, The causality-aware multi-objective optimization algorithm module uses the causal effect analysis results to guide the search process of the multi-objective evolutionary algorithm, and the guidance includes at least one of the following: key parameter guidance for population initialization based on causal effects, adaptive adjustment of evolutionary operators according to the causal sensitivity of parameters, or interpretation of the trade-off relationships in the Pareto optimal solution set based on causal paths.

9. An intelligent optimization system for the process parameters of laser cladding of a water turbine, according to claim 1, characterized in that, The system further includes a system integration and human-computer interaction module, which is used to integrate the data preparation and preprocessing module, the physics-informed multi-task prediction network construction and training module, the causal inference analysis module, and the causality-aware multi-objective optimization algorithm module, and provides a user interface to allow users to configure optimization tasks, monitor the optimization process, and visually display the optimization results including the Pareto optimal solution set and the corresponding causal explanations.

10. An intelligent optimization method for the process parameters of laser cladding of a water turbine, based on the intelligent optimization system for the process parameters of laser cladding of a water turbine according to any one of claims 1-9, characterized in that, It includes the following steps: Step 1: Obtain and preprocess the process parameters of the hydroturbine laser cladding and the corresponding cladding layer quality index data; Step 2: Based on the preprocessed process parameters and the preset physical control equation of laser cladding, construct and train a physics-informed multi-task neural network model to predict the cladding layer quality index; Step 3: Analyze the causal effect of the process parameters on the cladding layer quality index based on the output prediction results of the physics-informed multi-task neural network model or the preprocessed data; Step 4: Use the physics-informed multi-task neural network model as a surrogate model, and combine the causal effect analysis results to perform multi-objective optimization to obtain optimized process parameters.

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