Process industry system modeling method based on anti-noise hard constraint physical neural network

Abstract

The invention relates to a process industry system modeling method based on an anti-noise hard constraint physical neural network. The method comprises the following steps: firstly, constructing an anti-noise hard constraint physical neural network comprising a framework front end, an anti-noise hard constraint correction layer and an anti-noise loss function; based on the physical relationship between the input and the output of the required modeling system, constructing a linear equality constraint; then quantifying the uncertainty of each sensor in a system needing modeling, and configuring parameters of an anti-noise hard constraint correction layer based on the uncertainty and linear equality constraints; and finally, adopting an anti-noise loss function, and training the anti-noise hard constraint neural network after parameter configuration by using a noise data set to obtain a process industry system model. Compared with the prior art, the method has the advantages that the prediction accuracy of the built substitution model in the noisy input environment is improved while the physical consistency is ensured.

Description

Technical Field

[0001] This invention relates to the field of neural network modeling technology, and in particular to a method for modeling process industry systems based on noise-resistant hard-constraint physical neural networks. Background Technology

[0002] Due to the complexity of process industry systems, modeling them faces challenges such as high-dimensional nonlinearity, multivariate coupling, and the influence of various measurement noises. Existing modeling methods, such as first-principles models, often utilize the fundamental physical / chemical laws of the process system to provide mechanistic interpretation and robust extrapolation capabilities under data-scarce conditions. However, their application in actual production is severely limited because solving high-dimensional equations requires high computational costs, and mechanistic interpretation of complex nonlinear behavior is quite difficult or even infeasible. As an efficient alternative, neural networks can automatically extract features from data and accurately model nonlinear relationships in process systems through their powerful approximation capabilities. However, their black-box nature makes them lack interpretability, and predictions may violate physical constraints, limiting their deployment in safety-critical applications. In recent years, numerous studies on physically-informed neural networks have been proposed. These data-driven models that satisfy physical constraints combine mechanistic interpretability with data-driven flexibility, providing a new direction for modeling process industry systems. Accurate modeling of complex process industry systems with measurement noise by constructing appropriate physical neural networks will enable high-precision and high-efficiency digital transformation in the process industry.

[0003] The current mainstream approach to constructing physical information neural networks (PNNs) involves introducing a penalty term into the loss function to address constraint violations, as shown in References 1 and 2. This method of integrating physical constraints into the loss function degenerates into soft constraints, inherently lacking strict mathematical guarantees of constraint adherence. This inevitably leads to physical inconsistencies, fundamentally limiting their deployment in production. Reference 3 innovatively proposes a hard-constraint PNN framework, which utilizes a penalty term and augmented Lagrangian methods to improve constraint adherence during the training phase compared to traditional PNNs. However, this method cannot guarantee constraint adherence during extrapolation. Reference 4 enforces linear equality constraints through linear output transformation, but its constraint layer correction is performed post-hoc, failing to guide the previous model's learning process and neglecting constraint-based loss minimization during training, thus affecting prediction accuracy. To address these shortcomings, Reference 5 derives analytical solutions for the linear equality constraint layer using KKT conditions, establishing a KKT hard-constraint PNN. Its embedded constraint layer actively guides the optimization of the front-end neural network throughout the training process, achieving the training-time physical integration lacking in Reference 4.

[0004] While significant progress has been made in the development of physical neural networks with embedded linear equality hard constraints, as seen in references 3 and 5, these methods neglect the critical issue of measurement noise in the training data. This oversight is particularly pronounced given that real-world systems rely on sensor-acquired input / output data, which inherently contains measurement noise, as illustrated in reference 6. Reference 7 demonstrates that such noisy training data poses a significant challenge to constructing accurate physical information data-driven models. Although reference 8 advanced the field by proposing a mass-conserving hard-constrained physical neural network framework that considers output data noise, its idealized input assumptions limit its applicability in production practice, as real-world sensor data contains measurement noise in both input and output channels. Furthermore, since the constraint layer lacks analytical solutions, this method requires additional computational power for online optimization during model training and deployment to ensure model compliance with constraints, making it unsuitable for latency-sensitive applications such as real-time prediction systems.

[0005] Document 1: "Raissi, M., Perdikaris, P., Karniadakis, GE, 2019. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics. 378, 686–707. "; Document 2: "Karniadakis, GE, Kevrekidis, IG, Lu, L., Perdikaris, P.,Wang, S., Yang, L., 2021. Physics-informed machine learning. Nature ReviewsPhysics. 3 (6), 422–440. Document 3: "Lu, L., Pestourie, R., Yao, W., Wang, Z., Verdugo, F., Johnson, S.G., 2021. Physics-informed neural networks with hard constraints for inverse design. SIAM Journal on Scientific Computing. 43 (6), B1105–B1132. "; Document 4: "Ma, J., Agarwal, K., Sharma, P., Lang, Y., Zitney, S.E., Gorton, I., Agarwal, D., Miller, D. C., 2012. Enforcing elemental mass and energy balances for reduced order models. In: Proceedings of the 2012 AIChE Meeting. Pittsburgh, PA. "; Document 5: "Chen, H., Flores, G. E. C., Li, C., 2024. Physics-informed neural networks with hard linear equality constraints. Computers and Chemical Engineering. 189, 108764. "; Document 6: "Narasimhan, S., Cornelius, J., 1999. Data Reconciliation and Gross Error Detection. Elsevier. "; Document 7: "Yang, L., Meng, X., Karniadakis, G.E., 2021. B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data. Journal of Computational Physics. 425, 109913"; Document 8: "Mukherjee, A., Bhattacharyya, D., 2024. On the development of steady-state and dynamic mass-constrained neural networks using noisytransient data. Computers and Chemical Engineering. 187, 108722. "; In summary, existing technologies still have limitations in modeling complex process industrial systems, including the inability to simultaneously achieve physical consistency and data-driven flexibility, as well as the inability to resist various measurement noise effects. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a process industry system modeling method based on a noise-resistant hard-constraint physical neural network.

[0007] The objective of this invention can be achieved through the following technical solutions: According to one aspect of the present invention, a method for modeling process industry systems based on a noise-resistant hard-constraint physical neural network is provided, the method comprising the following steps: S1. Construct a noise-resistant hard constraint physical neural network, which includes a framework front-end, a noise-resistant hard constraint correction layer, and a noise-resistant loss function. S2. Based on the physical relationship between the input and output of the system to be modeled, construct linear equality constraints; S3. Quantify the uncertainty of each sensor in the required modeling system, and configure the parameters of the noise-resistant hard constraint correction layer based on the uncertainty and linear equality constraints. S4. Using a noise-resistant loss function, the noise-resistant hard-constraint neural network with configured parameters is trained using a noise dataset to obtain a process industry system model.

[0008] As a preferred technical solution, the framework front-end adopts the neural network paradigm, which is selected based on the specific production practice requirements of the process industry system to be modeled.

[0009] As a preferred technical solution, linear equality constraints: the physical relationship between the input and output of the system to be modeled. in, and This is a matrix of constant coefficients that encodes the physical conservation laws; It is a constant vector; It is the set of real numbers; The number of independent physical laws that the process industrial system to be modeled must follow; The number of input variables for the system to be modeled; The number of output variables for the system to be modeled.

[0010] As a preferred technical solution, the specific process of S3 includes: S31. Quantify the uncertainty of each sensor in the required modeling system, and generate the covariance matrix of sensor measurement noise based on the uncertainty. and ; S32. Based on the covariance matrix and linear equality constraints, configure the parameters of the noise-resistant hard constraint correction layer.

[0011] As a preferred technical solution, the sensor measurement noise in S31 follows a mean of zero and a covariance matrix of [missing information]. and Gaussian distribution of the sensor measurement noise and the system measurement input. Measurement output Real input Actual output The following relational equation is satisfied: in, This is real input. This is the actual output. Sample numbering, , is the sampling index. It is the set of real numbers; The number of input variables for the system to be modeled; The number of output variables for the system to be modeled.

[0012] As a preferred technical solution, the specific formula for configuring the parameters of the noise-resistant hard constraint correction layer in S32 is as follows: in, and These are the input-side optimization estimate and the output-side optimization estimate of the noise-resistant hard constraint correction layer, respectively. This is the predicted output of the model's front end; and These are the covariance matrices of the input-side sensor measurement noise and the output-side sensor measurement noise, respectively. and This is a matrix of constant coefficients that encodes the physical conservation laws; It is a constant vector; This is the input correlation coefficient matrix of the input-side correction layer; The output correlation coefficient matrix of the input-side correction layer; These are the constant parameters of the input-side correction layer; The input correlation coefficient matrix of the output-side correction layer; The output correlation coefficient matrix of the output-side correction layer; It is the identity matrix; These are the constant parameters of the output-side correction layer; This is to assist in calculating the matrix.

[0013] As a preferred technical solution, the specific process of S4 includes: S41. Collect and combine the noisy inputs and noisy outputs of each sensor in the required modeling system to generate a noisy dataset and set the training hyperparameters. S42. Based on the noise resistance loss function, construct the objective function, train the noise resistance hard constraint physical neural network with configured parameters based on the noise dataset, and supervise the training process using the objective function and the noise resistance loss function. S43. Output the trained noise-resistant hard-constraint physical neural network as a process industry system model.

[0014] As a preferred technical solution, the specific formula for the objective function in S42 is as follows: in, For noise reduction loss function, The set of parameters to be optimized includes all parameters of the noise-resistant hard-constrained physical neural network. This represents the total number of training samples in the noisy dataset.

[0015] As a preferred technical solution, the specific formula for the noise reduction loss function is as follows: in, It is the prediction output of the model front end. ; The parameter set of a noise-resistant hard-constraint physical neural network , for the Measurement input for each sample The front-end neural network is used to perform calculations, and the preliminary prediction results on the output side are obtained.

[0016] According to another aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, characterized in that the program, when executed by a processor, implements the process industry system modeling method based on a noise-resistant hard-constraint physical neural network as described above.

[0017] Compared with the prior art, the present invention has the following beneficial effects: 1. In this invention, by constructing a noise-resistant hard-constraint physical neural network, the modeling difficulty of complex systems is significantly reduced compared with the first-principles model. In this invention, the modeling process is completed by first initially constructing a noise-resistant hard-constraint physical neural network, then applying physical constraints and noise correction, and finally performing noise-resistant training. Compared with traditional data-driven models, it has stronger generalization ability and mechanistic interpretability while possessing data efficiency. It achieves the beneficial effect of improving the prediction accuracy of the established alternative model in noisy input environments while ensuring physical consistency.

[0018] 2. In this invention, the front-end neural network paradigm can be selected as needed to adapt to different production practice scenarios in various process industries, avoiding the limitations of fixed architectures and balancing modeling efficiency and fitting effects. Furthermore, this invention uses linear equation constraints to encode physical conservation laws, forcing the model to follow objective system laws, reducing the risk of overfitting in purely data-driven systems, and maintaining good generalization ability even when data is scarce or operating conditions change.

[0019] 3. In this invention, by generating the covariance matrix of sensor measurement noise based on uncertainty, and starting from the actual situation that both the input and output quantities of training data contain measurement noise during the system modeling process, a method for establishing a hard-constrained physical neural network that can predict noise-free output from noisy system input is proposed. This makes the method more practical in production compared to existing similar methods.

[0020] 4. In this invention, by configuring the parameters of the noise-resistant hard constraint correction layer based on the covariance matrix and linear equality constraints, the noise-resistant hard constraint correction layer can appropriately embed hard constraint mechanisms into the physical neural network, thereby generating the optimal correction amount that satisfies the constraints while considering prior noise knowledge. Compared with existing similar methods, the method proposed in this invention can significantly improve the prediction accuracy of the established model in noisy input environments while ensuring physical consistency. Furthermore, the noise-resistant hard constraint correction layer constructed in this way has an analytical solution, which mathematically guarantees that the established model can comply with the constraints during the training and prediction stages. At the same time, it eliminates the need for additional online optimization computing power during training and deployment, thereby maintaining a computational efficiency comparable to that of soft-constrained physical information neural networks.

[0021] 5. In this invention, an objective function is constructed based on a noise-resistant loss function. A noise-resistant hard-constraint physical neural network with configured parameters is trained on a noisy dataset. The objective function undergoes sample normalization to balance the influence weights of different samples, avoiding interference from extreme samples during training, thus making the model training more stable and improving overall modeling consistency. The loss function incorporates inverse weighting of the noise covariance matrix, assigning reasonable weights to high-noise samples. Simultaneously, it connects the output of the front-end neural network with the results of the correction layer, making supervised training more targeted and further enhancing the noise resistance effect. Attached Figure Description

[0022] Figure 1 This is a schematic diagram illustrating the steps of the process industry system modeling method based on a noise-resistant hard-constraint physical neural network in this invention. Figure 2 This is a schematic diagram of the architecture of the noise-resistant hard-constraint physical neural network in this invention; Figure 3 This is a schematic diagram of the fully connected neural network structure in this invention; Figure 4 This is a schematic diagram of the architecture of the dimethyl ether-diethyl ether synthesis system in the examples; Figure 5 This is a comparison chart of the root mean square error of each model in the examples on the training and validation sets of the dimethyl ether-diethyl ether synthesis system; Figure 6 This is a comparison chart of the root mean square error of each model on the test set of the dimethyl ether-diethyl ether synthesis system in the examples; Figure 7 This is a comparison chart of the absolute errors between the predicted values ​​and the noise-free true values ​​of each model on the test set of the dimethyl ether-diethyl ether synthesis system in the examples. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0024] This paper proposes a method for modeling noisy process industrial systems by constructing a noise-resistant hard-constraint physical neural network. First, the specific form of the front-end of the noise-resistant hard-constraint physical neural network framework is determined. Then, linear constraint equations are established based on the physical conservation laws obeyed by the system being modeled, and the parameters of the noise-resistant hard-constraint correction layer in the model are configured in conjunction with the uncertainties of the sensor measurements of each variable. Next, a noise dataset is generated by combining the noisy system input and output obtained from sensor measurements, and the model is trained using a noise-resistant loss function. The trained model can be directly extrapolated using the noisy system input to obtain the predicted value of the noise-free true system output. This modeling method combines mechanistic interpretability and data-driven flexibility, improving the prediction accuracy of the established alternative model in noisy input environments while ensuring physical consistency by embedding hard constraints and noise priors.

[0025] Example 1 In this embodiment, a process industry system modeling method based on a noise-resistant hard-constraint physical neural network is adopted. The method steps are as follows: Figure 1 As shown, it specifically includes: S1. Construct a noise-resistant hard constraint physical neural network, which includes a framework front end, a noise-resistant hard constraint correction layer, and a noise-resistant loss function. S2. Based on the physical relationship between the input and output of the system to be modeled, construct linear equality constraints; S3. Quantify the uncertainty of each sensor in the required modeling system, and configure the parameters of the noise-resistant hard constraint correction layer based on the uncertainty and linear equality constraints. S4. Using a noise-resistant loss function, the noise-resistant hard-constraint neural network with configured parameters is trained using a noise dataset to obtain a process industry system model.

[0026] In this embodiment, the method is specifically applied in the following steps: 1) Determine the specific form of the front end of the noise-resistant hard-constraint physical neural network framework.

[0027] Based on the requirements of production practice, the most suitable neural network paradigm is selected as the front-end approximator of the constructed noise-resistant hard-constraint physical neural network.

[0028] The noise-resistant hard-constraint physical neural network constructed in this scheme consists of a freely selectable data-driven approximator (front end) and a noise-resistant hard-constraint correction layer (back end) used to correct the front end, such as... Figure 2 As shown. This backend can be integrated with various neural network paradigms, including recurrent neural networks, convolutional neural networks, and graph neural networks. In this embodiment, to enable standardized performance benchmarking tests against existing hard-constrained neural network implementations, the framework's frontend adopts a fully connected neural network architecture. The basic structure of a fully connected neural network is as follows: Figure 3 As shown. The fully connected neural network used in this embodiment contains two hidden layers with a dimension of 32, and uses a modified linear unit as the activation function.

[0029] 2) Establish linear constraint equations based on the physical conservation laws obeyed by the modeled system.

[0030] Determine the input of the physical system being modeled and output The physical relationship between them can be expressed as a linear equality constraint, based on the conservation laws derived from fundamental engineering principles: in, and It is a matrix of constant coefficients that encodes the physical conservation laws, and It is a constant vector.

[0031] This embodiment focuses on a factory-level system composed of multiple subsystem units, and its process is as follows: Figure 4 As shown. Figure 4 The system achieves continuous processing of "feeding, extrusion, adsorption, backwashing / separation, and finished product output," while a supporting circulation unit maintains the system's material balance. A detailed explanation of each module and material flow direction is as follows: 1. Feeding and extrusion unit Input: Feed Material (MEW); Equipment: M1 (mixing / conveying equipment), B5 (pump), S10 (valve), D1 (squeezing tank), M2 (transfer pump); Function: Extrudes the MEW feed material to separate wastewater (labeled as wastewater CW) and discharges it from the system; the processed material is conveyed to the next unit by M2.

[0032] 2. Adsorption unit Input: Material from the extrusion unit; Equipment: HC (transfer pump), PLUG1 / PLUG2 (adsorption packing column, used for adsorption and purification of materials), S11 (valve). Auxiliary interface: BK-IN: Backwash feed inlet (material inlet for subsequent backwashing processes); Purging PU: An interface used to purge residual materials from the packed column after adsorption is complete; FRS-OUT: The outlet of the material after adsorption treatment (or the feed outlet of the packed column); Function: Adsorbs and purifies materials through PLUG1 / PLUG2 packing columns. After completion, the column can be cleaned through the purge port.

[0033] 3. Backwash / Separation Unit Input: Backwash material from the adsorption unit (marked RK-OUT); Equipment: B2 (transfer pump), S12 (valve), D2 / D3 / D4 (separation container); Auxiliary interface: Solvent METHOD (replenishing solvent for material separation); Output: Semi-finished product DMR: intermediate product after separation; Discharge DEE: Finished product material after final processing 4. Loop Unit Equipment: S1 (valve), B1 (circulating pump), M2 (mixing / transfer equipment); interface: RECV1 / RECV2: Material interface to be recycled (to return some materials within the system). WATER-CH: Water supply interface; METH: Refill interface; Function: To recycle a portion of the material back into the system (to merge with the material in the extrusion unit), while simultaneously replenishing water and solvent to maintain the material balance and processing stability of the system.

[0034] The factory produces methanol (Methanol, ), Ethanol E, Dimethyl ether (DME) was synthesized from W and water. ) and diethyl ether (DEE) The raw materials enter the pretreatment unit with the input stream, where waste liquid CW is first removed, and then the materials are sent to the reaction unit. The reaction products are separated and purified in the separation unit, and the heavier components are recycled. This embodiment aims to model a multi-input multi-output dimethyl ether-diethyl ether synthesis system by constructing a noise-resistant hard-constraint physical neural network, so as to predict the actual output mass flow rates of each component under given noisy input mass flow rates and noisy discharge mass flow rates. According to the law of mass conservation, the total input mass flow rate is equal to the total output mass flow rate. The linear constraint equations are shown in Table 1, where... , , .

[0035] Table 1. Definitions of quantities and linear constraint equations for the dimethyl ether-diethyl ether synthesis system. 3) Combine the uncertainties of each sensor in the system with the parameters of the noise-resistant hard constraint correction layer in the system constraint configuration model.

[0036] 301) Based on the uncertainties of each sensor in the system, determine and .

[0037] Based on the uncertainties of the sensors measuring each input and output in the modeled physical system, determine the sensor measurement noise. , covariance matrix and . , It follows a pattern with a mean of zero and covariance matrices of [missing information]. and The Gaussian distribution of the system's measured input. Measurement output Real input Actual output The following relational equation is satisfied: in, , , Indicates the sampling index.

[0038] In this embodiment, the measurement processes of each variable are independent, and the uncertainties of each sensor are known. and The matrix is ​​a diagonal array, and the percentage of the variance of each noise component relative to its maximum value is: , .

[0039] 302) Combine the constant coefficient matrix of the linear constraint equation to configure the parameters of the noise-resistant hard constraint correction layer.

[0040] Substituting the coefficient matrices into the algebraic expression of the proposed noise-resistant hard-constraint correction layer, the analytical expression of the noise-resistant hard-constraint correction layer is determined. This allows for simultaneous adjustment of the measurement input while considering prior noise knowledge. and neural network output The optimal correction amount that satisfies the constraints and achieves the minimum variance correction magnitude is obtained. and The letter expression for the noise-resistant hard-constraint correction layer is as follows: in: In this embodiment , , , , It has been determined that the analytical expression for the noise-resistant hard constraint correction layer can be determined by substituting it in.

[0041] 4) Use a noise-resistant loss function and train the model using a noisy dataset.

[0042] 401) A noise dataset is generated from the noisy input and noisy output measured by the combined sensors. , }, determine the optimizer and hyperparameters such as learning rate used for model training.

[0043] 402) Use a robust loss function to supervise the model training process. The robust loss function that uses a weighted norm to simultaneously supervise both input and output predictions is shown below: in: The dataset used in this embodiment for the dimethyl ether-diethyl ether synthesis system contains over 1200 pairs of noisy samples. All samples were normalized using the maximum absolute value scaling method to make the data distribution more reasonable and uniform. During model training, the Adam optimizer with an adaptive learning rate was used to accelerate convergence. The initial learning rate was set to 5e-3, and the batch size was 16. , , , , The expression for the noise reduction loss function can be obtained by substituting the given information.

[0044] 5) Use the trained model to extrapolate the noisy input to obtain the predicted value of the noise-free true output.

[0045] In actual production, the noisy input values ​​of the system measured by sensors are read, and the trained noise-resistant hard-constraint physical neural network can be used as a substitute model for the first-principles model of the original process industry system to obtain the predicted value of its corresponding noise-free true output.

[0046] In this embodiment, the dimethyl ether-diethyl ether synthesis system dataset is divided into training, validation, and test datasets in a 6:2:2 ratio. Fully connected neural networks (NNs), soft-constraint physical neural networks (PINNs), and Karush-Kuhn-Tucker condition-integrated physical neural networks (KKT-hPINNs) are selected as comparison schemes for standardized performance benchmark comparison tests. The model's performance is evaluated based on the root mean square error between the predicted and true values ​​of the noiseless output.

[0047] During the training phase, the terminal convergence and overfitting of the noise-resistant hard-constraint physical neural network constructed in this scheme and the compared model are examined on the training dataset. Figure 5 The figure shows a comparison of the root mean square errors (RMSEs) of various models on the training and validation sets of the dimethyl ether-diethyl ether synthesis system. In the figure, the green dashed and green solid lines represent the RMSEs of the NN model on the training and validation sets, respectively; the yellow dashed and yellow solid lines represent the RMSEs of the PINN model on the training and validation sets, respectively; the red dashed and red solid lines represent the RMSEs of the KKT-hPINN model on the training and validation sets, respectively; and the blue dashed and blue solid lines represent the RMSEs of the NR-hPINN (Noise-Resistant hybrid Physics-Informed Neural Network) on the training and validation sets, respectively. Figure 5 The learning curves shown indicate that, over the last 50 epochs (training rounds), this approach exhibits the smallest root mean square error (RMSE) among all models on the validation set, demonstrating better training convergence compared to other methods. The smallest difference between its RMSE on the training and validation sets indicates lower overfitting to the training set compared to other methods.

[0048] Table 2 Comparison of test indicators for modeling methods of dimethyl ether-diethyl ether synthesis system During the testing phase, the average root mean square error of each proxy model across ten tests is shown in Table 2 and... Figure 6 As shown, the noise-resistant hard-constraint physical neural network can reduce the test loss by 12.3% compared to the fully connected neural network, which is much greater than the 1.5% of the KKT-conditional hard-constraint physical neural network and the 3.7% of the soft-constraint physical neural network. Figure 6The graph shows the root mean square error (RMSE) of each model on the test set of the dimethyl ether-diethyl ether synthesis system (average of ten experimental results). Figure 6 The percentage means the improvement in performance of other models relative to the fully connected neural network; Figure 7 This is a comparison chart of the absolute errors of the predicted values ​​and the noise-free true values ​​of each model on the test set of the dimethyl ether-diethyl ether synthesis system (the average error of all corresponding output values ​​is taken at each sample point). Figure 7 The figure shows the absolute errors of the noise-resistant hard-constraint physical neural network and the KKT conditional hard-constraint physical neural network on each sample point of the test set. In the figure, the blue line represents the absolute error of the NR-hPINN method, and the red dashed line represents the absolute error of the KKT-hPINN method. Compared with the latter, the noise-resistant hard-constraint physical neural network has a smaller absolute error on more sample points.

[0049] The results above demonstrate that modeling using the noise-resistant hard-constraint physical neural network constructed in this scheme can provide more robust and reliable results when performing extrapolation tasks. The modeling process is completed by first initially constructing the noise-resistant hard-constraint physical neural network, then applying physical constraints and noise correction, and finally performing noise-resistant training. Compared with traditional data-driven models, this approach offers stronger generalization ability and mechanistic interpretability while maintaining data efficiency. It achieves the beneficial effect of improving the prediction accuracy of the established alternative model in noisy input environments while ensuring physical consistency.

[0050] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for modeling process industry systems based on noise-resistant hard-constraint physical neural networks, characterized in that, The method steps include: S1. Construct a noise-resistant hard constraint physical neural network, which includes a framework front end, a noise-resistant hard constraint correction layer, and a noise-resistant loss function. S2. Based on the physical relationship between the input and output of the system to be modeled, construct linear equality constraints; S3. Quantify the uncertainty of each sensor in the required modeling system, and configure the parameters of the noise-resistant hard constraint correction layer based on the uncertainty and linear equality constraints. S4. Using a noise-resistant loss function, the noise-resistant hard-constraint neural network with configured parameters is trained using a noise dataset to obtain a process industry system model.

2. The process industry system modeling method based on a noise-resistant hard-constraint physical neural network according to claim 1, characterized in that, The front end of the framework is based on the neural network paradigm, which is selected based on the specific production practice requirements of the process industry system to be modeled.

3. The process industry system modeling method based on a noise-resistant hard-constraint physical neural network according to claim 1, characterized in that, The linear equality constraint refers to the physical relationship between the input and output of the system to be modeled. in, and This is a matrix of constant coefficients that encodes the physical conservation laws; It is a constant vector; It is the set of real numbers; The number of independent physical laws that the process industrial system to be modeled must follow; The number of input variables for the system to be modeled; The number of output variables for the system to be modeled.

4. The process industry system modeling method based on a noise-resistant hard-constraint physical neural network according to claim 1, characterized in that, The specific process of S3 includes: S31. Quantify the uncertainty of each sensor in the required modeling system, and generate the covariance matrix of sensor measurement noise based on the uncertainty. and ; S32. Based on the covariance matrix and linear equality constraints, configure the parameters of the noise-resistant hard constraint correction layer.

5. The process industry system modeling method based on a noise-resistant hard-constraint physical neural network according to claim 4, characterized in that, The sensor measurement noise in S31 has a mean of zero and covariance matrices of [missing information]. and Gaussian distribution of the sensor measurement noise and the system measurement input. Measurement output Real input Actual output The following relational equation is satisfied: in, This is real input. This is the actual output. Sample numbering, , is the sampling index. It is the set of real numbers; The number of input variables for the system to be modeled; The number of output variables for the system to be modeled.

6. The process industry system modeling method based on a noise-resistant hard-constraint physical neural network according to claim 5, characterized in that, The specific formula for the parameters of the noise-resistant hard constraint correction layer in S32 is as follows: in, and These are the input-side optimization estimate and the output-side optimization estimate of the noise-resistant hard constraint correction layer, respectively. This is the predicted output of the model's front end; and These are the covariance matrices of the input-side sensor measurement noise and the output-side sensor measurement noise, respectively. and This is a matrix of constant coefficients that encodes the physical conservation laws; It is a constant vector; This is the input correlation coefficient matrix of the input-side correction layer; The output correlation coefficient matrix of the input-side correction layer; These are the constant parameters of the input-side correction layer; The input correlation coefficient matrix of the output-side correction layer; The output correlation coefficient matrix of the output-side correction layer; It is the identity matrix; These are the constant parameters of the output-side correction layer; This is to assist in calculating the matrix.

7. The process industry system modeling method based on a noise-resistant hard-constraint physical neural network according to claim 6, characterized in that, The specific process of S4 includes: S41. Collect and combine the noisy inputs and noisy outputs of each sensor in the required modeling system to generate a noisy dataset and set the training hyperparameters. S42. Based on the noise resistance loss function, construct the objective function, train the noise resistance hard constraint physical neural network with configured parameters based on the noise dataset, and supervise the training process using the objective function and the noise resistance loss function. S43. Output the trained noise-resistant hard-constraint physical neural network as a process industry system model.

8. The process industry system modeling method based on a noise-resistant hard-constraint physical neural network according to claim 7, characterized in that, The specific formula for the objective function in S42 is as follows: in, For noise reduction loss function, The set of parameters to be optimized includes all parameters of the noise-resistant hard-constrained physical neural network. This represents the total number of training samples in the noisy dataset.

9. The process industry system modeling method based on a noise-resistant hard-constraint physical neural network according to claim 8, characterized in that, The specific formula for the noise reduction loss function is as follows: in, It is the prediction output of the model front end. ; The parameter set of a noise-resistant hard-constraint physical neural network , for the Measurement input for each sample The front-end neural network is used to perform calculations, and the preliminary prediction results on the output side are obtained.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the process industry system modeling method based on noise-resistant hard-constraint physical neural networks as described in any one of claims 1-9.

Images