Dynamic Deviation Research Articles

Evaluation of Critical Dynamic Stress and Accumulative Plastic Strain of an Unbound Granular Material Based on Cyclic Triaxial Tests.

Critical dynamic stress (σcri) and accumulative plastic strain (εp) are primary indicators regarding the dynamic stability of unbound granular materials (UGMs). This study aims to seek an effective method to evaluate the dynamic stability of UGMs used in railway subgrades. First, the dynamic characteristics of an UGM used in railway subgrade bed construction were investigated by performing a series of large-scale cyclic triaxial tests, with the results showing that εp versus cycle number (N) curves can be categorized into stable, failure, and critical patterns. Grey relational analyses were then established, where the analyzed results demonstrated that the εp–N curve pattern and final accumulative plastic strain (εs) of the stable curves are strongly correlated with the moisture content (w), confining pressure (σ3), and dynamic deviator stress (σd). The analyzed grey relational grades distributed in a narrow range of 0.72 to 0.81, indicating that w, σ3, and σd have similar degrees of importance on determining the εp–N curve patterns and the values of εs of the UGM. Finally, a data processing method using a back-propagation (BP) neural network is introduced to analyze the test data, and an empirical approach is developed to evaluate the σcri (considering the effects of σ3 and w) and εs (considering the effects of σ3, w, and σd) of the UGM. The analyzed results illustrated that the developed method can effectively reflect the linear/non-linear relationships of σcri and εs with respect to σ3 and/or σd. The σcri approximately increases linearly with increasing σ3, and a simple empirical formula is proposed for the σcri. In addition, εs and its variation rate increase non-linearly with increasing σd but decrease non-linearly as σ3 increases.

Algorithm for controlling the process of buffer wastewater neutralization

In Ukraine, the condition of surface water near industrial enterprises is extremely critical. The operation of enterprises leads to intensive water pollution with industrial and domestic wastewater. Therefore, improving the quality of treatment facilities through the introduction of automated control systems is an urgent problem.
 For the operation of automated control systems for typical cleaning processes, a software package is required, which is developed on the basis of appropriate algorithmic software and mathematical models of processes. To obtain them, methods of mathematical and simulation modeling and block diagram method of algorithmization were used.
 In order to assess the quality of the developed algorithm for controlling the process of buffer wastewater neutralization during operation, a comparison of control system operation based on this algorithm with the most successful foreign variants of neutralization control systems was made. Simulation for the average values of operating parameters Q = 75 m3 / h, CP = 75 g / l, and Ck = 2 g / l at minimum b = 0.02 g / l pH and maximum buffer value b = 0.47 g / l pH, and also with unidirectional extreme combination of parameters Q = 50 m3 / h, CP = 100 g / l, b = 0,02 g / l pH and Q = 100 m3 / h, CP= 50 g / l, for minimum b = 0.02 g / l pH and maximum buffering value b = 0.47 g / l pH shows that the best quality of transient processes is for the control system operating on the basis of the developed algorithm. For any combination of parameters, the transients for this control system provide better quality transients. Studies have shown that the control system based on the developed algorithm in comparison with the previously proposed systems provides better process control by reducing the time of transients and reducing the dynamic deviation of the output parameters, which improves the quality of wastewater treatment.
 Given the non-stationary process and high requirements for the cleaning parameters, manual control of this process is beyond the power of even an experienced operator. The developed mathematical model describing the dynamics of the wastewater neutralization reactor with buffer properties and the process control algorithm made it possible to proceed to the development of the control system software, which is necessary for the automated control of this process.

Dynamical Large Deviations of Two-Dimensional Kinetically Constrained Models Using a Neural-Network State Ansatz.

We use a neural-network ansatz originally designed for the variational optimization of quantum systems to study dynamical large deviations in classical ones. We use recurrent neural networks to describe the large deviations of the dynamical activity of model glasses, kinetically constrained models in two dimensions. We present the first finite size-scaling analysis of the large-deviation functions of the two-dimensional Fredrickson-Andersen model, and explore the spatial structure of the high-activity sector of the South-or-East model. These results provide a new route to the study of dynamical large-deviation functions, and highlight the broad applicability of the neural-network state ansatz across domains in physics.

Fault detection and diagnosis of the air handling unit via an enhanced kernel slow feature analysis approach considering the time-wise and batch-wise dynamics

Air handling unit (AHU) is a typical special batch control process, exhibiting strong nonlinear property and two-directional dynamic characteristics which are the time-wise and batch-wise dynamic characteristics. Specifically, the time-wise dynamic characteristic corresponds to the evolution of different operating modes caused by the underlying driving forces which vary slowly in each running day (a batch run), while the batch-wise dynamic characteristic relates to the dynamic variations and deviations among different running days (batch runs). In order to further improve the AHU FDD performance through capturing the underlying driving forces of the AHU system and tackling the batch-wise dynamic property between different batch runs, in this paper, an enhanced kernel slow feature analysis (SFA) based FDD scheme is developed to detect and identify the faults of the nonlinear AHU system. Firstly, a three-way data based kernel SFA (TBKSFA) approach is proposed to detect the faults. In the proposed TBKSFA approach, the kernel trick is adopted in the SFA to sufficiently deal with the nonlinearity and the time-wise dynamic characteristic, and the multiway data analysis is employed to cope with the batch-wise dynamics among different batch runs by converting the three-way training dataset into a variable-wise unfolding two-way matrix. In addition, to handle the tough problem of nonlinearly identifying the fault pattern, a novel kernel discriminant SFA (KDSFA) model is further built by combining the kernel SFA with the discriminant analysis method. In the fault pattern diagnosis process, the proposed KDSFA is pairwisely implemented on the normal and fault datasets to calculate the fault direction, and the fault is then identified by computing the similar degrees of its own fault direction and the historical fault directions. At last, experiments and comparisons on the FDD performance of the developed approach are made using the experimental data provided by ASHRAE Research Project RP-1312. To be specific, the proposed TBKSFA based fault detection method is compared with the popular kernel principal component analysis (KPCA) method, the closely related kernel SFA method and the emerging manifold learning based kernel locality preserving projections (KLPP) method. While the developed KDSFA based fault pattern diagnosis scheme is compared with the conventional jointed angle analysis technique, the strongly linked DSFA based method and the rising artificial neural networks based long short-term memory(LSTM) classifier. Experimental results demonstrate that significant improvements can be achieved by the proposed approach compared with some other popular methods.

Braking Control System of Oilfield Minor Repair Machine Based on Wireless Sensor Network

Traditional minor repair machines have low control efficiency and low automation. In order to improve the brake control efficiency of the oilfield minor repair machine, the oilfield minor repair machine brake control system based on wireless sensor network is designed. The front-end controller collects the data of the oilfield repair machine through the wireless sensor and realizes the communication between the sensor nodes and the data interaction with the communication node through the field bus inside the equipment. The server uploads the processed data through the 3G network, and the server receives the data from the front-end controller and saves it in the database. The remote-control center accesses the server through the Internet to view the front-end controller data. The brake control module uses the expert fuzzy PID control method to control the speed, oil pressure, and operating status of the oilfield minor repair machine and sends the data to the front-end control center to complete the oilfield minor repair remote-control machine by sending control instructions. Experimental results show that the system can meet the braking control requirements of oilfield minor repair machines, the output can quickly track input changes, the braking control effect is good, the dynamic deviation of the machine can be reduced, and the braking control efficiency can be improved.

Layout-Dominated Dynamic Imbalanced Current Analysis and Its Suppression Strategy of Parallel SiC MOSFETs

The multichip power module is a popular application for large-capacity and high-frequency converters. However, the existence of an asymmetric circuit layout has a significant influence on the current sharing among parallel SiC metal-oxide-semiconductor field-effect transistors (MOSFETs). In this paper, the mechanism of the dynamic current imbalance resulting from the asymmetry of signal terminal confluence points (STCPs) is comprehensively investigated by theoretical analyses and simulation validations. It is demonstrated that the infinite norm of the common branch impedance coupling matrix (INC) can be used to characterize the dynamic current sharing performance. With an increase in the infinite norm, the dynamic current imbalance of parallel SiC MOSFETs gradually increases. Moreover, some significant discoveries are obtained. It is concluded that dynamic current imbalance is dominated by the asymmetry of the power source confluence point (PSCP). However, the asymmetry of the drain, gate, and auxiliary source confluence points does not exhibit a great effect on dynamic current sharing. Then, a novel circuit layout with an elliptical structure is proposed to suppress the dynamic current imbalance. Finally, some experimental tests are derived to validate the effectiveness of the designed layout. Compared with the commercial power module, experimental results show that the maximum dynamic imbalanced current with the proposed layout is reduced from 7.39 A to 1.37 A, and the largest dynamic current imbalanced deviation decreases from 28.66% to 5.11%.

Thermodynamic and structural properties of the ionic liquid binary system of 1-ethyl-3-methylimidazolium thiocyanate and methanol

A binary mixture of ionic liquid 1-ethyl-3-methylimidazolium thiocyanate ([C2mim][SCN]) and methanol was prepared along with the whole composition range. Thermodynamic properties such as densities, dynamic viscosities, and electrical conductivities of binary system were measured from 293.15 to 323.15 K at 101.3 KPa. The electrical conductivities dependences of IL mole fraction were graphically described by the Casteel–Amis four-parameter equation. The excess molar volumes (VE ) and dynamic viscosity deviations (Δη) of the binary mixture were calculated and satisfactorily fitted by the Redlich–Kister polynomial equation to reveal the interactions that exist among the components. For a deep understanding of the intermolecular interactions of the binary mixture, the infrared spectrum analysis was used to provide the observable changes related to the structural features, and the stable structures, energies of the complexes involving cation or anion of [C2mim][SCN] and methanol molecule were calculated by density functional theory calculations at B3LYP/6-311++G** level of calculation to evaluate the interaction situations of the IL and methanol.

Importance of dynamic lattice effects for crystal field excitations in the quantum spin ice candidate Pr2Zr2O7

Pr$_2$Zr$_2$O$_7$ is a pyrochlore quantum spin-ice candidate. Using Raman scattering spectroscopy we probe crystal electric field excitations of Pr$^{3+}$, and demonstrate the importance of their interactions with the lattice. We identify a vibronic interaction with a phonon that leads to a splitting of a doublet crystal field excitation at around 55~meV. We also probe a splitting of the non-Kramers ground state doublet of Pr$^{3+}$ by observing a double line of the excitations to the first excited singlet state $E^0_g \rightarrow A_{1g}$. We show that the splitting has a strong temperature dependence, with the doublet structure most prominent between 50~K and 100~K, and the weight of one of the components strongly decreases on cooling. We suggest a static or dynamic deviation of Pr$^{3+}$ from the position in the ideal crystal structure can be the origin of the effect, with the deviation strongly decreasing at low temperatures.

Dynamic system modelling and process monitoring based on long-term dependency slow feature analysis

Modern industrial processes are large-scale, highly complex systems with many units and equipment. The complex flow of mass and energy, as well as the compensation effects of closed-loop control systems, cause significant cross-correlation and autocorrelation between process variables. To operate the process systems stably and efficiently, it is crucial to uncover the inherent characteristics of both the variance structure and dynamic relationship. Compared with the original slow feature analysis (SFA) that can only model the one-step time dependence, long-term dependency slow feature analysis (LTSFA) proposed in this paper can understand the longer-term dynamics by an explicit expression of latent states of the process. An iterative algorithm is developed for the model parameter optimization and its convergency is proved. The model properties and theoretical comparison with existing dynamic models are presented. A process monitoring strategy is designed based on LTSFA. The results of two simulation case studies show that LTSFA has better system dynamics extraction capability, which reduces the violation rate of the residual for the 95% confidence interval from 40.4% to 3.2% compared to the original SFA, and can disentangle the quickly- and slowly-varying features. Several typical disturbances can be correctly identified by LTSFA. The monitoring results on the Tennessee Eastman process benchmark show the overall advantages of the proposed method both in the dynamic and nominal deviation detection and the monitoring accuracy

A large deviation theory perspective on nanoscale transport phenomena

Understanding transport processes in complex nanoscale systems, like ionic conductivities in nanofluidic devices or heat conduction in low dimensional solids, poses the problem of examining fluctuations of currents within nonequilibrium steady states and relating those fluctuations to nonlinear or anomalous responses. We have developed a systematic framework for computing distributions of time integrated currents in molecular models and relating cumulants of those distributions to nonlinear transport coefficients. The approach elaborated upon in this perspective follows from the theory of dynamical large deviations, benefits from substantial previous formal development, and has been illustrated in several applications. The framework provides a microscopic basis for going beyond traditional hydrodynamics in instances where local equilibrium assumptions break down, which are ubiquitous at the nanoscale.

Optimal sampling of dynamical large deviations via matrix product states.

The large deviation statistics of dynamical observables is encoded in the spectral properties of deformed Markov generators. Recent works have shown that tensor network methods are well suited to compute accurately the relevant leading eigenvalues and eigenvectors. However, the efficient generation of the corresponding rare trajectories is a harder task. Here, we show how to exploit the matrix product state approximation of the dominant eigenvector to implement an efficient sampling scheme which closely resembles the optimal (so-called "Doob") dynamics that realizes the rare events. We demonstrate our approach on three well-studied lattice models, the Fredrickson-Andersen and East kinetically constrained models, and the symmetric simple exclusion process. We discuss how to generalize our approach to higher dimensions.

Intelligent optimal control considering dynamic posture compensation for a cantilever roadheader

AbstractThe control of dynamic spatial posture for cantilever roadheader is one of the vital problems for intelligent mining, which directly affect the forming quality of cutting tunnel. Therefore, this paper proposed an intelligent optimal combination compensation strategy to adjust the real-time dynamic posture of cantilever roadheader. First, based on the topological structure analysis of cantilever roadheader, the structural loop compensation model for spatial posture deviation was established. Afterward, the principal component analysis (PCA) and multi-objective particle swarm optimization (MPSO) algorithm were applied to improve the analysis speed and accuracy of posture deviation. Finally, parallel dynamic cooperative optimization (PDCO) strategy was combined to achieve the accurate adjusting of posture deviation. The actual experimental and application results indicate that the intelligent optimal combination compensation strategy proposed in the paper can significantly improve the accuracy of the cutting tunnel. The intelligent optimal compensation strategy proposed in this paper transforms the transient spatial posture deviation into structural loop compensation, and implements by parallel cooperative strategy, finally to realize the fast analysis and efficient implementation of spatial dynamic posture deviation for cantilever roadheader during cutting process. The work of this paper provides an effective reference for intelligent deep and remote underground mining, and it can also be applied to effective control of dynamic spatial posture for intelligent engineering machinery products.

Simultaneous determination of five opium alkaloids in underground waters using molecularly imprinted polymer-modified magnetic nanoparticle based dispersive micro-solid phase extraction followed by high performance liquid chromatography

ABSTRACT In this work, we present a fast, simple and selective method for the extraction/preconcentration and determination of five opium alkaloids. This method is based on the combination of dispersive solid phase extraction with magnetic molecularly imprinted polymers (MMIP) and determination via high performance liquid chromatography. The surface modified Fe3O4 nanoparticles were synthesised in-situ, from a co-precipitation method by addition of a mixture of the methacrylic acid and ammonia to a mixture of Fe2+/Fe3+ under nitrogen atmosphere. MMIP was prepared from surface modified nanoparticles in the presence of ethylene glycol dimethyl acrylate as cross-linker and azobisisobutyronitrile as initiator and template molecule under reflux in acetonitrile. MMIPs for five natural occurring opium alkaloids, including morphine (MO), codeine (CO), thebaine (TE), noscapine (NO) and papaverine (PA) were prepared in the same manner. Structural characterisation and elucidation of both synthesised nanoprticles were performed by Fourier transform-infrared spectroscopy, scanning electron microscopy. X-ray diffraction and vibrating sample magnetometry. A precise chromatographic method was developed and coupled with extraction with MMIP nanoparticles for simultaneous preconcentration and determination of above-mentioned alkaloids in underground water samples. The limit of detection obtained 0.007, 0.007, 0.004, 0.003, 0.003 mg L−1 for MO, CO, TE, NO and PA, respectively and recoveries were about 97–102%. Linear dynamic range and relative standard deviation were 0.03–100 mg L−1 and less than 1.5% for each analyte.

Modeling of the electric drive of the main motion of the rolling cage as a multi-mass electromechanical system

The model of rolling stand of a thick-plate rolling mill 3000 has been designed in the work in order to determine the oscillations frequencies that occur during operation, the effect of their amplitude on the dynamic deviations of the speed of the working body from the specified one.Presented results of the research dynamic to rolling cage 3000 at presentation her as seven masses electromechanic system. Shown influence clearance in mechanical issue on dynamic of the mechanism.The research by the method of mathematical modeling in the design and operation of mechanical equipment is substantiated.The design diagram of mechanical part of the electromechanical system is presented.Using the simulation results it was confirmed that the influence of internal viscous friction in shafting on the oscillation damping is not significant in relation to the damping properties of electric drive.Therefore, in the first approximation, it can be ignored. The electric drive of the rolling stand was considered as a TP-D system with speed and current regulators at their standard settings to the modular optimum. To reduce the magnitude of the elastic moments in the kinematic chain of the stand the armature current intensity generator in the electric drive is used.Simulation of the processes was carried out in Simulink of the MATLAB package.Thestand model is designed according to design scheme and reflects the branching into two channels with their combination through an elastic element – the material that is rolled.Based on real geometry and taking into account the properties of material the stiffness of shafts of mechanical transmissions were calculated.The model was set to a rolling program with a variable speed – in order to compensate the thickness difference, which corresponds to modern technological trends.Comparing the simulation results, it was found that the presence of a gap provokes the appearance of self-oscillations, the damping of which in a real mechanical system will occur due to damping properties of the shafts.The damping of oscillations takes place due to the damping properties of the electric drive. The appearance of a gap in the spindles leads to an increase in the system vibration frequency (70-80 Hz).

Precise Reactive Power-Voltage Droop Control of Parallel Virtual Synchronous Generators That Considers Line Impedance

Problems such as high power coupling, low distribution accuracy, and insufficient reactive power-voltage droop accuracy occur when distributed generators are operated in parallel due to the influence of line impedance. The precise control of output reactive power and voltage is difficult to achieve using traditional virtual synchronous generator (VSG) control. Taking this into consideration, this study proposes a virtual synchronous generator reactive power-voltage integrated control strategy that considers line parameters to solve this problem. First, the impedance voltage drop of the line is compensated for in accordance with local information control to ensure the consistency of the control voltage in parallel operation of distributed generators and to realize the precise droop control of reactive power and the voltage of the point of common coupling (UPCC). Second, virtual negative impedance control is added to change the equivalent output impedance characteristics of the system and achieve power decoupling. On this basis, the active frequency and reactive voltage decoupling control effect of the improved control strategy is quantified and analyzed using the relative gain matrix. The accuracy of reactive power distribution and droop control is theoretically derived and analyzed by establishing a small-signal model of a two-machine parallel system. Finally, the accuracy and effectiveness of the proposed integrated control strategy are verified via a simulation model and an experimental platform for parallel operation. Results show that the proposed integrated control strategy can effectively solve the problems of power decoupling and accurate distribution, reduce system loop current, and realize accurate reactive power-voltage droop. Compared with the traditional VSG control strategy, the dynamic deviation of UPCC is reduced by at least 40% when a large-scale load disturbance occurs.

Dynamical Large Deviations for Plasmas Below the Debye Length and the Landau Equation

We consider a homogeneous plasma composed of $N$ particles of the same electric charge which interact through a Coulomb potential. In the large plasma parameter limit, classical kinetic theories justify that the empirical density is the solution of the Balescu-Guernsey-Lenard equation, at leading order. This is a law of large numbers. The Balescu-Guernsey-Lenard equation is approximated by the Landau equation for scales much smaller than the Debye length. In order to describe typical and rare fluctuations, we compute for the first time a large deviation principle for dynamical paths of the empirical density, within the Landau approximation. We obtain a large deviation Hamiltonian that describes fluctuations and rare excursions of the empirical density, in the large plasma parameter limit. We obtain this large deviation Hamiltonian either from the Boltzmann large deviation Hamiltonian in the grazing collision limit, or directly from the dynamics, extending the classical kinetic theory for plasmas within the Landau approximation. We also derive the large deviation Hamiltonian for the empirical density of $N$ particles, each of which is governed by a Markov process, and coupled in a mean field way. We explain that the plasma large deviation Hamiltonian is not the one of $N$ particles coupled in a mean-field way.

Generic Uncertainty Parameter Analysis and Optimization of Series–Series Wireless Power Transfer System for Robust Controller Design

In a typical wireless power transfer (WPT) system, the load, the mutual inductance, and the required tuning frequency can vary in a particular range. Variation of each parameter can substantially impact the dynamic characteristics of the system. Thus, they can be considered as sources of uncertainty in the system. To address this, robust control methods such as μ-synthesis are developed to deal with possible system uncertainties. This article first undertakes the generic dynamic analysis of the series–series WPT compensation network for two modes of operation, i.e., constant output voltage (COV) mode and constant output current (COC) mode, in the presence of three aforementioned uncertainty sources. Subsequently, the frequency detuning as a function of the compensation capacitor variation is explored and broadened as a technique to obtain the optimized compensation capacitor value that can lead to a plant with minimized dynamic deviations from its nominal system in the operating range between COC and COV modes. As such, this approach offers a design procedure for a least conservative robust controller, which can significantly improve the system performance. The optimized structure and the corresponding designed μ-synthesis controller are comprehensively elaborated. The theoretical achievements and experimental results show superior dynamic performance of the optimized structure and the corresponding designed controller in the presence of three uncertainty sources compared to the COC and COV modes of operation.

Coupling and coordination of socioeconomic and ecological environment in Wenchuan earthquake disaster areas: Case study of severely affected counties in southwestern China

The Chinese government established a counterpart support mechanism and ecological civilization construction to promote socioeconomic development and ecological protection after the Wenchuan earthquake. However, the contradiction between the ecological environment and socioeconomic is still has not changed fundamentally. How to coordinate the relationship between the socioeconomic and ecological environment in the disaster area has become a key issue to the sustainable development after the Wenchuan earthquake. The purpose of this paper is to research the coupling and coordination relationship between socioeconomic and ecological environment to provide reference for Wenchuan earthquake disaster area to achieve regional sustainable development goals (SDGs) and high-quality development. Based on this, the dynamic deviation maximization (DM) method and coupling coordination model (CCD) were used to calculate the indicator weight and the overall coordination relationship between socioeconomic (SE) and ecological environment (EE) in Wenchuan earthquake disaster area by using the data from 2005 to 2018. The results showed that the CCD of the Wenchuan earthquake disaster area has increased from 2005 to 2018. From the spatial characteristics, the comprehensive evaluation score of CCD decreased from northeast to southwest in the disaster area, and there is still a significant spatial difference in the disaster area. Besides, the interesting finding is that post-disaster reconstruction and recovery capacity are closely related to location factors, population factors and altitude factors. On this basis, the causes of regional differences are analyzed, and some corresponding concrete suggestions are proposed, involving strengthen the policies to prevent labor loss, expand the characteristic industries of each country according to local conditions, and increase investment in technological innovation.

Parameters design in active power control of virtual synchronous generator considering power-angle characteristic nonlinearity

This paper focuses on parameter-based design of active power control (APC) for virtual synchronous generator (VSG) in grid-connected mode. Compared to the current practice, we have taken the power-angle characteristic nonlinearity into account. APC parameters are related to the stability and performance of VSG, and the determination of parameters is linked to the synchronizing power coefficient (SPC). Also, the nonlinearity results in the SPC variation. This feature makes the selection of the reference value of SPC difficult. In the absence of suitable reference value, the performance shows a large deviation from reality and design, even the relative stability does not meet the requirements. To deal with this problem, we analyze the impact of SPC on relative stability and performance of VSG and propose a design methodology that takes only three steps to obtain the required parameters. As an illustrative example, we present a parameter-based design case of VSG with a rated power of 20 kW and take the hardware-in-the-loop experiment to validate. The results indicate that the required relative stability is always fulfilled, and the dynamic performance deviation of reality and design is found to be little.

Study on Cyclic Cumulative Deformation Characteristics and the Equivalent Cyclic Creep Model of Soft Clay

Suction caisson foundations can be used to anchor tension leg platforms. The soil at the bottom of the caisson undergoes both unloading and cyclic loading under wind and wave loads. However, the problem of cyclic cumulative deformation of soft clay under unloading has rarely been addressed. So, the strain cumulative deformation and strain softening characteristics of soft clay are studied by cyclic triaxial tests. The test results show that under low static deviator stress ratios and dynamic deviator stress ratios, the soil has a low level of strain accumulation and softening. As the dynamic deviator stress ratios increase, the cumulative cyclic deformation gradually increases, which rapidly develops in the early stage and tends to stabilize in the later stage. Moreover, the softening index gradually increases and is linearly related to the logarithm of the number of cycles. The cyclic cumulative deformation of the soil increases with increases in unloading stress and dynamic deviator stress, showing a creep characteristic of attenuation and then stabilization. Based on the tests, an equivalent cyclic creep model is established to describe the strain accumulation and softening of soil and verified through comparison with the test results. Then, the model is extended to a three-dimension model, and a finite element subroutine is developed for studying the strain cumulative deformation and strain softening characteristics of soft clay.