Principal axes of M-DOF structures Part I:Static loading

This paper is the first in a two-part series that discusses the principal axes of M-DOF structures subjected to static and dynamic loads. The primary purpose of this series is to understand the magnitude of the dynamic response of structures to enable better design of structures and control modification devices/systems. Under idealized design conditions, the structural responses are obtained by using single direction input ground motions in the direction of the intended control devices/systems, and by assuming that the responses of the structure is decoupleable in three mutually perpendicular directions. This standard practice has been applied to both new and retrofitted structures using various seismic protective systems. Very limited information is available on the effects of neglecting the impact of directional couplings (cross effects - of which torsion is a component) of the dynamic response of structures. In order to quantify such effects, it is necessary to examine the principal axes of structures under both static and dynamic loading. This first paper deals with quantitative definitions of principal axes and “cross effects” of three-dimensional structures under static load by using linear algebra. It shows theoretically that, for three-dimensional structures, such principal axes rarely exist. Under static loading conditions, the cross effect is typically small and negligible from the viewpoint of engineering applications. However, it provides the theoretical base for subsequent quantification of the response couplings under dynamic loads, which is reported in part II of this series.

Hydrologically induced orientation variations of a tri-axial Earth's principal axes based on satellite-gravimetric and hydrological models

The Earth is a tri-axial body, with unequal principal inertia moments, A, B and C. The corresponding principal axes a, b and c are determined by the mass distribution of the Earth, and their orientations vary with the mass redistribution. In this study, the hydrologically induced variations are estimated on the basis of satellite gravimetric data, including those from satellite laser ranging （SLR） and gravity recovery and climate experiment （GRACE）, and hydrological models from global land data assimilation system （GLDAS）. The longitude variations of a and b are mainly related to the variations of the spherical harmonic coefficients C 22 and S 22, which have been estimated to be consisting annual variations of about 1.6 arc seconds and 1.8 arc seconds, respectively, from gravity data. This result is confirmed by land surface water storage provided by the GLDAS model. If the atmospheric and oceanic signals are removed from the spherical harmonic coefficients C 21 and S 21, the agreement of the orientation series for c becomes poor, possibly due to the inaccurate background models used in pre-processing of the satellite gravimetric data. Determination of the orientation variations may provide a better understanding of various phenomena in the study of the rotation of a tri-axial Earth.

Principal axes of M-DOF structures PartⅡ:Dynamic loading

This paper is the second in a two-part series that discusses the principal axes of M-DOF structures subjected to static and dynamic loads.The primary purpose of this series is to understand the magnitude of the dynamie response of structures to enable better design of structures and response modification devices/systems.Under idealized design condi- tions,the structural responses are obtained by using single directinn input ground motions in the direction of the intended response modification devices/systems,and by assuming that the responses of the structure is deconpleable in three mutual- ly perpendicular directions.This standard practice has been applied to both new and retrofitted structures using various seis- mic protective systems.Very limited information is available on the effects of neglecting the impact of directional couplings (cross effects of which torsion is a component)of the dynamic response of structures.In order to quantify such effects,it is necessary to examine the principal axes of structures under both static and dynamic loading.In this twn-part series,the first paper is concerned with static loading,which provides definitions and fundamental formulations,with the conclusion that cross effects of a statically loaded M-DOF structure resulting from the lack of principal axes are of insignificant magnitude. However,under dynamic or earthquake loading,a relatively small amount of energy transferred across perpendicular direc- tions is accumulated,which may result in significant enlargement of the structural response.This paper deals with a formu- lation to define the principal axes of M-DOF structures under dynamic loading and develops quantitative measures to identify cross effects resuhing from the non-existence of principal axes.

Calibration and validation of a sand model considering the effects of wave-induced principal stress axes rotation

Principal stress axes rotation influences the stress-strain behavior of sand under wave loading. A constitutive model for sand, which considers principal stress orientation and is based on generalized plasticity theory, is proposed. The new model, which employs stress invariants and a discrete memory factor during reloading, is original because it quantifies model parameters using experimental data. Four sets of hollow torsion experiments were conducted to calibrate the parameters and predict the capability of the proposed model, which describes the effects of principal stress orientation on the behavior of sand. The results prove the effectiveness of the proposed calibration method.

3D DEM simulation of hard rock fracture in deep tunnel excavation induced by changes in principal stress magnitude and orientation

To achieve the loading of the stress path of hard rock,the spherical discrete element model(DEM)and the new flexible membrane technology were utilized to realize the transient loading of three principal stresses with arbitrary magnitudes and orientations.Furthermore,based on the deep tunnel of China Jinping Underground Laboratory II(CJPL-II),the deformation and fracture evolution characteristics of deep hard rock induced by excavation stress path were analyzed,and the mechanisms of transient loading-unloading and stress rotation-induced fractures were revealed from a mesoscopic perspective.The results indicated that the stressestrain curve exhibits different trends and degrees of sudden changes when subjected to transient changes in principal stress,accompanied by sudden changes in strain rate.Stress rotation induces spatially directional deformation,resulting in fractures of different degrees and orientations,and increasing the degree of deformation anisotropy.The correlation between the degree of induced fracture and the unloading magnitude of minimum principal stress,as well as its initial level is significant and positive.The process of mechanical response during transient unloading exhibits clear nonlinearity and directivity.After transient unloading,both the minimum principal stress and minimum principal strain rate decrease sharply and then tend to stabilize.This occurs from the edge to the interior and from the direction of the minimum principal stress to the direction of the maximum principal stress on theε1-ε3 plane.Transient unloading will induce a tensile stress wave.The ability to induce fractures due to changes in principal stress magnitude,orientation and rotation paths gradually increases.The analysis indicates a positive correlation between the abrupt change amplitude of strain rate and the maximum unloading magnitude,which is determined by the magnitude and rotation of principal stress.A high tensile strain rate is more likely to induce fractures under low minimum principal stress.

THE GENERAL STRESS STRAIN RELATION OF SOILS INVOLVING THE ROTATION OF PRINCIPAL STRESS AXES

In the light of matrix theory, the character of stress increment which causes the rotation of principal stress axes is analysed and the general stress increment is decomposed into two parts: coaxial part and rotational part. Based on these, the complex three dimensional (3-D) problem involving the rotation of principal stress axes is simplified to the combination of the 3-D coaxial model and the theory about pure rotation of principal stress axes that is only around one principal stress axes. The difficulty of analysis is reduced significantly. The concrete calculating method of general 3-D problem is provided and other applications are also presented.

Nonholonomic Theory of Principal-direction Orthonormal Basis for a Layer of Surfaces

In order to carry out tensor analysis in a neighborhood of a reference surface,the principal-direction orthogonal basis accompanying with Lame s coefficients or general curvilinear coordinate systems are widely used.A novel kind of field theory termed as the nonholonomic theory of the Principal-Direction Orthonormal Basis(PDOB)is presented systematically in the present paper,in which the formal Christoffel symbols are related directly to the principal and geodesic curvatures with respect to the principal directions of the surface.Furthermore,a systematic and simple way to determine the curvatures of the surface are presented with some examples.It provides a way to recognize qualitatively the bending property of a surface.

Principal Equatorial Null Geodesic Congruences in the Kerr Metric, and Their Quantum Propagators

Using the Raychaudhuri equation, we associate quantum probability amplitudes (propagators) to equatorial principal ingoing and outgoing null geodesic congruences in the Kerr metric. The expansion scalars diverge at the ring singularity;however, the propagators remain finite, which is an indication that at the quantum level singularities might disappear or, at least, become softened.

Mechanism of principal stress rotation and deformation failure behavior induced by excavation in roadways

The failure modes of rock after roadway excavation are diverse and complex.A comprehensive investigation of the internal stress field and the rotation behavior of the stress axis in roadways is essential for elucidating the mechanism of roadway failure.This study aimed to examine the spatial relationship between roadways and stress fields.The law of stress axis rotation under three-dimensional(3D)stress has been extensively studied.A stress model of roadways in the spatial stress field was established,and the far-field stress state at different spatial positions of the roadways was analyzed.A mechanical model of roadways under a 3D stress state was established using far-field stress solutions as boundary conditions.The distribution of principal stressesσ1,σ2 andσ3 around the roadways and the variation of the stress principal axis were solved.It was found that the stability boundary of the stress principal axis exhibits hysteresis when compared with that of the principal stress magnitudes.A numerical analysis model for spatial roadways was established to validate the distribution of principal stress and the mechanism of principal axis rotation.Research has demonstrated that the stress axis undergoes varying degrees of spatial rotation in different orientations and radial depths.Based on the distribution of principal stress and the rotation law of the stress principal axis,the entire evolution mechanism of the two stress adjustments to form the final failure form after roadway excavation has been revealed.The on-site detection results also corroborate the findings presented in this paper.The results provide a basis for the analysis of the failure mechanism under a 3D stress state.

Using deep neural networks coupled with principal component analysis for ore production forecasting at open-pit mines

Ore production is usually affected by multiple influencing inputs at open-pit mines.Nevertheless,the complex nonlinear relationships between these inputs and ore production remain unclear.This becomes even more challenging when training data(e.g.truck haulage information and weather conditions)are massive.In machine learning(ML)algorithms,deep neural network(DNN)is a superior method for processing nonlinear and massive data by adjusting the amount of neurons and hidden layers.This study adopted DNN to forecast ore production using truck haulage information and weather conditions at open-pit mines as training data.Before the prediction models were built,principal component analysis(PCA)was employed to reduce the data dimensionality and eliminate the multicollinearity among highly correlated input variables.To verify the superiority of DNN,three ANNs containing only one hidden layer and six traditional ML models were established as benchmark models.The DNN model with multiple hidden layers performed better than the ANN models with a single hidden layer.The DNN model outperformed the extensively applied benchmark models in predicting ore production.This can provide engineers and researchers with an accurate method to forecast ore production,which helps make sound budgetary decisions and mine planning at open-pit mines.

A Hybrid Optimization Approach of Single Point Incremental Sheet Forming of AISI 316L Stainless Steel Using Grey Relation Analysis Coupled with Principal Component Analysiss

We investigated the parametric optimization on incremental sheet forming of stainless steel using Grey Relational Analysis(GRA) coupled with Principal Component Analysis(PCA). AISI 316L stainless steel sheets were used to develop double wall angle pyramid with aid of tungsten carbide tool. GRA coupled with PCA was used to plan the experiment conditions. Control factors such as Tool Diameter(TD), Step Depth(SD), Bottom Wall Angle(BWA), Feed Rate(FR) and Spindle Speed(SS) on Top Wall Angle(TWA) and Top Wall Angle Surface Roughness(TWASR) have been studied. Wall angle increases with increasing tool diameter due to large contact area between tool and workpiece. As the step depth, feed rate and spindle speed increase,TWASR decreases with increasing tool diameter. As the step depth increasing, the hydrostatic stress is raised causing severe cracks in the deformed surface. Hence it was concluded that the proposed hybrid method was suitable for optimizing the factors and response.

Rock strength weakening subject to principal stress rotation:Experimental and numerical investigations

During the construction and operation of gas storage reservoirs,changes in the principal stress direction can induce fracture propagation under conditions of lower differential stress,potentially leading to failure in the surrounding rock.However,the weakening of strength due to pure stress rotation has not yet been investigated.Based on fracture mechanics,an enhanced Mohr-Coulomb strength criterion considering stress rotation is proposed and verified with experimental and numerical simulations.The micro-damage state and the evolution of the rock under the pure stress-rotation condition are analyzed.The findings indicate that differential stress exceeding the crack initiation stress is a prerequisite for stress rotation to promote the development of rock damage.As the differential stress increases,stress rotation is more likely to induce rock damage,leading to a transition from brittle to plastic failure,characterized by wider fractures and a more complex fracture network.Overall,a negative exponential relationship exists between the stress rotation angle required for rock failure and the differential stress.The feasibility of applying the enhanced criterion to practical engineering is discussed using monitoring data obtained from a mine-by tunnel.This study introduces new concepts for understanding the damage evolution of the surrounding rock under complex stress paths and offers a new theoretical basis for predicting the damage of gas storage reservoirs.

Robust Principal Component Analysis Integrating Sparse and Low-Rank Priors

Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.

A Modified Principal Component Analysis Method for Honeycomb Sandwich Panel Debonding Recognition Based on Distributed Optical Fiber Sensing Signals

The safety and integrity requirements of aerospace composite structures necessitate real-time health monitoring throughout their service life.To this end,distributed optical fiber sensors utilizing back Rayleigh scattering have been extensively deployed in structural health monitoring due to their advantages,such as lightweight and ease of embedding.However,identifying the precise location of damage from the optical fiber signals remains a critical challenge.In this paper,a novel approach which namely Modified Sliding Window Principal Component Analysis(MSWPCA)was proposed to facilitate automatic damage identification and localization via distributed optical fiber sensors.The proposed method is able to extract signal characteristics interfered by measurement noise to improve the accuracy of damage detection.Specifically,we applied the MSWPCA method to monitor and analyze the debonding propagation process in honeycomb sandwich panel structures.Our findings demonstrate that the training model exhibits high precision in detecting the location and size of honeycomb debonding,thereby facilitating reliable and efficient online assessment of the structural health state.

Principals’and Teachers’Awareness,Knowledge,and Differentiation of Privatization-A Secondary Publication

Based on the keynote report by Professor Martin Thrupp,this paper discusses the hollowing out of education provision by the state and the permeation of managerialism.It was pointed out that principals and boards of trustees in socioeconomically advantaged areas may not be willing to share their benefits with schools in less advantaged areas.The new liberal policies have hollowed out state provision of education,so the education system has come to rely heavily on private actors.This paper also presents the current stage of privatization in Japan and the principals’and teachers’perceptions of privatization.

Comparative Analysis of Differences among Northern,Jiangnan,and Lingnan Classical Private Gardens Using Principal Component Cluster Method

This paper investigates the design essence of Chinese classical private gardens,integrating their design elements and fundamental principles.It systematically analyzes the unique characteristics and differences among classical private gardens in the Northern,Jiangnan,and Lingnan regions.The study examines nine classical private gardens from Northern China,Jiangnan,and Lingnan by utilizing the advanced tool of principal component cluster analysis.Based on literature analysis and field research,273 variables were selected for principal component analysis,from which four components with higher contribution rates were chosen for further study.Subsequently,we employed clustering analysis techniques to compare the differences among the three types of gardens.The results reveal that the first principal component effectively highlights the differences between Jiangnan and Lingnan private gardens.The second principal component serves as the key to defining the types of Northern private gardens and distinguishing them from the other two types,and the third principal component indicates that Lingnan private gardens can be categorized into two distinct types as well.

Comparative assessment of the frying efficiency of standard and low linolenic rapeseed oils: Principal Component Analysis (PCA)

In this research,the performance of regular rapeseed oil(RSO)and modified low-linolenic rapeseed oil(LLRO)during frying was assessed using a frying procedure that commonly found in fast-food restaurants.Key physicochemical attributes of these oils were investigated.RSO and LLRO differed for initial linolenic acid(12.21%vs.2.59%),linoleic acid(19.15%vs.24.73%).After 6 successive days frying period of French fries,the ratio of linoleic acid to palmitic acid dropped by 54.49%in RSO,higher than that in LLRO(51.54%).The increment in total oxidation value for LLRO(40.46 unit)was observed to be significantly lower than those of RSO(42.58 unit).The changes in carbonyl group value and iodine value throughout the frying trial were also lower in LLRO compared to RSO.The formation rate in total polar compounds for LLRO was 1.08%per frying day,lower than that of RSO(1.31%).In addition,the formation in color component and degradation in tocopherols were proportional to the frying time for two frying oils.Besides,a longer induction period was also observed in LLRO(8.87 h)compared to RSO(7.68 h)after frying period.Overall,LLRO exhibited the better frying stability,which was confirmed by principal component analysis(PCA).

Optimizing data aggregation and clustering in Internet of things networks using principal component analysis and Q-learning

The Internet of things(IoT)is a wireless network designed to perform specific tasks and plays a crucial role in various fields such as environmental monitoring,surveillance,and healthcare.To address the limitations imposed by inadequate resources,energy,and network scalability,this type of network relies heavily on data aggregation and clustering algorithms.Although various conventional studies have aimed to enhance the lifespan of a network through robust systems,they do not always provide optimal efficiency for real-time applications.This paper presents an approach based on state-of-the-art machine-learning methods.In this study,we employed a novel approach that combines an extended version of principal component analysis(PCA)and a reinforcement learning algorithm to achieve efficient clustering and data reduction.The primary objectives of this study are to enhance the service life of a network,reduce energy usage,and improve data aggregation efficiency.We evaluated the proposed methodology using data collected from sensors deployed in agricultural fields for crop monitoring.Our proposed approach(PQL)was compared to previous studies that utilized adaptive Q-learning(AQL)and regional energy-aware clustering(REAC).Our study outperformed in terms of both network longevity and energy consumption and established a fault-tolerant network.

南方丘陵山地泡桐人工林的土壤肥力

以南方丘陵山地泡桐人工林为研究对象,按照全国第二次土壤普查分级标准对南方丘陵山地泡桐人工林土壤养分整体情况进行评级,并采用主成分分析法对南方丘陵山地泡桐人工林土壤肥力进行综合评价。结果表明:南方丘陵山地泡桐人工林土壤的全氮、碱解氮的平均质量分数分别为1.21 g·kg^(-1)、113.66 mg·kg^(-1),整体处于中上等级水平;全钾、速效钾、有机质的平均质量分数分别为13.07 g·kg^(-1)、68.17 mg·kg^(-1)、18.50 g·kg^(-1),整体处于中下等级水平;全磷平均质量分数为0.35 g·kg^(-1),整体处于低水平等级;有效磷的平均质量分数为2.68 mg·kg^(-1),整体处于很低等级水平。主成分分析结果表明:南方丘陵山地泡桐人工林的土壤综合肥力得分范围为-1.97~2.59,利用聚类分析法,可将115个样地土壤肥力划分为极高、高、中、低4个等级,各等级样地所占比例分别为6.09%、31.30%、43.48%、19.13%,说明土壤综合肥力以中等水平为主。不同种植区之间,土壤综合肥力差异较大,其中湖北省京山市、荆门市、钟祥市、咸宁市,泡桐人工林的土壤综合肥力整体水平最高;而湖北省崇阳县土壤综合肥力整体水平最差。

基于局部离群因子与隔离森林的激光超声缺陷检测

针对激光超声(LU)缺陷检测中最大振幅图存在伪像的问题,结合主成分分析(PCA)和两种无监督的机器学习算法局部离群因子(LOF)与隔离森林(IF),以实现对LU数据的无监督异常检测。首先,利用PCA算法对LU数据进行降维处理,减轻了LU数据的复杂度;其次,利用LOF算法和IF算法进行了数据异常值的识别分析,并利用累积分布函数和核密度估计确定异常值的阈值大小;最后,对比了LOF算法、IF算法以及最大振幅图的检测结果。结果表明:LOF算法有更优的缺陷识别精度和更低的误判率。