Organic Rankine cycle optimal configuration search method and device based on PINN and multi-objective optimization

Abstract

The invention discloses an organic Rankine cycle optimal configuration search method and device based on PINN and multi-objective optimization, and the method comprises the steps: firstly constructing a thermodynamic model of an organic Rankine cycle system, constructing a training data set and physical constraints based on the thermodynamic model, and then training a PINN pair network through the training data set, thereby obtaining the optimal configuration of the organic Rankine cycle system. Embedding a physical constraint in the loss function; the method comprises the following steps: training a PINN (Plural Index Neural Network), predicting a to-be-predicted design parameter by using the trained PINN to obtain a predicted cycle state parameter, finally calculating a plurality of organic Rankine cycle evaluation indexes according to the predicted cycle state parameter, constructing a target function, and carrying out multi-target optimization search by minimizing the target function to obtain final optimal configuration. According to the method, the calculation efficiency of system performance evaluation is remarkably improved, the optimal performance configuration of the ORC system under various working medium and operation conditions can be efficiently obtained by searching in a wide design space, and unification of optimization efficiency and prediction accuracy is achieved.

Description

Technical Field

[0001] This invention relates to the field of medium and low temperature waste heat recovery technology, and more specifically, to an optimal configuration search method and apparatus for organic Rankine cycles based on PINN and multi-objective optimization. Background Technology

[0002] With the rapid development of renewable energy and the increasing demand for waste heat recovery technology, the Organic Rankine Cycle (ORC) is widely used in geothermal energy, waste heat recovery, and other fields due to its ability to efficiently convert low-temperature thermal energy into mechanical work or electrical energy. Traditional ORC systems typically use water or other working fluids circulating between heat exchangers, expanders, and condensers, utilizing energy provided by heat sources for power conversion. While existing technologies can operate effectively within certain limits, they still face numerous challenges in practical applications, including low optimization efficiency, computational complexity, and poor adaptability.

[0003] Traditional ORC optimization methods mostly rely on explicit thermodynamic models. Empirical model-driven heuristic algorithms, by simplifying the model and employing heuristic search, possess a certain search efficiency. However, under complex operating conditions characterized by highly nonlinear systems, significant changes in the thermophysical properties of the working fluid, or strong coupling of multiple variables, empirical models struggle to accurately capture the true state of the system, limiting the accuracy and generalization of the optimization results. AI methods, such as data-driven LSTM, ANN, or BP fusion optimization algorithms, can effectively handle complex data, but lack explicit thermodynamic constraints and physical mechanism guidance. Under unobserved operating conditions or extreme conditions, the results are prone to deviating from actual physical laws, reducing the reliability of the model and the interpretability of engineering applications. Summary of the Invention

[0004] The purpose of this invention is to provide an organic Rankine cycle optimal configuration search method and apparatus based on PINN and multi-objective optimization. It employs Physical Information Neural Network (PINN), a deep learning method that combines data-driven approaches and physical constraints, enabling the neural network to learn complex thermodynamic system models while ensuring physical consistency. By embedding physical laws into the loss function, PINN automatically adheres to thermodynamic constraints such as energy and mass conservation while fitting data, overcoming the problem of poor physical consistency in traditional methods. Compared to traditional methods, PINN can effectively solve complex nonlinear problems, improving computational efficiency while maintaining high prediction accuracy, especially demonstrating stronger adaptability and optimization performance in handling multi-medium and multi-objective optimizations.

[0005] By introducing PINN, this invention effectively reduces computational load, improves optimization efficiency, and achieves precise balance in multi-objective optimization, overcoming the shortcomings of traditional methods in multi-medium selection, operating condition adaptability, and accuracy. Furthermore, the embedding of physical constraints in the PINN model makes the optimization results not only more consistent with thermodynamic laws but also significantly improves the system's stability and verifiability. Therefore, the purpose of this invention is to provide a novel ORC system optimization scheme by combining PINN with multi-objective optimization algorithms. This scheme can efficiently and accurately optimize multi-medium system design while ensuring physical consistency, thereby overcoming multiple limitations of existing technologies and improving the overall performance of ORC systems.

[0006] To achieve the above objectives, a first aspect of the present invention provides an organic Rankine cycle optimal configuration search method based on PINN and multi-objective optimization, comprising: A thermodynamic model of an organic Rankine cycle system is constructed. The design parameters are input into the thermodynamic model, and the cycle state parameters of each state point of the organic Rankine cycle system are output. The physical constraints are constructed by verifying and embedding the parameters of the saturation state point according to the energy conservation law that the evaporator and condenser follow in the thermodynamic model for heat absorption and dissipation. A training dataset is constructed based on the input design parameters and the output cycle state parameters. A physical information neural network PINN is constructed. PINN includes an input layer, a hidden layer, and an output layer. The input layer is used to receive the design parameters of the organic Rankine cycle system. The hidden layer adopts a multilayer perceptron structure to learn the complex nonlinear mapping relationship between the input design parameters and the output cycle state parameters. The output layer is used to predict the cycle state parameters of each state point of the organic Rankine cycle system as the performance index of the organic Rankine cycle system. The training dataset is input into PINN to train the network. Physical constraints are embedded in the loss function, and the network parameters are optimized by minimizing the loss function. The trained PINN is used to predict the design parameters to be predicted, and the predicted cyclic state parameters are obtained. Multiple organic Rankine cycle evaluation indices are calculated based on the predicted cycle state parameters, and an objective function is constructed based on the organic Rankine cycle evaluation indices. Multi-objective optimization search is performed by minimizing the objective function to obtain the final optimal configuration, where the optimal configuration is a set of optimal design parameters that satisfy the objective function.

[0007] In one implementation, a training dataset is constructed based on the input design parameters and the output cyclic state parameters, including: The input design parameters and the output loop state parameters are used to construct input-output pairs, which serve as the training dataset.

[0008] In one embodiment, the physical information neural network further includes an input preprocessing module for preprocessing the input design parameters.

[0009] In one implementation, the hidden layer includes a deep feature modeling module and a nonlinear interaction module. The deep feature modeling module is used to extract deep features from the preprocessed design parameters, and the nonlinear interaction module is used to model high-order interaction information using a multi-head attention mechanism based on the extracted deep features, and learn the complex nonlinear mapping relationship between the input design parameters and the output cyclic state parameters.

[0010] In one implementation, the construction of the loss function includes: A data error term is constructed based on the difference between the network prediction results and the actual data; Based on the law of conservation of energy, which states that the energy emitted by the heat source is equal to the energy received by the working fluid in the evaporator, and the heat dissipated by the working fluid inside the condenser is equal to the energy received by the cold source, an energy conservation loss term is constructed. Construct a loop state consistency loss term based on the relationship between the enthalpy values ​​of the states that the loop needs to maintain during operation; A loss function is constructed based on the data error term, the energy conservation loss term, and the cyclic state consistency loss term.

[0011] In one implementation, the constructed energy conservation loss term is:

[0012] in, This represents the energy conservation loss term. Indicates the mass flow rate of the heat source. This indicates the specific heat capacity of the heat source water and the cold source water. Indicates the inlet temperature of the heat source. Indicates the outlet temperature of the heat source. This represents the mass flow rate of the circulating working fluid. This refers to the process where the working fluid absorbs waste heat in the evaporator, and through heat exchange with an external heat source, heats the liquid and evaporates it into a gas. This refers to the process where high-temperature, high-pressure gas enters an expander, expands, and does work to drive a generator, converting mechanical energy into electrical energy. This refers to the process by which an expanded gas is cooled by a condenser, releasing heat and transforming into a liquid. This indicates the process of the cooled liquid flowing back to the evaporator. Indicates the outlet temperature of the cold source. Indicates the inlet temperature of the cold source; The constructed cyclic state consistency loss term is:

[0013] in, This represents the loss term for consistency in cyclic states. This represents a non-linear activation function.

[0014] In one implementation, a multi-objective optimization search is performed by minimizing the objective function to obtain the final optimal configuration, including: Initialize the particle swarm; The position and velocity of the particles are sampled; In each iteration, the PINN model is invoked based on the current particle position to obtain the corresponding cyclic state parameters. These cyclic state parameters are then used as input to the objective function to guide the particle's velocity and position updates. Obtain the particle's current position and optimal position; Determine whether the preset conditions have been met. If they have, output the optimal position of the particle as the optimal configuration.

[0015] Based on the same inventive concept, a second aspect of the present invention provides an organic Rankine cycle optimal configuration search device based on PINN and multi-objective optimization, comprising: The thermodynamic model building module is used to construct a thermodynamic model of an organic Rankine cycle system. The design parameters are input into the thermodynamic model, and the cycle state parameters of each state point of the organic Rankine cycle system are output. The physical constraints are embedded and constructed based on the energy conservation law that the evaporator and condenser follow in the thermodynamic model for heat absorption and dissipation, as well as the parameters of the saturation state point. A training dataset is constructed based on the input design parameters and the output cycle state parameters. The network construction module is used to build the physical information neural network PINN. PINN includes an input layer, a hidden layer and an output layer. The input layer is used to receive the design parameters of the organic Rankine cycle system. The hidden layer adopts a multilayer perceptron structure to learn the complex nonlinear mapping relationship between the input design parameters and the output cycle state parameters. The output layer is used to predict the cycle state parameters of each state point of the organic Rankine cycle system as the performance index of the organic Rankine cycle system. The network training module is used to input the training dataset into PINN to train the network, embed physical constraints into the loss function, and optimize the network parameters by minimizing the loss function; The prediction module is used to predict the design parameters to be predicted using the trained PINN, and obtain the predicted cyclic state parameters. The optimal configuration search module is used to calculate multiple organic Rankine cycle evaluation indices based on the predicted cycle state parameters, construct an objective function based on the organic Rankine cycle evaluation indices, and perform multi-objective optimization search by minimizing the objective function to obtain the final optimal configuration, where the optimal configuration is a set of optimal design parameters that satisfy the objective function.

[0016] Based on the same inventive concept, a third aspect of the present invention provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, provides the organic Rankine cycle optimal configuration search method based on PINN and multi-objective optimization described in the first aspect.

[0017] Based on the same inventive concept, a fourth aspect of the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the organic Rankine cycle optimal configuration search method based on PINN and multi-objective optimization described in the first aspect.

[0018] Compared with the prior art, the advantages and beneficial technical effects of the present invention are as follows: First, a thermodynamic model of the organic Rankine cycle system is constructed, and a training dataset and physical constraints are built based on this model. Then, the PINN network is trained using the training dataset, embedding the physical constraints into the loss function. Next, the trained PINN is used to predict the design parameters to be predicted, obtaining the predicted cycle state parameters. Finally, multiple organic Rankine cycle evaluation indices are calculated based on the predicted cycle state parameters, and an objective function is constructed. Multi-objective optimization search is performed by minimizing the objective function to obtain the final optimal configuration. During the training process of the neural network, thermodynamic constraint equations are explicitly embedded to ensure strict adherence to the laws of conservation of energy and mass. Simultaneously, the model is trained based on cycle running data, learning the complex nonlinear mapping relationship between the input design parameters and the cycle state parameters. This method not only significantly improves the computational efficiency of system performance evaluation but also possesses good generalization ability, adapting to various operating boundaries and design parameter conditions. While maintaining physical consistency, it uncovers inherent coupling characteristics that are difficult to analyze using traditional explicit models. Furthermore, this invention embeds the trained PINN model into a multi-objective PSO optimization algorithm, replacing the traditional thermodynamic iterative calculation process, as a fast and high-fidelity performance prediction module. By searching within a broad design space, the optimal performance configuration of the ORC system under various working fluids and operating conditions can be efficiently obtained, achieving a balance between optimization efficiency and prediction accuracy. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 A flowchart of an organic Rankine cycle optimal configuration search method based on PINN and multi-objective optimization provided in an embodiment of the present invention; Figure 2 A detailed flowchart illustrating the implementation of the organic Rankine cycle optimal configuration search method based on PINN and multi-objective optimization provided in this embodiment of the invention. Figure 3 This is a schematic diagram of the organic Rankine cycle in an embodiment of the present invention; Figure 4 This is a schematic diagram of the complete model of organic Rankine cycle optimal configuration search based on PINN and multi-objective optimization in an embodiment of the present invention; Figure 5 This is a block diagram of the organic Rankine cycle optimal configuration search device for PINN and multi-objective optimization in an embodiment of the present invention. Detailed Implementation

[0021] The key points and inventive aspects to be protected by this invention include: (1) Optimal configuration search for multi-working-medium ORC based on a hybrid model and framework of PINN and multi-objective optimization algorithm One of the core technological innovations of this invention is the construction of a hybrid optimization framework based on a Physical Information Neural Network (PINN) and a multi-objective optimization algorithm, used to achieve optimal configuration search for multiple working media in Organic Rankine Cycle (ORC) systems. Traditional ORC system optimization relies on explicit physical models, while this invention, by replacing the traditional explicit physical model with the PINN model, significantly improves computational efficiency through rapid training and prediction. This framework not only supports optimization of multiple working media but also enables global search across a broad design space to find the optimal configuration. This innovation allows the system to simultaneously consider multiple working media and optimize the design parameters of the ORC system for different operating conditions and requirements.

[0022] (2) Prediction model of thermodynamic parameters of multi-working-fluid organic Rankine cycle based on PINN Another key technical aspect of this invention is the multi-working-fluid ORC thermodynamic parameter prediction model based on PINN. Unlike artificial neural network models, the PINN model ensures the physical consistency and accuracy of the system by embedding physical constraint terms into the network's loss function. This model not only possesses physical interpretability, clearly reflecting changes in the thermophysical properties of the working fluid and their impact on system performance, but also exhibits high generalization ability, adapting to different working fluids and varying operating conditions. PINN can provide higher prediction accuracy and stronger adaptability when facing complex operating conditions and strongly coupled systems.

[0023] (3) Calculate performance indicators by predicting auxiliary intermediate terms. The third innovation of this invention is to indirectly predict the final performance indicators (such as thermal efficiency and power output) of the ORC system by predicting auxiliary intermediate terms. Unlike traditional methods that directly predict the final performance, this invention predicts the intermediate thermodynamic parameters (such as enthalpy, temperature, and pressure) of the system through PINN, and then calculates the performance indicators based on these intermediate terms. This method is more consistent with the actual laws of thermodynamic processes and is more computationally reasonable, providing more accurate and reliable performance predictions. Furthermore, this method enhances the verifiability of the model, facilitating comparison and verification with actual experimental data.

[0024] This embodiment provides an organic Rankine cycle optimal configuration search method based on PINN and multi-objective optimization. Please refer to [link to relevant documentation]. Figure 1 ,include: S1: Construct a thermodynamic model of the organic Rankine cycle system, input the design parameters into the thermodynamic model, output the cycle state parameters of each state point of the organic Rankine cycle system, construct physical constraints based on the energy conservation law that the evaporator and condenser follow in heat absorption and dissipation in the thermodynamic model and the parameter verification of the saturation state point, and construct a training dataset based on the input design parameters and the output cycle state parameters.

[0025] like Figure 3 As shown, the embodiment of this invention first demonstrates how to construct a thermodynamic model based on a subcritical organic Rankine cycle (ORC) and then train and optimize it using a Physical Information Neural Network (PINN). First, a thermodynamic model of the ORC system is constructed. This model considers the main components of the ORC system, including the processes from the condenser to the pump, then to the evaporator, and back to the condenser, referred to as processes 1, 2, 3, and 4. Process 1 involves the working fluid absorbing waste heat in the evaporator, heating the liquid and evaporating it into a gas through heat exchange with an external heat source. Process 2 involves the high-temperature, high-pressure gas entering the expander, expanding and doing work to drive a generator, converting mechanical energy into electrical energy. Process 3 involves the expanded gas being cooled by the condenser, releasing heat and turning back into liquid. Process 4 involves the cooled liquid flowing back to the evaporator, where the generator and expander are connected to convert shaft work into electrical energy. In all these processes, it is assumed that the system operates under steady-state conditions, neglecting factors such as heat loss, pressure loss, and changes in kinetic and potential energy at pipes and connections. By using the heat source temperature, the pinch temperature difference between the evaporator and condenser, and the narrow point temperature difference, and by utilizing the energy conservation law property library and verifying the saturation parameters, the cyclic state parameters (such as temperature, pressure, enthalpy, and mass flow rate) at each state point in the system can be derived. Among these, the energy conservation law that the evaporator and condenser follow in heat absorption and dissipation, and the parameter verification at the saturation state point are embedded in PINN as physical constraints to ensure that the model follows the laws of thermodynamics during the prediction process.

[0026] The training dataset is constructed based on the input design parameters and the output cyclic state parameters, including: The input design parameters and the output loop state parameters are used to construct input-output pairs, which serve as the training dataset.

[0027] In this implementation scheme, the design parameters of the ORC system include: heat source inlet temperature, cold source inlet temperature, evaporation pressure, condensation pressure, etc., and the cycle state parameters include temperature, pressure, enthalpy, mass flow rate, etc.

[0028] S2: Construct a physical information neural network PINN. PINN includes an input layer, a hidden layer, and an output layer. The input layer is used to receive the design parameters of the organic Rankine cycle system. The hidden layer adopts a multilayer perceptron structure to learn the complex nonlinear mapping relationship between the input design parameters and the output cycle state parameters. The output layer is used to predict the cycle state parameters of each state point of the organic Rankine cycle system, which serve as the performance index of the organic Rankine cycle system.

[0029] In this invention, PINN is used to learn the complex thermodynamic behavior of a system through data-driven learning and serves as a performance prediction module in a multi-objective optimization framework. Specifically: 1. Input Layer Design: The input layer receives the design parameters and control variables of the ORC system. These parameters and variables have a significant impact on the operation and performance of the system. Design parameters include heat source inlet temperature, cold source inlet temperature, pump efficiency, expander efficiency, etc.; control variables include heat exchanger temperature difference, heat source inlet temperature, working fluid, and critical temperature and pressure that vary with the working fluid, etc.

[0030] The input layer contains multiple neurons, each corresponding to one input parameter. Specifically, it includes:

[0031] The physical information neural network also includes an input preprocessing module, which is used to preprocess the input design parameters.

[0032] Because the original input data differs significantly in distribution, scale, and outlier sensitivity, directly inputting it into the model would affect training stability and cause prediction bias. Therefore, the input data needs to undergo a series of preprocessing operations. First, one-hot encoding is used for the working fluid category variables to eliminate pseudo-order relationships introduced by non-numerical variables; second, standardization and normalization methods are applied to continuous variables to make their distribution closer to a zero-mean, unit-variance form; finally, RobustScaler (a data preprocessing tool) is introduced to scale input variables containing outliers to improve the model's tolerance and robustness to boundary conditions. These processing operations not only improve the numerical stability of model training but also provide a standardized data foundation for subsequent feature modeling.

[0033] 2. Hidden Layer Design: The hidden layers are a crucial component of the PINN model, used to learn the complex nonlinear relationship between input and output. In its design, PINN employs a Multilayer Perceptron (MLP) structure, with each layer containing multiple neurons. By abstracting features layer by layer, it progressively approximates the nonlinear mapping relationship between input and output. Each neuron converts the input signal into an output signal through an activation function, thus forming the information transmission chain in the neural network. Thermodynamic constraints are embedded in these hidden layers to ensure that the output of each layer conforms to physical laws.

[0034] Suppose the neural network has L layers, where the output of the l-th layer is h(l) and the input is x, then the formula for calculating the l-th layer is: (1) Among them, W (l) Let b be the weight matrix of the l-th layer. (l) For the bias term, σ (l) It is an activation function), while h (0) =x is the input layer. The output of each layer is non-linearly transformed through an activation function, progressively extracting higher-order features from the input data. In PINN, the hidden layers not only need to fit the data but also satisfy physical constraints. To this end, a physical constraint term is added to the output value of each hidden layer, which is explicitly reflected in the loss function.

[0035] Optionally, the hidden layer includes a deep feature modeling module and a nonlinear interaction module. The deep feature modeling module is used to extract deep features from the preprocessed design parameters, and the nonlinear interaction module is used to model high-order interaction information based on the extracted deep features using a multi-head attention mechanism, and learn the complex nonlinear mapping relationship between the input design parameters and the output cyclic state parameters.

[0036] Specifically, the multi-head attention mechanism is the core structure in the PINN model that constructs the nonlinear mapping relationship between input and output. Its design directly affects the model's ability to express the features of complex systems and its ability to control physical consistency. The PINN network constructed in this paper adopts a multilayer perceptron (MLP) as its basic structure, and introduces a multi-head attention mechanism, residual connections, and a Squeeze-and-Excitation (SE) attention mechanism to enhance the diversity of feature representation and the selectivity of physical features.

[0037] The primary function of this layer is to nonlinearly upscale the original input, mapping it from a low-dimensional state space to a more expressive high-dimensional feature space, thus providing a foundation for subsequent nonlinear interaction modeling. Based on this feature space, the model further introduces a multi-head attention mechanism to model higher-order interaction information. The multi-head attention mechanism can model interaction patterns between different dimensions in parallel across multiple independent representation subspaces, effectively handling the complex nonlinear dependencies between variables such as temperature, pressure, and enthalpy in the ORC system. Each attention head learns to focus on different feature combinations through independent weights, thereby enhancing the model's ability to express multi-scale relationships.

[0038] In deep network structures, to ensure stable gradient propagation and information retention, this implementation introduces layer normalization and residual connection structures in the multi-head attention module. The former helps improve numerical stability during training, while the latter avoids the gradient vanishing problem that occurs after the network is deepened. Furthermore, the module includes a standard feedforward network structure to enhance local nonlinear modeling capabilities. To further improve the model's ability to distinguish the importance of different input channels, the network integrates an SE attention mechanism (channel attention mechanism) in deep feature modeling. This mechanism compresses, activates, and reweights each channel feature, enabling the model to adaptively determine which variables are more critical to the current output. In the context of ORC systems operating across different media, the influence of different input dimensions on state variables such as enthalpy and flow rate is not consistent. The SE mechanism provides a learnable feature selection mechanism, significantly improving the model's adaptability and generalization performance under complex conditions.

[0039] 3. Output layer design The output layer is used to predict the cycle state parameters of the organic Rankine cycle system at various state points, which serve as key performance indicators of the ORC system, such as enthalpy, temperature, and mass flow rate.

[0040] The cyclic state parameters of the output layer serve as predictions for several key performance indicators of the ORC system. These outputs are directly related to the system's operating efficiency and can be used as predictive aids in calculating the final evaluation indicators.

[0041] S3: Input the training dataset into PINN to train the network, embed physical constraints into the loss function, and optimize the network parameters by minimizing the loss function.

[0042] The loss function consists of a data error term and a physical constraint term. The data error term minimizes the difference between the network's predicted values ​​and the actual data, while the physical constraint term ensures that the network follows the laws of thermodynamics.

[0043] Specifically, the construction of the loss function includes: A data error term is constructed based on the difference between the network prediction results and the actual data; Based on the law of conservation of energy, which states that the energy emitted by the heat source is equal to the energy received by the working fluid in the evaporator, and the heat dissipated by the working fluid inside the condenser is equal to the energy received by the cold source, an energy conservation loss term is constructed. Construct a loop state consistency loss term based on the relationship between the enthalpy values ​​of the states that the loop needs to maintain during operation; A loss function is constructed based on the data error term, the energy conservation loss term, and the cyclic state consistency loss term.

[0044] In practical implementation, the loss function in a physical information neural network consists of a data error term and a physical constraint term. Specifically, the physical constraint loss term includes an energy conservation loss term and an energy transfer loss term. These components together ensure that the neural network not only minimizes data errors but also adheres to thermodynamic laws and physical constraints.

[0045] (1) Data error term The data error term is used to minimize the difference between the neural network's predictions and the actual data. A commonly used metric is the mean squared error (MSE). The data error term can be expressed as:

[0046] Where: N is the number of samples, and M is the number of output variables. and These are the predicted and actual values ​​of the i-th sample and the j-th output variable, respectively. This term ensures that the neural network's output is as close as possible to the actual observed data, thereby improving prediction accuracy.

[0047] (2) Physical loss item Based on physical laws, the physical embedding constraints of this algorithm are set as follows: According to the law of conservation of energy, the energy emitted by the heat source is equal to the energy received by the working fluid in the evaporator, and the heat dissipated by the working fluid inside the condenser is equal to the energy received by the cold source. The specific formula is as follows.

[0048]

[0049] The energy conservation loss term LE is reflected by calculating the residual between the enthalpy difference and the actual heat, and its specific form is as follows:

[0050] The loop needs to maintain the following relationship between the enthalpy values ​​of the states:

[0051] The cycle-state consistency loss term LS ensures the monotonicity of the predicted output enthalpy by penalizing instances where h4>h3>h2>h1 is not satisfied. Specifically, it takes the following form:

[0052] Where ReLU(X) = max(0,x).

[0053] (3) Total loss function Combining the above factors, the total loss function of PINN is:

[0054] Wherein, λ1, λ2, and λ3 are weight functions. Their weights are set to 1, 0.8, and 0.5 respectively to balance prediction accuracy and physical consistency, ensuring that the network can efficiently fit the data during training without deviating from the basic physical logic. By minimizing this loss function, PINN can achieve accurate prediction and optimization of ORC system performance while maintaining physical consistency.

[0055] S4: Use the trained PINN to predict the design parameters to be predicted, and obtain the predicted cyclic state parameters.

[0056] S5: Calculate multiple organic Rankine cycle evaluation indices based on the predicted cycle state parameters, construct an objective function based on the organic Rankine cycle evaluation indices, and perform multi-objective optimization search by minimizing the objective function to obtain the final optimal configuration, where the optimal configuration is a set of optimal design parameters that satisfy the objective function.

[0057] Please see Figure 2 This is a detailed flowchart illustrating the implementation of the organic Rankine cycle optimal configuration search method based on PINN and multi-objective optimization provided in this embodiment of the invention. First, parameters and variables (design parameters) are set. Then, a traversal search is performed. The design parameters are input into a trained PINN prediction module, which outputs the corresponding cycle state parameters. The trained PINN prediction module is obtained by training a dataset derived from a thermodynamic model. The model training process explicitly embeds thermodynamic constraint equations to ensure that the model follows the laws of conservation of energy and mass. The cycle state parameters output by the model are used to construct the objective function in the subsequent multi-objective optimization algorithm. Multi-objective optimization is then performed, including index determination and optimization iteration. It is determined whether the maximum number of iterations has been reached; if so, the optimal configuration is output.

[0058] Please see Figure 4This is a schematic diagram of the complete model for the search of optimal configuration of organic Rankine cycle based on PINN and multi-objective optimization in an embodiment of the present invention. The whole includes thermodynamic modeling, PINN module and multi-objective optimization algorithm, in which the index function is the objective function.

[0059] The optimal configuration is obtained by performing a multi-objective optimization search by minimizing the objective function, including: Initialize the particle swarm; The position and velocity of the particles are sampled; In each iteration, the PINN model is invoked based on the current particle position to obtain the corresponding cyclic state parameters. These cyclic state parameters are then used as input to the objective function to guide the particle's velocity and position updates. Obtain the particle's current position and optimal position; Determine whether the preset conditions have been met. If they have, output the optimal position of the particle as the optimal configuration.

[0060] Specifically, the following final organic Rankine cycle evaluation metrics are calculated based on the output values ​​of PINN:

[0061] in, For thermal efficiency, For efficiency, For Carnot cycle efficiency, This refers to relative efficiency.

[0062] In multi-objective optimization, multiple performance objective functions are defined, such as thermal efficiency and thermal efficiency. These objective functions are combined with weights to form a comprehensive objective function, which guides the optimization process to find the optimal solution.

[0063] Evaluation criteria: The fitness of each combination of design parameters is evaluated by the performance prediction values ​​(cyclic state parameters) output by the trained PINN model. Optimization Process: Multi-objective optimization finds the optimal solution through global search. The optimization process continues until the set termination conditions are met (such as reaching the maximum number of iterations or fitness convergence). During this process, the optimization algorithm explores the balance between multiple objective functions within the design space, ultimately obtaining the optimal design configuration. For example, the applicable heat source temperature for different working fluids can assist in selecting application scenarios; the pinch point temperature difference and narrow point temperature difference of the evaporator and condenser help in designing the performance of the heat exchanger; and the temperature and pressure conditions at various internal state points, as well as the optimized performance indicators, can be derived as a reference.

[0064] Obtaining the optimal solution: After multiple optimization iterations, the optimization algorithm converges to a set of optimal solutions. Each solution represents a design configuration that achieves an optimal balance among multiple objective functions. Finally, the best design scheme is selected to achieve the optimal performance of the ORC system in multiple performance indicators such as thermal efficiency and power output.

[0065] In its specific implementation, this invention proposes a multi-objective optimization method based on the coupling of multi-objective particle swarm optimization (MOPSO) and physical information neural networks. This method, while ensuring physical consistency, incorporates Pareto optimality theory to reveal the trade-offs between multiple performance indicators (including net output power, thermodynamic efficiency, power generation efficiency, and relative efficiency) and obtain a set of mutually independent optimal solutions, providing a decision-making basis for the efficient operation and structural matching of ORC systems.

[0066] In this framework, the optimization problem is modeled as a vector multi-objective minimization problem of the following form:

[0067] in, The design parameters (input parameters) for the ORC system include variables such as working fluid type (coded), critical pressure, heat source inlet temperature, heat exchanger inlet and outlet temperature difference, and minimum heat transfer temperature difference. This represents the multi-objective performance function evaluated by the PINN model and obtained through thermal calculations. The negative sign is used to unify it into a minimization problem, which is achieved by minimizing... This maximizes the values ​​of thermal efficiency, thermal efficiency, and relative thermal efficiency simultaneously.

[0068] Each particle represents a feasible solution in the design space, and its initial position and velocity are sampled from a uniform distribution within the physically feasible range:

[0069] , The initial position and velocity of the i-th particle are represented. The particle's position is passed to the PINN module as an input parameter. PINN quickly predicts the enthalpy and mass flow rate of each state point of the system based on the embedded energy conservation and state equations, avoiding a large amount of numerical simulation in traditional cyclic simulation.

[0070] In each iteration, the particle's position and velocity are updated using the following formula:

[0071] in, Let be the velocity of the i-th particle in the (t+1)-th iteration. Let be the velocity of the i-th particle in the t-th iteration. Let i be the position of the i-th particle in the t-th iteration. Let i be the position of the i-th particle in the (t+1)-th iteration. This represents the optimal position in the history of an individual particle. The guided solution is selected from the external Pareto archive; ω is the inertia coefficient. , These are self-learning factors and social learning factors, respectively. , ~U(0,1) is a random perturbation factor.

[0072] The key lies in constructing the Pareto optimal solution set. In multi-objective optimization, there is no absolute comparison of superiority or inferiority between solutions; judgment is made only in the sense of "dominance." If for a solution... and ,have:

[0073] Then it is called Dominate .

[0074] in, , Solution and The corresponding fitness value is calculated by normalizing the objective optimization index using the objective function of formula (13). The Pareto optimal solution is defined as the solution that is not dominated by any other solution. This set constitutes the so-called Pareto Front, which is geometrically represented as a curve (surface) or a compromise curve in the multi-objective space, representing the optimal performance trade-off state achievable by the current search. MOPSO hierarchically stratifies the current population through non-dominated sorting, extracts non-dominated particles and stores them in the external elite archive, and uses the crowding distance mechanism to maintain the diversity of the solution set. When the external archive exceeds the capacity limit, solutions located in dense regions are deleted first. In each generation, each particle randomly selects a non-dominated solution from the archive as a guide individual when updating its speed, thereby maintaining the diversity and exploratory nature of the search direction.

[0075] The MOPSO optimization process terminates when any of the following conditions are met: the maximum number of iterations is reached; or the Pareto front converges within a preset threshold over several consecutive iterations. The final output Pareto solution set is a set of design schemes that are independent of each other across all performance metrics, covering the entire optimization range and demonstrating multiple possible configurations of the system in terms of performance trade-offs. During the optimization process, the PINN model is closely linked to each iteration of MOPSO. In each iteration, MOPSO calls the PINN model based on the current particle position (i.e., design parameters) to obtain the corresponding performance evaluation results (cyclic state parameters). These evaluation results serve as input to the fitness function (objective function), guiding the particle's velocity and position updates. In this way, the combination of MOPSO and PINN not only enables efficient searching of large-scale design spaces but also ensures that the optimization results satisfy physical constraints.

[0076] In general, the advantages and beneficial technical effects of the present invention include: (1) Significantly Improved Optimization Efficiency: Compared with the use of traditional explicit thermodynamic calculation models for the optimal exploration of organic Rankine cycles, this invention significantly improves optimization efficiency by using a Physical Information Neural Network (PINN). The PINN model can quickly learn the thermodynamic behavior under different working fluids and complete a global search for multiple working fluids in a short time, reducing computation time and resource consumption. This method can efficiently handle complex nonlinear systems and optimize the configuration of multiple working fluids, greatly improving the efficiency of the optimization process.

[0077] (2) Improved prediction accuracy and physical interpretability: This invention uses PINN to embed physical constraints, which provides higher prediction accuracy compared to traditional data-driven deep learning models (such as ANN). By introducing physical laws such as energy conservation and saturation state into the neural network, PINN not only improves the accuracy of performance prediction, but also enhances the physical interpretability of the model, avoiding the shortcomings of traditional methods that lack physical basis.

[0078] (3) Enhanced generalization and adaptability of the model: PINN can accurately predict the performance of ORC systems under different operating boundaries and design parameters. Compared with the limitations of traditional simplified thermodynamic models, PINN maintains adherence to physical laws through nonlinear mapping learning during the training process, and has stronger generalization and adaptability, enabling it to cope with various complex operating conditions.

[0079] (4) More reasonable and verifiable performance evaluation: By training PINN with experimental data, this invention can fully learn complex nonlinear relationships during the training process while adhering to thermodynamic constraints, thus providing a more accurate performance evaluation. By predicting intermediate parameters (such as enthalpy, temperature, pressure, etc.) instead of directly predicting the final performance index, not only can better physical constraints be set to improve the physical interpretability and accuracy of the model, but also the process parameters of all state points can be obtained through reverse calculation. Finally, the rationality of the prediction can be verified through the corresponding calculation index, which enhances the verifiability of the model and facilitates the verification of consistency with the actual results.

[0080] Based on the same inventive concept, this embodiment discloses an organic Rankine cycle optimal configuration search device based on PINN and multi-objective optimization. Please refer to [link to relevant documentation]. Figure 5 ,include: Thermodynamic model construction module 101 is used to construct a thermodynamic model of an organic Rankine cycle system. The design parameters are input into the thermodynamic model, and the cycle state parameters of each state point of the organic Rankine cycle system are output. The physical constraints are embedded and constructed based on the energy conservation law that the evaporator and condenser follow in the thermodynamic model for heat absorption and dissipation, as well as the parameters of the saturation state point. A training dataset is constructed based on the input design parameters and the output cycle state parameters. Network building module 102 is used to build a physical information neural network PINN. PINN includes an input layer, a hidden layer and an output layer. The input layer is used to receive the design parameters of the organic Rankine cycle system. The hidden layer adopts a multilayer perceptron structure to learn the complex nonlinear mapping relationship between the input design parameters and the output cycle state parameters. The output layer is used to predict the cycle state parameters of each state point of the organic Rankine cycle system as the performance index of the organic Rankine cycle system. The network training module 103 is used to input the training dataset into PINN to train the network, embed physical constraints in the loss function, and optimize the network parameters by minimizing the loss function; The prediction module 104 is used to predict the design parameters to be predicted using the trained PINN, and obtain the predicted cyclic state parameters. The optimal configuration search module 105 is used to calculate multiple organic Rankine cycle evaluation indices based on the predicted cycle state parameters, construct an objective function based on the organic Rankine cycle evaluation indices, and perform multi-objective optimization search by minimizing the objective function to obtain the final optimal configuration, where the optimal configuration is a set of optimal design parameters that satisfy the objective function.

[0081] Based on the same inventive concept, the present invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the organic Rankine cycle optimal configuration search method based on PINN and multi-objective optimization of Embodiment 1.

[0082] Based on the same inventive concept, the present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in Embodiment 1.

[0083] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0084] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0085] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various modifications and variations to the embodiments of the invention without departing from the spirit and scope of the invention. Thus, if these modifications and variations of the embodiments of the invention fall within the scope of the claims of the invention and their equivalents, the invention also intends to include these modifications and variations.

Claims

1. A method for searching the optimal configuration of an organic Rankine cycle based on PINN and multi-objective optimization, characterized in that, The application relates to a method for predicting the performance of an organic Rankine cycle system. The method comprises the following steps: a thermodynamic model of the organic Rankine cycle system is constructed, design parameters are input into the thermodynamic model, and cycle state parameters of each state point of the organic Rankine cycle system are output; physical constraints are embedded in the thermodynamic model according to the energy conservation law followed by heat absorption and heat dissipation of an evaporator and a condenser and parameters of saturated state points; a training data set is constructed based on the input design parameters and the output cycle state parameters; a physical information neural network (PINN) is constructed, the PINN comprises an input layer, a hidden layer and an output layer, the input layer is used for receiving the design parameters of the organic Rankine cycle system, the hidden layer adopts a multilayer perceptron structure and is used for learning a complex nonlinear mapping relationship between the input design parameters and the output cycle state parameters, and the output layer is used for predicting the cycle state parameters of each state point of the organic Rankine cycle system as performance indicators of the organic Rankine cycle system; the training data set is input into the PINN to train the network, physical constraints are embedded in a loss function, and network parameters are optimized by minimizing the loss function; the trained PINN is used to predict the design parameters to be predicted, and predicted cycle state parameters are obtained; 2. The method of claim 1, wherein the method is based on a PINN and multi-objective optimization for optimal configuration search of an organic Rankine cycle. a plurality of organic Rankine cycle evaluation indicators are calculated according to the predicted cycle state parameters, a target function is constructed based on the organic Rankine cycle evaluation indicators, multi-objective optimization search is performed by minimizing the target function, and finally, an optimal configuration is obtained, wherein the optimal configuration is a set of optimal design parameters meeting the target function. The training data set is constructed based on the input design parameters and the output cycle state parameters, which comprises the following steps:

3. The method of claim 1, wherein the method is based on a PINN and multi-objective optimization for optimal configuration search of an organic Rankine cycle. input-output pairs of the input design parameters and the output cycle state parameters are constructed as the training data set.

4. The method of claim 3, wherein the method is based on PINN and multi-objective optimization for optimal configuration search of ORC. The PINN further comprises an input preprocessing module used for preprocessing the input design parameters.

5. The method of claim 1, wherein, The hidden layer comprises a deep feature modeling module and a nonlinear interaction module, the deep feature modeling module is used for extracting deep features from the preprocessed design parameters, and the nonlinear interaction module is used for learning a complex nonlinear mapping relationship between the input design parameters and the output cycle state parameters according to the extracted deep features. The construction of the loss function comprises the following steps: a data error term is constructed according to the difference between the network prediction result and the real data; an energy conservation loss term is constructed according to the energy conservation law that the energy emitted by a heat source is equal to the energy received by a working medium in an evaporator and the energy emitted by a working medium in a condenser is equal to the energy received by a cold source; a cycle state consistency loss term is constructed according to the enthalpy value size relationship of state points that need to be kept during the operation of the cycle; 6. The method of claim 1, wherein the method is based on a PINN and multi-objective optimization for optimal configuration search of an organic Rankine cycle. the loss function is constructed according to the data error term, the energy conservation loss term and the cycle state consistency loss term. wherein, represents an energy conservation loss term, represents a heat source mass flow rate, represents the specific heat capacity of the heat source water and the cold source water, represents a heat source inlet temperature, represents a heat source outlet temperature, represents a circulating working medium mass flow rate, represents a process in which the working medium absorbs waste heat in the evaporator, heats and evaporates the liquid into gas through heat exchange with an external heat source, represents a process in which the high-temperature and high-pressure gas enters the expander, drives the generator to convert mechanical energy into electrical energy through expansion work, represents a process in which the expanded gas is cooled by the condenser, releases heat and is converted into liquid, represents a process in which the cooled liquid flows back to the evaporator, represents a cold source outlet temperature, represents a cold source inlet temperature; The constructed energy conservation loss term is: wherein, represents a cycle consistency loss term, represents a nonlinear activation function.

7. The method of claim 1, wherein the method is based on a PINN and multi-objective optimization for optimal configuration search of an organic Rankine cycle. The constructed cycle state consistency loss term is: The multi-objective optimization search by minimizing the target function to obtain the final optimal configuration comprises the following steps: a particle swarm is initialized; positions and speeds of the particles are sampled; in each iteration, a PINN model is called according to the current particle position to obtain corresponding cycle state parameters, the cycle state parameters are taken as inputs of the target function to guide the speed and position updating of the particles. Obtaining the current position and the optimal position of the particle; Determining whether a preset condition is reached, and outputting the optimal position of the particle as the optimal configuration if the preset condition is reached.

8. An organic Rankine cycle optimal configuration search device based on PINN and multi-objective optimization, characterized by, The method comprises the following steps: a thermodynamic model construction module, configured to construct a thermodynamic model of an organic Rankine cycle system, input design parameters into the thermodynamic model, and output cycle state parameters of each state point of the organic Rankine cycle system, and to construct a training data set based on the input design parameters and the output cycle state parameters according to the energy conservation law followed by heat absorption and heat dissipation of an evaporator and a condenser in the thermodynamic model and the physical constraints checked according to parameters of saturated state points; a network construction module, configured to construct a physics-informed neural network (PINN), the PINN comprising an input layer, a hidden layer, and an output layer, wherein the input layer is configured to receive the design parameters of the organic Rankine cycle system, the hidden layer adopts a multi-layer perceptron structure and is configured to learn a complex nonlinear mapping relationship between the input design parameters and the output cycle state parameters, and the output layer is configured to predict the cycle state parameters of each state point of the organic Rankine cycle system as performance indicators of the organic Rankine cycle system; a network training module, configured to input the training data set into the PINN to train the network, embed the physical constraints in a loss function, and optimize network parameters by minimizing the loss function; a prediction module, configured to predict the design parameters to be predicted by using the trained PINN to obtain predicted cycle state parameters; an optimal configuration search module, configured to calculate a plurality of organic Rankine cycle evaluation indicators according to the predicted cycle state parameters, construct an objective function based on the organic Rankine cycle evaluation indicators, and perform multi-objective optimization search by minimizing the objective function to obtain a final optimal configuration, wherein the optimal configuration is a set of optimal design parameters satisfying the objective function.

9. A computer-readable storage medium, characterized in that, A computer program is stored thereon, and the program is executed by a processor to implement the PINN and multi-objective optimization-based optimal configuration search method of an organic Rankine cycle according to any one of claims 1 to 7.

10. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the program to implement the PINN and multi-objective optimization-based optimal configuration search method of an organic Rankine cycle according to any one of claims 1 to 7.

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