A material drying cycle prediction method and device based on dynamic physical constraints

Abstract

The application discloses a material drying cycle prediction method and device based on dynamic physical constraints, and belongs to the technical field of industrial drying process optimization and artificial intelligence. The method comprises the following steps: obtaining a small sample amount of training samples; the training samples comprise a drying cycle and a plurality of input features affecting moisture content; a PINN neural network model is constructed, the plurality of input features affecting the moisture content are taken as inputs, the drying cycle is taken as an output, and the PINN neural network model is trained; a loss function is constructed to supervise the training process, and a trained prediction model is obtained; the loss function comprises a data fitting loss, a physical law loss and a monotonicity loss; obtaining to-be-predicted data, inputting the to-be-predicted data into the prediction model, and obtaining a predicted drying cycle. The application can improve the prediction accuracy under the condition of a small sample.

Description

Technical Field

[0001] This invention relates to the fields of industrial drying process optimization and artificial intelligence technology, and in particular to a method and apparatus for predicting material drying cycles based on dynamic physical constraints. Background Technology

[0002] Industrial drying is a key unit operation in chemical, food, and pharmaceutical industries. The precision of its process control directly determines the uniformity of product moisture content, energy consumption efficiency, and the reliability of continuous equipment operation. Taking a drum dryer system as an example, its dynamic process exhibits typical multi-physics coupling characteristics: the heat and mass transfer of the material is simultaneously regulated by operating parameters such as drum rotation speed, filling rate, and inlet air temperature, and is also closely related to physical properties such as particle size distribution and initial humidity. The nonlinear interaction of these variables poses a severe challenge to drying kinetic modeling. Establishing a high-precision drying cycle prediction model not only provides a quantitative basis for equipment parameter optimization but is also a core prerequisite for achieving intelligent and energy-saving operation.

[0003] Current modeling methods have significant limitations in industrial applications. While data-driven methods can capture complex nonlinear relationships through deep learning, their performance is highly dependent on the size and quality of the training samples. Data acquisition in industrial drying processes is often limited by high sensor deployment costs, measurement noise interference under harsh operating conditions, and data sparsity caused by batch production. This leads to a sharp increase in the prediction variance of conventional neural networks under small sample conditions, making it difficult to meet the accuracy requirements of control systems.

[0004] Therefore, it is necessary to provide a method that can accurately predict the drying cycle of materials under small sample conditions. Summary of the Invention

[0005] This invention provides a method and apparatus for predicting material drying cycles based on dynamic physical constraints, which can solve the problem of low prediction accuracy in related technologies. The technical solution is as follows: On the one hand, a method for predicting material drying cycles based on dynamic physical constraints is provided, the method comprising: Obtain a small number of training samples; the training samples include: drying cycle and multiple input features that affect moisture content; A PINN neural network model was constructed, taking multiple input features affecting moisture content as input and the drying cycle as output, and the PINN neural network model was trained. The training process is supervised by a constructed loss function to obtain a trained prediction model; the loss function includes: data fitting loss, physical law loss, and monotonicity loss; the physical law loss is used to ensure the rationality of the mechanism, and the monotonicity loss is used to maintain the physical relationship between variables; Acquire the data to be predicted and input the data to be predicted into the prediction model to obtain the drying cycle of the prediction output; the data to be predicted includes multiple input features that affect the moisture content.

[0006] On the other hand, a material drying cycle prediction device based on dynamic physical constraints is provided, the device comprising: An acquisition unit is used to acquire a small number of training samples; the training samples include: drying cycle and multiple input features that affect moisture content; The building unit is used to build the PINN neural network model. It takes multiple input features that affect moisture content as input and the drying cycle as output to train the PINN neural network model. The training unit is used to supervise the training process using a constructed loss function to obtain a trained prediction model. The loss function includes: data fitting loss, physical law loss, and monotonicity loss. The physical law loss is used to ensure the rationality of the mechanism, and the monotonicity loss is used to maintain the physical relationship between variables. A prediction unit is used to acquire data to be predicted and input the data to be predicted into the prediction model to obtain the predicted drying cycle; the data to be predicted includes multiple input features that affect the moisture content.

[0007] On the other hand, a computer device is provided, the computer device including a memory and a processor, the memory for storing computer programs, and the processor for executing the computer programs stored in the memory to implement the steps of the material drying cycle prediction method based on dynamic physical constraints described above.

[0008] On the other hand, a computer-readable storage medium is provided, wherein a computer program is stored therein, and when the computer program is executed by a processor, the steps of the material drying cycle prediction method based on dynamic physical constraints described above are implemented.

[0009] On the other hand, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps of the material drying cycle prediction method based on dynamic physical constraints described above.

[0010] The technical solution provided by this invention can bring at least the following beneficial effects: This invention employs a PINN neural network to process multiple input features that affect moisture content, enabling the capture of dynamic dependencies during the drying process. By introducing physical law loss and monotonicity loss into the loss function, explicit physical constraints are imposed on the model to ensure the rationality of the mechanism and maintain the physical relationships between variables. This avoids overfitting or extrapolation distortion of pure data under small sample conditions, thereby improving the prediction accuracy under small sample conditions. Attached Figure Description

[0011] 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.

[0012] Figure 1 This is a flowchart of a material drying cycle prediction method based on dynamic physical constraints provided by an embodiment of the present invention; Figure 2 This is a structural diagram of a material drying cycle prediction device based on dynamic physical constraints provided in an embodiment of the present invention; Figure 3 This is a hardware architecture diagram of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0013] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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 some embodiments of the present invention, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0014] Please refer to Figure 1 This invention provides a method for predicting the drying cycle of materials based on dynamic physical constraints, the method comprising: Step 100: Obtain a small number of training samples; the training samples include: drying cycle and multiple input features that affect moisture content; Step 102: Construct the PINN neural network model by taking multiple input features that affect moisture content as inputs and the drying cycle as outputs, and train the PINN neural network model. Step 104: Supervise the training process using the constructed loss function to obtain the trained prediction model; the loss function includes: data fitting loss, physical law loss and monotonicity loss; the physical law loss is used to ensure the rationality of the mechanism, and the monotonicity loss is used to maintain the physical relationship between variables; Step 106: Obtain the data to be predicted and input the data to be predicted into the prediction model to obtain the drying cycle of the prediction output; the data to be predicted includes multiple input features that affect the moisture content.

[0015] In this embodiment of the invention, a PINN neural network is used to process multiple input features that affect moisture content, which can capture the dynamic dependencies in the drying process. Physical law loss and monotonicity loss are introduced into the loss function to impose explicit physical constraints on the model to ensure the rationality of the mechanism and maintain the physical relationship between variables. This avoids overfitting or extrapolation distortion of pure data under small sample conditions and improves the prediction accuracy under small sample conditions.

[0016] The following description Figure 1 The execution method for each step is shown.

[0017] First, for step 100, obtain a small number of training samples.

[0018] In this embodiment of the invention, the training samples include: a drying cycle and multiple input features affecting the moisture content. The training samples further include: an initial moisture content and a target moisture content. The drying cycle is the drying time from the initial moisture content to the target moisture content. It is understood that the target moisture content is less than the initial moisture content.

[0019] For the initial moisture content and target moisture content of the training samples, there are two possible scenarios: Scenario 1: The initial moisture content and the target moisture content are the same in different training samples. In other words, by using different input feature values ​​to dry the material so that its moisture content can be dried from the same initial moisture content to the same target moisture content, the required drying cycle needs to be predicted.

[0020] Scenario 2: The initial moisture content and target moisture content are not exactly the same in different training samples. In other words, different input feature values ​​are used to dry the material so that the material's moisture content can be dried from a given initial moisture content to the desired target moisture content, requiring prediction of the required drying cycle.

[0021] When the initial moisture content and target moisture content of the training samples correspond to different situations, the design of the loss function will not be entirely the same. The design of the loss function for situation one and situation two will be explained separately in the following sections.

[0022] Regardless of whether the initial moisture content and target moisture content of the training samples correspond to Case 1 or Case 2 above, in this embodiment of the invention, the multiple input features used to influence the moisture content may include: drum rotation speed rpm, fill ratio fill_ratio, air temperature air_temp, airflow speed air_flow, wall temperature wall_temp, inlet air humidity and particle size.

[0023] In this embodiment of the invention, training samples can be obtained experimentally. To address the problem of poor prediction accuracy of neural network models under conditions of small sample sizes, sensitivity analysis and boundary constraints can be used to expand the sample size.

[0024] Specifically, the sample expansion method is as follows: For each training sample that has been acquired so far, perform the following: Calculate the sensitivity of the training sample to each input feature; Based on the sensitivity of the training sample to each input feature, noise is generated, and the generated noise is used to inject noise into the corresponding input feature of the training sample; wherein, the noise amplitude of the generated noise is inversely proportional to the sensitivity. By utilizing physical boundary constraints, a specified number of perturbation samples are generated, and these perturbation samples are used as training samples.

[0025] Here, sensitivity (sens) represents the degree of response of the drying cycle prediction to changes in input characteristics. Sensitivity is calculated by taking the partial derivatives (i.e., gradients) of the physical prediction with respect to air temperature and wall temperature. Specifically: The physical model is used to obtain physical prediction values ​​for the training samples; The physical prediction value phys_pred is used as a two-dimensional function of air temperature air_temp and wall temperature wall_temp. The dT_air = value for each sample point is calculated numerically. phys_pred / air_temp and dT_wall= phys_pred / wall_temp; Construct a 7-dimensional sensitivity vector: the first two dimensions are |dT_air| and |dT_wall|, and the sensitivity of the remaining input features is set to zero; this vector is used for data augmentation. The larger the absolute value of the temperature gradient, the more sensitive the drying time is to the temperature, and the smaller the corresponding feature perturbation needs to be to prevent the generation of unreasonable samples.

[0026] In this embodiment of the invention, the physical model is constructed based on the heat and mass transfer theory. This physical model can calculate the rate of change of water content driven by physics based on the current input characteristics and the current water content, and then output the physical prediction value based on the rate of change of water content.

[0027] Noise is a random vector with the same dimension as the input features, and its magnitude is inversely proportional to the normalized sensitivity. The noise magnitude, noise_scale, can be calculated using the following formula: noise_scale = α + β ×(1 - sens) α = 0.03 (basic noise), β = 0.07 (scaling factor).

[0028] The higher the sensitivity (the closer sens is to 1), the lower the noise; when the sensitivity is 0, the noise reaches its maximum (0.10).

[0029] Noise is directly injected into the corresponding input features of the training sample to generate perturbed samples. Specifically: first, the standard deviation σ of each input feature in the training set is calculated; then, a standard normal random vector Z is generated; the noise N = noise_scale × σ × Z is calculated, and the perturbed sample is X_perturbed = X_original + N. X_original is the original training sample.

[0030] Furthermore, for samples near the value boundaries, the noise amplitude is automatically amplified; at the same time, the noise direction is constrained to satisfy physical monotonicity. For example, for negatively correlated features (such as air_temp), the noise is mainly positive to reflect the rule that "as temperature increases, drying time decreases".

[0031] Physical boundary constraints define the value range of each input feature. Perturbation samples are obtained by adding noise that satisfies sensitivity and monotonicity constraints to the original training samples, and then truncating them according to the boundary constraints. For example, the original sample is [rpm=50, fill_ratio=0.3, air_temp=60, air_flow=5, wall_temp=50, humidity=0.01, particle_size=5]; after adding noise, it may become [52, 0.31, 61.5, 4.8, 51.2, 0.0102, 4.9]. If a certain dimension (such as humidity) exceeds the preset range (such as >0.02), it is directly truncated to the boundary value (such as set to 0.02).

[0032] Furthermore, in order to improve the prediction accuracy under small sample size conditions, in addition to the multiple input features mentioned above that affect moisture content, the training samples may also include cross features composed of any two input features.

[0033] Furthermore, when selecting which two input features to combine to obtain cross features, the contribution of each cross feature to the model's predicted output can be used for selection. Specifically, Feature Importance Analysis (SHAP) can be used to calculate the feature importance analysis value of each cross feature, and the cross features with the highest analysis values ​​are selected as the final cross features.

[0034] Preferably, the multiple input features used to influence the moisture content may further include: a cross feature consisting of air temperature and wall temperature, a cross feature consisting of airflow velocity and inlet air humidity, and a cross feature consisting of filling rate and particle size.

[0035] The cross-feature composed of air temperature and wall temperature can be expressed as the product of air temperature and wall temperature; that is, air_temp × wall_temp. The drying process is affected by both convective heat transfer (air temperature) and conductive heat transfer (wall temperature), and their product can better characterize the overall heat source intensity.

[0036] The cross-feature composed of airflow velocity and inlet air humidity can be calculated as follows: Calculate the difference between 1 and the inlet air humidity, and then multiply this difference by the airflow velocity. This product is taken as the cross-feature composed of airflow velocity and inlet air humidity; that is, air_flow × (1 - humidity). Airflow velocity represents air flow capacity, and (1 - humidity) represents the air's drying potential (the lower the humidity, the stronger the drying capacity). The product of the two better reflects the actual dehumidification capacity.

[0037] The cross-feature composed of fill ratio and particle size can be expressed as the product of fill ratio and particle size; that is, fill_ratio × particle_size. Fill ratio affects the exposed area and mixing degree of particles within the drum, while particle size affects the heat and mass transfer surface area and the internal moisture diffusion path. The product of the two can reflect the effective drying area or drying difficulty per unit volume of material.

[0038] These interactive features are designed to capture the nonlinear, coupled physical effects between input features that are difficult to express with simple linear models or independent feature inputs.

[0039] In this embodiment of the invention, the generation of perturbation samples using directional perturbation guided by physical laws ensures the physical rationality of the generated samples. Furthermore, the selection of cross-features—comprising air temperature and wall temperature, airflow velocity and inlet air humidity, and packing ratio and particle size—to enrich the input features is not a simple feature combination, but rather a design based on drying kinetics. Specifically, the cross-feature composed of air temperature and wall temperature reflects the coupling effect of heat transfer between the cylinder wall and air; the cross-feature composed of airflow velocity and inlet air humidity characterizes the drying potential, i.e., the ability of air to remove moisture; and the cross-feature composed of packing ratio and particle size describes the influence of material loading density on drying.

[0040] Then, explanations will be given for step 102, "Constructing a PINN neural network model, taking multiple input features that affect moisture content as inputs and the drying cycle as outputs, and training the PINN neural network model", and for step 104, "Using the constructed loss function to supervise the training process and obtain the trained prediction model".

[0041] In one embodiment of the present invention, the architecture of the PINN neural network model may include, in sequence according to the processing order of the input features, a fully connected layer, a first residual block, an attention module, a second residual block, and an output layer.

[0042] The fully connected layer is used to extract features from the multidimensional features of the input. The first residual block is used to analyze the relationship between signals in depth. The attention module is used to assign higher weights to the dimensional features that have the greatest impact on the drying time of the current working condition. The second residual block is used to weight the dimensional features according to the weights to perform data fusion at a deeper level. The output layer is used to predict the output drying cycle.

[0043] In one implementation, the residual blocks can be designed using the `resBlock` function. Each residual block can contain two fully connected layers and skip connections, effectively mitigating the vanishing gradient problem. The attention module can employ a parallel path design, first generating attention weights through two layers, `attn_fc1` and `attn_fc2`, and then multiplying them with the main path features. The input to the attention module comes directly from the output of the first residual block (`res1_lrelu2`), allowing it to focus on high-sensitivity features in the physical equations. The network ultimately constructs complete connections using the `connectLayers` function, forming a data flow path of "input - residual block 1 - attention weighting - residual block 2 - output".

[0044] In this embodiment of the invention, the loss function includes data fitting loss, physical law loss, and monotonicity loss; the physical law loss is used to ensure the rationality of the mechanism, and the monotonicity loss is used to maintain the physical relationship between variables.

[0045] The data fitting loss is the difference between the predicted and actual values ​​of the drying cycle. The following sections will explain the physical law loss and the monotonicity loss separately.

[0046] In this embodiment of the invention, the physical law loss is the mean square error calculated between the predicted value output by the PINN neural network model and the physical prediction value; wherein, when the initial moisture content and target moisture content of the training samples correspond to the above-mentioned situation one, the physical prediction value is determined as follows: A1: Calculate the temperature effect using airflow velocity and particle size; In this embodiment of the invention, the temperature effect is used to characterize that the higher the temperature, the shorter the drying time.

[0047] In one implementation, the Nusselt number can be used to calculate the temperature effect, reflecting the relative influence of air temperature and wall temperature on the drying process. Specifically, the Reynolds number can be calculated using airflow velocity and particle size, then the Nusselt number on the air side and wall side can be calculated using the Reynolds number, followed by the heat transfer coefficient using the Nusselt number, then the air heat transfer weight and wall heat transfer weight using the heat transfer coefficient, and finally the weighted temperature can be calculated using the air heat transfer weight and wall heat transfer weight. The temperature effect is obtained based on the reciprocal of the weighted temperature. It is evident that the air heat transfer weight and wall heat transfer weight are dynamically changing and need to be calculated based on different input features, thus reflecting the dominant heat transfer mechanism under different operating conditions. The temperature effect is calculated based on the reciprocal of the weighted temperature, conforming to the physical law that the drying rate is proportional to the temperature. This temperature effect is predicted through a physical loss term constrained neural network. The weight of the physical loss term constraint needs to decay exponentially with each training epoch, for example, from an initial 0.3 to a final 0.01, thereby achieving dynamic equilibrium.

[0048] The Reynolds number Re is calculated using the following formula: The air-side Nusselt number and the wall-side Nusselt number are calculated using the following formulas: Where Re is the Reynolds number, Nu_air is the air-side Nusselt number, and Nu_wall is the wall-side Nusselt number.

[0049] The heat transfer coefficient can be calculated using the following formula: Where h_air is the air-side heat transfer coefficient and h_wall is the wall-side heat transfer coefficient.

[0050] The temperature effect temp_effect is calculated using the following formula: Where temp_weight_air is the air heat transfer weight, temp_weight_wall is the wall heat transfer weight, temp_sum is the weighted temperature, air_temp is the air temperature, and wall_temp is the wall temperature.

[0051] A2: Calculate the particle size effect using particle size and drum rotation speed; The particle size effect, size_effect, is calculated using the following formula: The particle size effect calculation takes into account the influence of particle size and drum rotation speed on mass transfer.

[0052] A3: Calculate the humidity effect using inlet air humidity; The humidity effect is calculated using the following formula: The humidity effect can characterize the air drying potential; the lower the humidity, the shorter the drying time.

[0053] A4: Calculate the coupling effect between airflow and filling rate using airflow velocity, filling rate, and drum speed; The coupling effect between airflow and fill ratio is used to simulate airflow velocities under different fill ratios. The calculation method for the coupling effect differs depending on the fill ratio. In one implementation: When the fill rate is less than a first threshold, for example, 15%, then airflow dominates: When the fill rate is greater than the first threshold and less than the second threshold, for example, the second threshold is 40%, then the airflow velocity and drum speed are coupled: When the fill rate exceeds the second threshold, the roller speed becomes the dominant factor. A5: The product of temperature effect, particle size effect, humidity effect and coupling effect is determined as the physical prediction value; this physical prediction value is dimensionless and positively correlated with the drying cycle.

[0054] The physical prediction value phys_pred is calculated using the following formula: The physical prediction value is calculated by integrating all effects. This physical prediction value is a dimensionless exponent that is proportional to the actual drying time.

[0055] After obtaining the physical prediction value, the physical law loss can be calculated using the following formula: physLoss = mse(predictions, phys_target) Wherein, physLoss is the physical law loss, predictions are the drying cycle predictions (standardized drying times) output by the PINN neural network model for multiple input features in the training samples, phys_target is the standardized physical prediction value of phys_pred, and mse is used to calculate the mean square error between the two.

[0056] When the initial moisture content and target moisture content of the training samples correspond to Case 2 above, then in the method for determining the physical prediction value corresponding to Case 1 above, the physical prediction value phys_pred is multiplied by the parameter DDC(M0,Mt). M0 is the initial moisture content, and Mt is the target moisture content.

[0057] In one implementation, DDC(M0,Mt) can be any one of DDC_A and DDC_B, and DDC_A and DDC_B are calculated as follows: DDC_A = (M0 - Mt) / (1 - Mt) The numerator (M0 - Mt) is the total amount of water to be removed (assuming a dry basis moisture content), and the denominator (1 - Mt) is a normalization factor used to account for the weakening of the drying potential when the target moisture content is extremely low (due to the reduction in the driving force of the vapor pressure difference in the air). As Mt approaches 0, the DDC tends towards M0, highlighting the high difficulty of the final stage.

[0058] DDC_B = log( (M0 - Me) / (Mt - Me) ) This is a derivation based on classical drying kinetics (such as the Lewis model). Me represents the equilibrium moisture content of the material (which can be considered a constant or estimated from the inlet air humidity).

[0059] In this embodiment of the invention, the monotonicity loss is a penalty term that, during model training, forces the relationship between specific input features and output predictions to conform to known physical laws, thereby significantly improving the interpretability and physical consistency of the model. This mechanism primarily constrains the feature-output relationship that has been scientifically validated during the drying process.

[0060] Monotonicity loss is used to define the constraint direction of input features through monotonicity labeling. 1 indicates positive correlation, meaning an increase in feature value leads to an increase in drying time; -1 indicates negative correlation, meaning an increase in feature value leads to a decrease in drying time; and 0 indicates no constraint. Specifically, air temperature, wall temperature, and airflow velocity are labeled as -1, meaning an increase in these input features should shorten drying time; inlet air humidity is labeled as 1, meaning an increase in inlet air humidity will prolong the drying process; the cross feature composed of air temperature and wall temperature is labeled as -1; the cross feature composed of airflow velocity and inlet air humidity (1-humidity) is labeled as -1; and other input features are labeled as 0.

[0061] During the gradient calculation phase of model training, the monotonicity loss is reflected through a gradient penalty term. For each training batch, the model calculates the gradient of the output drying cycle prediction with respect to each input feature; For input features marked as negatively correlated, if the gradient of the input feature is positive, it indicates that the increase in the feature value leads to an increase in the predicted value of the drying cycle, which is contrary to the physical law, so a positive penalty is applied; if the gradient of the input feature is negative, a negative penalty is applied. For an input feature that is labeled as positively correlated, if the gradient of the input feature is positive, a negative penalty is applied; if the gradient of the input feature is negative, a positive penalty is applied.

[0062] The ReLU (grad) penalty is the core mechanism of monotonic loss. ReLU(x) = max(0,x), meaning it takes the larger value between x and 0. During training, grad represents the gradient (partial derivative) of the predicted value in the drying cycle with respect to a certain input feature. The sign is used to reflect the monotonic relationship between the feature and the predicted value: a positive gradient means that an increase in the feature increases the predicted value; a negative gradient means that an increase in the feature decreases the predicted value. For example, for a pre-set negatively correlated feature, we expect grad < 0; if the actual grad > 0 (violating physical laws), then ReLU(grad) > 0, triggering the penalty; if grad ≤ 0, then ReLU(grad) = 0, with no penalty. Therefore, this penalty term only adds a positive value to the total loss when the model learns a direction that violates the prior monotonic relationship, thereby forcing the gradient sign to conform to physical laws.

[0063] This ensures that the model does not establish feature relationships that violate basic physical laws during the learning process.

[0064] After obtaining the physical law loss and monotonicity loss using the above scheme, the following total loss can be obtained: totalLoss=dataLoss+lambda_dynamic×physLoss+penalty_weight×monotonic_penalty Where totalLoss is the total loss, dataLoss is the data fitting loss, physLoss is the physical law loss, monotonic_penalty is the monotonicity loss, lambda_dynamic is the physical weight, and penalty_weight is the penalty weight.

[0065] It should be noted that the physical weights employ a dynamic decay strategy, decreasing exponentially with each training epoch. decay_factor=max(0.01, 1 - epoch / decay_epochs) lambda_dynamic=lambda_initial×decay_factor+lambda_final×(1 - decay_factor) Wherein, decay_factor is the decay factor, used to control the decay rate of physical weights; epoch is the number of training epochs; decay_epochs is the decay period, used to control the number of training epochs for the physical constraint to transition from the initial physical weights to the final physical weights. The larger the decay_epochs, the slower the decay process and the longer the physical constraint weights remain at a high level; the smaller the decay, the faster the decay; lambda_dynamic is the physical weight, lambda_initial is the initial physical weight, and lambda_final is the final physical weight.

[0066] In one implementation, the initial physical weight can be 0.3, and the final physical weight can be 0.01.

[0067] Furthermore, in addition to the exponential decay of physics weights with each training epoch as described above, a performance feedback mechanism can be used to adjust the physics weights. Specifically, during model validation, when the validation set MAPE exceeds 10%, an error adjustment factor is automatically used to amplify the physics weights to strengthen physical constraints and correct overfitting or deviation from the trend. This can be achieved through dynamic adjustment in the following manner: error_factor = 1 + 0.5×tanh(0.2×(current_mape - 10)); lambda_dynamic = max(0.005, min(0.8, lambda_decay×error_factor)); Where error_factor is the error adjustment factor, current_mape is the current mean absolute percentage error, lambda_dynamic is the physical weight, and lambda_decay is the base decay weight.

[0068] Ultimately, the physics weights are limited to the range [0.005, 0.8] to prevent extreme values. This design ensures strong physics guidance in the early stages of training, focuses on data fitting in the later stages, and automatically strengthens physics constraints when model performance deteriorates.

[0069] It should be noted that the penalty weights employ a dynamic decay strategy, decreasing exponentially with each training epoch. penalty_weight = 0.7×e (-epoch / numEpochs) Where penalty_weight is the penalty weight, epoch is the number of training epochs, and numEpochs is the preset total number of training epochs.

[0070] This design allows the model to strictly adhere to physical constraints in the early stages of training, while gradually relaxing the constraints in the later stages to better fit the details of the data.

[0071] In each training round, the total loss is used to supervise the training process. The weights of different losses change dynamically in each training round. Once the model is trained, a well-trained prediction model is obtained.

[0072] To verify the effectiveness of the prediction model (DD-PINN) in this invention, it was compared with five typical machine learning models, including unconstrained basic deep neural networks (DDNN), particle swarm optimization-backpropagation hybrid model (PSO-BP), particle swarm optimization-support vector machine hybrid model (PSO-SVM), random forest (RF), and Bayesian optimization-extreme gradient boosting tree hybrid model (BO-XGboost). Performance evaluation included root mean square error (RMSE), mean absolute percentage error (MAPE), and coefficient of determination (R²). 2 Three indicators. The training and prediction accuracy results based on 100 sets of drying process data samples are shown in Table 1, where the numbers after DD-PINN and DDNN models indicate the enhancement sample quantity setting.

[0073] Table 1: Comparison of Training and Prediction Accuracy Results Among Six Types of Models The results show that the DD-PINN model exhibits a significant advantage on the test set. In terms of overall performance, among traditional machine learning models, BO-XGboost performs best, with a test set RMSE of 452.9 seconds, MAPE of 31.9%, and R² of 0.7608, but still significantly lower than DD-PINN. Notably, the performance of the DD-PINN model continuously improves with the increase in the number of augmented samples. When the number of augmented samples is 5, the test set RMSE drops to 134.2 seconds (a 70.4% reduction compared to BO-XGboost), the MAPE is optimized to 4.6% (a relative reduction of 85.6%), and the R² reaches a high of 0.9964, approaching the ideal prediction level. In contrast, the DDNN model without physical constraints, under the same augmentation conditions (DDNN-5), shows significantly worse test set RMSE (255.6 seconds) and MAPE (9.1%) than DD-PINN-5, validating the effectiveness of physical constraints. From the perspective of training stability, the performance fluctuation range of each enhanced version of DD-PINN on the test set (RMSE 134.2-257.8 seconds) is much smaller than that of DDNN (183.8-1192.4 seconds), indicating that physical constraints can effectively suppress overfitting. Specifically, regarding prediction accuracy, DD-PINN-5's MAPE (4.6%) is more than an order of magnitude higher than traditional methods such as PSO-BP (52.5%) and PSO-SVM (41.4%), and its R² value (0.9964) is closest to the theoretical maximum of 1 among all compared models, fully demonstrating the reliability of this method in the drying cycle prediction task. These experimental results systematically confirm that the method of this invention can overcome the performance bottleneck of traditional machine learning in complex industrial scenarios.

[0074] Please refer to Figure 2 This invention provides a material drying cycle prediction device based on dynamic physical constraints, the device comprising: The acquisition unit 200 is used to acquire a small number of training samples; the training samples include: drying cycle and multiple input features that affect moisture content; The building unit 202 is used to build a PINN neural network model, taking multiple input features that affect moisture content as input and the drying cycle as output to train the PINN neural network model; Training unit 204 is used to supervise the training process using a constructed loss function to obtain a trained prediction model; the loss function includes: data fitting loss, physical law loss and monotonicity loss; the physical law loss is used to ensure the rationality of the mechanism, and the monotonicity loss is used to maintain the physical relationship between variables; The prediction unit 206 is used to acquire the data to be predicted and input the data to be predicted into the prediction model to obtain the drying cycle of the prediction output; the data to be predicted includes multiple input features that affect the moisture content.

[0075] In one embodiment of the present invention, the multiple input features used to influence the moisture content include: drum speed rpm, fill ratio, air temperature air_temp, airflow speed air_flow, wall temperature wall_temp, inlet air humidity, and particle size.

[0076] In one embodiment of the present invention, the plurality of input features for influencing moisture content further include: a cross feature consisting of air temperature and wall temperature, a cross feature consisting of airflow velocity and inlet air humidity, and a cross feature consisting of filling rate and particle size.

[0077] In one embodiment of the present invention, the physical law loss is: the mean square error calculated based on the predicted value output by the PINN neural network model and the physical predicted value; the physical predicted value is determined as follows: Calculate the temperature effect using airflow velocity and particle size; The particle size effect is calculated using particle size and drum rotation speed; Calculate the humidity effect using inlet air humidity; The coupling effect between airflow and filling rate is calculated using airflow velocity, filling rate, and drum rotation speed; The product of temperature effect, particle size effect, humidity effect, and coupling effect is determined as the physical prediction value; this physical prediction value is dimensionless and positively correlated with the drying cycle.

[0078] In one embodiment of the present invention, the calculation of temperature effect using airflow velocity and particle size includes: Calculate the Reynolds number using airflow velocity and particle size; Calculate the air-side Nusselt number and the wall-side Nusselt number using the Reynolds number; The heat transfer coefficient is calculated using the Nusselt number, and the air heat transfer weight and wall heat transfer weight are calculated using the heat transfer coefficient. The weighted temperature is calculated using the air heat transfer weight and the wall heat transfer weight, and the temperature effect is obtained based on the reciprocal of the weighted temperature.

[0079] In one embodiment of the present invention, the physical weights of the physical law loss adopt a dynamic decay strategy, which decays exponentially with the number of training rounds: decay_factor=max(0.01, 1 - epoch / decay_epochs) lambda_dynamic=lambda_initial×decay_factor+lambda_final×(1 - decay_factor) Wherein, decay_factor is the decay factor, used to control the decay rate of physical weights; epoch is the number of training epochs; decay_epochs is the decay period, used to control the number of training epochs from the initial physical weights to the final physical weights; lambda_dynamic is the physical weight, lambda_initial is the initial physical weight, and lambda_final is the final physical weight.

[0080] It should be noted that the material drying cycle prediction device based on dynamic physical constraints provided in the above embodiments is only an example of the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the material drying cycle prediction device based on dynamic physical constraints provided in the above embodiments and the material drying cycle prediction method based on dynamic physical constraints belong to the same concept. The specific implementation process is detailed in the method embodiments and will not be repeated here.

[0081] Embodiments of this application also provide a computer device, please refer to... Figure 3 The computer device includes a processor and a memory, the memory storing at least one instruction, at least one program, code set or instruction set, the at least one instruction, at least one program, code set or instruction set being loaded and executed by the processor to implement the material drying cycle prediction method based on dynamic physical constraints provided in the above method embodiments.

[0082] Embodiments of this application also provide a computer-readable storage medium storing at least one instruction, at least one program, code set, or instruction set, wherein the at least one instruction, at least one program, code set, or instruction set is loaded and executed by a processor to implement the material drying cycle prediction method based on dynamic physical constraints provided in the above-described method embodiments.

[0083] Embodiments of this application also provide a computer program product, which includes a computer program. A processor of a computer device reads the computer program from a computer-readable storage medium and executes the computer program, causing the computer device to perform the material drying cycle prediction method based on dynamic physical constraints as described in any of the above embodiments.

[0084] For ease of description, the above systems or devices are described separately as various modules or units based on their functions. Of course, in implementing this application, the functions of each unit can be implemented in one or more software and / or hardware components.

[0085] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of this application.

[0086] Finally, it should be noted that in this document, relational terms such as first, second, third, and fourth are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus.

[0087] The above description is only a preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of this application, and these improvements and modifications should also be considered within the scope of protection of this application.

Claims

1. A method for predicting material drying cycles based on dynamic physical constraints, characterized in that, The method includes: Obtain a small number of training samples; the training samples include: drying cycle and multiple input features that affect moisture content; A PINN neural network model was constructed, taking multiple input features affecting moisture content as input and the drying cycle as output, and the PINN neural network model was trained. The training process is supervised by a constructed loss function to obtain a trained prediction model; the loss function includes: data fitting loss, physical law loss, and monotonicity loss; the physical law loss is used to ensure the rationality of the mechanism, and the monotonicity loss is used to maintain the physical relationship between variables; Acquire the data to be predicted and input the data to be predicted into the prediction model to obtain the drying cycle of the prediction output; the data to be predicted includes multiple input features that affect the moisture content.

2. The method according to claim 1, characterized in that, The multiple input features used to influence moisture content include: drum speed, filling rate, air temperature, airflow velocity, wall temperature, inlet air humidity, and particle size.

3. The method according to claim 2, characterized in that, The multiple input features used to influence moisture content also include: a cross feature consisting of air temperature and wall temperature, a cross feature consisting of airflow velocity and inlet air humidity, and a cross feature consisting of fill rate and particle size.

4. The method according to claim 2, characterized in that, The physical law loss is the mean square error calculated between the predicted value output by the PINN neural network model and the physical predicted value; the physical predicted value is determined as follows: Calculate the temperature effect using airflow velocity and particle size; The particle size effect is calculated using particle size and drum rotation speed; Calculate the humidity effect using inlet air humidity; The coupling effect between airflow and filling rate is calculated using airflow velocity, filling rate, and drum rotation speed; The product of temperature effect, particle size effect, humidity effect, and coupling effect is determined as the physical prediction value; this physical prediction value is dimensionless and positively correlated with the drying cycle.

5. The method according to claim 4, characterized in that, The calculation of temperature effect using airflow velocity and particle size includes: Calculate the Reynolds number using airflow velocity and particle size; Calculate the air-side Nusselt number and the wall-side Nusselt number using the Reynolds number; The heat transfer coefficient is calculated using the Nusselt number, and the air heat transfer weight and wall heat transfer weight are calculated using the heat transfer coefficient. The weighted temperature is calculated using the air heat transfer weight and the wall heat transfer weight, and the temperature effect is obtained based on the reciprocal of the weighted temperature.

6. The method according to any one of claims 1-5, characterized in that, The physical weights for the physical law loss employ a dynamic decay strategy, decreasing exponentially with each training epoch. decay_factor=max(0.01, 1 - epoch / decay_epochs) lambda_dynamic=lambda_initial×decay_factor+lambda_final×(1 - decay_factor) Wherein, decay_factor is the decay factor, used to control the decay rate of physical weights; epoch is the number of training epochs; decay_epochs is the decay period, used to control the number of training epochs from the initial physical weights to the final physical weights; lambda_dynamic is the physical weight, lambda_initial is the initial physical weight, and lambda_final is the final physical weight.

7. A material drying cycle prediction device based on dynamic physical constraints, characterized in that, The device includes: An acquisition unit is used to acquire a small number of training samples; the training samples include: drying cycle and multiple input features that affect moisture content; The building unit is used to build the PINN neural network model. It takes multiple input features that affect moisture content as input and the drying cycle as output to train the PINN neural network model. The training unit is used to supervise the training process using a constructed loss function to obtain a trained prediction model. The loss function includes: data fitting loss, physical law loss, and monotonicity loss. The physical law loss is used to ensure the rationality of the mechanism, and the monotonicity loss is used to maintain the physical relationship between variables. A prediction unit is used to acquire data to be predicted and input the data to be predicted into the prediction model to obtain the predicted drying cycle; the data to be predicted includes multiple input features that affect the moisture content.

8. A computer device, characterized in that, The computer device includes a memory and a processor. The memory is used to store computer programs, and the processor is used to execute the computer programs stored in the memory to implement the steps of the method according to any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the steps of the method described in any one of claims 1-6.

10. A computer program product, characterized in that, Includes a computer program, which, when executed by a processor, implements the steps of the method according to any one of claims 1-6.

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