Orthogonal expansion of ground motion and PDEM-based seismic response analysis of nonlinear structures

This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.

Design and selection of an artificial diet for the coconut black-headed caterpillar, Opisina arenosella, based on orthogonal array analysis

Opisina arenosella has been an outbreak pest of coconut trees in southern China since 2013. To develop efficient control methods for this invasive pest, adequate rearing protocols are desirable. In this study, an orthogonal array of artificial diets with 11 factors at 3 levels was deployed for both 2 nd–4 th and 5 th–6 th instar larvae of O. arenosella. Biological parameters including survival time of larvae, development time from larva to pupa, pupation rate, emergence rate, and pupal weight were monitored to reveal the most important components in the diet formulas. Biological parameters in O. arenosella were most affected by brewer’s yeast, sucrose, ascorbic acid, and wheat germ. Statistical analysis indicated that different diet combinations supported optimum performance of biological parameters for 2 nd–4 th and 5 th–6 th instar larvae. The validity of the optimization predicted by the orthogonal array analysis was confirmed in a follow-up bioassay with similar optimized diets for both 2 nd–4 th and 5 th–6 th instar larvae. The optimal artificial diet has great potential for the mass rearing technique, and can provide valuable results for using parasitoids in biological control of O. arenosella.

Analysis of the regional spectral properties in northwestern South China Sea based on an empirical orthogonal function

This study presents an analysis of the spectral characteristics of remote sensing reflectance(Rrs)in northwestern South China Sea based on the in situ optical and water quality data for August 2018.Rrswas initially divided into four classes,classes A to D,using the max-classification algorithm,and the spectral properties of whole Rrs were characterized using the empirical orthogonal function(EOF)analysis.Subsequently,the dominant factors in each EOF mode were determined.The results indicated that more than 95%of the variances of Rrs are partly driven by the back-scattering characteristics of the suspended matter.The initial two EOF modes were well correlated with the total suspended matter and back-scattering coefficient.Furthermore,the first EOF modes of the four classes of Rrs(A-D Rrs-EOF1)significantly contributed to the total variances of each Rrs class.In addition,the correlation coefficients between the amplitude factors of class A-D Rrs-EOF1 and the variances of the relevant water quality and optical parameters were better than those of the unclassified ones.The spectral shape of class ARrs-EOF1 was governed by the absorption characteristic of chlorophyll a and colored dissolved organic matter(CDOM).The spectral shape of class B Rrs-EOF1 was governed by the absorption characteristic of CDOM since it exhibited a high correlation with the absorption coefficient of CDOM(ag(λ)),whereas the spectral shape of class C Rrs-EOF1 was governed by the back-scattering characteristics but not affected by the suspended matter.The spectral shape of class D Rrs-EOF1 exhibited a relatively good correlation with all the water quality parameters,which played a significant role in deciding its spectral shape.

Flutter Analysis of Aircraft Wing Using Equivalent-Plate Models with Orthogonal Polynomials

A method of equivalent simplification,using equivalent-plate models(EPMs),is developed.It is to achieve goals of rapid modeling and effective analysis in structural dynamics and flutter analysis of complex wing structures.It is on the assumption that the wing structures discussed are composed of skin,beams and ribs,and the different plate units(such as skin,beam web,rib web)are not distinguished in modeling,which is to avoid the complex pre-processing and make it more generalized.Taking the effect of transverse shear deformation into consideration,the equivalence is based on the first-order shear deformation theory,and it can import the model files of MSC/NASTRAN and process the information to accomplish the equivalent modeling.The Ritz method is applied with the Legendre polynomials,which is used to define the geometry,structure and displacements of the wing.Particularly,the selection of Legendre polynomials as trial functions brings good accuracy to the modeling and can avoid the ill-conditions.This is in contrast to the EPM method based on the classical plate theory.Through vibration and flutter analysis,the results obtained by using EPM agree well with those obtained by the finite element method,which indicates the accuracy and effectiveness in vibration and flutter analysis of the EPM method.

A General Model for Analysis of Sound Radiation from Orthogonally Stiffened Laminated Composite Plates

A general theoretical model is developed to investigate the sound radiation from an infinite orthogonally stiffened plate under point excitation force. The plate can be metallic or composite, and fluid loading is also considered in the research. The first order shear deformation theory is used to account for the transverse shear deformation. The motion of the equally spaced stiffeners is examined by considering their bending vibrations and torsional movements. Based on the periodic structure theory and the concepts of the equivalent dynamic flexibility of the plate, the generalized vibro-acoustic equation of the model is obtained by applying the Fourier transform method. The generalized model that can be solved numerically is validated by comparing model predictions with the existing results. Numerical calculations are performed to investigate the effects of the location of the excitation, the spacing of the stiffeners, the plate thickness, the strengthening form and the fiber orientation on the sound radiation characteristic of the orthogonaUy stiffened plate, and some practical conclusions are drawn from these parameter studies.

Orthogonal design of experiment and analysis of abrasive water jet cutting on carbon fiber reinforced composites

The carbon fiber reinforced composite is a new type of composite material with an excellent property in strength and elastic modulus,and has found extensive applications in aerospace,energy,automotive industry and so on.However,this composite has a strict requirement on processing techniques,for example,brittle damage or delamination often exists in conventional processing techniques.Abrasive water jet machining technology is a new type of green machining technique with distinct advantages such as high-energy and thermal distortion free.The use of abrasive water jet technique to process carbon fiber composite materials has become a popular trend since it can significantly improve the processing accuracy and surface quality of carbon fiber composite materials.However,there are too many parameters that affect the quality of an abrasive water jet machining.At present,few studies are carried out on the parameter optimization of such a machining process,which leads to the unstable quality of surface processing.In this paper,orthogonal design of experiment and regression analysis were employed to establish the empirical model between cutting surface roughness and machining process parameters.Then a verified model was used to optimize the machining process parameters for abrasive water jet cutting carbon fiber reinforced composites.

Fuzzy Analysis Method for Orthogonal Test on Seed Propagation of Eurya chinensis

Fuzzy analysis method for orthogonal test was used to study the effect of different sowing depth, seed soaking time, illumination intensity and culture soil on the seed germination rate of Eurya chinensis. The results showed that the effect of seed soaking time on the sowing and seedling of Eurya chinensis was the biggest, and the ethers were illumination intensity, sowing depth and culture soil. The germi- nation rate was the highest when composite soil was used as culture soil and seeds were soaked for 48 h and sowed in topsoil, and a layer of sunshade net was used.

MODEL AND PERFORMANCE ANALYSIS OF FMT SYSTEM AND ORTHOGONAL FILTERBANKS

An orthogonal multi-carrier modulation-Filtered Multi-Tone (FMT) modulation, is evaluated in this paper. The objective of this paper is to model the FMT system with polyphase fil- terbank network, design its synthesis/analysis orthogonal filterbanks and analyze their performance. Oversampled and critically sampled cases of FMT system are discussed in detail. Perfect Reconstruc- tion (PR) properties of M parallel orthogonal subchannels in the case of critically sampled is derived from filterbank polyphase decomposition. Diverse types of prototype filters which include Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) are designed and analyzed. Performance analysis of orthogonal filterbanks which are implemented by these prototype filters are proposed and compared respectively. Simulation results of FMT orthogonal filterbanks are presented. In the end, the application prospect of FMT is discussed.

Global Comprehensive Sensitivity Analysis of Arch Dam Construction Parameters Based on Orthogonal Experiment

The construction of arch dams exhibits high uncertainty. Sensitivity analysis of construction parameters is important for the design and optimization of dam construction duration. However, current research cannot fully consider the combined influences of multiple parameters on the total construction. To effectively analyze the duration of arch dam construction, this study proposes a global comprehensive sensitivity analysis method in view of the whole process of arch dam construction based on an orthogonal experiment. This method could comprehensively consider the influence of the construction parameters that may lead to the uncertainty of construction duration. In addition, this method is able to identify the key parameters that may have a significant effect on duration uncertainty and sums up the general rules of combined parameters’ interaction effect, which provides a scientific basis for reasonable optimization of the duration of dam construction. © 2017, Tianjin University and Springer-Verlag GmbH Germany.

CAPS(Covariance Analysis Program Developed at Shanghai Observatory)的原理、结构和使用

推导了在Givens－Gentleman正交变换形式下的考察协方差分析理论，给出一些重要的统计量，如考察协方差矩阵、摄动矩阵等在此形式下的表达式。在理论分析的基础上给出编写CAPS时采用的详细流程图，并介绍在使用CAPS时应注意的一些问题。

Influence of multiple structural parameters on interior ballistics based on orthogonal test methods

Influence of multiple structural parameters on the performance of a gun launch system driven by highpressure reactive gases is important for structural design and performance adjustment.A coupled lumped parameter model was utilized to predict the propellant combustion,and a dynamic finite element method was applied to approximate the mechanical interactions between the projectile and the barrel.The combustion and the mechanical interactions were coupled through a user subroutine interface in ABAQUS.The correctness and the capability of the finite element approximations in capturing small structural changes were validated by comparing predicted resistance with experiments.Based on the coupled model,the influence of structural parameters of a medium-caliber gun on the system performance was investigated.In order to reduce the research costs,orthogonal tests were designed to investigate the comprehensive effects of the parameters.According to statistical analysis,the important order of the structural parameters on the launching process was obtained.The results indicate that the influence of the width of the rotating band stands out among the studied parameters in the gun.The work provides a method to investigate the influence of multiple parameters on system performance and gives guidance for controlling the system performance.

Cavitation Optimization for a Centrifugal Pump Impeller by Using Orthogonal Design of Experiment

Cavitation is one of the most important performance of centrifugal pumps. However, the current optimization works of centrifugal pump are mostly focusing on hydraulic efficiency only, which may result in poor cavitation performance. Therefore, it is necessary to find an appropriate solution to improve cavitation performance with acceptable efficiency. In this paper, to improve the cavitation performance of a centrifugal pump with a vaned diffuser, the influence of impeller geometric parameters on the cavitation of the pump is investigated using the orthogonal design of experiment （DOE） based on computational fluid dynamics. The impeller inlet diameter D1, inlet incidence angle Aft, and blade wrap angle ~0 are selected as the main impeller geometric parameters and the orthogonal experiment of L9（3＂3） is performed. Three-dimensional steady simulations for cavitation are conducted by using constant gas mass fraction model with second-order upwind, and the predicated cavitation performance is validated by laboratory experiment. The optimization results are obtained by the range analysis method to improve cavitation performance without obvious decreasing the efficiency of the centrifugal pump. The internal flow of the pump is analyzed in order to identify the flow behavior that can affect cavitation performance. The results show that D1 has the greatest influence on the pump cavitation and the final optimized impeller provides better flow distribution at blade leading edge. The final optimized impeller accomplishes better cavitation and hydraulic performance and the NPSHR decreases by 0.63m compared with the original one. The presented work supplies a feasible route in engineering practice to optimize a centrifugal pump impeller for better cavitation performance.

Research on the Reliability Tolerance Analysis Method of Electromagnetic Relay in Aerospace

Electromagnetic relay in aerospace is one of the main electronic components in aerospace electronic systems for information transfer, control and power distribution, and its reliability will influence the reliability of the whole aerospace electronic systems. Reliability design is the key technique of electromagnetic relay reliability engineering. This paper synthetically analyzes the present reliability design methods, and presents the reliability tolerance analyzing mathematic models of electromagnetic force basing on orthogonal design, mechanical spring force basing on probability statistics theory, and matching characteristics of electromagnetic force and mechanical spring force basing on method of stressstrength interference. Some instructive conclusions are draw by researching on the reliability tolerance of some type electromagnetic relay in aerospace.

Sensitivity Analysis,Determination and Optimization of Granite RHT Parameters

The RHT model has 34 parameters,among which 19 parameters can be obtained by experiments or theoretical calculations and the remaining 15 parameters are difficult to acquire.In this study,firstly,10 Hopkinson impact tests were conducted to acquire the typical stress-strain curves of granite under dynamic loads.Through the sensitivity analysis,it is found that 13 of the 15 difficult-acquired parameters are effective to affect the shape of the stress-strain curve,and the other two parameters have no effect.Following the initial determination of model parameters with reference to the concrete RHT model,a new approach is proposed to optimize the 13 influential parameters through the LS-DYNA numerical simulation and orthogonal experiments.Finally,the determined granite RHT model parameters are verified by the results of Hopkinson impact tests conducted in this study and the bullet penetration test by Wang et al.Both results of the numerical simulations are in a good agreement with the tested results,which validates the suitability of the proposed method to acquire RHT model parameters for granite and the other rocks.

On Frequency Sensitivity and Mode Orthogonality of Flexible Robotic Manipulators

This paper presents sensitivity analysis of vibration frequencies of flexible manipulators with respect to variations of systems parameters such as rotational inertia of hub, and mass, moment, and side of tip load. Both Euler-Bernoulli and Timoshenko dynamical models of flexible manipulators are discussed. By using variational method, sensitivity indices are obtained with explicit expressions for measuring the sensitivity of frequencies. Based on variational formulations, a novel method for deriving the orthogonal relations among vibration modal shape functions of flexible manipulators is introduced. With this method, the orthogonal relations can be derived easily without invoking the tedious process of differentiation and integration by part, as commonly used in their derivation. © 2014 Chinese Association of Automation.

Direct linear discriminant analysis based on column pivoting QR decomposition and economic SVD

A direct linear discriminant analysis algorithm based on economic singular value decomposition （DLDA/ESVD） is proposed to address the computationally complex problem of the conventional DLDA algorithm, which directly uses ESVD to reduce dimension and extract eigenvectors corresponding to nonzero eigenvalues. Then a DLDA algorithm based on column pivoting orthogonal triangular （QR） decomposition and ESVD （DLDA/QR-ESVD） is proposed to improve the performance of the DLDA/ESVD algorithm by processing a high-dimensional low rank matrix, which uses column pivoting QR decomposition to reduce dimension and ESVD to extract eigenvectors corresponding to nonzero eigenvalues. The experimental results on ORL, FERET and YALE face databases show that the proposed two algorithms can achieve almost the same performance and outperform the conventional DLDA algorithm in terms of computational complexity and training time. In addition, the experimental results on random data matrices show that the DLDA/QR-ESVD algorithm achieves better performance than the DLDA/ESVD algorithm by processing high-dimensional low rank matrices.

Numerical study of AE and DRA methods in sandstone and granite in orthogonal loading directions

The directional dependency of the acoustic emission （AE） and deformation rate analysis （DRA） methods was analyzed, based on the contact bond model in the two-dimensional particle flow code （PFC2D） in two types of rocks, the coarse-grained sandstone and Aue granite. Each type of rocks had two shapes, the Brazilian disk and a square shape. The mechanical behaviors of the numerical model had already been verified to be in agreement with those of the physical specimens in previous research. Three loading protocols with different loading cycles in two orthogonal directions were specially designed in the numerical tests. The results show that no memory effect is observed in the second loading in the orthogonal direction. However, both the cumulative crack number of the second loading and the differential strain value at the inflection point are influenced by the first loading in the orthogonal direction.

Mathematical model for abrasive suspension jet cutting based on orthogonal test design

This paper describes the application of orthogonal test design coupled with non-linear regression analysis to optimize abrasive suspension jet （AS J） cutting process and construct its cutting model. Orthogonal test design is applied to cutting stainless steel. Through range analysis on experiment results, the optimal process conditions for the cutting depth and the kerr ratio of the bottom width to the top width can be determined. In addition, the analysis of ranges and variances are all employed to identify various factors： traverse rate, working pressure, nozzle diameter, standoff distance which denote the importance order of the cutting parameters affecting cutting depth and the kerf ratio of the bottom width to the top width. ~rthermore, non-linear regression analysis is used to establish the mathematical models of the cutting parameters based on the cutting depth and the kerr ratio. Finally, the verification experiments of cutting parameters＇ effect on cutting performance, which show that optimized cutting parameters and cutting model can significantly improve the prediction of the cutting ability and quality of ASJ.

Feature analysis of stratospheric wind and temperature fields over the Antigua site by rocket data

The wind and temperature fields at 20 to 55 km above the Antigua launch site(17°N,61°W)were analyzed by using sounding rocket data published by the research organization on Stratosphere-Troposphere Processes and their Role in Climate(SPARC).The results showed distinct variations in the wind and temperature fields at different heights from the 1960s to the 1990s.The overall zonal wind speed showed a significant increasing trend with the year,and the overall change in meridional wind speed showed a falling trend from 1976 to 1990,whereas the temperature field showed a significant cooling trend from 1964 to 1990.The times the trends mutated varied at different levels.By taking the altitudes at 20,35,and 50 km as representatives,we found that the zonal wind speed trend had mutated in 1988,1986,and 1986,respectively;that the meridional wind speed trend had mutated in 1990,1986,and 1990,respectively;and that the temperature trend had mutated separately in 1977,1973,and 1967,respectively.Characteristics of the periodic wind and temperature field variations at different heights were also analyzed,and obvious differences were found in time scale variations across the different layers.The zonal and meridional wind fields were basically characterized as having a significant periodic variation of 5 years across the three layers,and each level was characterized as having a periodic variation of less than 5 years.Temperature field variation at the three levels was basically characterized as occurring in 10-year and 5-year cycles.

Influence of radial forging process on strain inhomogeneity of hollow gear shaft using finite element method and orthogonal design

Due to the current trend towards lightweight design in automotive industry,hollow stepped gear shafts for automobile and its radial forging process are widely investigated.Utilizing coupled finite element thermo-mechanical model,radial forging process of a hollow stepped gear shaft for automobile was simulated.The optimal combination of three process parameters including initial temperature,rotation rate and radial reduction was also selected using orthogonal design method.To examine the strain inhomogeneity of the forging workpiece,the strain inhomogeneity factor was introduced.The results reveal that the maximum effective strain and the minimum effective strain appeared in the outermost and innermost zones of different cross sections for the hollow stepped gear shaft,respectively.Optimal forging parameters are determined as a combination of initial temperature of 780°C,rotation rate of 21°/stroke and radial reduction of 3 mm.