Approximate solutions of the Alekseevskii–Tate model of long-rod penetration

The Alekseevskii–Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets. However, due to the nonlinear nature of the equations, the rod(tail) velocity, penetration velocity, rod length, and penetration depth were obtained implicitly as a function of time and solved numerically By employing a linear approximation to the logarithmic relative rod length, we obtain two sets of explicit approximate algebraic solutions based on the implicit theoretica solution deduced from primitive equations. It is very convenient in the theoretical prediction of the Alekseevskii–Tate model to apply these simple algebraic solutions. In particular, approximate solution 1 shows good agreement with the theoretical(exact) solution, and the first-order perturbation solution obtained by Walters et al.(Int. J. Impac Eng. 33:837–846, 2006) can be deemed as a special form of approximate solution 1 in high-speed penetration. Meanwhile, with constant tail velocity and penetration velocity approximate solution 2 has very simple expressions, which is applicable for the qualitative analysis of long-rod penetration. Differences among these two approximate solutions and the theoretical(exact) solution and their respective scopes of application have been discussed, and the inferences with clear physical basis have been drawn. In addition, these two solutions and the first-order perturbation solution are applied to two cases with different initial impact velocity and different penetrator/target combinations to compare with the theoretical(exact) solution. Approximate solution 1 is much closer to the theoretical solution of the Alekseevskii–Tate model than the first-order perturbation solution in both cases, whilst approximate solution 2 brings us a more intuitive understanding of quasi-steady-state penetration.

EXTENSION OF CONVEX MODELS AND ITS IMPROVEMENT ON THE APPROXIMATE SOLUTION

In this paper, by means of combining non-probabilistic convex modeling with perturbation theory, an improvement is made on the first order approximate solution in convex models of uncertainties. Convex modeling is extended to largely uncertain and non-convex sets of uncertainties and the combinational convex modeling is developed. The presented method not only extends applications of convex modeling, but also improves its accuracy in uncertain problems and computational efficiency. The numerical example illustrates the efficiency of the proposed method.

A simplified approximate model of compressible hypervelocity penetration

A simplified approximate model considering rod/target material's compressibility is proposed for hypervelocity penetration.We study the effect of shockwaves on hypervelocity penetration whenever the compressibility of the rod is much larger,analogously,and much less than that of the target,respectively.The results show that the effect of shockwaves is insignificant up to 12 km/s,so the shockwave is neglected in the present approximate model.The Murnaghan equation of state is adopted to simulate the material behaviors in penetration and its validity is proved.The approximate model is finally reduced to an equation depending only on the penetration velocity and a simple approximate solution is achieved.The solution of the approximate model is in agreement with the result of the complete compressible model.In addition,the effect of shockwaves on hypervelocity penetration is shown to weaken material's compressibility and reduce the interface pressure of the rod/target,and thus the striking/protective performance of the rod/target is weakened,respectively.We also conduct an error analysis of the interface pressure and penetration efficiency.With a velocity change of 1.6 times the initial sound speed for the rod or target,the error of the approximate model is very small.For metallic rod-target combinations,the approximate model is applicable even at an impact velocity of 12 km/s.

Sampled-data Observer Design for a Class of Stochastic Nonlinear Systems Based on the Approximate Discrete-time Models

In this paper,we studied the approximate sampleddata observer design for a class of stochastic nonlinear systems.Euler-Maruyama approximation was investigated in this paper because it is the basis of other higher precision numerical methods,and it preserves important structures of the nonlinear systems.Also,the form of Euler-Maruyama model is simple and easy to be calculated.The results provide a reference for sampled-data observer design method for such stochastic nonlinear systems,and may be useful to many practical control applications,such as tracking control in mechanical systems.And the effectiveness of the approach is demonstrated by a simulation example.

Tree-Based Solution Frameworks for Predicting Tunnel Boring Machine Performance Using Rock Mass and Material Properties

Tunnel Boring Machines(TBMs)are vital for tunnel and underground construction due to their high safety and efficiency.Accurately predicting TBM operational parameters based on the surrounding environment is crucial for planning schedules and managing costs.This study investigates the effectiveness of tree-based machine learning models,including Random Forest,Extremely Randomized Trees,Adaptive Boosting Machine,Gradient Boosting Machine,Extreme Gradient Boosting Machine(XGBoost),Light Gradient Boosting Machine,and CatBoost,in predicting the Penetration Rate(PR)of TBMs by considering rock mass and material characteristics.These techniques are able to provide a good relationship between input(s)and output parameters;hence,obtaining a high level of accuracy.To do that,a comprehensive database comprising various rock mass and material parameters,including Rock Mass Rating,Brazilian Tensile Strength,and Weathering Zone,was utilized for model development.The practical application of these models was assessed with a new dataset representing diverse rock mass and material properties.To evaluate model performance,ranking systems and Taylor diagrams were employed.CatBoost emerged as the most accurate model during training and testing,with R2 scores of 0.927 and 0.861,respectively.However,during validation,XGBoost demonstrated superior performance with an R2 of 0.713.Despite these variations,all tree-based models showed promising accuracy in predicting TBM performance,providing valuable insights for similar projects in the future.

A novel excitation controller using support vector machines and approximate models

This paper proposes a novel excitation controller using support vector machines （SVM） and approximate models. The nonlinear control law is derived directly based on an input-output approximation method via Taylor expansion, which not only avoids complex control development and intensive computation, but also avoids online learning or adjustment. Only a general SVM modelling technique is involved in both model identification and controller implementation. The robustness of the stability is rigorously established using the Lyapunov method. Several simulations demonstrate the effectiveness of the proposed excitation controller.

APPROXIMATE POWER OF HETEROSCEDASTICITY TEST IN NONLINEAR MODELS WITH ARIMA（0,1,0） ERRORS

This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power calculations for the score test of heteroscedasticity in European rabbit data （Ratkowsky, 1983）. Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a wide range of parameter configurations.

An Efficient Constrained Model Predictive Control Algorithm Based on Approximate Computation

The on line computational burden related to model predictive control (MPC) of large scale constrained systems hampers its real time applications and limits it to slow dynamic process with moderate number of inputs. To avoid this, an efficient and fast algorithm based on aggregation optimization is proposed in this paper. It only optimizes the current control action at time instant k , while other future control sequences in the optimization horizon are approximated off line by the linear feedback control sequence, so the on line optimization can be converted into a low dimensional quadratic programming problem. Input constraints can be well handled in this scheme. The comparable performance is achieved with existing standard model predictive control algorithm. Simulation results well demonstrate its effectiveness.

SVM Approximate-based Internal Model Control Strategy

一台支持向量机器(SVM ) 近似底的内部模型控制(IMC ) 策略为同步发电机的蒸气 valving 控制被介绍。建议 SVM IMC 策略包括二主要部分：在内部模型结构的 SVM 近似反的控制器和无常赔偿。SVM 反的控制器经由泰勒扩大用一条输入产量近似途径直接被导出，并且没有进一步的联机训练，它通过非线性的系统鉴定被实现。而且，一个坚韧性过滤器在内部模型结构被用于无常赔偿。模拟为蒸气 valving 控制显示出 SVM IMC 策略的有效性。

An Analytic Approximate Solution of the SIR Model

The SIR(D) epidemiological model is defined through a system of transcendental equations, not solvable by elementary functions. In the present paper those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, originating, piece-wisely, from generalized logistic functions: they ensure exact (in the numerical sense) asymptotic values, besides to be quite practical to use, for example with fit to data algorithms;moreover they unveil a useful feature, that in fact, at least with very strict approximation, is also owned by the (numerical) solutions of the exact equations. The novelties in the work are: the way the approximate equations are obtained, using simple, analytic geometry considerations;the easy and practical formulation of the final approximate solutions;the mentioned useful feature, never disclosed before. The work’s method and result prove to be robust over a range of values of the well known non-dimensional parameter called basic reproduction ratio, that covers at least all the known epidemic cases, from influenza to measles: this is a point which doesn’t appear much discussed in analogous works.

A Class of Generalized Approximate Inverse Solvers for Unsymmetric Linear Systems of Irregular Structure Based on Adaptive Algorithmic Modelling for Solving Complex Computational Problems in Three Space Dimensions

A class of general inverse matrix techniques based on adaptive algorithmic modelling methodologies is derived yielding iterative methods for solving unsymmetric linear systems of irregular structure arising in complex computational problems in three space dimensions. The proposed class of approximate inverse is chosen as the basis to yield systems on which classic and preconditioned iterative methods are explicitly applied. Optimized versions of the proposed approximate inverse are presented using special storage (k-sweep) techniques leading to economical forms of the approximate inverses. Application of the adaptive algorithmic methodologies on a characteristic nonlinear boundary value problem is discussed and numerical results are given.

A novel robust adaptive controller for EAF electrode regulator system based on approximate model method

The electrode regulator system is a complex system with many variables, strong coupling and strong nonlinearity, while conventional control methods such as proportional integral derivative （PID） can not meet the requirements. A robust adaptive neural network controller （RANNC） for electrode regulator system was proposed. Artificial neural networks were established to learn the system dynamics. The nonlinear control law was derived directly based on an input-output approximating method via the Taylor expansion, which avoids complex control development and intensive computation. The stability of the closed-loop system was established by the Lyapunov method. The current fluctuation relative percentage is less than ±8% and heating rate is up to 6.32 ℃/min when the proposed controller is used. The experiment results show that the proposed control scheme is better than inverse neural network controller （INNC） and PID controller （PIDC）.

The Research of Role Tree-Based Access Control Model

Towards the crossing and coupling permissions in tasks existed widely in many fields and considering the design of role view must rely on the activities of the tasks process,based on Role Based Accessing Control (RBAC) model,this paper put forward a Role Tree-Based Access Control (RTBAC) model. In addition,the model definition and its constraint formal description is also discussed in this paper. RTBAC model is able to realize the dynamic organizing,self-determination and convenience of the design of role view,and guarantee the least role permission when task separating in the mean time.

IMPROVED AERODYNAMIC APPROXIMATION MODEL WITH CASE-BASED REASONING TECHNIQUE FOR MDO OF AIRCRAFT

To increase the efficiency of the multidisciplinary optimization of aircraft, an aerodynamic approximation model is improved. Based on the study of aerodynamic approximation model constructed by the scaling correction model, case-based reasoning technique is introduced to improve the approximation model for optimization. The aircraft case model is constructed by utilizing the plane parameters related to aerodynamic characteristics as attributes of cases, and the formula of case retrieving is improved. Finally, the aerodynamic approximation model for optimization is improved by reusing the correction factors of the most similar aircraft to the current one. The multidisciplinary optimization of a civil aircraft concept is carried out with the improved aerodynamic approximation model. The results demonstrate that the precision and the efficiency of the optimization can be improved by utilizing the improved aerodynamic approximation model with ease-based reasoning technique.

RBMDO Using Gaussian Mixture Model-Based Second-Order Mean-Value Saddlepoint Approximation

Actual engineering systems will be inevitably affected by uncertain factors.Thus,the Reliability-Based Multidisciplinary Design Optimization(RBMDO)has become a hotspot for recent research and application in complex engineering system design.The Second-Order/First-Order Mean-Value Saddlepoint Approximate(SOMVSA/-FOMVSA)are two popular reliability analysis strategies that are widely used in RBMDO.However,the SOMVSA method can only be used efficiently when the distribution of input variables is Gaussian distribution,which significantly limits its application.In this study,the Gaussian Mixture Model-based Second-Order Mean-Value Saddlepoint Approximation(GMM-SOMVSA)is introduced to tackle above problem.It is integrated with the Collaborative Optimization(CO)method to solve RBMDO problems.Furthermore,the formula and procedure of RBMDO using GMM-SOMVSA-Based CO(GMM-SOMVSA-CO)are proposed.Finally,an engineering example is given to show the application of the GMM-SOMVSA-CO method.

Beam Approximation for Dynamic Analysis of Launch Vehicles Modelled as Stiffened Cylindrical Shells

A beam approximation method for dynamic analysis of launch vehicles modelled as stiffened cylindrical shells is proposed.Firstly,an initial beam model of the stiffened cylindrical shell is established based on the cross-sectional area equivalence principle that represents the shell skin and its longitudinal ribs as a beam with annular cross-section,and the circumferential ribs as lumped masses at the nodes of the beam elements.Then,a fine finite element model(FE model)of the stiffened cylindrical shell is constructed and a modal analysis is carried out.Finally,the initial beam model is improved through model updating against the natural frequencies and mode shapes of the fine FE model of the shell.To facilitate the comparison between the mode shapes of the fine FE model of the stiffened shell and the equivalent beam model,a weighted nodal displacement coupling relationship is introduced.To prevent the design parameters used in model updating from converging to incorrect values,a pre-model updating procedure is added before the proper model updating.The results of two examples demonstrate that the beam approximation method presented in this paper can build equivalent beam models of stiffened cylindrical shells which can reflect the global longitudinal,lateral and torsional vibration characteristics very well in terms of the natural frequencies.

Dynamics of Jaynes-Cummings Model in the Absence of Rotating-Wave Approximation

The Jaynes-Cummings model （JCM） is studied in the absence of the rotating-wave approximation （RWA） by a coherent-state expansion technique. In comparison with the previous paper in which the coherent-state expansion was performed only to the third order, we carry out in this paper a complete expansion to demonstrate exactly the dynamics of the JCM without the RWA. Our study gives a systematic method to solve the non-RWA problem, which would be useful in various physical systems, e.g., in a system with an ultracold trapped ion experiencing the running waves of lasers.

Integrating a novel irrigation approximation method with a process-based remote sensing model to estimate multi-years'winter wheat yield over the North China Plain

Accurate estimation of regional winter wheat yields is essential for understanding the food production status and ensuring national food security.However,using the existing remote sensing-based crop yield models to accurately reproduce the inter-annual and spatial variations in winter wheat yields remains challenging due to the limited ability to acquire irrigation information in water-limited regions.Thus,we proposed a new approach to approximating irrigations of winter wheat over the North China Plain(NCP),where irrigation occurs extensively during the winter wheat growing season.This approach used irrigation pattern parameters(IPPs)to define the irrigation frequency and timing.Then,they were incorporated into a newly-developed process-based and remote sensing-driven crop yield model for winter wheat(PRYM–Wheat),to improve the regional estimates of winter wheat over the NCP.The IPPs were determined using statistical yield data of reference years(2010–2015)over the NCP.Our findings showed that PRYM–Wheat with the optimal IPPs could improve the regional estimate of winter wheat yield,with an increase and decrease in the correlation coefficient(R)and root mean square error(RMSE)of 0.15(about 37%)and 0.90 t ha–1(about 41%),respectively.The data in validation years(2001–2009 and 2016–2019)were used to validate PRYM–Wheat.In addition,our findings also showed R(RMSE)of 0.80(0.62 t ha–1)on a site level,0.61(0.91 t ha–1)for Hebei Province on a county level,0.73(0.97 t ha–1)for Henan Province on a county level,and 0.55(0.75 t ha–1)for Shandong Province on a city level.Overall,PRYM–Wheat can offer a stable and robust approach to estimating regional winter wheat yield across multiple years,providing a scientific basis for ensuring regional food security.

Speech Enhancement Based on Approximate Message Passing

To overcome the limitations of conventional speech enhancement methods, such as inaccurate voice activity detector(VAD) and noise estimation, a novel speech enhancement algorithm based on the approximate message passing(AMP) is adopted. AMP exploits the difference between speech and noise sparsity to remove or mute the noise from the corrupted speech. The AMP algorithm is adopted to reconstruct the clean speech efficiently for speech enhancement. More specifically, the prior probability distribution of speech sparsity coefficient is characterized by Gaussian-model, and the hyper-parameters of the prior model are excellently learned by expectation maximization(EM) algorithm. We utilize the k-nearest neighbor(k-NN) algorithm to learn the sparsity with the fact that the speech coefficients between adjacent frames are correlated. In addition, computational simulations are used to validate the proposed algorithm, which achieves better speech enhancement performance than other four baseline methods-Wiener filtering, subspace pursuit(SP), distributed sparsity adaptive matching pursuit(DSAMP), and expectation-maximization Gaussian-model approximate message passing(EM-GAMP) under different compression ratios and a wide range of signal to noise ratios(SNRs).

Research on Approximate Calculation of Preventive Maintenance Period in Machinery Systems under Random Distribution

Approximate calculation methods of prevention maintenance period under the random distribution are given,and three kinds of approximate calculation models of prevention maintenance period based on different security demands are come up with according to maintenance problems of machinery systems in modern enterprise and starting with different demands of systems. And then,how to make certain the best maintenance period by using the approximate calculation methods is illustrated by an exam- ple.