Due to global energy depletion,solar energy technology has been widely used in the world.The output power of the solar energy systems is affected by solar radiation.Accurate short-term forecasting of solar radiation c...Due to global energy depletion,solar energy technology has been widely used in the world.The output power of the solar energy systems is affected by solar radiation.Accurate short-term forecasting of solar radiation can ensure the safety of photovoltaic grids and improve the utilization efficiency of the solar energy systems.In the study,a new decomposition-boosting model using artificial intelligence is proposed to realize the solar radiation multi-step prediction.The proposed model includes four parts:signal decomposition(EWT),neural network(NARX),Adaboost and ARIMA.Three real solar radiation datasets from Changde,China were used to validate the efficiency of the proposed model.To verify the robustness of the multi-step prediction model,this experiment compared nine models and made 1,3,and 5 steps ahead predictions for the time series.It is verified that the proposed model has the best performance among all models.展开更多
Ice accretion on aircraft poses a critical threat to flight safety by significantly altering aerodynamic performance.This study presents a novel numerical framework for ice accretion prediction,developed by extending ...Ice accretion on aircraft poses a critical threat to flight safety by significantly altering aerodynamic performance.This study presents a novel numerical framework for ice accretion prediction,developed by extending the Myers model and incorporating an advanced multi-step approach.The proposed framework integrates ice layer growth into the modeling of unsteady water film dynamics and introduces a revised criterion for determining the icing condi-tion.A multi-step scheme,accounting for the continuous variation of physical parameters,is implemented to enhance computational accuracy.The framework is validated through simulations on both 2D and 3D configurations.For the NACA0012 airfoil,the model demonstrates strong adaptability to both rime and glaze ice scenarios,with simulated ice shapes and thicknesses showing close agreement with experimental data,especially under low-temperature rime ice scenarios.In glaze ice cases,the framework effectively captures the leading-edge ice thickness and horn formation,albeit with minor positional deviations.For the GLC-305 swept wing,the approach accurately reproduces the primary ice shape features and overall thickness distribution.However,discrepancies in icing extent and thickness persist under rime scenarios due to the limitations of the single-step strategy.In glaze ice scenarios,the model captures the general trend of ice horn development,though positional and thickness deviations remain.Overall,the developed framework improves the precision of ice accretion simulations and offers a promising tool for advancing aircraft safety.Future research will aim to refine the multi-step framework to further improve its robustness and accuracy in complex,3D icing environments.展开更多
By adopting cyclic increment loading and unloading method, time-independent and time-dependent strains can be separated. It is more reasonable to describe the reversible and the irreversible deformations of sample sep...By adopting cyclic increment loading and unloading method, time-independent and time-dependent strains can be separated. It is more reasonable to describe the reversible and the irreversible deformations of sample separately during creep process. A nonlinear elastic-visco-plastic rheological model is presented to characterize the time-based deformational behavior of hard rock. Specifically, a spring element is used to describe reversible instantaneous elastic deformation. A reversible nonlinear visco-elastic （RNVE） model is developed to characterize recoverable visco-elastic response. A combined model, which contains a fractional derivative dashpot in series with another Hook’s body, and a St. Venant body in parallel with them, is proposed to describe irreversible visco-plastic deformation. Furthermore, a three-stage damage equation based on strain energy is developed in the visco-plastic portion and then nonlinear elastic-visco-plastic rheological damage model is established to explain the trimodal creep response of hard rock. Finally, the proposed model is validated by a laboratory triaxial rheological experiment. Comparing with theoretical and experimental results, this rheological damage model characterizes well the reversible and irreversible deformations of the sample, especially the tertiary creep behavior.展开更多
Considering chaotic time series multi-step prediction, multi-step direct prediction model based on partial least squares （PLS） is proposed in this article, where PLS, the method for predicting a set of dependent var...Considering chaotic time series multi-step prediction, multi-step direct prediction model based on partial least squares （PLS） is proposed in this article, where PLS, the method for predicting a set of dependent variables forming a large set of predictors, is used to model the dynamic evolution between the space points and the corresponding future points. The model can eliminate error accumulation with the common single-step local model algorithm~ and refrain from the high multi-collinearity problem in the reconstructed state space with the increase of embedding dimension. Simulation predictions are done on the Mackey-Glass chaotic time series with the model. The satisfying prediction accuracy is obtained and the model efficiency verified. In the experiments, the number of extracted components in PLS is set with cross-validation procedure.展开更多
Accurately predicting motion responses is a crucial component of the design process for floating offshore structures.This study introduces a hybrid model that integrates a convolutional neural network(CNN),a bidirecti...Accurately predicting motion responses is a crucial component of the design process for floating offshore structures.This study introduces a hybrid model that integrates a convolutional neural network(CNN),a bidirectional long short-term memory(BiLSTM)neural network,and an attention mechanism for forecasting the short-term motion responses of a semisubmersible.First,the motions are processed through the CNN for feature extraction.The extracted features are subsequently utilized by the BiLSTM network to forecast future motions.To enhance the predictive capability of the neural networks,an attention mechanism is integrated.In addition to the hybrid model,the BiLSTM is independently employed to forecast the motion responses of the semi-submersible,serving as benchmark results for comparison.Furthermore,both the 1D and 2D convolutions are conducted to check the influence of the convolutional dimensionality on the predicted results.The results demonstrate that the hybrid 1D CNN-BiLSTM network with an attention mechanism outperforms all other models in accurately predicting motion responses.展开更多
The role of heating load forecasts in the energy transition is significant,given the considerable increase in the number of heat pumps and the growing prevalence of fluctuating electricity generation.While machine lea...The role of heating load forecasts in the energy transition is significant,given the considerable increase in the number of heat pumps and the growing prevalence of fluctuating electricity generation.While machine learning methods offer promising forecasting capabilities,their black-box nature makes them difficult to interpret and explain.The deployment of explainable artificial intelligence methodologies enables the actions of these machine learning models to be made transparent.In this study,a multi-step forecast was employed using an Encoder–Decoder model to forecast the hourly heating load for an multifamily residential building and a district heating system over a forecast horizon of 24-h.By using 24 instead of 48 lagged hours,the simulation time was reduced from 92.75 s to 45.80 s and the forecast accuracy was increased.The feature selection was conducted for four distinct methods.The Tree and Deep SHAP method yielded superior results in feature selection.The application of feature selection according to the Deep SHAP values resulted in a reduction of 3.98%in the training time and a 8.11%reduction in the NRMSE.The utilisation of local Deep SHAP values enables the visualisation of the influence of past input hours and individual features.By mapping temporal attention,it was possible to demonstrate the importance of the most recent time steps in a intrinsic way.The combination of explainable methods enables plant operators to gain further insights and trustworthiness from the purely data-driven forecast model,and to identify the importance of individual features and time steps.展开更多
We consider the problem of approximation of the solution of the backward stochastic differential equations in Markovian case.We suppose that the forward equation depends on some unknown finite-dimensional parameter.Th...We consider the problem of approximation of the solution of the backward stochastic differential equations in Markovian case.We suppose that the forward equation depends on some unknown finite-dimensional parameter.This approximation is based on the solution of the partial differential equations and multi-step estimator-processes of the unknown parameter.As the model of observations of the forward equation we take a diffusion process with small volatility.First we establish a lower bound on the errors of all approximations and then we propose an approximation which is asymptotically efficient in the sense of this bound.The obtained results are illustrated on the example of the Black and Scholes model.展开更多
In this paper, the tumor-immune dynamics are simulated by solving a nonlinear system of differential equations. The fractional-order mathematical model incorporated with three Michaelis-Menten terms to indicate the sa...In this paper, the tumor-immune dynamics are simulated by solving a nonlinear system of differential equations. The fractional-order mathematical model incorporated with three Michaelis-Menten terms to indicate the saturated effect of immune response, the limited immune response to the tumor and to account the self-limiting production of cytokine interleukin-2. Two types of treatments were considered in the mathematical model to demonstrate the importance of immunotherapy. The limiting values of these treatments were considered, satisfying the stability criteria for fractional differential system. A graphical analysis is made to highlight the effects of antigenicity of the tumor and the fractionM-order derivative on the tumor mass.展开更多
The reasoning chain generated by the large language models(LLMs)during the reasoning process is often susceptible to illusions that lead to incorrect reasoning steps.Such misleading intermediate reasoning steps may tr...The reasoning chain generated by the large language models(LLMs)during the reasoning process is often susceptible to illusions that lead to incorrect reasoning steps.Such misleading intermediate reasoning steps may trigger a series of errors.This phenomenon can be alleviated by using validation methods to obtain feedback and adjust the reasoning process,similar to the human reflective process.In this paper,we propose a collaborative reasoning framework for mathematical reasoning called CRMR,where a generator is responsible for generating structured intermediate reasoning and a verifier provides detailed feedback on each step of the reason-ing.In particular,we formulate a rigorous form of structured intermediate reasoning called step-by-step rationale(SSR).We evaluated the CRMR framework not only on mathematical word problems but also conducted experiments using open-source and closed-source models with different parameter sizes independently.The results show that our method fully exploits the inference capabilities of the models and achieves significant results on the dataset compared to a single model.展开更多
基金Project(2020TJ-Q06)supported by Hunan Provincial Science&Technology Talent Support,ChinaProject(KQ1707017)supported by the Changsha Science&Technology,ChinaProject(2019CX005)supported by the Innovation Driven Project of the Central South University,China。
文摘Due to global energy depletion,solar energy technology has been widely used in the world.The output power of the solar energy systems is affected by solar radiation.Accurate short-term forecasting of solar radiation can ensure the safety of photovoltaic grids and improve the utilization efficiency of the solar energy systems.In the study,a new decomposition-boosting model using artificial intelligence is proposed to realize the solar radiation multi-step prediction.The proposed model includes four parts:signal decomposition(EWT),neural network(NARX),Adaboost and ARIMA.Three real solar radiation datasets from Changde,China were used to validate the efficiency of the proposed model.To verify the robustness of the multi-step prediction model,this experiment compared nine models and made 1,3,and 5 steps ahead predictions for the time series.It is verified that the proposed model has the best performance among all models.
文摘Ice accretion on aircraft poses a critical threat to flight safety by significantly altering aerodynamic performance.This study presents a novel numerical framework for ice accretion prediction,developed by extending the Myers model and incorporating an advanced multi-step approach.The proposed framework integrates ice layer growth into the modeling of unsteady water film dynamics and introduces a revised criterion for determining the icing condi-tion.A multi-step scheme,accounting for the continuous variation of physical parameters,is implemented to enhance computational accuracy.The framework is validated through simulations on both 2D and 3D configurations.For the NACA0012 airfoil,the model demonstrates strong adaptability to both rime and glaze ice scenarios,with simulated ice shapes and thicknesses showing close agreement with experimental data,especially under low-temperature rime ice scenarios.In glaze ice cases,the framework effectively captures the leading-edge ice thickness and horn formation,albeit with minor positional deviations.For the GLC-305 swept wing,the approach accurately reproduces the primary ice shape features and overall thickness distribution.However,discrepancies in icing extent and thickness persist under rime scenarios due to the limitations of the single-step strategy.In glaze ice scenarios,the model captures the general trend of ice horn development,though positional and thickness deviations remain.Overall,the developed framework improves the precision of ice accretion simulations and offers a promising tool for advancing aircraft safety.Future research will aim to refine the multi-step framework to further improve its robustness and accuracy in complex,3D icing environments.
基金Project(BK20150005)supported by the Natural Science Foundation of Jiangsu Province for Distinguished Young Scholars,ChinaProject(2015XKZD05)supported by the Fundamental Research Funds for the Central Universities,China
文摘By adopting cyclic increment loading and unloading method, time-independent and time-dependent strains can be separated. It is more reasonable to describe the reversible and the irreversible deformations of sample separately during creep process. A nonlinear elastic-visco-plastic rheological model is presented to characterize the time-based deformational behavior of hard rock. Specifically, a spring element is used to describe reversible instantaneous elastic deformation. A reversible nonlinear visco-elastic （RNVE） model is developed to characterize recoverable visco-elastic response. A combined model, which contains a fractional derivative dashpot in series with another Hook’s body, and a St. Venant body in parallel with them, is proposed to describe irreversible visco-plastic deformation. Furthermore, a three-stage damage equation based on strain energy is developed in the visco-plastic portion and then nonlinear elastic-visco-plastic rheological damage model is established to explain the trimodal creep response of hard rock. Finally, the proposed model is validated by a laboratory triaxial rheological experiment. Comparing with theoretical and experimental results, this rheological damage model characterizes well the reversible and irreversible deformations of the sample, especially the tertiary creep behavior.
文摘Considering chaotic time series multi-step prediction, multi-step direct prediction model based on partial least squares （PLS） is proposed in this article, where PLS, the method for predicting a set of dependent variables forming a large set of predictors, is used to model the dynamic evolution between the space points and the corresponding future points. The model can eliminate error accumulation with the common single-step local model algorithm~ and refrain from the high multi-collinearity problem in the reconstructed state space with the increase of embedding dimension. Simulation predictions are done on the Mackey-Glass chaotic time series with the model. The satisfying prediction accuracy is obtained and the model efficiency verified. In the experiments, the number of extracted components in PLS is set with cross-validation procedure.
基金the National Natural Science Foundation of China (Grant No. 52301322)the Jiangsu Provincial Natural Science Foundation (Grant No. BK20220653)+1 种基金the National Science Fund for Distinguished Young Scholars (Grant No. 52025112)the Key Projects of the National Natural Science Foundation of China (Grant No. 52331011)
文摘Accurately predicting motion responses is a crucial component of the design process for floating offshore structures.This study introduces a hybrid model that integrates a convolutional neural network(CNN),a bidirectional long short-term memory(BiLSTM)neural network,and an attention mechanism for forecasting the short-term motion responses of a semisubmersible.First,the motions are processed through the CNN for feature extraction.The extracted features are subsequently utilized by the BiLSTM network to forecast future motions.To enhance the predictive capability of the neural networks,an attention mechanism is integrated.In addition to the hybrid model,the BiLSTM is independently employed to forecast the motion responses of the semi-submersible,serving as benchmark results for comparison.Furthermore,both the 1D and 2D convolutions are conducted to check the influence of the convolutional dimensionality on the predicted results.The results demonstrate that the hybrid 1D CNN-BiLSTM network with an attention mechanism outperforms all other models in accurately predicting motion responses.
基金the German Federal Ministry for Economic Affairs and Climate Action in the framework of the research program EnOB:ML-EBESR 03EN1076B.
文摘The role of heating load forecasts in the energy transition is significant,given the considerable increase in the number of heat pumps and the growing prevalence of fluctuating electricity generation.While machine learning methods offer promising forecasting capabilities,their black-box nature makes them difficult to interpret and explain.The deployment of explainable artificial intelligence methodologies enables the actions of these machine learning models to be made transparent.In this study,a multi-step forecast was employed using an Encoder–Decoder model to forecast the hourly heating load for an multifamily residential building and a district heating system over a forecast horizon of 24-h.By using 24 instead of 48 lagged hours,the simulation time was reduced from 92.75 s to 45.80 s and the forecast accuracy was increased.The feature selection was conducted for four distinct methods.The Tree and Deep SHAP method yielded superior results in feature selection.The application of feature selection according to the Deep SHAP values resulted in a reduction of 3.98%in the training time and a 8.11%reduction in the NRMSE.The utilisation of local Deep SHAP values enables the visualisation of the influence of past input hours and individual features.By mapping temporal attention,it was possible to demonstrate the importance of the most recent time steps in a intrinsic way.The combination of explainable methods enables plant operators to gain further insights and trustworthiness from the purely data-driven forecast model,and to identify the importance of individual features and time steps.
基金This work was done with partial financial support of the RSF grant number 14-49-10079.
文摘We consider the problem of approximation of the solution of the backward stochastic differential equations in Markovian case.We suppose that the forward equation depends on some unknown finite-dimensional parameter.This approximation is based on the solution of the partial differential equations and multi-step estimator-processes of the unknown parameter.As the model of observations of the forward equation we take a diffusion process with small volatility.First we establish a lower bound on the errors of all approximations and then we propose an approximation which is asymptotically efficient in the sense of this bound.The obtained results are illustrated on the example of the Black and Scholes model.
文摘In this paper, the tumor-immune dynamics are simulated by solving a nonlinear system of differential equations. The fractional-order mathematical model incorporated with three Michaelis-Menten terms to indicate the saturated effect of immune response, the limited immune response to the tumor and to account the self-limiting production of cytokine interleukin-2. Two types of treatments were considered in the mathematical model to demonstrate the importance of immunotherapy. The limiting values of these treatments were considered, satisfying the stability criteria for fractional differential system. A graphical analysis is made to highlight the effects of antigenicity of the tumor and the fractionM-order derivative on the tumor mass.
基金supported by the National Natural Science Foundation of China(No.62176052)Natural Science Foundation of Shanghai,China(No.21ZR1401700)AI-Enhanced Research Program of Shanghai Municipal Education Commission(No.SMEC-AI-DHUZ-05).
文摘The reasoning chain generated by the large language models(LLMs)during the reasoning process is often susceptible to illusions that lead to incorrect reasoning steps.Such misleading intermediate reasoning steps may trigger a series of errors.This phenomenon can be alleviated by using validation methods to obtain feedback and adjust the reasoning process,similar to the human reflective process.In this paper,we propose a collaborative reasoning framework for mathematical reasoning called CRMR,where a generator is responsible for generating structured intermediate reasoning and a verifier provides detailed feedback on each step of the reason-ing.In particular,we formulate a rigorous form of structured intermediate reasoning called step-by-step rationale(SSR).We evaluated the CRMR framework not only on mathematical word problems but also conducted experiments using open-source and closed-source models with different parameter sizes independently.The results show that our method fully exploits the inference capabilities of the models and achieves significant results on the dataset compared to a single model.
