Grouping response method for equivalent static wind loads based on a modified LRC method

Wind loading is one of the most important loads for controlling the design of large-span roof structures. Equivalent static wind loads, which can generally aim at determining a specific response, are widely used by structural designers. A method for equivalent static wind loads applicable to multi-responses is proposed in this paper. A modified load- response-correlation （LRC） method corresponding to a particular peak response is presented, and the similarity algorithm implemented for the group response is described. The main idea of the algorithm is that two responses can be put into one group if the value of one response is close to that of the other response, when the structure is subjected to equivalent static wind loads aiming at the other response. Based on the modified LRC, the grouping response method is put forward to construct equivalent static wind loading. This technique can simultaneously reproduce peak responses for some grouped responses. To verify its computational accuracy, the method is applied to an actual large-span roof structure. Calculation results show that when the similarity of responses in the same group is high, equivalent static wind loads with high accuracy and reasonable magnitude of equivalent static wind distribution can be achieved.

General Expression of LRC Method in Estimation of Bridge’s Equivalent Static Wind Load

According to the relationship between load and response, the equivalent static wind load(ESWL) of a structure can be estimated by load-response correlation(LRC) method, which can be accurately used to estimate the background ESWL of a structure. The derivation of the classical expression of LRC formula is based on a specific command response at a critical position, and the ESWL distribution has only one form in this case. In this paper, a general expression of LRC formula is derived based on a specific command response at all positions. For the general expression, ESWLs can be expressed by load-response correlation coefficients, response-response correlation coefficients, RMS values of the fluctuating wind loads, and peak factor in the form of matrices. By comparing the expressions of LRC method, it was found that the classical expression was only one form of the general one. The general expression which introduces the response-response correlation coefficients provided more options for structural engineers to estimate ESWLs and offered further insights into the LRC method. Finally, a cable-stayed bridge, a rigid three span continuous girder bridge, and a suspension bridge were used to verify the correctness of the general expression of LRC method.

Distribution of background equivalent static wind load on high-rise buildings

In this paper,the along-wind and cross-wind fluctuating load distributions along the height of high-rise buildings and their correlations are obtained through simultaneous pressure measurements in a wind tunnel.Some typical methods proposed in some relative litera-tures,i.e.,load-response correlation(LRC),and quasi-mean load(QML)and gust load envelope(GLE)methods,are verified in terms of their accuracy in describing the background equivalent static wind load distribution on high-rise buildings.Based on the results,formulae of the distribution of background equivalent static load on high-rise buildings with typical shapes are put forward.It is shown that these formulae are of high accuracy and practical use.

Data-driven Static Equivalence with Physics-informed Koopman Operators

With deployment of measurement units,fitting static equivalent models of distribution networks(DNs)by linear regression has been recognized as an effective method in power flow analysis of a transmission network.Increasing volatility of measurements caused by variable distributed renewable energy sources makes it more difficult to accurately fit such equivalent models.To tackle this challenge,this letter proposes a novel data-driven method to improve equivalency accuracy of DNs with distributed energy resources.This letter provides a new perspective that an equivalent model can be regarded as a mapping from internal conditions and border voltages to border power injections.Such mapping can be established through 1)Koopman operator theory,and 2)physical features of power flow equations at the root node of a DN.Performance of the proposed method is demonstrated on the IEEE 33-bus and IEEE 136-bus test systems connected to a 661-bus utility system.

A Precision-Positioning Method for a High-Acceleration Low-Load Mechanism Based on Optimal Spatial and Temporal Distribution of Inertial Energy

High-speed and precision positioning are fundamental requirements for high-acceleration low-load mechanisms in integrated circuit （IC） packaging equipment. In this paper, we derive the transient nonlinear dynamicresponse equations of high-acceleration mechanisms, which reveal that stiffness, frequency, damping, and driving frequency are the primary factors. Therefore, we propose a new structural optimization and velocity-planning method for the precision positioning of a high-acceleration mechanism based on optimal spatial and temporal distribution of inertial energy. For structural optimization, we first reviewed the commonly flexible multibody dynamic optimization using equivalent static loads method （ESLM）, and then we selected the modified ESLM for optimal spatial distribution of inertial energy; hence, not only the stiffness but also the inertia and frequency of the real modal shapes are considered. For velocity planning, we developed a new velocity-planning method based on nonlinear dynamic-response optimization with varying motion conditions. Our method was verified on a high-acceleration die bonder. The amplitude of residual vibration could be decreased by more than 20% via structural optimization and the positioning time could be reduced by more than 40% via asymmetric variable velocity planning. This method provides an effective theoretical support for the precision positioning of high-acceleration low-load mechanisms.

A new framework for evaluating along-wind responses of a transmission tower

In this paper, an analytical framework to evaluate the along-wind-induced dynamic responses of a transmission tower is presented. Two analytical models and a new method are developed： （1） a higher mode generalized force spectrum （GFS） model of the transmission tower is deduced; （2） an analytical model that includes the contributions of the higher modes is further derived as a rational algebraic formula to estimate the structural displacement response; and （3） a new approach, applying load with displacement （ALD） instead of force, to solve the internal force of transmission tower is given. Unlike conventional methods, the ALD method can avoid calculating equivalent static wind loads （ESWLs）. Finally, a transmission tower structure is used as a numerical example to verify the feasibility and accuracy of the ALD method.

Crack detection using integrated signals from dynamic responses of girder bridges

An innovative approach for the identification of cracks from the dynamic responses of girder bridges was proposed.One of the key steps of the approach was to transform the dynamical responses into the equivalent static quantities by integrating the excitation and response signals over time.A sliding-window least-squares curve fitting technique was then utilized to fit a cubic curve for a short segment of the girder.The moment coefficient of the cubic curve can be used to detect the locations of multiple cracks along a girder bridge.To validate the proposed method,prismatic girder bridges with multiple cracks of various depths were analyzed.Sensitivity analysis was conducted on various effects of crack depth,moving window width,noise level,bridge discretization,and load condition.Numerical results demonstrate that the proposed method can accurately detect cracks in a simply-supported or continuous girder bridges,the five-point equally weighted algorithm is recommended for practical applications,the spacing of two discernable cracks is equal to the window length,and the identified results are insensitive to noise due to integration of the initial data.

Seismic Design Loads of Truss Arch Frames with Ceilings subjected to Vertical and Horizontal Earthquake Motions

Spatial structures such as a gymnasium and an exhibition hall often use ceilings because of enhancing sound effects and reducing heating bills. Although the ceiling members fell down on a large scale due to the seismic motion according to the past great earthquake disaster reports, structural engineers particularly do not carry out the seismic design. The study gives structural engineers the equivalent static loads for the design of the earthquake-proof design of the ceiling system. In particular, it is significant to investigate the dynamic behavior and the applied seismic loads for the complicated vibration of the long span arch building structures with RC columns.

State Key Laboratory of Power Grid Safety and Energy Conservation,China Electric Power Research Institute,Beijing,China

The power system is experiencing a higher penetration of renewable energy generations(REGs).The short circuit ratio(SCR)and the grid impedance ratio(GIR)are two indices to quantify the system strength of the power system with REGs.In this paper,the critical short circuit ratio(CSCR)is defined as the corresponding SCR when the system voltage is in the critical stable state.Through static voltage stability analysis,the mathematical expression of the CSCR considering the impact of GIR is derived.The maximum value of CSCR is adopted as the critical value to distinguish the weak power system.Based on the static equivalent circuit analysis,it is proved that the CSCR is still effective to evaluate critical system strength considering the interactive impact among REGs.Finally,we find that the GIR can be neglected and the SCR can be used individually to evaluate the system strength when SCR>2 or GIR>5.The correctness and rationality of the CSCR and its critical value are validated on ADPSS.