Equivalent linear model for seismic damage evaluation of single-degree-of-freedom systems representing reinforced concrete structures considering cyclic degradation behavior

In this study,a novel equivalent damping ratio model that is suitable for reinforced concrete(RC)structures considering cyclic degradation behavior is developed,and a new equivalent linearization analysis method for implementing the proposed equivalent damping ratio model for use in seismic damage evaluation is presented.To this end,Ibarra’s peak-oriented model,which incorporates an energy-based degradation rule,is selected for representing hysteretic behavior of RC structure,and the optimized equivalent damping for predicting the maximum displacement response is presented by using the empirical method,in which the effect of cyclic degradation is considered.Moreover,the relationship between the hysteretic energy dissipation of the inelastic system and the elastic strain energy of the equivalent linear system is established so that the proposed equivalent linear system can be directly integrated with the Park-Ang seismic model to implement seismic damage evaluation.Due to the simplicity of the equivalent linearization method,the proposed method provides an efficient and reliable way of obtaining comprehensive insight into the seismic performance of RC structures.The verification demonstrates the validity of the proposed method.

Deterioration of equivalent thermal conductivity of granite subjected to heating-cooling treatment

Understanding the thermal conductivity of granite is critical for many geological and deep engineering applications.The heated granite was subjected to air-,water-,and liquid nitrogen(LN2-)coolings in this context.The transient hot-wire technique was used to determine the equivalent thermal conductivity(ETC)of the granite before and after treatment.The deterioration mechanism of ETC is analyzed from the meso-perspective.Finally,the numerical model is used to quantitatively study the impact of cooling rate on the microcrack propagation and heat conduction characteristics of granite.The results show that the ETC of granite is not only related to the heating temperature,but also affected by the cooling rate.The ETC of granite decreases nonlinearly with increasing heating temperature.A faster cooling rate causes a greater decrease in ETC at the same heating temperature.The higher the heating temperature,the stronger the influence of cooling rate on ETC.The main explanation for the decrease in ETC of granite is the increase in porosity and microcrack density produced by the formation and propagation of pore structure and microcracks during heating and cooling.Further analysis displays that the damage of granite at the heating stage is induced by the difference in thermal expansion and elastic properties of mineral particles.At the cooling stage,the faster cooling rate causes a higher temperature gradient,which in turn produces greater thermal stress.As a result,it not only causes new cracks in the granite,but also aggravates the damage at the heating stage,which induces a further decrease in the heat conduction performance of granite,and this scenario is more obvious at higher temperatures.

An equivalent target plate damage probability calculation mathematics model and damage evaluation method

Aiming at the requirement of damage testing and evaluation of equivalent target plate based on the explosion of intelligent ammunition, this paper proposes a novel method for damage testing and evaluation method of circumferential equivalent target plate. Leveraging the dispersion characteristics parameters of fragment, we establish a calculation model of the fragment power situation and the damage calculation model under the condition of fragment ultimate penetration equivalent target plate. The damage model of equivalent target plate involves the fragment dispersion density, the local perforation damage criterion, the tearing damage model, and the damage probability. We use the camera to obtain the image of the equivalent target plate with fragment perforation, and research the algorithm of fragment distribution position recognition and fragment perforation area calculation method on the equivalent target plate by image processing technology. Based on the obtained parameters of the breakdown position and perforation area of fragments on equivalent target plate, we apply to damage calculation model of equivalent target plate, and calculate the damage probability of each equivalent target plate, and use the combined probabilistic damage calculation method to obtain the damage evaluation results of the circumferential equivalent target plate in an intelligent ammunition explosion experiment. Through an experimental testing, we verify the feasibility and rationality of the proposed damage evaluation method by comparison, the calculation results can reflect the actual damage effect of the equivalent target plate.

An efficient approach for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations

An efficient approach is proposed for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations.The concentrated plastic hinges,described by the Bouc-Wen model,are assumed to occur at the two ends of a linear-elastic beam element.The auxiliary differential equations governing the plastic rotational displacements and their corresponding hysteretic displacements are replaced with linearized differential equations.Then,the two sets of equations of motion for the original nonlinear system can be reduced to an expanded-order equivalent linearized equation of motion for equivalent linear systems.To solve the equation of motion for equivalent linear systems,the nonstationary random vibration analysis is carried out based on the explicit time-domain method with high efficiency.Finally,the proposed treatment method for initial values of equivalent parameters is investigated in conjunction with parallel computing technology,which provides a new way of obtaining the equivalent linear systems at different time instants.Based on the explicit time-domain method,the key responses of interest of the converged equivalent linear system can be calculated through dimension reduction analysis with high efficiency.Numerical examples indicate that the proposed approach has high computational efficiency,and shows good applicability to weak nonlinear and medium-intensity nonlinear systems.

Analysis of secondary makeup characteristics of drill collar joint and prediction of downhole equivalent impact torque of Well SDTK1

Based on the three-dimensional elastic-plastic finite element analysis of the 8"(203.2 mm)drill collar joint,this paper studies the mechanical characteristics of the pin and box of NC56 drill collar joints under complex load conditions,as well as the downhole secondary makeup features,and calculates the downhole equivalent impact torque with the relative offset at the shoulder of internal and external threads.On the basis of verifying the correctness of the calculation results by using measured results in Well GT1,the prediction model of the downhole equivalent impact torque is formed and applied in the first extra-deep well with a depth over 10000 m in China(Well SDTK1).The results indicate that under complex loads,the stress distribution in drill collar joints is uneven,with relatively higher von Mises stress at the shoulder and the threads close to the shoulder.For 203.2 mm drill collar joints pre-tightened according to the make-up torque recommended by American Petroleum Institute standards,when the downhole equivalent impact torque exceeds 65 kN·m,the preload balance of the joint is disrupted,leading to secondary make-up of the joint.As the downhole equivalent impact torque increases,the relative offset at the shoulder of internal and external threads increases.The calculation results reveal that there exists significant downhole impact torque in Well SDTK1 with complex loading environment.It is necessary to use double shoulder collar joints to improve the impact torque resistance of the joint or optimize the operating parameters to reduce the downhole impact torque,and effectively prevent drilling tool failure.

An improved algorithm based on equivalent sound velocity profile method at large incident angle

With the development of ultra-wide coverage technology,multibeam echo-sounder(MBES)system has put forward higher requirements for localization accuracy and computational efficiency of ray tracing method.The classical equivalent sound speed profile(ESSP)method replaces the measured sound velocity profile(SVP)with a simple constant gradient SVP,reducing the computational workload of beam positioning.However,in deep-sea environment,the depth measurement error of this method rapidly increases from the central beam to the edge beam.By analyzing the positioning error of the ESSP method at edge beam,it is discovered that the positioning error increases monotonically with the incident angle,and the relationship between them could be expressed by polynomial function.Therefore,an error correction algorithm based on polynomial fitting is obtained.The simulation experiment conducted on an inclined seafloor shows that the proposed algorithm exhibits comparable efficiency to the original ESSP method,while significantly improving bathymetry accuracy by nearly eight times in the edge beam.

An abnormal carbody swaying of intercity EMU train caused by low wheel-rail equivalent conicity and damping force unloading of yaw damper

Low-frequency carbody swaying phenomenon often occurs to railway vehicles due to hunting instability,which seriously deteriorates the ride comfort of passengers.This paper investigates low-frequency carbody swaying through experimental analysis and numerical simulation.In the tests,the carbody acceleration,the wheel-rail profiles,and the dynamic characteristics of dampers were measured to understand the characteristics of the abnormal carbody vibration and to find out its primary contributor.Linear and nonlinear numerical simulations on the mechanism and optimization measures were carried out to solve this carbody swaying issue.The results showed that the carbody swaying is the manifest of carbody hunting instability.The low equivalent conicity and the decrease of dynamic damping of the yaw damper are probably the cause of this phenomenon.The optimization measures to increase the equivalent conicity and dynamic damping of the yaw damper were put forward and verified by on-track tests.The results of this study could enrich the knowledge of carbody hunting and provide a reference for solving abnormal carbody vibrations.

Force Analysis of the Overconstrained Mechanisms Based on Equivalent Stiffness Considering Limb Axial Deformation

Overconstrained mechanism has the advantages of large bearing capacity and high motion reliability,but its force analysis is complex and difficult because the mechanism system contains overconstraints.Considering the limb axial deformation,taking typical 2SS+P and 7-SS passive overconstrained mechanisms,2SPS+P and 7-SPS active overconstrained mechanisms,and 2SPS+P and 7-SPS passive-input overconstrained mechanisms as examples,a new force analysis method based on the idea of equivalent stiffness is proposed.The equivalent stiffness matrix of passive overconstrained mechanism is derived by combining the force balance and deformation compatibility equations with consideration of axial elastic limb deformations.The relationship between the constraint wrench magnitudes and the external force,limb stiffness is established.The equivalent stiffness matrix of active overconstrained mechanism is derived by combining the force balance and displacement compatibility equations.Here,the relationship between the magnitudes of the actuated wrenches and the external force,limb stiffness is investigated.Combining with the equivalent stiffness of the passive overconstrained mechanism,an analytical relationship between the actuated forces of passive-input overconstrained mechanism and the output displacement,limb stiffness is explored.Finally,adaptability of the equivalent stiffness to overconstrained mechanisms is discussed,and the effect of the limb stiffness on overconstrained mechanisms force distribution is revealed.The research results provide a theoretical reference for the design,research and practical application of overconstrained mechanism.

Generalized-Extended-State-Observer and Equivalent-Input-Disturbance Methods for Active Disturbance Rejection: Deep Observation and Comparison

Active disturbance-rejection methods are effective in estimating and rejecting disturbances in both transient and steady-state responses.This paper presents a deep observation on and a comparison between two of those methods:the generalized extended-state observer(GESO)and the equivalent input disturbance(EID)from assumptions,system configurations,stability conditions,system design,disturbance-rejection performance,and extensibility.A time-domain index is introduced to assess the disturbance-rejection performance.A detailed observation of disturbance-suppression mechanisms reveals the superiority of the EID approach over the GESO method.A comparison between these two methods shows that assumptions on disturbances are more practical and the adjustment of disturbance-rejection performance is easier for the EID approach than for the GESO method.

Retrieving chlorophyll content and equivalent water thickness of Moso bamboo(Phyllostachys pubescens) forests under Pantana phyllostachysae Chao-induced stress from Sentinel-2A/B images in a multiple LUTs-based PROSAIL framework

Biochemical components of Moso bamboo(Phyllostachys pubescens)are critical to physiological and ecological processes and play an important role in the material and energy cycles of the ecosystem.The coupled PROSPECT with SAIL(PROSAIL)radiative transfer model is widely used for vegetation biochemical component content inversion.However,the presence of leaf-eating pests,such as Pantana phyllostachysae Chao(PPC),weakens the performance of the model for estimating biochemical components of Moso bamboo and thus must be considered.Therefore,this study considered pest-induced stress signals associated with Sentinel-2A/B images and field data and established multiple sets of biochemical canopy reflectance look-up tables(LUTs)based on the PROSAIL framework by setting different parameter ranges according to infestation levels.Quantitative inversions of leaf area index(LAI),leaf chlorophyll content(LCC),and leaf equivalent water thickness(LEWT)were derived.The scale conversions from LCC to canopy chlorophyll content(CCC)and LEWT to canopy equivalent water thickness(CEWT)were calculated.The results showed that LAI,CCC,and CEWT were inversely related with PPC-induced stress.When applying multiple LUTs,the p-values were<0.01;the R2 values for LAI,CCC,and CEWT were 0.71,0.68,and 0.65 with root mean square error(RMSE)(normalized RMSE,NRMSE)values of 0.38(0.16),17.56μg cm-2(0.20),and 0.02 cm(0.51),respectively.Compared to the values obtained for the traditional PROSAIL model,for October,R2 values increased by 0.05 and 0.10 and NRMSE decreased by 0.09 and 0.02 for CCC and CEWT,respectively and RMSE decreased by 0.35μg cm-2 for CCC.The feasibility of the inverse strategy for integrating pest-induced stress factors into the PROSAIL model,while establishing multiple LUTs under different pest-induced damage levels,was successfully demonstrated and can potentially enhance future vegetation parameter inversion and monitoring of bamboo forest health and ecosystems.

New correlations for evaluating the equivalent bare charge mass for a cased charge

Munitions contain casings that consume explosive energy.The blast load(e.g.,peak overpressure and maximum impulse)intensity generated by ammunition explosion will be lower than that generated by a bare charge with equal mass.To evaluate the blast load of a cased charge under different conditions,the equivalent bare mass needs to be calculated.However,the accuracy of existing correlations strongly depends on the empirical determination of relevant controlling parameters and lacks theoretical clarification.In this paper,new correlations are proposed based on a more rigorous theoretical derivation,considering both the mechanical behaviors of the casing’s material and the change of the polytropic exponent during the expansion process of the explosion products.The controlling parameters are attributed to the rupture radius ratio and the polytropic exponent of detonation products expansion to casing rupture state.The reasonability is validated by both comprehensive numerical simulations with dynamic mechanical constitutive model and theoretical derivations.The results calculated by the new correlation show better agreement with the experimental results than those calculated by previous correlations,and the results difference is explained in more consistency with the thermos-physical properties of the charge and mechanical behaviors of casing material.Furthermore,the correlation of the cased-to-bare impulse ratio is also theoretically improved,providing a more accurate theoretical basis for both the equivalent bare mass and impulse evaluation for a cased charge.

Time-varying gravity field model of Sichuan-Yunnan region based on the equivalent mass source model

High-precision time-varying gravity field is an effective way to study the internal mass movement and understanding the spatio-temporal evolution process of the geodynamic system.Compared to the satellite gravity measurement,the repeated terrestrial gravity observation can provide a more high-order signal related to the shallow crust and subsurface.However,the suitable and unified method for gravity model estimation is a key problem for further applications.In this study,we introduce the spherical hexahedron element to simulate the field source mass and forward model the change of gravity field located at the Sichuan-Yunnan region(99—104°E,23—29°N)in the four epochs from 2015 to 2017.Compared to the experimental results based on Slepian or spherical harmonics frequency domain method,this alternative approach is suitable for constructing the equivalent mass source model of regional-scale gravity data,by introducing the first-order smooth prior condition of gravity time-varying signal to suppress the high-frequency component of the signal.The results can provide a higher spatial resolution reference for regional gravity field modeling in the Sichuan-Yunnan region.

A Lagrangian Trajectory Analysis of Azimuthally Asymmetric Equivalent Potential Temperature in the Outer Core of Sheared Tropical Cyclones

In this study,the characteristics of azimuthally asymmetric equivalent potential temperature(θ_(e))distributions in the outer core of tropical cyclones(TCs)encountering weak and strong vertical wind shear are examined using a Lagrangian trajectory method.Evaporatively forced downdrafts in the outer rainbands can transport low-entropy air downward,resulting in the lowestθ_(e)in the downshear-left boundary layer.Quantitative estimations ofθ_(e)recovery indicate that air parcels,especially those originating from the downshear-left outer core,can gradually revive from a low entropy state through surface enthalpy fluxes as the parcels move cyclonically.As a result,the maximumθ_(e)is observed in the downshear-right quadrant of a highly sheared TC.The trajectory analyses also indicate that parcels that move upward in the outer rainbands and those that travel through the inner core due to shear make a dominant contribution to the midlevel enhancement ofθ_(e)in the downshear-left outer core.In particular,the former plays a leading role in suchθ_(e)enhancements,while the latter plays a secondary role.As a result,moist potential stability occurs in the middle-to-lower troposphere in the downshear-left outer core.

Multi-domain equivalent method for prediction of elastic modulus of complex fractured rock mass

Reliable estimation of deformation and failure behaviors of fractured rock mass is important for practical engineering design.This study proposes a multi-domain equivalent method for fracture network to estimate the deformation properties of complex fractured rock mass.It comprehends both the advantages of the discrete fracture network model and the equivalent continuum model to capture the features of discontinuities explicitly while reducing computational intensity.The complex fracture network is stochastically split into a number of subfracture networks according to the domain,length or angle.An analytical solution is derived to infer theoretically the relationship between the elastic moduli of the original complex fractured rock mass and the split subfractured rock masses by introducing a correction term based on the deformation superposition principle.Numerical simulations are conducted to determine the elastic moduli of split subfractured rock masses using universal distinct element code(UDEC),while the elastic modulus of the original model is estimated based on the currently proposed analytical relationship.The results show that the estimation accuracy with the current domainbased splitting model is far superior compared to those with the other two splitting models.Thus,the estimation method of elastic modulus of complex fractured rock mass based on domain splitting mode of fracture network is identified as the multi-domain equivalent method proposed in this paper.The reliability of this method is evaluated,and its high computational efficiency is demonstrated through exemplification with regard to different geometric configurations for stochastically artificial discrete fracture network.The proposed multi-domain equivalent method constructs the theoretical framework except for the regression analysis hypothesis compared to the density-reduced model equivalent method.

Research on Equivalent Modeling Method of AC-DC Power Networks Integrating with Renewable Energy Generation

Along with the increasing integration of renewable energy generation in AC-DC power networks,investigating the dynamic behaviors of this complex system with a proper equivalent model is significant.This paper presents an equivalent modeling method for the AC-DC power networks with doubly-fed induction generator(DFIG)based wind farms to decrease the simulation scale and computational burden.For the AC-DC power networks,the equivalent modeling strategy in accordance with the physical structure simplification is stated.Regarding the DFIG-based wind farms,the equivalent modeling based on the sequential identification of multi-machine parameters using the improved chaotic cuckoo search algorithm(ICCSA)is conducted.In light of the MATLAB simulation platform,a two-zone four-DC interconnected power grid with wind farms is built to check the efficacy of the proposed equivalentmodelingmethod.Fromthe simulation analyses and comparative validation in different algorithms and cases,the proposed method can precisely reflect the steady and dynamic performance of the demonstrated system under N-1 and N-2 fault scenarios,and it can efficiently achieve the parameter identification of the wind farms and fulfill the equivalent modeling.Consequently,the proposed approach’s effectiveness and suitability are confirmed.

Cost-Effective Monitoring of the Fuel Air Equivalence-Ratio with a Lambda Sensor and a Microcontroller in a Downdraft Biomass Gasifier

The operation of biomass treatment devices such as gasifiers is based on the control of key parameters that play an important role in product formation. These include: temperature, excess oxygen, relative humidity and biomass composition. This work focuses on excess oxygen and temperature. Unfortunately, flue gas oxygen analyzers are expensive and not accessible to small industries. However, the equivalence ratio is linked to excess oxygen and has the advantage of not depending on biomass composition. This study therefore focuses on the design and development of a device for controlling this equivalence ratio by measuring oxygen concentration using a self-propelled Lambda probe, and a system for monitoring this equivalence ratio using an Arduino Uno 3 microcontroller. The temperature is recorded with an accuracy of ±1.5°C. For a heating time of 10 minutes, the response time to temperature change is around 3 seconds, which is sufficient for the device to function properly. This simple device is an efficient and cost-effective means of checking the equivalence ratio.

From“Semantic Equivalence”to“Verve Reproduction”—Exploration on Xu Yuanchong’s English Translation of the Analects

This paper focuses on the English translation of Xu Yuanchong’s Analects,explains in depth the theory of semantic equivalence and the theory of verve reproduction.It analyzes the application and integration of these two theories by Xu Yuanchong in detail.Through a comprehensive textual analysis,this paper summarizes the remarkable achievements of the English translation of the Analects,such as the accurate transmission of semantics and the vivid reproduction of cultural charm,which is expected to bring new thinking directions and valuable references to the study of the English translation of the Analects.

Special Relativity’s “Newtonization” in Complex “Para-Space”: The Two Theories Equivalence Question

Complex model, say C3, of “para-space” as alternative to the real M4 Minkowski space-time for both relativistic and classical mechanics was shortly introduced as reference to our previous works on that subject. The actual aim, however, is an additional analysis of the physical and para-physical phenomena’ behavior as we formally transport observable mechanical phenomena [motion] to non-real interior of the complex domain. As it turns out, such procedure, when properly set, corresponds to transition from relativistic to more classic (or, possibly, just classic) kind of the motion. This procedure, we call the “Newtonization of relativistic physical quantities and phenomena”, first of all, includes the mechanical motion’s characteristics in the C3. The algebraic structure of vector spaces was imposed and analyzed on both: the set of all relativistic velocities and on the set of the corresponding to them “Galilean” velocities. The key point of the analysis is realization that, as a matter of fact, the relativistic theory and the classical are equivalent at least as for the kinematics. This conclusion follows the fact that the two defined structures of topological vector spaces i.e., the structure imposed on sets of all relativistic velocities and the structure on set of all “Galilean” velocities, are both diffeomorphic in their topological parts and are isomorphic as the vector spaces. As for the relativistic theory, the two approaches: the hyperbolic (“classical” SR) with its four-vector formalism and Euclidean, where SR is modeled by the complex para-space C3, were analyzed and compared.

Subsidence prediction method based on equivalent mining height theory for solid backfilling mining

Based on the characteristics of strata movement of solid backfilling mining technology, the surface subsidence prediction method based on the equivalent mining height theory was proposed, and the parameters selection guideline of this method was also described. While comparing the parameters of caving mining with equivalent height, the subsidence efficient can be calculated according to the mining height and bulk factor of sagging zone and fracture zone, the tangent of main influence angle of solid backfilling mining is reduced by 0.2-0.5（while it cannot be less than 1.0）. For sake of safety, offset of the inflection point is set to zero, and other parameters, such as horizontal movement coefficient and main propagation angle are equal to the corresponding parameters of caving mining with equivalent height. In the last part, a case study of solid backfilling mining subsidence prediction was described. The results show the applicability of this method and the difference of the maximum subsidence point between the prediction and the observation is less than 5%.

Effect of gas bubble on cell voltage oscillations based on equivalent circuit simulation in aluminum electrolysis cell

A method to investigate the effect of gas bubble on cell voltage oscillations was established. The whole aluminum electrolysis cell was treated as a resistance circuit, and the dynamic simulation of the cell equivalent circuit was modeled with Matlab/Simulink simulation software. The time-series signals of cell voltage and anode current were obtained under different bubble conditions, and analyzed by spectral and statistical analysis methods. The simulation results show that higher bubble release frequency has a significant effect on the cell voltage oscillations. When the bubble coverage of one anode block exceeds 80%, the cell voltage may exceed its normal fluctuation amplitude. The simulation also proves that the anode effect detected by computer in actual production is mainly the whole cell anode effect.