Large Deflection Dynamic Response Analysis of Flexible Hull Beams by the Multibody System Method

In this paper the large deflection dynamic problems of Euler beams are investigated. The vibration control equations are derived based on the multibody system method. A numerical procedure for solving the resulting differential algebraic equations is presented on the basis of the Newmark direct integration method combined with the Newton-Raphson iterative method. The sub beams are treated as small deformation in the convected coordinate systems, which can greatly simplify the deformation description. The rigid motions of the sub beams are taken into account through the motions of the convected coordinate systems. Numerical ex- amples are carried out, where results show the effectiveness of the proposed method.

Fluidized bed control system based on inverse system method

The invertible of the Large Air Dense Medium Fluidized Bed (ADMFB) were studied by introducing the concept of the inverse system theory of nonlinear systems. Then the ADMFB, which was a multivariable, nonlinear and coupled strongly system, was decoupled into independent SISO pseudo-linear subsystems. Linear controllers were designed for each of subsystems based on linear systems theory. The practice output proves that this method improves the stability of the ADMFB obviously.

Dynamical System Method for Solving Ill-Posed Operator Equations

Two dynamical system methods are studied for solving linear ill-posed problems with both operator and right-hand nonexact. The methods solve a Cauchy problem for a linear operator equation which possesses a global solution. The limit of the global solution at infinity solves the original linear equation. Moreover, we also present a convergent iterative process for solving the Cauchy problem.

Legendre-Weighted Residual Methods for System of Fractional Order Differential Equations

The numerical approach for finding the solution of fractional order systems of boundary value problems (BPVs) is derived in this paper. The implementation of the weighted residuals such as Galerkin, Least Square, and Collocation methods are included for solving fractional order differential equations, which is broadened to acquire the approximate solutions of fractional order systems with differentiable polynomials, namely Legendre polynomials, as basis functions. The algorithm of the residual formulations of matrix form can be coded efficiently. The interpretation of Caputo fractional derivatives is employed here. We have demonstrated these methods numerically through a few examples of linear and nonlinear BVPs. The results in absolute errors show that the present method efficiently finds the numerical solutions of fractional order systems of differential equations.

Simplified Method of Stability Analysis of Nonlinear Systems without Using of Lyapunov Concept

In this paper a new simplified method of stability study of dynamical nonlinear systems is proposed as an alternative to using Lyapunov’s method. Like the Lyapunov theorem, the new concept describes a sufficient condition for the systems to be globally stable. The proposed method is based on the assumption that, not only the state matrix contains information on the stability of the systems, but also the eigenvectors. So, first we will write the model of nonlinear systems in the state-space representation, then we use the eigenvectors of the state matrix as system stability indicators.

Using Pearson’s System of Curves to Approximate the Distributions of the Difference between Two Correlated Estimates of Signal-to-Noise Ratios: The Cases of Bivariate Normal and Bivariate Lognormal Distributions

Background: The signal-to-noise ratio (SNR) is recognized as an index of measurements reproducibility. We derive the maximum likelihood estimators of SNR and discuss confidence interval construction on the difference between two correlated SNRs when the readings are from bivariate normal and bivariate lognormal distribution. We use the Pearsons system of curves to approximate the difference between the two estimates and use the bootstrap methods to validate the approximate distributions of the statistic of interest. Methods: The paper uses the delta method to find the first four central moments, and hence the skewness and kurtosis which are important in the determination of the parameters of the Pearsons distribution. Results: The approach is illustrated in two examples;one from veterinary microbiology and food safety data and the other on data from clinical medicine. We derived the four central moments of the target statistics, together with the bootstrap method to evaluate the parameters of Pearsons distribution. The fitted Pearsons curves of Types I and II were recommended based on the available data. The R-codes are also provided to be readily used by the readers.

AI-Enhanced Performance Evaluation of Python, MATLAB, and Scilab for Solving Nonlinear Systems of Equations: A Comparative Study Using the Broyden Method

This research extensively evaluates three leading mathematical software packages: Python, MATLAB, and Scilab, in the context of solving nonlinear systems of equations with five unknown variables. The study’s core objectives include comparing software performance using standardized benchmarks, employing key performance metrics for quantitative assessment, and examining the influence of varying hardware specifications on software efficiency across HP ProBook, HP EliteBook, Dell Inspiron, and Dell Latitude laptops. Results from this investigation reveal insights into the capabilities of these software tools in diverse computing environments. On the HP ProBook, Python consistently outperforms MATLAB in terms of computational time. Python also exhibits a lower robustness index for problems 3 and 5 but matches or surpasses MATLAB for problem 1, for some initial guess values. In contrast, on the HP EliteBook, MATLAB consistently exhibits shorter computational times than Python across all benchmark problems. However, Python maintains a lower robustness index for most problems, except for problem 3, where MATLAB performs better. A notable challenge is Python’s failure to converge for problem 4 with certain initial guess values, while MATLAB succeeds in producing results. Analysis on the Dell Inspiron reveals a split in strengths. Python demonstrates superior computational efficiency for some problems, while MATLAB excels in handling others. This pattern extends to the robustness index, with Python showing lower values for some problems, and MATLAB achieving the lowest indices for other problems. In conclusion, this research offers valuable insights into the comparative performance of Python, MATLAB, and Scilab in solving nonlinear systems of equations. It underscores the importance of considering both software and hardware specifications in real-world applications. The choice between Python and MATLAB can yield distinct advantages depending on the specific problem and computational environment, providing guidance for researchers and practitioners in selecting tools for their unique challenges.

Nonlinear Control for Autonomous Underwater Glider Motion Based on Inverse System Method

Autonomous underwater gliders are highly effcient,buoyancy-driven,winged autonomous underwater vehicles. Their dynamics are multivariable nonlinear systems. In addition,the gliders are underactuated and diffcult to maneuver,and also dependent on their operational environment. To confront these problems and to design an effective controller,the inverse system method was used to decouple the original system into two independent single variable linear subsystems. The stability of the zero dynamics was analyzed,and an additional closed-loop controller for each linear subsystem was designed by sliding mode control method to form a type of composite controller. Simulation results demonstrate that the derived nonlinear controller is able to cope with the aforementioned problems simultaneously and satisfactorily.

Progressive Collapse Resistance of a New Staggered Story Isolated System

A new staggered isolated system developed from the mid-story isolated system is the new staggered story isolated system. There are not many studies on this structure currently. In this study, an 18-story new staggered story isolated system model is established using SAP2000. The dynamic nonlinear dynamic alternate method is used to analyze the structure against progressive collapse. Results show that the structure has good resistance to progressive collapse, and there is no progressive collapse under each working condition. The progressive collapse does not occur for the case of removing only one vertical structural member of the new staggered of isolated system. The side column has big influence on this isolated structures’ progressive collapse;the removal of vertical structural member of the isolation layer has less impact on the structure than the removal of the bottom vertical structural member. After the removing of the member, the internal force of the structure will be redistributed, and the axial force of the adjacent columns will change obviously, showing a trend of “near large and far small”.

Approximation Maintenance When Adding a Conditional Value in Set-Valued Ordered Decision Systems

The integration of set-valued ordered rough set models and incremental learning signify a progressive advancement of conventional rough set theory, with the objective of tackling the heterogeneity and ongoing transformations in information systems. In set-valued ordered decision systems, when changes occur in the attribute value domain, such as adding conditional values, it may result in changes in the preference relation between objects, indirectly leading to changes in approximations. In this paper, we effectively addressed the issue of updating approximations that arose from adding conditional values in set-valued ordered decision systems. Firstly, we classified the research objects into two categories: objects with changes in conditional values and objects without changes, and then conducted theoretical studies on updating approximations for these two categories, presenting approximation update theories for adding conditional values. Subsequently, we presented incremental algorithms corresponding to approximation update theories. We demonstrated the feasibility of the proposed incremental update method with numerical examples and showed that our incremental algorithm outperformed the static algorithm. Ultimately, by comparing experimental results on different datasets, it is evident that the incremental algorithm efficiently reduced processing time. In conclusion, this study offered a promising strategy to address the challenges of set-valued ordered decision systems in dynamic environments.

Study on Sex Ratio of Lampreys Based on Simulated Ecosystem-Food Web Model

Lampreys, as an important participant in the ecosystem, play an irreplaceable role in the stability of nature. A variety of models were used to simulate ecosystems and food webs, and the dynamic evolution of multiple populations was solved. The temporal changes of the biomass and the health of the ecosystem affected by the population of Lampreys in other ecological niches were solved. For problem 1, Firstly, a simple natural ecosystem is simulated based on the threshold model and BP neural network model. The dynamic change of the sex ratio of lampreys population and the fluctuation of ecosystem health value were found to generate time series maps. Lampreys overprey on low-niche animals, which damages the overall stability of the ecosystem. For problem 2, We used the Lotka-Volterra model to construct ecological competition between lampreys and primary consumers and predators. Then, the Lotka-Volterra equations were solved, and a control group without gender shift function was set up, which reflected the advantages and disadvantages of the sex-regulated characteristics of lampreys in the natural environment. For problem 3, The ecosystem model established in question 1 was further deepened, and the food web was simulated by the Beverton-Holt model and the Logistic time-dependent differential equations model. The parameters of the food web model were input into the neurons of the ecosystem model, and the two models were integrated to form an overall biosphere model. The output layer of the ecosystem neural network was input into the food web Beverton-Holt and Logistic differential equations, and finally, the three-dimensional analytical solution was obtained by numerical simulation. Then Euler method is used to obtain the exact value of the solution surface. The Random forest model was used to predict the future development of lampreys and other ecological niches. For problem 4, By investigating relevant literature, we normalized the populations of lampreys and a variety of fish as well as other ecological niche animals, plants and microorganisms in the same water area, set different impact weights of lampreys, constructed weight evaluation matrix, and obtained positive and negative ideal solution vectors and negative correlation proximity by using TOPSIS comprehensive evaluation method. It is concluded that many kinds of fish are greatly affected by the sex regulation of lampreys.

Performance Analysis of Thermal Energy System with Linear System Method

The paper addresses the system performance of coal-fired power unit with changed auxiliary system or other local heat disturbance. The idea of state space model is imported and the universal formula for the calculation of system performance output is deduced on the system state equation. Two important vector of system are worked out under linear system assumption and transform. The transfer matrix is the characteristics of system itself and is constant for a similar condition, which greatly facilitates the analysis. The concept of thermal disturbance vector is proposed to construct the thermal disturbance input easily. The method can be helpful for analyzing any thermal disturbance input satisfying the assumption and also for supplementing the correction means of performance test. An example of 600MW power unit is presented to demonstrate its availability.

VIRTUAL SYSTEM METHOD FOR SYSTEM TREE

A machine, or other type of 'system' , can often be divided into several subsystems (components)and these subsystems again can be divided into sevreral subsystems (second generation). This process forms a system tree. To assess the reliability of the machine based on data from the trials of components of the machine, virtual system method is employed. It is proved in the paper that the lower confident limit of the reliability of the machine set by the virtual system method is level consistent and asymptotically optimal while the one set by Lindstrom-Maddens method is not.

Galerkin-Bernstein Approximations for the System of Third-Order Nonlinear Boundary Value Problems

This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in detail, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory. .

NEW EXACT TRAVELLING WAVE SOLUTIONS OF NONLINEAR WAVE EQUATIONS USING THE DYNAMICAL SYSTEM METHOD

By the method of dynamical system, we construct the exact travelling wave solu- tions of a new Hamiltonian amplitude equation and the Ostrovsky equation. Based on this method, the new exact travelling wave solutions of the new Hamiltonian am- plitude equation and the Ostrovsky equation, such as solitary wave solutions, kink and anti-kink wave solutions and periodic travelling wave solutions, are obtained, respectively.

Revealing the Hidden Mathematical Beauties of the Cayley-Hamilton Method

The inversion of a non-singular square matrix applying a Computer Algebra System (CAS) is straightforward. The CASs make the numeric computation efficient but mock the mathematical characteristics. The algorithms conducive to the output are sealed and inaccessible. In practice, other than the CPU timing, the applied inversion method is irrelevant. This research-oriented article discusses one such process, the Cayley-Hamilton (C.H.) [1]. Pursuing the process symbolically reveals its unpublished hidden mathematical characteristics even in the original article [1]. This article expands the general vision of the original named method without altering its practical applications. We have used the famous CAS Mathematica [2]. We have briefed the theory behind the method and applied it to different-sized symbolic and numeric matrices. The results are compared to the named CAS’s sealed, packaged library commands. The codes are given, and the algorithms are unsealed.

A FIELD METHOD FOR SOLVING THE EQUATIONS OF MOTION OF NONHOLONOMIC SYSTEMS

In this paper,the field method for solving the equations of motion of holonomic nonconservative systems is extended to nonholonomic systems with constant mass and with variable mass.Two examples are given to illustrate its application.

The method of variation on parameters for integration of a generalized Birkhoffian system

This paper focuses on studying the integration method of a generalized Birkhoffian system.The method of variation on parameters for the dynamical equations of a generalized Birkhoffian system is presented.The procedure for solving the problem can be divided into two steps：the first step,a system of auxiliary equations is constructed and its general solution is given;the second step,the parameters are varied,and the solution of the problem is obtained by using the properties of generalized canonical transformation.The method of variation on parameters for the generalized Birkhoffian system is of universal significance,and we take a nonholonomic system and a nonconservative system as examples to illustrate the application of the results of this paper.

Modeling Method for Flexible Energy Behaviors in CNC Machining Systems

CNC machining systems are inevitably confronted with frequent changes in energy behaviors because they are widely used to perform various machining tasks. It is a challenge to understand and analyze the flexible energy behaviors in CNC machining systems. A method to model flexible energy behaviors in CNC machining systems based on hierarchical objected-oriented Petri net(HOONet) is proposed. The structure of the HOONet is constructed of a high-level model and detail models. The former is used to model operational states for CNC machining systems, and the latter is used to analyze the component models for operational states. The machining parameters having great impacts on energy behaviors in CNC machining systems are declared with the data dictionary in HOONet models. A case study based on a CNC lathe is presented to demonstrate the proposed modeling method. The results show that it is effective for modeling flexible energy behaviors and providing a fine-grained description to quantitatively analyze the energy consumption of CNC machining systems.

Preparation of hydro-sodalite from fly ash using a hydrothermal method with a submolten salt system and study of the phase transition process

Hydro-sodalites are zeolitic materials with a wide variety of applications.Fly ash is an abundant industrial solid waste,rich in silicon and aluminum,from which hydro-sodalite can be synthesized.However,traditional hydrothermal synthesis methods are complex and cannot produce high-purity products.Therefore,there is a demand for processing routes to obtain high-purity hydro-sodalites.In the present study,high-purity hydro-sodalite(90.2 wt%)was prepared from fly ash by applying a hydrothermal method to a submolten salt system.Samples were characterized by powder X-ray diffraction(XRD),scanning electron microscopy(SEM),thermogravimetry and differential thermal analysis(TG–DTA),and Fourier transform infrared spectroscopy(FTIR)to confirm and quantify conversion of the raw material into the product phase.Purity of the samples prepared with an H2O/Na OH mass ratio of 1.5 and an H2O/fly ash mass ratio of 10 was calculated and the conversion process of the product phase was studied.Crystallinity of the product was influenced more by the Na OH concentration,less by the H2O/fly ash mass ratio.The main reaction process of the system is that the Si O ions produced by dissolution of the vitreous body in the fly ash and Na+ions in the solution reacted on the destroyed mullite skeleton to produce hydro-sodalite.This processing route could help mitigate processing difficulties,while producing high-purity hydro-sodalite from fly ash.