Search Results (64)

Rainfall infiltration is one of the main factors inducing slope instability, while the spatial heterogeneity and uncertainty of soil parameters have profound impacts on slope response characteristics and stability evolution. Traditional deterministic analysis methods struggle to reveal the dynamic risk evolution process of the system under heavy rainfall. Therefore, this paper proposes an uncertainty analysis framework combining Karhunen–Loève Expansion (KLE) random field theory, Polynomial Chaos Kriging (PCK) surrogate modeling, and Monte Carlo simulation to efficiently quantify the probabilistic characteristics and spatial risks of rainfall-induced slope instability. First, for key strength parameters such as cohesion and internal friction angle, a two-dimensional random field with spatial correlation is constructed to realistically depict the regional variability of soil mechanical properties. Second, a PCK surrogate model optimized by the LARS algorithm is developed to achieve high-precision replacement of finite element calculation results. Then, large-scale Monte Carlo simulations are conducted based on the surrogate model to obtain the probability distribution characteristics of slope safety factors and potential instability areas at different times. The research results show that the slope enters the most unstable stage during the middle of rainfall (36–54 h), with severe system response fluctuations and highly concentrated instability risks. Deterministic analysis generally overestimates slope safety and ignores extreme responses in tail samples. The proposed method can effectively identify the multi-source uncertainty effects of slope systems, providing theoretical support and technical pathways for risk early warning, zoning design, and protection optimization of slope engineering during rainfall periods. Full article

Many authors analyze the prediction of chaos in a Josephson junction with quadratic damping by the Melnikov technique. Due to the lack of an explicit presentation of the Melnikov integral, the researchers apply numerical methods and illustrative examples to verify a good agreement between the numerical method and the analytical one. The reader has difficulty navigating and touching upon Melnikov’s elegant theory and, in particular, the formulation of the Melnikov criterion for the possible occurrence of chaos in a dynamical system, based solely on the provided illustrations of dependencies between the main parameters of the model under consideration. The statements in a number of publications devoted to this interesting topic, such as “It is easy to see that Melnikov’s integrals are finite and not zero. It is possible to see that the transverse zeros of the Melnikov function”, do not shed enough light on the origin of the “horseshoe”-type chaos. In this paper we will try to shed additional light on this important problem. A new planar system corresponding to the N-generalized Josephson junction with quadratic damping with many free parameters is considered, which may be of interest to specialists in the field of engineering sciences. Prediction of chaos in the proposed model by the Melnikov technique is closely related to the problem of approximately simultaneously finding all roots (simple or multiple) of generalized trigonometric polynomials. Several simulations are composed. We also demonstrate some specialized modules for investigating the dynamics of the model. One application about generating stochastic construction for possible control over oscillations is also discussed. Full article

Unstable technological processes, such as turbulent gas and hydrodynamic flows, generate time series that deviate sharply from the assumptions of classical statistical forecasting. These signals are shaped by stochastic chaos, characterized by weak inertia, abrupt trend reversals, and pronounced low-frequency contamination. Traditional extrapolators, including linear and polynomial models, therefore act only as weak forecasters, introducing systematic phase lag and rapidly losing directional reliability. To address these challenges, this study introduces an evolutionary boosting framework within a multi-expert system (MES) architecture. Each expert is defined by a compact genome encoding training-window length and polynomial order, and experts evolve across generations through variation, mutation, and selection. Unlike conventional boosting, which adapts only weights, evolutionary boosting adapts both the weights and the structure of the expert pool, allowing the system to escape local optima and remain responsive to rapid environmental shifts. Numerical experiments on real monitoring data demonstrate consistent error reduction, highlighting the advantage of short windows and moderate polynomial orders in balancing responsiveness with robustness. The results show that evolutionary boosting transforms weak extrapolators into a strong short-horizon forecaster, offering a lightweight and interpretable tool for proactive control in environments dominated by chaotic dynamics. Full article

Rotating detonation engines (RDEs) are expected to have higher specific work and efficiency, but the high-temperature transonic flow delivered by the combustor poses relevant design and technological difficulties. This work proposes a 1D model for turbine internal cooling design which can be used to explore multiple design options during the preliminary design of the cooling system. Being based on an energy balance applied to an infinitesimal control volume, the model is general and can be adapted to other applications. The model is applied to design a cooling system for a pre-existing stator blade geometry. Both the inputs and the outputs of the 1D simulation are in good agreement with the values found in the literature. Subsequently, 1D results are compared to a full conjugate heat transfer (CHT) simulation. The agreement on the internal heat transfer coefficient is excellent and is entirely within the uncertainty of the correlation. Despite some criticality in finding agreement with the thermal power distribution, the Mach number, the total pressure drop, and the coolant temperature increase in the cooling channels are accurately predicted by the 1D code, thus confirming its value as a preliminary design tool. To guarantee the integrity of the blade at the extremities, a cooling solution with coolant injection at the leading and trailing edge is studied. A finite element analysis of the cooled blade ensures the structural feasibility of the cooling system. The computational economy of the 1D code is then exploited to perform a global sensitivity analysis using a polynomial chaos expansion (PCE) surrogate model to compute Sobol’ indices. Full article

To address the challenges of transient voltage stability in modern power systems with high renewables penetration, this paper proposes a multiple stability margin indexes-oriented online risk evaluation and adjustment framework based on a digital twin platform. The System Voltage Deviation Index (S_VDI) is first introduced as a quantitative metric to assess transient voltage stability from time-domain simulation results, capturing the system’s dynamic response under large disturbances. An arbitrary Polynomial Chaos (aPC) expansion combined with Sobol sensitivity analysis is then employed to model the nonlinear relationship between S_VDI and uncertain inputs such as wind power, photovoltaic output, and dynamic load variations, enabling accurate identification of key nodes influencing stability. Furthermore, an emergency control optimization model is developed that jointly considers voltage, frequency, and rotor angle stability margins, as well as the economic costs of load shedding, with a trajectory sensitivity-based local linearization technique applied to enhance computational efficiency. The proposed method is validated on a hybrid AC/DC test system (CSEE-VS), and results show that, compared with a traditional control strategy, the optimized approach reduces total load shedding from 322.59 MW to 191.40 MW, decreases economic cost from 229.18 to 178.11, and improves the transient rotor angle stability index from 0.31 to 0.34 and the transient frequency stability index from 0.3162 to 1.511, while maintaining acceptable voltage stability performance. These findings demonstrate that the proposed framework can accurately assess online operational risks, pinpoint vulnerable nodes, and generate cost-effective, stability-guaranteeing control strategies, showing strong potential for practical deployment in renewable-integrated power grids. Full article

Process designs based on deterministic simulations without considering parameter uncertainty or variability have a high probability of failing to meet specifications. In this work, uncertainty and global sensitivity analyses were applied to a biogas upgrading membrane process implemented in the COCO simulator (CAPE-OPEN to CAPE-OPEN), considering both controlled and non-controlled scenarios. A user-defined model code was developed to simulate gas separation membrane stages, and a preliminary study of membrane parameter uncertainty was performed. In addition, a unit generating combinations of uncertainty factors was developed to interact with the simulator’s parametric tool. Global sensitivity analyses were carried out using the Morris method and Sobol’ indices obtained by Polynomial Chaos Expansion, allowing for the ranking and quantification of the influence of feed variability and membrane parameter uncertainty on product streams and process utilities. Results showed that when feed variability was ±10%, its effect exceeded the uncertainty of the membrane parameters. Uncertainty analysis using the Monte Carlo propagation method provided lower and upper tolerance limits for the main responses. Relative gaps between tolerance limits and mean product flows were 8–9% at a feed variability of 5% and 14–18% at a feed variability of 10%, while relative tolerance gaps resulting from composition were smaller (0.4–1.2%). Full article

This study investigates the dynamics of dust acoustic periodic waves in a three-component, unmagnetized dusty plasma system using generalized $(r^{\star },q^{\star })$ distributions. First, boundary conditions are applied to reduce the model to a second-order nonlinear ordinary differential equation. The Galilean transformation is subsequently applied to reformulate the second-order ordinary differential equation into an unperturbed dynamical system. Next, phase portraits of the system are examined under all possible conditions of the discriminant of the associated cubic polynomial, identifying regions of stability and instability. The Runge–Kutta method is employed to construct the phase portraits of the system. The Hamiltonian function of the unperturbed system is subsequently derived and used to analyze energy levels and verify the phase portraits. Under the influence of an external periodic perturbation, the quasi-periodic and chaotic dynamics of dust ion acoustic waves are explored. Chaos detection tools confirm the presence of quasi-periodic and chaotic patterns using Basin of attraction, Lyapunov exponents, Fractal Dimension, Bifurcation diagram, Poincaré map, Time analysis, Multi-stability analysis, Chaotic attractor, Return map, Power spectrum, and 3D and 2D phase portraits. In addition, the model’s response to different initial conditions was examined through sensitivity analysis. Full article

In this paper, we provide a novel extended mixed differential model that is appealing to users because of its numerous free parameters. The motivation of this research arises from the opportunity for a general investigation of some outstanding classical and novel dynamical models. The higher energy levels known in the literature can be governed by appropriately added correction factors. Furthermore, the different applications of the considered model can be achieved only after a proper parameter calibration. All these necessitate the use of diverse optimization and approximation techniques. The proposed extended model is especially useful in the important field of decision making, namely the antenna array theory. This is due to the possibility of generating high-order Melnikov polynomials. The work is a natural continuation of the authors’ previous research on the topic of chaos generation via the term ${x\left|x\right|}^{a-1}$. Some specialized modules for investigating the dynamics of the proposed oscillators are provided. Last but not least, the so-defined dynamical model can be of interest for scientists and practitioners in the area of antenna array theory, which is an important part of the decision-making field. The stochastic control of oscillations is also the subject of our consideration. The underlying distributions we use may be symmetric, asymmetric or strongly asymmetric. The same is true for the mass in the tails, too. As a result, the stochastic control of the oscillations we purpose may exhibit a variety of possible behaviors. In the final section, we raise some important issues related to the methodology of teaching Master’s and PhD students. Full article

The accuracy of the blade pitch angle (BPA) motion in controllable pitch propellers (CPPs) is considered crucial for the efficacy and reliability of marine propulsion systems. The pitch adjustment process of CPPs is highly complex and influenced by various uncertain factors. A parametric kinematic model for the pitch adjustment process for CPPs was established, incorporating the geometric dimensions and material surface friction coefficients caused during workpiece production as uncertainty parameters. The aim was to establish the correspondence between these uncertainty parameters and the BPA of CPPs. A large dataset was generated by batch calling on Adams. Based on the collected dataset, five surrogate models (e.g., deep neural network (DNN), Kriging, support vector regression (SVR), random forest (RF), and polynomial chaos expansion Kriging (PCK)) were constructed to predict the BPA. Among these, the DNN approach demonstrated the highest prediction accuracy. Accordingly, the influence of uncertainties on the BPA was investigated using the DNN model, focusing on variations in the slider width, crank pin diameter, crank disc diameter, piston rod–slider friction coefficient, crank pin–slider friction coefficient, and hub bearing–crank disc friction coefficient. The high-fidelity model established in this study can replace the kinematic model of the CPP pitch adjustment process, significantly improving computational efficiency. The research findings also provide important references for the design optimization of CPPs. Full article

In renewable energy generation, uncertainties mainly refer to power output fluctuations caused by the intermittency, variability, and forecasting errors of wind and photovoltaic power. These uncertainties have adverse effects on the secure operation of the power systems. Probabilistic load supply capability (LSC) serves as an effective perspective for evaluating power system security under uncertainties. Therefore, this paper studies the influence of renewable energy generation on probabilistic LSC to quantify the impact of these uncertainties on the secure operation of the power systems. Global sensitivity analysis (GSA) is introduced for the first time into probabilistic LSC evaluation. It can quantify the impact of renewable energy generation on the system’s LSC and rank the importance of renewable energy power stations based on GSA indices. GSA necessitates multiple rounds of probabilistic LSC evaluation, which is computationally intensive. To address it, this paper introduces a novel probabilistic repeated power flow (PRPF) algorithm, which employs a basis-adaptive sparse polynomial chaos expansion (BASPCE) model as a surrogate model for the original repeated power flow model, thereby accelerating the probabilistic LSC evaluation. Finally, the effectiveness of the proposed methods is verified through case studies on the IEEE 39-bus system. This study provides a practical approach for analyzing the impact of renewable generation uncertainties on power system security, contributing to more informed planning and operational decisions. Full article

The increase in new energy grid connections has reduced the supply-side regulation capability of the power system. Traditional economic dispatch methods are insufficient for addressing the flexibility limitations in the system’s balancing capabilities. Consequently, this study presents a day-ahead scheduling method for renewable energy systems that balances flexibility and economy. This approach establishes a dual-layer optimized scheduling model. The upper-layer model focuses on the economic efficiency of unit start-up and shut-down, utilizing a particle swarm algorithm to identify unit combinations that comply with minimum start-up and shut-down time constraints. In contrast, the lower-layer model addresses the dual uncertainties of generation and load. It employs the Generalized Polynomial Chaos approximation to create an opportunity-constrained model aimed at minimizing unit generation and curtailment costs while maximizing flexibility supply capability. Additionally, it calculates the probability of flexibility supply-demand insufficiency due to uncertainties in demand response resource supply and system operating costs, providing feedback to the upper-layer model. Ultimately, through iterative solutions of the upper and lower models, a day-ahead scheduling plan that effectively balances flexibility and economy is derived. The proposed method is validated using a simulation of the IEEE 30-bus system case study, demonstrating its capability to balance system flexibility and economy while effectively reducing the risk of insufficient supply-demand balance. Full article

As magnetic field strength in Magnetic Resonance Imaging (MRI) technology increases, maintaining the specific absorption rate (SAR) within safe limits across human head tissues becomes challenging due to the formation of standing waves at a shortened wavelength. Compounding this challenge is the uncertainty in the dielectric properties of head tissues, which notably affects the SAR induced by the radiofrequency (RF) coils in an ultra-high-field (UHF) MRI system. To this end, this study introduces a computational framework to quantify the impacts of uncertainties in head tissues’ dielectric properties on the induced SAR. The framework employs a surrogate model-assisted Monte Carlo (MC) technique, efficiently generating surrogate models of MRI observables (electric fields and SAR) and utilizing them to compute SAR statistics. Particularly, the framework leverages a high-dimensional model representation technique, which constructs the surrogate models of the MRI observables via univariate and bivariate component functions, approximated through generalized polynomial chaos expansions. The numerical results demonstrate the efficiency of the proposed technique, requiring significantly fewer deterministic simulations compared with traditional MC methods and other surrogate model-assisted MC techniques utilizing machine learning algorithms, all while maintaining high accuracy in SAR statistics. Specifically, the proposed framework constructs surrogate models of a local SAR with an average relative error of 0.28% using 289 simulations, outperforming the machine learning-based surrogate modeling techniques considered in this study. Furthermore, the SAR statistics obtained by the proposed framework reveal fluctuations of up to 30% in SAR values within specific head regions. These findings highlight the critical importance of considering dielectric property uncertainties to ensure MRI safety, particularly in 7 T MRI systems. Full article

Chaotic maps have been widely studied in the field of cryptography for their complex dynamics. However, chaos-based cryptosystems have not been widely used in practice. One important reason is that the following requirements of practical engineering applications are not taken into account: computational complexity and difficulty of hardware implementation. In this paper, based on the demand for information security applications, we modify the local structure of the three-dimensional Intertwining Logistic chaotic map to improve the efficiency of software calculation and reduce the cost of hardware implementation while maintaining the complex dynamic behavior of the original map. To achieve the goal by reducing the number of floating point operations, we design a mechanism that can be decomposed into two processes. One process is that the input parameters value of the original system is fixed to $2^k$ by Scale index analysis. The other process is that the transcendental function of the original system is replaced by a nonlinear polynomial. We named the new map as “Simple intertwining logistic”. The basic chaotic dynamic behavior of the new system for controlling parameter is qualitatively analyzed by bifurcation diagram and Lyapunov exponent; the non-periodicity of the sequence generated by the new system is quantitatively evaluated by using Scale index technique based on continuous wavelet change. Fuzzy entropy (FuzzyEn) is used to evaluate the randomness of the new system in different finite precision digital systems. The analysis and evaluation results show that the optimized map could achieve the designed target. Then, a novel scheme for generating pseudo-random numbers is proposed based on new map. To ensure its usability in cryptographic applications, a series of analysis are carried out. They mainly include key space analysis, recurrence plots analysis, correlation analysis, information entropy, statistical complexity measure, and performance speed. The statistical properties of the proposed pseudo random number generator (PRNG) are tested with NIST SP800-22 and DIEHARD. The obtained results of analyzing and statistical software testing shows that, the proposed PRNG passed all these tests and have good randomness. In particular, the speed of generating random numbers is extremely rapid compared with existing chaotic PRNGs. Compared to the original chaotic map (using the same scheme of random number generation), the speed is increased by 1.5 times. Thus, the proposed PRNG can be used in the information security. Full article

In previous studies, customer preferences were assumed to be static when modeling their preferences based on online reviews. However, in fact, customer preferences for products are dynamic and changing over time. Few research has been conducted to model dynamic customer preferences as the time series data of customer preference are difficult to be obtained. Based on online reviews, an adaptive neuro fuzzy inference system (ANFIS) was introduced to model customer preferences, which can take into account the fuzzy nature of customers’ emotions and the nonlinearity of the model. However, ANFIS is plagued with black box problems, and the nonlinearity of the model cannot be directly demonstrated. To address the above research issues, a multi-objective chaos optimization algorithm (MOCOA)-based ANFIS approach is proposed to generate customer preferences models by using online reviews, which has explicit nonlinear inputs. Firstly, a sentiment analysis approach is used to derive information from online reviews by periods, which is used as the time series data sets of the proposed model. A MOCOA is combined into ANFIS to identify the nonlinear inputs, which include single items, interactive items, and terms of second order and/or higher-order terms. Consequently, the fuzzy rules in ANFIS are expressed in polynomial form, which allows for the explicit representation of the nonlinearity between customer preferences and product attributes. A case study of sweeping robots is used to compare the validation results of the proposed approach with those of ANFIS, subtractive cluster-based ANFIS, fuzzy c-means-based ANFIS, and K-means-based ANFIS. Moreover, the proposed approach provides better performance than the other four approaches in terms of mean relative error and variance of error. Full article

Landing of supersonic transport (SST) suffers from a large uncertainty due to its highly sensitive aerodynamic properties in the subsonic domain, as well as the wind gusts around runways. At the vehicle design stage, a landing trajectory optimization under wind uncertainty in a multi-objective solution space is desired to explore the possible trade-off in its key flight performance metrics. The proposed algorithm solves this robust constrained multi-objective optimal control problem by integrating non-intrusive polynomial chaos expansion into a constrained evolutionary algorithm. The computationally tractable optimization is made possible through the conversion of a probabilistic problem into an equivalent deterministic representation while maintaining a form of the multi-objective problem. The generated guidance trajectories achieve a significant reduction of the uncertainty in their terminal states with a marginal modification in the control history of the deterministic solutions, validating the importance of the consideration of robustness in trajectory optimization. Full article