Uncertain Model Research Articles

Adaptive Two-Degree-of-Freedom Robust Gain-Scheduling Control Strategy

This study introduces a novel tracking control strategy tailored to aeroengines, which are highly nonlinear and characterized by significant uncertainty. The proposed method entails a robust extended Kalman filter (REKF) enhanced by a forgetting factor for improved performance. An accompanying augmented, mixed onboard adaptive model based on the REKF precisely estimates and manages engine performance degradation. This advanced model effectively counters the degradation term in the perturbation block of the engine’s uncertain model. Using this strategic approach, a robust gain-scheduling controller was constructed and was found to outperform its predecessors, marking a notable advancement in control system design. Controlling twin rotor multi-input, multi-output (MIMO) systems is a highly complex process due to model uncertainties and unpredictable external disturbances. To address these challenges, we constructed an adaptive two-degree-of-freedom robust gain-scheduling controller (ATDF-RGSC) using a mixed sensitivity approach. Rigorous performance analysis confirms that this controller offers enhanced robustness, faster tracking, and more precise disturbance attenuation compared to other methods. These advanced control strategies successfully manage uncertainties and disturbances, improving performance metrics in both simulated and experimental scenarios. The proposed method may significantly enhance the safety and reliability of aeroengines and MIMO systems in practical applications.

A portfolio optimization model under uncertain random environment

<p>Uncertain events frequently occur in today’s financial markets. Consequently, the issue of portfolio selection is becoming increasingly significant. This paper thoroughly considers the complexities of stock returns in real-world scenarios and employs uncertain differential equations (UDE), uncertain time series analysis (UTSA), stochastic differential equations (SDE), and random time series analysis (RTSA) to predict stock returns, thereby enhancing the accuracy of these predictions. Furthermore, this paper addresses investors’ preferences and the limitations of using variance as a measure of investment risk. It introduces a risk preference factor and proposes an uncertain random mean-lower variance model. Finally, a genetic algorithm is utilized to solve the model, and numerical simulations are conducted to demonstrate the model’s practicality.<strong></strong></p>

Modeling China’s Per Capita Disposable Income by Uncertain Statistics

Uncertain statistics is a set of mathematical techniques for collecting, analyzing and interpreting data by uncertainty theory. There are mainly three modeling methods in uncertain statistics: uncertain time series analysis, uncertain regression analysis, and uncertain differential equation. This paper applies these tools to modeling China’s per capita disposable income, and employs uncertain hypothesis test to determine whether the estimated uncertain statistical models fit China’s per capita disposable income. In addition, this paper shows that it is necessary to use uncertain statistics instead of probability statistics to model China’s per capita disposable income by investigating the corresponding residuals.

Gaia/GSP-spec spectroscopic properties of γ Doradus pulsators

Context. The third Data Release of the ESA Gaia mission has provided a large sample of new gravity-mode pulsators, among which more than 11 600 are γ Dor stars. Aims. The goal of the present work is to present the spectroscopic parameters of these γ Dor pulsators estimated by the GSP-Spec module that analysed millions of Gaia spectra. Such a parametrisation could help confirm their γ Dor nature and provide their chemo-physical properties. Methods. The Galactic positions, kinematics, and orbital properties of these new Gaia pulsators were examined in order to define a sub-sample belonging to the Milky Way thin disc, in which these young stars should preferentially be found. The stellar luminosities, radii, and astrometric surface gravities were estimated without adopting any priors from uncertain stellar evolution models. These parameters, combined with the GSP-Spec effective temperatures, spectroscopic gravities, and metallicities were then validated by comparison with recent literature studies. Results. Most stars are found to belong to the Galactic thin disc, as expected. It is also found that the derived luminosities, radii, and astrometric surface gravities are high quality and have values typical of genuine γ Dor pulsators. Moreover, we show that Teff and [M/H] of pulsators with high enough S/N spectra or slow to moderate rotation rates are robust. This allowed to define a sub-sample of genuine slow-rotating Gaiaγ Dor pulsators. Their Teff were found to be between ∼6500 and ∼7800 K, log(g) is around 4.2, and the luminosities and stellar radii peak at ∼5 L⊙ and ∼1.7 R⊙, The median metallicity is close to the Solar value, although γ Dor with higher and lower metallicities by about ±0.5 dex were also identified. The [α/Fe] content is fully consistent with the chemical properties of the Galactic disc. Conclusions.Gaia/DR3 spectroscopic properties of γ Dor stars therefore confirm the nature of these pulsators and allow to chemo-physically parametrise a new large sample of such stars. Moreover, future Gaia data releases should drastically increase the number of γ Dor stars with parameters spectroscopically derived with good precision.

Reconstruction of exposure to volatile organic compounds from venous blood concentration and an uncertain physiologically-based pharmacokinetic model

Physiologically-based pharmacokinetic modeling was applied to determine exposures to volatile organic compounds, specifically focusing on m-xylene. Passive diffusion was used to describe permeation through the skin. The proposed model agreed with the experimental data and allowed researchers to monitor the concentration profiles in different compartments. The study also focused on the impact of parameter uncertainty on the model predictions. Local and global sensitivity analyses evaluated the influence of partition parameters, diffusion coefficients in the skin, and metabolic parameters on the blood concentration. Both methods show that the Michaelis-Menten kinetics and the lean tissue:blood partition coefficients contributed the most to the total variability. A reverse dosimetry approach used the measured biomarker level to estimate the exposure dose in four hours. The results aligned with experimental data when simulations were conducted using random parameters selected within twenty-five percent of the mean.

Modeling and analysis of uncertain Bass diffusion model driven by uncertain Liu process

The Bass diffusion model is one of the most influential models for predicting the diffusion of new products and technologies, but the diffusion process will be affected by some uncertain factors. Usually, such kinds of uncertain factors are characterized as stochastic processes. However, in many cases, this approach can lead to uncertain issues. Therefore, in this article, a Bass diffusion model that incorporates the uncertainty theory is studied. First, we present an uncertain Bass diffusion model where the uncertain disturbance is modeled as an uncertain Liu process. Then, the existence and uniqueness of the uncertain Bass diffusion model are analyzed. Moreover, the uncertain Bass diffusion model is solved by using the 99-α-Runge-Kutta method. Finally, we carry out a numerical simulation on the output of the integrated circuit industry in China by using uncertain differential equations and stochastic differential equations. The results show that modeling with uncertain differential equations is superior to using stochastic differential equations.

Ridge estimation for uncertain autoregressive moving average model with imprecise observations

An uncertain time series is a sequence of imprecisely observed values arranged in chronological order, whose main purpose is to predict future values based on previously observed values. It is significant to select an appropriate parameter estimation method in uncertain time series analysis. Firstly, the paper transforms a one-order uncertain autoregressive moving average model into an uncertain autoregressive model by the iterative method. Secondly, the ridge method is used to estimate the unknown parameters in the uncertain autoregressive moving average model, in which the shrinkage parameter is determined by ridge trace analysis. Thirdly, the forecast value and confidence interval are acquired by the residual analysis of the fitted model. Finally, two examples are provided to verify the validity and feasibility of the method. The result shows that the ridge method can effectually cut down the affection of outliers and improve the prediction accuracy compared with the least square estimation.

Model uncertainty quantification of a degradation model of miter gates using normalizing flow-based likelihood-free inference

Degradation modeling is essential for failure prognostics of miter gates and subsequent risk-informed maintenance or operational decision-making. Typically, degradation models are formulated based on certain assumptions and simplifications and may not fully capture the complexity of underlying degradation mechanisms. Even minor errors in such models may lead to significant discrepancies in failure prognostics due to error accumulation over time. Aiming to improve the accuracy of the degradation model and ensure reliable failure prognostics, this article proposes a degradation model updating framework for miter gates using normalizing flow-based likelihood-free inference, accounting for both model parameter uncertainty and model form uncertainty (i.e., model bias). The proposed work consists of two phases: the offline training phase and the online updating phase. During the offline training phase, the unknown model bias term is modeled as a random noise with uncertain standard deviation. Synthetic data are then generated using a physical model based on prior knowledge of the uncertain model parameters and model bias. The synthetic data are utilized to train an inference model, which has a summary network for data compression and a conditional invertible neural network for parameter estimation. In the online updating phase, the trained inference model uses strain observations to obtain posterior samples. The Gaussian mixture model and dual particle filter techniques are utilized to recursively update posterior samples, thereby improving the estimation accuracy. Subsequently, model bias is inversely estimated using the degradation model, which uses the updated model parameters and the gap length from the inference model. Following that, a regression model is constructed to correct the biases inherent in the simplified degradation model. This process is implemented iteratively over time to perform continuous model updating and failure prognostics. Results of a case study demonstrate the efficacy of the proposed framework in reducing both model parameter uncertainty and recovering model biases and thereby improving the accuracy of failure prognostics of miter gates.

Robust load frequency control in interval power systems via reduced-order generalized active disturbance rejection control

Abrupt load changes, structural discrepancies, and parametric uncertainties cause degraded performance of the high-order power systems. This situation creates a problematic endeavor while analyzing the performance of such high-order systems. Hence, a simple and efficient lower-order control methodology can be deployed to sort out the issues related to load frequency control (LFC) in such systems. This study resolves the LFC problem in parametric bounded power systems by developing a worst-case reduced-order generalized active disturbance rejection control (WRGADRC) method. The core concept of the proposed technique entails that a controller will perform well in nominal scenarios if it performs satisfactorily in worst-case conditions. Therefore, an interval system’s worst-case reduced-order model is first obtained from its different uncertain models; the reduced order controller is then designed using the GADRC technique. The proposed scheme is rigorously validated on various parametric bounded minimum and non-minimum phase single-area and multi-area power systems, instilling confidence in its ability to achieve minimum frequency deviation in multiple scenarios. The supremacy of the proposed scheme is highlighted over some well-established control techniques in the literature related to the LFC problem.

Positioning anti-sway control method for tower crane based on improved MFAC

A model-free adaptive control (MFAC) based on partial format is proposed for the complex modeling and uncertain model parameters of the tower crane (TC) in this paper. Firstly, considering the complexity of the TC nonlinear system, the data model of the TC is obtained through the partial format dynamic linearization method. Then, a model-free adaptive controller is designed for the TC, incorporating the change rate of the tracking error and its derivative into the objective function to address the inefficiency of traditional model-free controllers in controlling TCs. The convergence and stability of the proposed controller are also proved. To further improve the dynamic performance of the system, a tracking differentiator (TD) is introduced after the input signal. Finally, MATLAB simulation and experiments are conducted to verify that the proposed method can achieve precise trolley positioning while suppressing the load swing angle.

Research on network time reliability evaluation method based on uncertainty theory

In view of the problem that existing network time reliability assessment methods often only consider the impact of inherent uncertainty, while ignoring the impact of epistemic uncertainty caused by insufficient fault information on reliability assessment results, a new method based on uncertainty theory is proposed. According to the node range of network reliability, two types of measurement parameters of single node pair and multi-node pair time reliability are designed. The extended uncertain network model is proposed to directly model the epistemic uncertainty characteristics on nodes and links, and further single node and multi-node pair time reliability algorithms based on the most reliable path and the most reliable extended uncertain subnetwork are designed. Finally, taking a six-node network and the backbone network of China Education and Research Network (CERNET) as examples, the method is applied to evaluate two time reliability indicators, verifying the correctness and effectiveness of the method.

Enchanting dynamics: Juvenile and adult predators with prey model in an intuitionistic fuzzy environment

This study represents an interaction model including juvenile and adult predators along with prey, involving key characteristics like the inability of juvenile predators to reproduce, the impact of adult predators on juvenile growth rates and the transformation of some juveniles to adulthood. Furthermore, it is supposed that adult predators intake prey for sustenance, and the logistic growth of prey is assumed in the non-appearance of adult predators. Intra-species competition among adult predators, together with predation of juveniles and chasing, is conveyed. To tackle the imprecise biological parameters, most parametric values are considered as triangular intuitionistic fuzzy numbers. The model is further processed into an intuitionistic fuzzy model using the Hukuhara derivative and Yager’s ranking method is implemented to make the model crispified. Non-negativity and boundedness of the model are explored, after that, an investigation of possible equilibrium points is discussed. Local and global stability analyses close to these points are supervised. The study accentuates the significant influence of uncertain model parameters on the solution. Especially, uncertain estimates of intra-species competition among adult predators remarkably regulate the model’s stability. Extended uncertainty in intra-species competition for prey, although, is discovered to stabilize the system. In addition, increased consumption of juvenile predators by adult predators is observed to provide the system’s instability.

Uncertain Logistic Population Model with Allee Effect

By considering the influence of various uncertain noises, we established an uncertain Logistic population model with Allee effect, which was characterized by an uncertain differential equation. Firstly, we obtained the solution of the model, and discussed the stability of the equilibrium state. Secondly, the unknown parameters in the model were estimated by using the generalized moment estimation method under the framework of uncertainty theory. Finally, the parameter estimations of the model and the properties of the solution were explained by an example analysis.

Music statistics: uncertain logistic regression models with applications in analyzing music

Music statistics: uncertain logistic regression models with applications in analyzing music

Quantifying the Role of Calibration Strategies on Surface‐Subsurface Hydrologic Model Performance

ABSTRACTDistributed, coupled surface‐groundwater hydrologic models are high‐dimensional, given the necessity to reflect the spatially diverse nature of complex hydrologic processes. Furthermore, inverse/inference problems involving these high‐dimensional models are naturally ill‐posed, given the limited information content of state observations that are typically assimilated. Many inversion/inference algorithms do not cope well with high dimensionality, leaving the practitioner to make subjective choices related to uncertain model inputs. The objective of this study is to evaluate the impact of these subjective calibration choices within a formal sensitivity analysis, uncertainty analysis, and parameters estimation (SA‐UA‐PE) framework on model testing for a surface‐subsurface hydrologic model. In doing so, we address the concepts of ‘over‐parameterisation’ and ‘under‐parameterisation’. We completed a series of numerical experiments, testing several otherwise subjective aspects of the calibration process: (1) the number (5, 10, 15, 20) and type (soil, aquifer, land surface, channel) of calibration parameters selected); (2) the type of state observations assimilated (streamflow, groundwater head); and (3) the length of testing period (1 to 14 years), using monthly streamflow and groundwater head as testing data. The experiments were completed for models of the Winnebago River watershed (Minnesota, Iowa), (significant tile drainage) and the Nanticoke River watershed (Delaware, Maryland (significant groundwater‐channel interactions). The selected hydrologic model is SWAT+, using the gwflow module for physically based groundwater storage and flow modelling, and simulations are run for the 2000–2015 period. Through this process, we found that increasing the number of parameters from 5 to 15 improves the representation of streamflow, principally through an improvement of groundwater storage representation and baseflow generation, but minimal improvement when increasing to 20 parameters. Therefore, the SA‐UA‐PE process can be optimised based on an ideal number of parameters that yield adequate results while maintaining a lower computational burden. The method presented here can be used for any watershed, using integrated surface‐subsurface hydrologic models.

Variable selection for uncertain regression models based on elastic net method

On one hand, determining the exact number of explanatory variables in uncertain regression analysis is often challenging, as real-world scenarios are interconnected. On the other hand, it’s worth noting that even when the number of variables is determined, some variables may have minimal impact on the response variable, and retaining them would only increase the complexity of the model. Therefore, variable selection methods can help eliminate variables with minimal impact to enhance the simplicity and interpretability of the model. In light of this, this paper first introduces a novel variable selection strategy based on the elastic net method to address the variable selection problem in uncertain regression models. This method not only offers the flexibility to simplify uncertain regression analysis into Lasso estimation or Ridge estimation but also exhibits extremely high efficiency in variable selection. Secondly, to address the issue of determining tuning parameters, we introduce the cross-validation method to ensure optimal model performance. Furthermore, we propose an uncertain hypothesis testing method based on imprecise observational data, which can help us assess the suitability of estimated parameters. Finally, through a series of numerical examples, we validate the feasibility and effectiveness of this method.

Future increase in extreme El Niño supported by past glacial changes

El Niño events, the warm phase of the El Niño–Southern Oscillation (ENSO) phenomenon, amplify climate variability throughout the world1. Uncertain climate model predictions limit our ability to assess whether these climatic events could become more extreme under anthropogenic greenhouse warming2. Palaeoclimate records provide estimates of past changes, but it is unclear if they can constrain mechanisms underlying future predictions3–5. Here we uncover a mechanism using numerical simulations that drives consistent changes in response to past and future forcings, allowing model validation against palaeoclimate data. The simulated mechanism is consistent with the dynamics of observed extreme El Niño events, which develop when western Pacific warm pool waters expand rapidly eastwards because of strongly coupled ocean currents and winds6,7. These coupled interactions weaken under glacial conditions because of a deeper mixed layer driven by a stronger Walker circulation. The resulting decrease in ENSO variability and extreme El Niño occurrence is supported by a series of tropical Pacific palaeoceanographic records showing reduced glacial temperature variability within key ENSO-sensitive oceanic regions, including new data from the central equatorial Pacific. The model–data agreement on past variability, together with the consistent mechanism across climatic states, supports the prediction of a shallower mixed layer and weaker Walker circulation driving more frequent extreme El Niño genesis under greenhouse warming.

Privacy Protection in Mobile Big Data: Challenges and Solutions

The pervasive use of mobile big data has profoundly altered daily life, providing unprecedented convenience and efficiency. However, with the proliferation of mobile devices and the explosive growth of data volume, the issue of user privacy protection has become increasingly severe. Location information and semantic information, as the two core components of mobile big data, can directly reflect users’ behavioral trajectories and thought dynamics, underscoring the importance of privacy protection. Although existing technologies can protect user data to a certain extent, traditional methods struggle to address increasingly sophisticated attack techniques in the face of evolving privacy threats. A comprehensive privacy protection scheme for mobile big data was proposed in this study, with a focus on two main areas: the privacy protection of location-based and semantic-based mobile big data. For location information protection, an uncertain graph model was employed to effectively resist combined attacks by jointly protecting the user layer and the location layer. For semantic information protection, a hypergraph clustering method was used to structurally protect the user layer and the semantic layer, enhancing the privacy security of semantic information. This study not only addresses existing gaps but also provides new solutions for mobile big data privacy protection, offering significant theoretical and practical value.

Fuzzy-stochastic distributional robust approach for microalgae-based bio-plastic supply chain with new sustainability aspects

The current study offers a sustainable supply chain model that can be used to identify opportunities and constraints for the future of the microalgae-based bio-diesel and bio-plastic industry. The network’s carbon emissions are restricted by an uncertain constraint that allows for flexibility in controlling emissions as needed. The social constraints of the model provides a transparent depiction of labour needs in dynamic business landscape and foster women’s empowerment through a preference coefficient. The proposed model introduces a new upside risk measures under fuzzy-stochastic setting to quantify the upward financial risk. To characterize and manage the model uncertainty, a fuzzy-stochastic distributional robust model is presented. Credibility distribution is utilized to handle fuzzy uncertainty, while box and polyhedral uncertainty sets are included to handle stochastic uncertainty. After that, tractable deterministic formulations of the uncertain model for two ambiguity sets are presented to solve the model. Finally, a number of insights are obtained by means of five test problems that are implemented in Python and resolved by one exact and five meta-heuristic algorithms. Experiments indicate that, when faced with uncertainty, two robust models have produced more stable solutions (16.23% and 19.67% higher stability, respectively) than nominal stochastic model. Further, a 4.68% decline in total cost and 3.27% increment in bio-diesel production can be achieved by increasing bio-diesel conversion rate to 10%. In addition, a 9.09% downturn in total cost and 10.44% rise in bio-plastic production can be obtained by 10% increment in bio-plastic conversion rate. Moreover, 45.38% more woman labours can be recruited by increasing the preference coefficient from −0.2 to +0.2.

Stochastic control of geological carbon storage operations using geophysical monitoring and deep reinforcement learning

Geological carbon storage (GCS) is the process of injecting and storing carbon dioxide (CO2) in the subsurface to reduce greenhouse gas emissions. Safe and profitable GCS operations require effective decision-making in the presence of uncertain geological models, a process which can often be facilitated with geophysical monitoring. In this study, we examine how sequential decision-making algorithms can be combined with geophysical measurements for the optimal control of GCS operations. Specifically, we develop an artificial intelligence model using deep reinforcement learning (DRL) that takes geophysical time-lapse gravity and well pressure monitoring data as input and delivers an optimal CO2 injection policy. The objective of the problem at hand is to maximize the profit of a hypothetical GCS operation while mitigating the potential for induced seismicity, by training DRL agents using combined geostatistical, reservoir and geophysical simulation. Comparisons against two benchmarks – a constant injection strategy and an injection schedule optimized using a commercial reservoir simulator toolbox – show that the stochastic control of such operations from subsurface monitoring data using deep reinforcement learning is feasible. Evaluation results show that DRL agent behavior generates profits which are on average 1 to 8 percent higher than what is possible through a constant injection approach. Furthermore, we show that DRL can generate optimal injection policies applicable to the true (yet previously unseen) subsurface given carefully managed levels of uncertainty.