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Extracting to enhance the accuracy of diagnosing bearing faults in steam turbines, a novel approach focused on extracting key fault features from vibration signals is introduced. Recognizing the complex, non-linear, and non-stationary nature of bearing vibration signals, our strategy involves a sensitivity analysis utilizing a multivariate diagnostic algorithm. The process begins with collecting vibration data from defective bearings via the TMI system. This data is then subjected to Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), enabling the integration of adaptive noise for the extraction of in-depth information. Following this, an analysis in both time and frequency domains — post Fast Fourier Transform (FFT) — is conducted on the decomposed signals, forming the basis of a diagnostic features database. To streamline data analysis and boost the model’s computational efficiency, a combination of eXtreme Gradient Boosting (XGBoost) and Mutual Information Criterion (MIC) is applied for dimensionality reduction. Furthermore, a deep belief network (DBN) is implemented to develop a precise fault diagnosis model for the bearings in rotating machinery. By incorporating sensitivity analysis, a diagnostic matrix is crafted, facilitating highly accurate fault identification. The superiority of this diagnostic algorithm is corroborated by testing with real on-site data and a benchmark database, demonstrating its enhanced diagnostic capabilities relative to other feature selection techniques.

In the context of the increasing global economic policy uncertainty (EPU) and the gradual reduction of US Treasuries holdings in many countries, based on the ADCC-GARCH model and sensitivity analysis, we find that the relative increase of instability in the global economic system will affect foreign investors’ decision-making of investing in the US Treasuries, especially during the high uncertainty period. Shocks in global uncertainty significantly and negatively explain most samples’ time-varying correlations with a lag of one or two months. To some extent, the sustainability and investors’ inherent understanding of US Treasuries’ safety has been shaken in the recent years. Our findings hold important implications for both foreign investors and financial advisors who are interested in US Treasuries.

This study aims to analyze the effect of internship participation on university graduates’ overall employability and uses Korea’s Graduate Occupational Mobility Survey data in order to track university graduates’ employment prospects. Our findings reveal that participation in internships increases the employability of young adults, and that this impact is slightly greater for male college graduates than for female college graduates. Meanwhile, in order to supplement the reliability of our results, we conducted additional analytical tests, including a placebo test and an intensive sensitivity analysis test. It turns out that the estimated treatment effects on the placebo outcomes are of a small magnitude, with no statistical significance. In the analysis which includes simulated confounders, it appears that the risk of omitting relevant confounders does not threaten the baseline estimates.

Emergency departments (EDs) are among the most intensive and dynamic departments in hospital systems. This study considers the resource allocation problem at the ED of a hospital with two objective functions: the length of stay (LS) and wasted resources. The numbers of doctors, nurses, lab technicians, and other medical equipment must be constantly determined to effectively operate EDs with the two objective functions, representing the satisfaction of patients and unnecessary costs, respectively. The ED system is evaluated with a discrete event simulation (DES) model. Furthermore, a Pareto optimal set of solutions is approximated using the quantile-relaxed multiple objective probabilistic branch and bound (QR-MOPBnB), which was developed as an extension algorithm of MOPBnB to improve efficiency. QR-MOPBnB iteratively branches the solution space into subregions and identifies the subregions that are the most promising to be close to the Pareto optimal set. Using QR-MOPBnB, the trade-off between the LS and wasted resources is illustrated for decision makers to appropriately determine the ideal design based on their preferences, and the relaxed Pareto optimal set with statistical quality assurance provides further insights similar to those obtained through sensitivity analysis.

Nonlinear evolution equations appear in various branches of physics, including fluid dynamics, solid mechanics, quantum mechanics, and other fields. They are essential for describing systems where interactions and nonlinearity play a significant role, providing a more accurate representation of real-world phenomena than linear equations in certain cases. The study of nonlinear evolution equations involves exploring their solutions, stability properties, and the behavior of the systems they describe over time. In this study, we provide plenty of analytical solutions to a very recently proposed water wave model using the modified generalized exponential rational function, modified extended tanh-function, and the $exp(-\phi (\xi ))$-expansion methods. To examine the dynamic characteristics of these results, we displayed three-dimensional (3D), contour, and two-dimensional (2D) visual representations of specific solutions. The outcomes reveal a multitude of novel solutions, emphasizing the robustness and effectiveness of the applied methodologies. It is important to note that all the solutions derived in this study are original and have not been previously documented in the existing literature. These novel solutions hold significant value for researchers in the realms of fluids and plasma physics, providing insights into the dynamics of nonlinear waves within various physical systems. Furthermore, this research contributes to a deeper understanding of the nature of nonlinear waves prevalent in seas and oceans, offering valuable knowledge for the broader study of such phenomena.

Here attention is focused on the (1+1)-dimensional Sawada–Kotera (SK) model that is prominent in mathematical physics and engineering to analyze plasmas and coherent systems for communication. Our techniques offer fresh perspectives on the model’s attributes and structure, deepening our comprehension of the underlying dynamics. First, the SK model is reduced to ordinary differential equations by constructing the Lie symmetries and using the associated transformation. Graphs are used to build and display invariant solutions. This strategy has caused the revelation of novel constant solutions that have not been found in the previous works. We offer new understandings of nature and changes observed during the SK derivation by taking advantage of the Lie symmetries powerful tools. Next, the fluctuating layout of proposed framework is examined from several perspectives such as sensitivity and bifurcation analysis. We examined the bifurcation analysis of planar dynamical system by using bifurcation theory. We also include an external periodic perturbation term that breaks regular patterns in the perturbed dynamical system. Graphical structures are provided to display the invariant solutions. The sensitivity of the SK model is determined to be strong after sensitivity analysis under different initial conditions. These results are fascinating, fresh, and conceptually useful for understanding the suggested framework. In mathematics and the applied sciences, forecasting and learning about new technologies are greatly aided by the dynamic aspect of system processing.

The objective of this study is to numerically investigate and compare the characteristics of two distinct hybrid nanofluids EG-MoS₂-SiO₂ and H₂O-Cu-Al₂O₃ flowing steadily over a channel created by two non-parallel absorbent porous walls. Further, the considered fluid flow is under the influence of exponential space-based heat source, viscous dissipation, Joule heating, radiation, and external magnetic field. The nonlinear partial differential equations and subjecting boundary conditions of the flow are transformed into a system of nonlinear ordinary differential equations through suitable similarity transformations and are solved by combining the shooting technique with the traditional Runge–Kutta method. The consequential results are produced utilizing MATLAB software. The comparisons of the velocity profiles, temperature profiles, surface drag, and Nusselt number for both hybrid nanofluids are illustrated as graphs. The findings indicate that H₂O-Cu-Al₂O₃ exhibits better velocity profiles, EG-MoS₂-SiO₂ displays enhanced temperature profiles, while H₂O-Cu-Al₂O₃ has improved skin friction and Nusselt number. It is noteworthy to mention that numerous industries, including manufacturing, power generation, chemical processes, microelectronics, and transportation, depend on improving heat transfer coefficients. Hence, the significance and novelty of this work lie in the evaluation of optimization and sensitivity analysis of the EG-MoS₂-SiO₂ hybrid nanofluid to enhance heat transmission using Response Surface Methodology.

In this paper, we construct a COVID-19 dynamic model that included both the initial and reinfected population compartments, and conduct a structural identifiability analysis of the model parameters to ensure the robustness of the parameter fitting results. We use some actual statistical data from North Carolina to fit the model and estimate the values of some important parameters. In order to accurately fit the parameters in the model, we improve the physics-informed neural networks (PINNs) method in this paper, so that the fitting results can be reproduced on Matlab. The results of this study show that the transmission capacity of the virus in the reinfected person is only slightly lower than that of the first infected person, and vaccination is not effective in reducing the transmission rate of the virus. The death rate of the reinfected is much higher than that of the first infected person. Finally, we conduct a cost-effectiveness study using optimal control methods and found that, while it is easier to reduce reinfection by combining multiple strategies, the most effective strategy for reducing reinfection is to increase treatment cure rates and reduce direct or indirect contact among those who have recovered.

Vaccination and prevention are commonly employed strategies in disease control. However, the influence of sexual preferences on the spread of sexually transmitted infections (STIs) remains underexplored due to the lack of adequate mathematical models. This study addresses this gap by evaluating the impact of sexual preferences on STIs transmission and providing a tool for implementing more effective control policies. We develop two models that describe STIs transmission dynamics in populations with exclusively same-sex or opposite-sex contacts. Later, we introduce a third, more general model that integrates both scenarios. Sensitivity analysis reveals that prevention often outperforms vaccination in effectiveness. Our findings highlight the critical need for tailoring control policies. In the cases of sexual preferences, it is paramount to pay attention to the group with the highest local basic reproduction number, underscoring the importance of customized strategies in disease management.

Pneumonia is one of the major causes of death among children under five years of age and adults over 65, with more than 2 million deaths occurring in developing countries every year. The efforts for early detection, effective treatment, and minimizing the transmission of pneumonia are possible if the dynamics of the disease are well understood. In most countries or communities, hospitals have limited capacity to accommodate those who are sick. Therefore, individuals can be treated as outpatients or in community-based care depending on the severity of the infection. In this research, a model for the transmission dynamics of pneumonia is developed to determine the effect of disinfecting the pathogen-contaminated environment, and community-based care on the disease mitigation process. The basic properties of the model including positivity and boundedness, the basic reproduction number (${{ℛ}}_0$), existence and stability of equilibria were determined as well as the conditions for existence of backward bifurcation, a scenario where reducing ${{ℛ}}_0$ below 1 may not be enough to eradicate the disease. Sensitivity analysis was performed using the Latin Hypercube Sampling Scheme to determine the parameters with the greatest influence on the reproduction number. The results revealed that transmission rate through the contaminated environment and contact rate through person-to-person have the most significant potential of increasing the disease burden if unabated, while effective treatment and increased decay rate of microbes from the environment have the greatest potential of containing the number of infections. Numerical simulations were performed to illustrate the analytical results as well as establish the long-term behavior of the disease. It was observed that introducing community-based care can accelerate the containment of the disease as well as reducing the number of deaths in the population. In addition, a higher frequency of environmental disinfection is associated with lower infection cases not only around the peaks but also in the long term. We recommend that the community-based care be enhanced in the disease management process to cater for settings where resources are limited. To ensure proper implementation of community-based care services, training of community-based caregivers on the transmission dynamics of the disease, its management and prevention strategies is mandatory. More still, practicing proper hygiene, and applying multiple combinations of control measures including vaccination and isolation of the infected is essential if the disease is to be contained in a shorter time.

Maintaining a reliable water treatment plant is paramount for a consistent and dependable supply of safe drinking water to communities. This study employs an integrated approach, leveraging advanced methodologies including Markov processes, supplementary variable technique, and Laplace transformation. The research seeks to comprehensively model the plant’s dynamic behavior, transitions between operational states, and the influence of maintenance practices. By employing these methodologies, the research aims to enhance the precision of critical reliability metrics such as reliability and availability. The study further incorporates thorough cost analysis, shedding light on the economic implications of reliability-enhancing measures. Additionally, sensitivity analysis is employed to identify critical variables influencing plant performance and economic efficiency. The insights garnered from this study are expected to provide a sophisticated understanding of the water treatment plant’s performance, fostering effective decision-making strategies to optimize maintenance protocols and ensure the uninterrupted delivery of clean and secure water to communities.

Drive-by inspection of bridge damage using a passing vehicle’s dynamic response has great potential in bridge damage identification. Among the current drive-by methodologies, the methods based on bridge modeling have been proposed for the quantitative identification of bridge damage and bridge surface roughness. However, the coupling of bridge damage and unknown surface roughness increases the difficulty of the identification problem and most previous studies conduct the identification task of bridge damage or bridge surface roughness separately. In this paper, a novel method is proposed for the identification of joint bridge damage and bridge surface roughness based on the residual bridge deflections from the front and rear wheels contact points of an instrumented passing vehicle. The vehicle–bridge interaction is analyzed using a half-car model of a four degrees of freedom (4-DOF) with front and rear vehicle wheels. First, the vehicle–bridge unknown forces and displacement of the vehicle axles are identified by the generalized Kalman filter under unknown input (GKF-UI) proposed by the authors. The sensors can be installed conveniently on the vehicle body due to GKF-UI. Then, the residual bridge deflections from the front and rear vehicle wheels contact points are utilized to eliminate the effect of road surface roughness. Afterward, bridge structural damage is identified based on the sensitivity analysis of residual bridge deflections from the front and rear contact points with $l$1-norm regularization. Finally, bridge road surface roughness is estimated based on the identified unknown forces and updated bridge model with damage. The results of numerical identification examples demonstrate the effectiveness of the proposed method for the identification of joint bridge damage and surface roughness.

In structural damage detection (SDD) studies, regularization techniques have shown potential for improving ill-posedness. However, existing methods based on regularization techniques cannot yield satisfactory results for the SDD problem involving regional damages. Based on the sparse distribution characteristics of regional damages in the finite element (FE) model, this study proposes a novel SDD method that integrates sensitivity analysis of modal parameters with overlapping group sparse regularization. First, the relationship between modal parameters and structural damages is established based on sensitivity analysis. Then, the overlapping group sparsity of regional damages is analyzed and the objective function for SDD can be defined. Finally, a grouping matrix is introduced to transform the objective function from overlapping to non-overlapping group sparse regularization. To evaluate the effectiveness of the proposed method, both numerical simulations and experimental studies are employed, and comparative studies are conducted with the SDD method based on the $l_1$-norm regularization. The identification results indicate that the proposed method can handle regional damages in the FE model and identify both single and multiple damages well.

The stochastic dynamical ${\rho }^4$ equation is utilized as a robust framework for modeling the behavior of complex systems characterized by randomness and nonlinearity, with applications spanning various scientific fields. The aim of this paper is to employ an analytical method to identify stochastic traveling wave solutions of the dynamical ${\rho }^4$ equation. Novel hyperbolic and rational functions are investigated through this method. A Galilean transformation is applied to reformulate the model into a planar dynamical system, which enables a comprehensive qualitative analysis. Additionally, the emergence of chaotic and quasi-periodic patterns following the introduction of a perturbation term is addressed. Simulation results indicate that significant changes in the systems’ dynamic behavior are caused by adjusting the amplitude and frequency parameters. Our findings indicate the impact of the method on system dynamics and its efficacy in analyzing solitons and phase behavior in nonlinear models. These discoveries provide fresh perspectives on how the suggested method can lead to notable shifts in the systems’ dynamic behavior. The effectiveness and practicality of the proposed methodology in scrutinizing soliton solutions and phase visualizations across diverse nonlinear models are underscored by these revelations.

In this research, the influences of quadratic Boussinesq approximation and quadratic thermal radiation on the heat transfer analysis of magnetized Sisko nanofluid flow with Cattaneo–Christov heat flux through stretching surfaces are studied. The formulated mathematical model is solved by the finite difference technique, and heat transfer rate and skin friction coefficients are computed for acting parameters, i.e., magnetic field, Eckert number, Forchheimer parameter, thermal relaxation parameter, radiation parameter, porosity parameter and Biot number. For sensitivity analysis, the response surface method (RSM) with a face-centered central composite design is utilized. The RSM is elucidated by applying nonlinear regression, analysis of variance and goodness of fit. The results indicate that the friction coefficient and Nusselt number have positive sensitivities for the Forchheimer parameter. The heat transfer rate decreases with an increase in magnetic field, Biot number and thermal relaxation parameter values for shear thickening $(n>1)$ and shear thinning $(n<1)$. Further for $n<1$, a one unit increase in $A_1$ leads to a 33% drop in SFC and 48% in LNN; and an increase of 8 units in $F_r$ leads to a 67.18% rise in LNN.

In this paper, we study an SS_vEIQR model with nonlinear contact rate, isolation rate and vaccination rate driven by media coverage. First, the basic reproduction number $R_0$ is derived. Then, the threshold dynamics of the disease are obtained in terms of $R_0$: when $R_0\le 1$, the global stability of the disease-free equilibrium is obtained by constructing an appropriate Lyapunov function; when $R_0>1$, the sufficient conditions to prove the globally stability of endemic equilibrium are obtained by applying the geometric method into the four-dimensional system, which needs to estimate the Lozinski$ǐ$ measure of a $6\times 6$ matrix. Further, we conduct some numerical simulations to validate our theoretical results, and analyze the impact of media coverage on disease transmission, the results show that media coverage could effectively suppress the spread of the disease and reduce the number of infected individuals. Finally, through the sensitivity analysis of $R_0$, we obtain some measures to control the spread of the disease, such as reducing contact, strengthening isolation and vaccination.

In this paper, we propose an Echinococcosis model with logistic growth. After giving the basic reproductive number $R_0$, we prove that $R_0$ can be used to govern the threshold dynamics of the model: if $R_0<1$, the disease will go to extinction, while if $R_0>1$, the disease will persist. Based on the data of Echinococcosis in Ürümqi, Xinjiang, China during 2006–2016, we estimate the parameters in the model and calculate that $R_0=1.42$ (95% CI [0.767, 4.327]). The results show that Echinococcosis is endemic in Ürümqi, China. In addition, we obtain that $\mathrm{\text{MAPE}}=3.54$% and $\mathrm{\text{RMSPE}}=3.87$%, which indicates that the model has certain reliability and rationality. Furthermore, we carry out the sensitivity analysis of the model parameters to identify the key factors affecting the prevalence of Echinococcosis, and the effective control efforts are suggested focusing on reducing the proportion rate from sheep to dogs and increasing the recovery rate of dogs to curb the prevalence of Echinococcosis in Ürümqi, China.

This paper incorporates generalized nonlinear vaccination rate and temporary immunity into the infectious disease models and presents the corresponding system. The qualitative results show that the disease-free equilibrium point and the endemic equilibrium point are globally asymptotically stable under some certain conditions. The local sensitivity analysis reveals that the importance of the critical parameters to the effective reproduction number $R_v$ in the order from high to low is $\mu$, $\mathrm{\Lambda }$, $𝜃$, $\gamma$ and $\xi$, respectively. The global sensitivity analysis shows that the parameters which impact on the effective reproduction number $R_v$ are $\alpha$, $𝜃$, $\mu$, $\beta$, $\mathrm{\Lambda }$, $p$, $\alpha$, $\xi$ and $\gamma$ in the descending order. Based on the dynamical behavior and the sensitivity analysis of the considered system, the controlling measures are presented to prevent and control the infectious diseases: (1) increasing the nonlinear vaccination rate of the susceptible subpopulation, (2) controlling the number of immigrants to infectious areas, (3) increasing vaccination coverage of immigrants and newborns and (4) improving the effectiveness of vaccines and reducing the rate of immune loss.

We propose new mathematical models based on ordinary differential equations to investigate the transmission dynamics of infectious diseases by adding a hospitalization compartment $H$ into the classic $SIS$ and $SIR$ models. The models incorporate a general incidence rate between susceptibles and infected individuals and a nonlinear recovery rate for hospitalized individuals. We rigorously analyze the existence, local stabilities, and global stabilities of equilibria and derive threshold conditions determining whether the disease dies out or persists. As an application of our $SIH$ model, we perform a case study with an endemic of COVID-19, conduct data fitting and sensitivity analysis for model parameters, and present simulation results to emphasize the role of the hospitalization rate.

Brucellosis, as a prevalent zoonosis caused by Brucella, primarily spreads in northern pastoral regions of China. The high levels of perceived risk about brucellosis before 2009 were largely suspected in Jilin province, as well as its effect in stemming the transmission of brucellosis. We will devise two epidemic models to investigate the effects of spontaneous changes in herder’s behavior awareness on the transmission of brucellosis. The global dynamics of these models will be thoroughly analyzed. The models are utilized to fit the data of newly infected cases of brucellosis in Jilin province from 2002–2020. The vital information-induced parameters of brucellosis have been estimated by the Markov Chain Monte Carlo (MCMC) method. The basic reproduction numbers are calculated as $R_0=1.767$ prior to 2009 and $R_0=0.921$ after 2009. Moreover, our findings indicate that a one-year delay in the implementation of pilot work in Jilin province by the government would result in a 50% increase in the peak number of newly infected brucellosis cases, surpassing 5000. On the contrary, if the government were to implement the pilot work in Jilin province one year ahead of schedule, there would be a 40% reduction in the peak number of newly infected brucellosis cases. Furthermore, the results suggest that enhancing the voluntary detection and protection rate is more effective than increasing voluntary rates. Information-induced detection and protection play a crucial role in curbing the spread of brucellosis. The increase in the reactivity factor of voluntary detection $C$ from 0.00128 to 0.0128 will result in a reduction of the incidence rate of human brucellosis cases to less than 1 per 100,000, enabling the achievement of the national control target seven years ahead of schedule. The insights shed herein may be conductive to suppress the spread of brucellosis in other areas.