Defining the We-map Reference Frames and Providing Mathematical Expressions for Transformation Relations

We-map is an interactive mobile map that can be easily communicated and applied on personal electronic devices,such as personal computers and mobile phones.Therefore,the study of direction systems and coordinate systems is critical,and exploring reference frames is essential in direction and coordinate systems.Despite its significance,existing research on We-map lacks specific solutions for the exploration of reference frames is indispensable for the establishment of accurate direction and coordinate systems.In this paper,we endeavor to address this gap by elucidating the significance of We-map reference frames,defining them with mathematical constraints,summarizing their nature and characteristics,deriving their transformation relationships and representing them through mathematical formulars and equations.Our work contributes to the fundamental theory of We-map and provides valuable systems and support for the mathematical foundation of We-map,map production,and platform development.Ultimately,this research serves to advance the development of We-map.

Resilience-incorporated seismic risk assessment of precast concrete frames with“dry”connections

A resilience-incorporated risk assessment framework is proposed and demonstrated in this study to manifest the advantageous seismic resilience of precast concrete frame(PCF)structures with“dry”connections in terms of their low damage and rapid recovery.The framework integrates various uncertainties in the seismic hazard,fragility,capacity,demand,loss functions,and post-earthquake recovery.In this study,the PCF structures are distinguished from ordinary reinforced concrete frame(RCF)structures by characterizing multiple limit states for the PCF based on its unique damage mechanisms.Accordingly,probabilistic story-wise pushover analyses are performed to yield story-wise capacities for the predefined limit states.In the seismic resilience analysis,a step-wise recovery model is proposed to idealize the functionality recovery process,with separate considerations of the repair and non-repair events.The recovery model leverages the economic loss and downtime to delineate the stochastic post-earthquake recovery curves for the resilience loss estimation.As such,contingencies in the probabilistic post-earthquake repairs are incorporated and the empirical judgments on the recovery parameters are largely circumvented.The proposed framework is demonstrated through a comparative study between two“dry”connected PCFs and one RCF designed as alternative structural systems for a prototype building.The results from the risk quantification indicate that the PCFs show reduced loss hazards and lower expected losses relative to the RCF.Particularly,the PCF equipped with energy dissipation devices at the“dry”connections largely reduces the expected economic loss,downtime,and resilience loss by 29%,56%,and 60%,respectively,compared to the RCF.

New tangent stiffness matrix for geometrically nonlinear analysis of space frames

A three-dimensional beam element is derived based on the principle of stationary total potential energy for geometrically nonlinear analysis of space frames. A new tangent stiffness matrix, which allows for high order effects of element deformations, replaces the conventional incremental secant stiffness matrix. Two deformation stiffness matrices due to the variation of axial force and bending moments are included in the tangent stiffness. They are functions of element deformations and incorporate the coupling among axial, lateral and torsional deformations. A correction matrix is added to the tangent stiffness matrix to make displacement derivatives equivalent to the commutative rotational degrees of freedom. Numerical examples show that the proposed dement is accurate and efficient in predicting the nonlinear behavior, such as axial-torsional and flexural-torsional buckling, of space frames even when fewer elements are used to model a member.

A Note on Tight Frames

Suppose that Φ(x)∈L 2(R) with compact support and V= span{Φ(x-k)|k∈Z}. In this note, we prove that if {Φ(x-k)k|k∈Z} is tight frame with bound 1 in V, then {Φ(x-k)|k∈Z} must be an orthonormal basis of V.

Perturbations of Generalized Frames in a Hilbert Space

In the paper, we study the stability of Hilbert space generalized frames under perturbations. We get some results that are in spirit close to classical results for discrete frames, due to OLE Christensen.

SEPARATED FRAMES

In this paper we shall offer a separation axiom for frames inspired by the Hausdorff separation axiom for topological spaces. We call it separated condition. This is a condition on topology OX equivalent to the T O space X being Hausdorff. The class of separated frames includes that of strong Hausdorff frames and that of S frames. We shall show that the class of separated frames is a class closed under the formation of coproducts and subspaces, and the space Fil( L ) is Hausdorff for any separated frame L . Therefore there is a contravariant adjunction between the category TOP 2 of Hausdorff topological spaces and the category FRAM 2 of separated frames.

APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES

In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.

SOME RESULTS ON CONTROLLED FRAMES IN HILBERT SPACES

We use two appropriate bounded invertible operators to define a controlled frame with optimal frame bounds. We characterize those operators that produces Parseval controlled frames also we state a way to construct nearly Parseval controlled frames. We intro- duce a new perturbation of controlled frames to obtain new frames from a given one. Also we reduce the distance of frames by appropriate operators and produce nearly dual frames from two given frames which are not dual frames for each other.

Automatic Method for Synchronizing Workpiece Frames in Twin-robot Nondestructive Testing System

The workpiece frames relative to each robot base frame should be known in advance for the proper operation of twin-robot nondestructive testing system. However, when two robots are separated from the workpieces, the twin robots cannot reach the same point to complete the process of workpiece frame positioning. Thus, a new method is proposed to solve the problem of coincidence between workpiece frames. Transformation between two robot base frames is initiated by measuring the coordinate values of three non-collinear calibration points. The relationship between the workpiece frame and that of the slave robot base frame is then determined according to the known transformation of two robot base frames, as well as the relationship between the workpiece frame and that of the master robot base frame. Only one robot is required to actually measure the coordinate values of the calibration points on the workpiece. This requirement is beneficial when one of the robots cannot reach and measure the calibration points. The coordinate values of the calibration points are derived by driving the robot hand to the points and recording the values of top center point（TCP） coordinates. The translation and rotation matrices relate either the two robot base frames or the workpiece and master robot. The coordinated are solved using the measured values of the calibration points according to the Cartesian transformation principle. An optimal method is developed based on exponential mapping of Lie algebra to ensure that the rotation matrix is orthogonal. Experimental results show that this method involves fewer steps, offers significant advantages in terms of operation and time-saving. A method used to synchronize workpiece frames in twin-robot system automatically is presented.

Ductility demands on buckling-restrained braced frames under earthquake loading

Accurate estimates of ductility demands on buckling-restrained braced frames(BRBFs)are crucial to performance-based design of BRBFs.An analytical study on the seismic behavior of BRBFs has been conducted at the ATLSS Center,Lehigh University to prepare for an upcoming experimental program.The analysis program DRAIN-2DX was used to model a one-bay,four-story prototype BRBF including material and geometric nonlinearities.The buckling- restrained brace(BRB)model incorporates both isotropic and kinematic hardening.Nonlinear static pushover and time- history analyses were performed on the prototype BRBF.Performance objectives for the BRBs were defined and used to evaluate the time-history analysis results.Particular emphasis was placed on global ductility demands and ductility demands on the BRBs.These demands were compared with anticipated ductility capacities.The analysis results,along with results from similar previous studies,are used to evaluate the BRBF design provisions that have been recommended for codification in the United States.The results show that BRB maximum ductility demands can be as high as 20 to 25.These demands significantly exceed those anticipated by the BRBF recommended provisions.Results from the static pushover and time- history analyses are used to demonstrate why the ductility demands exceed those anticipated by the recommended provisions. The BRB qualification testing protocol contained in the BRBF recommended provisions is shown to be inadequate because it requires only a maximum ductility demand of at most 7.5.Modifications to the testing protocol are recommended.

Damage Tolerance Assessment of a Brake Unit Bracket for High-Speed Railway Welded Bogie Frames

The brake unit bracket of a bogie frame is an important load-carrying component, particularly under emergency start/stop conditions. Conventional infinite/safe life approaches provide an over-conservative recommendation for the allowable strength and lifetime, which hinders the lightweight design of modern railway vehicles. In this study, to ensure the reliability and durability of a brake unit bracket, an attempt was made to integrate the nominal stress method and an advanced damage tolerance method. First, a complex bogie frame was modelled using solid elements instead of plate and beam elements. A hot spot stress region on the bracket was found under an eight-stage load spectrum obtained from the Wuhan–Guangzhou high-speed railway line. Based on the probability of foreign damage, a semi-elliptical surface crack was then assumed for residual life assessment. The results obtained by the cumulative damage and damage tolerance methods show that the brake unit bracket can operate for over 30 years. Moreover, even if a 2-mm depth crack exists, the brake unit bracket can be safely operated for more than 2.27 years, with the hope that the crack can be detected in subsequent maintenance procedures. Finally, an appropriate safety margin was suggested which provides a basis for the life prediction and durability assessment of brake unit brackets of high-speed railways.

Methodology to Evaluate Fatigue Damage of High-Speed Train Welded Bogie Frames Based on On-Track Dynamic Stress Test Data

The current method of estimating the fatigue life of railway structures is to calculating the equivalent stress amplitude based on the measured stress data. However, the random of the measured data is not considered. In this paper, a new method was established to compute the equivalent stress amplitude to evaluate the fatigue damage based on the measurable randomness, since the equivalent stress is the key parameter for assessment of structure fatigue life and load derivation. The equivalent stress amplitude of a high-speed train welded bogie frame was found to obey normal distribution under uniform operation route that verified by on-track dynamic stress data, and the proposed model is, in effect, an improved version of the mathematical model used to calculate the equivalent stress amplitude. The data of a long-term, on-track dynamic stress test program was analyzed to find that the normal distribution parameters of equivalent stress amplitude values differ across different operation route. Thus, the fatigue damage of the high-speed train welded bogie frame can be evaluated by the proposed method if the running schedule of the train is known a priori. The results also showed that the equivalent stress amplitude of the region connected to the power system is more random than in other regions of the bogie frame.

Evaluation of the fishbone model in simulating the seismic response of multistory reinforced concrete moment-resisting frames

The fishbone model is a simplified numerical model for moment-resisting frames that is capable of modelling the effects of column-beam strength and stiffness ratios. The applicability of the fishbone model in simulating the seismic responses of reinforced concrete moment-resisting frames of different sets of column-beam strength and stiffness ratios are evaluated through nonlinear static, dynamic and incremental dynamic analysis on six prototype buildings of 4-, 8-and 12-stories. The results show that the fishbone model is practically accurate enough for reinforced concrete frames, although the assumption of equal joint rotation does not hold in all cases. In addition to the ground motion characteristics and the number of stories in the structures, the accuracy of the model also varies with the column-beam stiffness and strength ratios. The model performs better for strong column-weak beam frames, in which the lateral drift patterns are better controlled by the continuous stiffness provided by the strong columns. When the inelastic deformation is large, the accuracy of the model may be subjected to large record-to-record variability. This is especially the case for frames of weak columns.

Experimental study on seismic behaviors of steel-concrete composite frames

Steel-concrete composite frames are seeing increased use in earthquake region because of their excellent structural characteristics, including high strength, stiffness, and good ductility. However, there exist gaps in the knowledge of seismic behavior and the design provisions for these structures. In order to better understand the seismic behaviors of composite frame systems, eight steel-concrete composite frames were designed. These composite frames were composed of steel-concrete composite beams and concrete filled steel tube columns. The axial compression ratio of column, slenderness ratio and linear stiffness ratio of beam to column were selected as main design parameters. The low reversed cyclic loading tests of composite frame system were carried out. Based on test results, the seismic behaviors of composite frames such as failure mode, hysteresis curve, strength degradation, rigidity degradation, ductility and energy dissipation were studied. Known from the test phenomenon, the main cause of damage is the out-of-plane deformation of steel beam and the yielding destruction of column heel. The hysteretic loops of composite frame appear a spindle shape and no obvious pinch phenomenon. The results demonstrate that this type of composite frame has favorable seismic behaviors. Furthermore, the effects of design parameters on seismic behaviors were also discussed. The results of the experiment show that the different design parameter has different influence rule on seismic behaviors of composite frame.

Pushover analysis of reinforced concrete frames considering shear failure at beam-column joints

Since most current seismic capacity evaluations of reinforced concrete （RC） frame structures are implemented by either static pushover analysis （PA） or dynamic time history analysis, with diverse settings of the plastic hinges （PHs） on such main structural components as columns, beams and walls, the complex behavior of shear failure at beam-column joints （BCJs） during major earthquakes is commonly neglected. This study proposes new nonlinear PA procedures that consider shear failure at BCJs and seek to assess the actual damage to RC structures. Based on the specifications of FEMA-356, a simplified joint model composed of two nonlinear cross struts placed diagonally over the location of the plastic hinge is established, allowing a sophisticated PA to be performed. To verify the validity of this method, the analytical results for the capacity curves and the failure mechanism derived from three different full-size RC frames are compared with the experimental measurements. By considering shear failure at BCJs, the proposed nonlinear analytical procedures can be used to estimate the structural behavior of RC frames, including seismic capacity and the progressive failure sequence of joints, in a precise and effective manner.

Evaluating the inelastic displacement ratios of moment-resisting steel frames designed according to the Egyptian code

Seismic codes estimate the maximum displacements of building structures under the design-basis earthquakes by amplifying the elastic displacements under the reduced seismic design forces with a deflection amplification factor(DAF). The value of DAF is often estimated as ρ× R, where R is the force reduction factor and ρ is the inelastic displacement ratio that accounts for the inelastic action of the structure according to the definition presented by FEMA P695. The purpose of this study is to estimate the ρ-ratio of moment resisting steel frames(MRSFs) designed according to the Egyptian code. This is achieved by conducting a series of elastic and inelastic time-history analyses by two sets of earthquakes on four MRSFs designed according to the Egyptian code and having 2, 4, 8 and 12 stories. The earthquakes are scaled to produce maximum story drift ratios(MSDRs) of 1.0%, 1.5%, 2.0% and 2.5%. The mean values of the ρ-ratio are calculated based on the displacement responses of the investigated frames. The results obtained in this study indicate that the consideration of ρ for both the roof drift ratios(RDRs) and the MSDRs equal to 1.0 is a reasonable estimation for MRSFs designed according to the Egyptian code.

Some New Inequalities for Wavelet Frames on Local Fields

Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. Finding general and verifiable conditions which imply that the wavelet systems are wavelet frames is among the core problems in time-frequency analysis. In this article, we establish some new inequalities for wavelet frames on local fields of positive characteristic by means of the Fourier transform. As an application, an improved version of the Li-Jiang inequality for wavelet frames on local fields is obtained.

Compressed data separation via dual frames based split-analysis with Weibull matrices

In this paper, we consider data separation problem, where the original signal is composed of two distinct subcomponents, via dual frames based Split-analysis approach. We show that the two distinct subcomponents, which are sparse in two diff erent general frames respectively, can be exactly recovered with high probability, when the measurement matrix is a Weibull random matrix （not Gaussian） and the two frames satisfy a mutual coherence property. Our result may be significant for analysing Split-analysis model for data separation.

A SUFFICIENT CONDITION FOR AFFINE FRAMES WITH MATRIX DILATION

A sufficient condition for affine frame with an arbitrary matrix dilation is presented. It is based on the univariate case by Shi, and generalizes the univariate results of Shi, Casazza and Christensen from one dimension with an arbitrary real number a （a 〉 1） dilation to higher dimension with an arbitrary expansive matrix dilation.

Study on establishment of standardized load spectrum on bogie frames of high-speed trains

Establishing structural load spectrum under actual operating conditions is a major problem in structural fatigue life analysis. This study introduces the load measuring method for the bogie frame structure. The load-measuring frame based on quasi-static can measure different load systems synchronously. The t-test method is employed to evaluate the least test time of deducing the parent distribution. In order to fit the load spectrum distribution accurately, the kernel density estimation method is employed which is based on the sample characteristics. The expansion factor method is used to deduce the maximum load. The formula of standardized load spectrum derives from the deduced maximum load, the linear factor between operating condition length and cumulative frequency and the parent distribution of each load system. The damage consistency criterion is performed by solving the objective function with constraint conditions. The calibrated damage provides a suitable representation of the real damage under actual operating conditions. By processing and analyzing the load spectrum and stress spectrum data of the measured lines, it is verified that the standardized load spectrum established in this paper is superior to the European specification and the Japanese specification in evaluating the fatigue reliability of the structure.