High-Order Models of Nonlinear and Dispersive Wave in Water of Varying Depth with Arbitrary Sloping Bottom

High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of mu(= h/lambda, depth to deep-water wave length ratio) and epsilon(= a/h, wave amplitude to depth ratio) for velocity potential, particle velocity vector, pressure and the Boussinesq-type equations for surface elevation eta and horizontal velocity vector (U) over right arrow at any given level in water are given. Then, the exact explicit expressions to the fourth order of mu are derived. Finally, the linear solutions of eta, (U) over right arrow, C (phase-celerity) and C-g (group velocity) for a constant water depth are obtained. Compared with the Airy theory, excellent results can be found even for a water depth as large as the wave legnth. The present high-order models are applicable to nonlinear regular and irregular waves in water of any varying depth (from shallow to deep) and bottom slope (from mild to steep).

A Comparative Study of Fractional Order Models on State of Charge Estimation for Lithium Ion Batteries

State of charge(SOC)estimation for lithium ion batteries plays a critical role in battery management systems for electric vehicles.Battery fractional order models(FOMs)which come from frequency-domain modelling have provided a distinct insight into SOC estimation.In this article,we compare five state-of-the-art FOMs in terms of SOC estimation.To this end,firstly,characterisation tests on lithium ion batteries are conducted,and the experimental results are used to identify FOM parameters.Parameter identification results show that increasing the complexity of FOMs cannot always improve accuracy.The model R(RQ)W shows superior identification accuracy than the other four FOMs.Secondly,the SOC estimation based on a fractional order unscented Kalman filter is conducted to compare model accuracy and computational burden under different profiles,memory lengths,ambient temperatures,cells and voltage/current drifts.The evaluation results reveal that the SOC estimation accuracy does not necessarily positively correlate to the complexity of FOMs.Although more complex models can have better robustness against temperature variation,R(RQ),the simplest FOM,can overall provide satisfactory accuracy.Validation results on different cells demonstrate the generalisation ability of FOMs,and R(RQ)outperforms other models.Moreover,R(RQ)shows better robustness against truncation error and can maintain high accuracy even under the occurrence of current or voltage sensor drift.

Sliding Mode Control Design via Reduced Order Model Approach

This paper presents a design of continuous-time sliding mode control for the higher order systems via reduced order model. It is shown that a continuous-time sliding mode control designed for the reduced order model gives similar performance for thc higher order system. The method is illustrated by numerical examples. The paper also introduces a technique for design of a sliding surface such that the system satisfies a cost-optimality condition when on the sliding surface.

Fractional Order Modeling of Human Operator Behavior with Second Order Controlled Plant and Experiment Research

Modeling human operator's dynamics plays a very important role in the manual closed-loop control system, and it is an active research area for several decades. Based on the characteristics of human brain and behavior, a new kind of fractional order mathematical model for human operator in single-input single-output(SISO) systems is proposed. Compared with the traditional models based on the commonly used quasilinear transfer function method or the optimal control theory method, the proposed fractional order model has simpler structure with only few parameters, and each parameter has explicit physical meanings. The actual data and experiment results with the second-order controlled plant illustrate the effectiveness of the proposed method.

Derivation of a second-order model for Reynolds stress using renormalization group analysis and the two-scale expansion technique

With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples：turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder （GL） model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.

What Does a First Order Model Tell Us about PEEP Wave Maneuvers?

Patients with acute respiratory distress syndrome (ARDS) are currently treated with a lung protective ventilation strategy and the application of positive end-expiratory pressure (PEEP), sometimes in combination with recruitment maneuvers. In this study, the respiratory system elastance and airway resistance of each breath before, during and after a specific recruitment maneuver (PEEP wave maneuver) were analyzed in two patient groups, ARDS and control group. A reduction of elastance after the maneuver was observed in ARDS patients. In addition, only healthy lungs exhibited a reduction of the elastance during the course of the maneuver, while the lungs of ARDS patients didn’t show that reduction of elastance. The capability of PEEP wave maneuvers to improve lung ventilation was shown and the dynamic behavior of the elastance after the maneuver was illustrated. Healthy lungs adapt faster to changes in mechanical ventilation than the lungs of ARDS patients.

Analytical Higher-Order Model for Flexible and Stretchable Sensors

The stretchable sensor wrapped around a foldable airfoil or embedded inside of it has great potential for use in the monitoring of the structural status of the foldable airfoil.The design methodology is important to the development of the stretchable sensor for status monitoring on the foldable airfoil.According to the requirement of mechanical flexibility of the sensor,the combined use of a layered flexible structural formation and a strain isolation layer is implemented.An analytical higher-order model is proposed to predict the stresses of the strain-isolation layer based on the shear-lag model for the safe design of the flexible and stretchable sensors.The normal stress and shear stress equations in the constructed structure of the sensors are obtained by the proposed model.The stress distribution in the structure is investigated when bending load is applied to the structures.The numerical results show that the proposed model can predict the variation of normal stress and shear stress along the thickness of the strain-isolation（polydimethylsiloxane）layer accurately.The results by the proposed model are in good agreement with the finite element method,in which the normal stress is variable while the shear stress is invariable along the thickness direction of strain-isolation layer.The high-order model is proposed to predict the stresses of the layered structure of the flexible and stretchable sensor for monitoring the status of the foldable airfoil.

FAW-Volkswagen’s build-to-order model

This paper represents an attempt to: 1) conduct a systematic analysis of the build-to-order model and concomitant process change FAW-Volkswagen Automobile Co., Ltd. adopted 1 ; 2) elaborate on how Chinese automakers should restructure and improve themselves along the value chain under the build-to-order model in order to acquire new competitive advantages; and 3) modify the value chain under the build-to-order model according to the findings of the case analysis based on a review of value chain and customization theories. This study shows that the build-to-order model is an important way for Chinese automakers to effectively handle the production and market relationship. Order management enables automakers to effectively understand and gauge market demand, reduce inventory costs, reasonably arrange production capacity planning and concentrate on advantageous resources to plan corporate production and operation. Under the build-to-order model, scientific market forecast and time management can be combined with a certain margin of safety in inventory to effectively cope with domestic automotive market fluctuations.

基于Ordered Probit模型的人车冲突安全影响因素研究

为探究和定量分析人车冲突严重程度的影响因素,通过采集3个信号交叉口的人车冲突视频数据,利用T-Analyst标定人车轨迹并计算冲突指标(PET),采用85%位累计频率曲线法划分人车冲突等级;从人、车、路及环境特征中选取10个因素作为变量,构建Ordered Probit模型,以确立人车冲突严重程度的显著影响因素,并通过边际效应定量分析不同显著因素的影响程度。研究结果表明:行人闯红灯情况、年龄、行人交通量、人行道占用情况、人行道起点终点、车辆速度变化及车流量是人车冲突严重程度的显著因素,相较于各自参考量,行人闯红灯、车辆加速通过冲突点、人行道起点及老年人造成严重冲突的概率分别增加8.2%,5.9%,5.1%,4.4%;相较于低流量的交通流,较高流量的车流和行人交通流使得严重冲突的概率分别增加3.7%,2.5%,但人行道占用使得严重冲突的概率下降6.8%。研究结果可为信号交叉口行人过街交通安全设施的设计和实施提供理论依据。

基于Ordered Logit模型的民办高校科研成果转化影响因素研究

为研究民办高校科研成果转化影响因素,在专家访谈和实地调研的基础上,对K高校、C高校、B高校、Z高校等民办高校教师发放调查问卷收集数据,应用Ordered Logit模型对其影响因素进行了实证分析。分析发现,科研经费支持力度与科研成果数量之间呈正相关关系,高校科研平台设置与服务地方经济建设之间呈正相关关系,高校科研管理制度与科研成果转化成效之间呈正相关关系。由此得出结论:我国民办高校科研成果转化与服务地方经济能力有待提升,民办高校科研成果转化的金融支持不够灵活、公共服务平台不够健全,完善民办高校科研管理制度是提高科研成果转化效率的重要保障。

Fourth-Order Predictive Modelling: II. 4th-BERRU-PM Methodology for Combining Measurements with Computations to Obtain Best-Estimate Results with Reduced Uncertainties

This work presents a comprehensive fourth-order predictive modeling (PM) methodology that uses the MaxEnt principle to incorporate fourth-order moments (means, covariances, skewness, kurtosis) of model parameters, computed and measured model responses, as well as fourth (and higher) order sensitivities of computed model responses to model parameters. This new methodology is designated by the acronym 4th-BERRU-PM, which stands for “fourth-order best-estimate results with reduced uncertainties.” The results predicted by the 4th-BERRU-PM incorporates, as particular cases, the results previously predicted by the second-order predictive modeling methodology 2nd-BERRU-PM, and vastly generalizes the results produced by extant data assimilation and data adjustment procedures.

Second-Order MaxEnt Predictive Modelling Methodology. I: Deterministically Incorporated Computational Model (2nd-BERRU-PMD)

This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2nd-BERRU-PMD. The attribute “2nd” indicates that this methodology incorporates second-order uncertainties (means and covariances) and second-order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best- Estimate Results with Reduced Uncertainties” and the last letter (“D”) in the acronym indicates “deterministic,” referring to the deterministic inclusion of the computational model responses. The 2nd-BERRU-PMD methodology is fundamentally based on the maximum entropy (MaxEnt) principle. This principle is in contradistinction to the fundamental principle that underlies the extant data assimilation and/or adjustment procedures which minimize in a least-square sense a subjective user-defined functional which is meant to represent the discrepancies between measured and computed model responses. It is shown that the 2nd-BERRU-PMD methodology generalizes and extends current data assimilation and/or data adjustment procedures while overcoming the fundamental limitations of these procedures. In the accompanying work (Part II), the alternative framework for developing the “second- order MaxEnt predictive modelling methodology” is presented by incorporating probabilistically (as opposed to “deterministically”) the computed model responses.

Second-Order MaxEnt Predictive Modelling Methodology. II: Probabilistically Incorporated Computational Model (2nd-BERRU-PMP)

This work presents a comprehensive second-order predictive modeling (PM) methodology based on the maximum entropy (MaxEnt) principle for obtaining best-estimate mean values and correlations for model responses and parameters. This methodology is designated by the acronym 2nd-BERRU-PMP, where the attribute “2nd” indicates that this methodology incorporates second- order uncertainties (means and covariances) and second (and higher) order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best-Estimate Results with Reduced Uncertainties” and the last letter (“P”) in the acronym indicates “probabilistic,” referring to the MaxEnt probabilistic inclusion of the computational model responses. This is in contradistinction to the 2nd-BERRU-PMD methodology, which deterministically combines the computed model responses with the experimental information, as presented in the accompanying work (Part I). Although both the 2nd-BERRU-PMP and the 2nd-BERRU-PMD methodologies yield expressions that include second (and higher) order sensitivities of responses to model parameters, the respective expressions for the predicted responses, for the calibrated predicted parameters and for their predicted uncertainties (covariances), are not identical to each other. Nevertheless, the results predicted by both the 2nd-BERRU-PMP and the 2nd-BERRU-PMD methodologies encompass, as particular cases, the results produced by the extant data assimilation and data adjustment procedures, which rely on the minimization, in a least-square sense, of a user-defined functional meant to represent the discrepancies between measured and computed model responses.

Fourth-Order Predictive Modelling: I. General-Purpose Closed-Form Fourth-Order Moments-Constrained MaxEnt Distribution

This work (in two parts) will present a novel predictive modeling methodology aimed at obtaining “best-estimate results with reduced uncertainties” for the first four moments (mean values, covariance, skewness and kurtosis) of the optimally predicted distribution of model results and calibrated model parameters, by combining fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses to model parameters. Underlying the construction of this fourth-order predictive modeling methodology is the “maximum entropy principle” which is initially used to obtain a novel closed-form expression of the (moments-constrained) fourth-order Maximum Entropy (MaxEnt) probability distribution constructed from the first four moments (means, covariances, skewness, kurtosis), which are assumed to be known, of an otherwise unknown distribution of a high-dimensional multivariate uncertain quantity of interest. This fourth-order MaxEnt distribution provides optimal compatibility of the available information while simultaneously ensuring minimal spurious information content, yielding an estimate of a probability density with the highest uncertainty among all densities satisfying the known moment constraints. Since this novel generic fourth-order MaxEnt distribution is of interest in its own right for applications in addition to predictive modeling, its construction is presented separately, in this first part of a two-part work. The fourth-order predictive modeling methodology that will be constructed by particularizing this generic fourth-order MaxEnt distribution will be presented in the accompanying work (Part-2).

Second-Order MaxEnt Predictive Modelling Methodology. III: Illustrative Application to a Reactor Physics Benchmark

This work illustrates the innovative results obtained by applying the recently developed the 2nd-order predictive modeling methodology called “2nd- BERRU-PM”, where the acronym BERRU denotes “best-estimate results with reduced uncertainties” and “PM” denotes “predictive modeling.” The physical system selected for this illustrative application is a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. This benchmark is modeled using the neutron transport Boltzmann equation (involving 21,976 uncertain parameters), the solution of which is representative of “large-scale computations.” The results obtained in this work confirm the fact that the 2nd-BERRU-PM methodology predicts best-estimate results that fall in between the corresponding computed and measured values, while reducing the predicted standard deviations of the predicted results to values smaller than either the experimentally measured or the computed values of the respective standard deviations. The obtained results also indicate that 2nd-order response sensitivities must always be included to quantify the need for including (or not) the 3rd- and/or 4th-order sensitivities. When the parameters are known with high precision, the contributions of the higher-order sensitivities diminish with increasing order, so that the inclusion of the 1st- and 2nd-order sensitivities may suffice for obtaining accurate predicted best- estimate response values and best-estimate standard deviations. On the other hand, when the parameters’ standard deviations are sufficiently large to approach (or be outside of) the radius of convergence of the multivariate Taylor-series which represents the response in the phase-space of model parameters, the contributions stemming from the 3rd- and even 4th-order sensitivities are necessary to ensure consistency between the computed and measured response. In such cases, the use of only the 1st-order sensitivities erroneously indicates that the computed results are inconsistent with the respective measured response. Ongoing research aims at extending the 2nd-BERRU-PM methodology to fourth-order, thus enabling the computation of third-order response correlations (skewness) and fourth-order response correlations (kurtosis).

Adding-Point Strategy for Reduced-Order Hypersonic Aerothermodynamics Modeling Based on Fuzzy Clustering

Reduced order models（ROMs） based on the snapshots on the CFD high-fidelity simulations have been paid great attention recently due to their capability of capturing the features of the complex geometries and flow configurations. To improve the efficiency and precision of the ROMs, it is indispensable to add extra sampling points to the initial snapshots, since the number of sampling points to achieve an adequately accurate ROM is generally unknown in prior, but a large number of initial sampling points reduces the parsimony of the ROMs. A fuzzy-clustering-based adding-point strategy is proposed and the fuzzy clustering acts an indicator of the region in which the precision of ROMs is relatively low. The proposed method is applied to construct the ROMs for the benchmark mathematical examples and a numerical example of hypersonic aerothermodynamics prediction for a typical control surface. The proposed method can achieve a 34.5% improvement on the efficiency than the estimated mean squared error prediction algorithm and shows same-level prediction accuracy.

Static aeroelastic analysis including geometric nonlinearities based on reduced order model

This paper describes a method proposed for modeling large deflection of aircraft in nonlinear aeroelastic analysis by developing reduced order model（ROM）.The method is applied for solving the static aeroelastic and static aeroelastic trim problems of flexible aircraft containing geometric nonlinearities;meanwhile,the non-planar effects of aerodynamics and follower force effect have been considered.ROMs are computational inexpensive mathematical representations compared to traditional nonlinear finite element method（FEM） especially in aeroelastic solutions.The approach for structure modeling presented here is on the basis of combined modal/finite element（MFE） method that characterizes the stiffness nonlinearities and we apply that structure modeling method as ROM to aeroelastic analysis.Moreover,the non-planar aerodynamic force is computed by the non-planar vortex lattice method（VLM）.Structure and aerodynamics can be coupled with the surface spline method.The results show that both of the static aeroelastic analysis and trim analysis of aircraft based on structure ROM can achieve a good agreement compared to analysis based on the FEM and experimental result.

Reduced order model for unsteady aerodynamic performance of compressor cascade based on recursive RBF

Based on Recursive Radial Basis Function(RRBF)neural network,the Reduced Order Model(ROM)of compressor cascade was established to meet the urgent demand of highly efficient prediction of unsteady aerodynamics performance of turbomachinery.One novel ROM called ASA-RRBF model based on Adaptive Simulated Annealing(ASA)algorithm was developed to enhance the generalization ability of the unsteady ROM.The ROM was verified by predicting the unsteady aerodynamics performance of a highly-loaded compressor cascade.The results show that the RRBF model has higher accuracy in identification of the dimensionless total pressure and dimensionless static pressure of compressor cascade under nonlinear and unsteady conditions,and the model behaves higher stability and computational efficiency.However,for the strong nonlinear characteristics of aerodynamic parameters,the RRBF model presents lower accuracy.Additionally,the RRBF model predicts with a large error in the identification of aerodynamic parameters under linear and unsteady conditions.For ASA-RRBF,by introducing a small-amplitude and highfrequency sinusoidal signal as validation sample,the width of the basis function of the RRBF model is optimized to improve the generalization ability of the ROM under linear unsteady conditions.Besides,this model improves the predicting accuracy of dimensionless static pressure which has strong nonlinear characteristics.The ASA-RRBF model has higher prediction accuracy than RRBF model without significantly increasing the total time consumption.This novel model can predict the linear hysteresis of dimensionless static pressure happened in the harmonic condition,but it cannot accurately predict the beat frequency of dimensionless total pressure.

Active Control Law Design for Flutter/LCO Suppression Based on Reduced Order Model Method

Active stability augmentation system is an attractive and promising technology to suppress flutter and limit cycle oscillation (LCO). In order to design a good active control law, the control plant model with low order and high accuracy must be provided, which is one of the most important key points. The traditional model is based on low fidelity aerodynamics model such as panel method, which is unsuitable for transonic flight regime. The physics-based high fidelity tools, reduced order model (ROM) and CFD/CSD coupled aeroservoelastic solver are used to design the active control law. The Volterra/ROM is applied to constructing the low order state space model for the nonlinear unsteady aerodynamics and static output feedback method is used to active control law design. The detail of the new method is demonstrated by the Goland+ wing/store system. The simulation results show that the effectiveness of the designed active augmentation system, which can suppress the flutter and LCO successfully.

State of charge estimation by square root cubature particle filter approach with fractional order model of lithium-ion battery

In this paper, a square root cubature particle filter approach was designed to estimate the state of charge of lithium-ion battery,which not only enhanced the numerical stability and guaranteed positive definiteness of the state covariance, but also increased accuracy and decreased computation quantity. Due to the fractional characteristics of the battery capacitance, a fractional order model was used to formulate the lithium-ion battery. Considering the high accuracy and easy convergence, a particle swarm optimization algorithm was utilized to identify the model parameters. The above-mentioned approach was modelled and translated into C code, which was downloaded into battery control unit of battery management system for experimental validation. Two kinds of dynamic cycles were utilized to validate the proposed approach at different temperatures, where both unscent Kalman filter and cubature Kalman filter were compared with the proposed approach. Experimental results indicate that the proposed approach has better accuracy and robustness, and fractional order model is more accurate than integer order model.Therefore, the square root cubature particle filter with fractional order model of lithium-ion battery is a good candidate to estimate the state of charge.