Prediction and Output Estimation of Pattern Moving in Non-Newtonian Mechanical Systems Based on Probability Density Evolution

A prediction framework based on the evolution of pattern motion probability density is proposed for the output prediction and estimation problem of non-Newtonian mechanical systems,assuming that the system satisfies the generalized Lipschitz condition.As a complex nonlinear system primarily governed by statistical laws rather than Newtonian mechanics,the output of non-Newtonian mechanics systems is difficult to describe through deterministic variables such as state variables,which poses difficulties in predicting and estimating the system’s output.In this article,the temporal variation of the system is described by constructing pattern category variables,which are non-deterministic variables.Since pattern category variables have statistical attributes but not operational attributes,operational attributes are assigned to them by posterior probability density,and a method for analyzing their motion laws using probability density evolution is proposed.Furthermore,a data-driven form of pattern motion probabilistic density evolution prediction method is designed by combining pseudo partial derivative(PPD),achieving prediction of the probability density satisfying the system’s output uncertainty.Based on this,the final prediction estimation of the system’s output value is realized by minimum variance unbiased estimation.Finally,a corresponding PPD estimation algorithm is designed using an extended state observer(ESO)to estimate the parameters to be estimated in the proposed prediction method.The effectiveness of the parameter estimation algorithm and prediction method is demonstrated through theoretical analysis,and the accuracy of the algorithm is verified by two numerical simulation examples.

High-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer based on probability density evolution method

This paper proposed an efficient research method for high-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer.Firstly,the dynamic model of projectile motion is established considering the flexible deformation of the barrel and the interaction between the projectile and the barrel.Subsequently,the accuracy of the dynamic model is verified based on the external ballistic projectile attitude test platform.Furthermore,the probability density evolution method(PDEM)is developed to high-dimensional uncertainty quantification of projectile motion.The engineering example highlights the results of the proposed method are consistent with the results obtained by the Monte Carlo Simulation(MCS).Finally,the influence of parameter uncertainty on the projectile disturbance at muzzle under different working conditions is analyzed.The results show that the disturbance of the pitch angular,pitch angular velocity and pitch angular of velocity decreases with the increase of launching angle,and the random parameter ranges of both the projectile and coupling model have similar influence on the disturbance of projectile angular motion at muzzle.

Probabilistic Response and Short-Term Extreme Load Estimation of Offshore Monopile Wind Turbine Towers by Probability Density Evolution Method

A new analysis framework based on probability density evolution method(PDEM)and its Chebyshev collocation solution are introduced to predict the dynamic response and short-term extreme load of offshore wind turbine(OWT)towers subjected to random sea state.With regard to the stochastic responses,random function method is employed to generate samples of sea elevation,the probability density evolution equation(PDEE)is solved to calculate time-variant probability density functions of structural responses.For the probabilistic load estimation,a FAST model of NREL 5MW offshore turbine is established to obtain samples of bending moment at the tower base.The equivalent extreme event theory is used to construct a virtual stochastic process(VSP)to assess the short-term extreme load.The results indicate that the proposed approach can predict time-variant probability density functions of the structural responses,and shows good agreement with Monte Carlo simulations.Additionally,the predicted short-term extreme load can capture the fluctuation at the tail of the extreme value distribution,thus is more rational than results from the typical distribution models.Overall,the proposed method shows good adaptation,precision and efficiency for the dynamic response analysis and load estimation of OWT towers.

Semi-analytical modeling of tokamak density evolution

Tokamak plasma density evolution is generally modeled by a diffusion-convection equation in cylindrical geometry. By using a semi-analytical approach, we solve such an equation for a given diffusion coefficient and inward convection velocity as an arbitrary function of the radial position. Through variable separation, a Sturm-Liouville-type eigenvalue problem is solved, thereby constructing a complete set of orthogonal eigenfunctions. Based on the decomposition of the solution, the initial function, and the source function in these eigenfunctions, several problems of practical interest about the density evolution are analyzed. They include the density evolution, with boundary density not being zero; the density profile with internal transport barrier; the damping profile during particle source being shut-down. Results are found to be qualitatively consistent with the tokamak experiments.

Operator Semi-group of Density Evolution Equation for a Repairable Redundant System with Two Same Components

For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution, the probability densities of the system in some state at time t were determined by a group of ordinary and partial differential equations, called density evolution equations. It was proved that the time dependent solution of the density evolution equations uniquely exists and strongly converges to its steady state density solution by a semi group method. In this proof, it is not necessary to suppose that the repair rate function is bounded. The technique of the proof is valuable for many density evolution equations.

C_0-Semigroup Method of the Density Evolution Equation for M/M/∞ Model

In this paper, the existence, uniqueness, and asymptotic behavior of the solution of the density evolution equation for M/M/∞ model was studied by the semigroup theory of linear operators.

Typhoon hazard assessment at the site-specific scale based on the probability density evolution method and its application on the southeast coast of China

Herein, a typhoon hazard assessment method at the site-specific scale is proposed. This method integrates the nonlinear threedimensional wind field model and the probability density evolution method. At the site-specific scale, the track of a typhoon near the engineering site is approximated via a straight line. The wind field model is utilized to calculate the wind speed at the surface given the gradient wind field at the top of the boundary layer. A comparison between the simulated and observed wind histories for Typhoon Hagupit that made landfall in Guangdong Province demonstrates the fidelity of the wind field model. The probability density evolution method is utilized to calculate the propagation of the randomness from the basic random variables toward the extremities of the typhoon surface wind. To model the probability distribution of the basic random variables, several candidate distributions are considered to fit the observations. Akaike information criterion and Anderson-Darling distance are used for selecting the preferred probability distribution model. The adequacy of the probability density evolution method in assessing typhoon hazards is verified by comparing the results with those generated by Monte Carlo simulations. The typhoon wind hazards estimated by the present study are compared with those proposed by other studies and the design code, and the differences are analyzed and discussed. The results of the proposed method provide the reasonable probabilistic model for the assessment of the structural reliability and the improvement of community resilience in the typhoon-prone areas.

A novel refined dynamic model of high-speed maglev train-bridge coupled system for random vibration and running safety assessment

Running safety assessment and tracking irregularity parametric sensitivity analysis of high-speed maglev train-bridge system are of great concern,especially need perfect refinement models in which all properties can be well characterized based on various stochastic excitations.A three-dimensional refined spatial random vibration analysis model of high-speed maglev train-bridge coupled system is established in this paper,in which multi-source uncertainty excitation can be considered simultaneously,and the probability density evolution method(PDEM)is adopted to reveal the system-specific uncertainty dynamic characteristic.The motion equation of the maglev vehicle model is composed of multi-rigid bodies with a total 210-degrees of freedom for each vehicle,and a refined electromagnetic force-air gap model is used to account for the interaction and coupling effect between the moving train and track beam bridges,which are directly established by using finite element method.The model is proven to be applicable by comparing with Monte Carlo simulation.By applying the proposed stochastic framework to the high maglev line,the random dynamic responses of maglev vehicles running on the bridges are studied for running safety and stability assessment.Moreover,the effects of track irregularity wavelength range under different amplitude and running speeds on the coupled system are investigated.The results show that the augmentation of train speed will move backward the sensitive wavelength interval,and track irregularity amplitude influences the response remarkably in the sensitive interval.

Uncertainty quantification of mechanism motion based on coupled mechanism—motor dynamic model for ammunition delivery system

In this paper,a dynamic modeling method of motor driven electromechanical system is presented,and the uncertainty quantification of mechanism motion is investigated based on this method.The main contribution is to propose a novel mechanism-motor coupling dynamic modeling method,in which the relationship between mechanism motion and motor rotation is established according to the geometric coordination of the system.The advantages of this include establishing intuitive coupling between the mechanism and motor,facilitating the discussion for the influence of both mechanical and electrical parameters on the mechanism,and enabling dynamic simulation with controller to take the randomness of the electric load into account.Dynamic simulation considering feedback control of ammunition delivery system is carried out,and the feasibility of the model is verified experimentally.Based on probability density evolution theory,we comprehensively discuss the effects of system parameters on mechanism motion from the perspective of uncertainty quantization.Our work can not only provide guidance for engineering design of ammunition delivery mechanism,but also provide theoretical support for modeling and uncertainty quantification research of mechatronics system.

Joint probability density function of the stochastic responses of nonlinear structures

The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.

Implementation of low-density parity-check codes decoder for CCSDS standard

The complexity/performance balanced decoder for low-density parity-check （LDPC） codes is preferred in practical wireless communication systems. A low complexity LDPC decoder for the Consultative Committee for Space Data Systems （CCSDS） standard is achieved in DSP. An ap- proximate decoding algorithm, normalized rain-sum algorithm, is used in the implementation for its low amounts of computation. To reduce the performance loss caused by the approximation, the pa- rameters of the normalized min-sum algorithm are determined by calculating and finding the mini- mum value of thresholds through density evolution. The minimum value which indicates the best per- formance of the decoding algorithm is corresponding with the optimized parameters. In implementa- tion, the memory cost is saved by decomposing the parity-check matrix into submatrices to store and the computation of passing message in decoding is accelerated by using the intrinsic function of DSP. The performance of the decoder with optimized factors is simulated and compared with the ideal BP decoder. The result shows they have about the same performance.

Phase Evolution Study and Optimization of the Heat Treatment Process for High Current Capacity Bi-2223 Tapes

Powder in tube process（PIT） was adopted for the fabrication of single filament Bi-2223 tapes, and a heat treatment process including the first heat treatment（HT1）, intermediate rolling（IR）, and second heat treatment（HT2） was performed. The phase evolution mechanism and microstructure changes during these heat treatment processes were systematically discussed. The influences of HT1 parameters on the phase evolution process of Bi-2223 tapes were discussed. With the optimized HT1 process, a proper Bi-2223 content of about 90% was achieved. HT2 process was also optimized by adding a post annealing process. An obvious increase of current capacity was obtained due to the enhancement of intergrain connections. Single filament Bi-2223 tapes with the critical current of Ic-90 A were fabricated with the optimized sintering process.

Design of two-dimensional spatially coupled LDPC codes for combating burst erasures

Spatially-coupled low-density parity-check(SC-LDPC)codes are prominent candidates for fu-ture communication standards due to their‘threshold saturation’properties.However,when facing burst erasures,the decoding process will stop and the decoding performances will dramatically de-grade.To improve the ability of burst erasure corrections,this paper proposes a two-dimensional SC-LDPC(2D-SC-LDPC)codes constructed by parallelly connecting two asymmetric SC-LDPC coupled chains for resistance to burst erasures.Density evolution algorithm is presented to evaluate the as-ymptotic performances against burst erasures,by which the maximum correctable burst erasure length can be computed.The analysis results show that the maximum correctable burst erasure lengths of the proposed 2D-SC-LDPC codes are much larger than the SC-LDPC codes and the asym-metric SC-LDPC codes.Finite-length performance simulation results of the 2D-SC-LDPC codes over the burst erasure channel confirm the excellent asymptotic performances.

Simulated and experimental investigation on discontinuous dynamic recrystallization of a near-α TA15 titanium alloy during isothermal hot compression in βsingle-phase field

A cellular automaton（CA） modeling of discontinuous dynamic recrystallization（DDRX） of a near-α Ti-6Al-2Zr-1Mo-1V（TA15） isothermally compressed in the β single phase field was presented.In the CA model,nucleation of the β-DDRX and the growth of recrystallized grains（re-grains） were considered and visibly simulated by the CA model.The driving force of re-grain growth was provided by dislocation density accumulating around the grain boundaries.To verify the CA model,the predicted flow stress by the CA model was compared with the experimental data.The comparison showed that the average relative errors were10.2%,10.1%and 6%,respectively,at 1.0,0.1 and 0.01 s^-1 of 1020 ℃,and were 10.2%,11.35%and 7.5%,respectively,at 1.0,0.1and 0.01 s^-1 of 1050 ℃.The CA model was further applied to predicting the average growth rate,average re-grain size and recrystallization kinetics.The simulated results showed that the average growth rate increases with the increasing strain rate or temperature,while the re-grain size increases with the decreasing strain rate;the volume fraction of recrystallization decreases with the increasing strain rate or decreasing temperature.

On the hydro-mechanical behaviour of MX80 bentonite-based materials

Bentonite-based materials have been considered in many countries as engineered barrier/backfilling materials in deep geological disposal of high-level radioactive waste.During the long period of waste storage,these materials will play an essential role in ensuring the integrity of the storage system that consists of the waste canisters,the engineered barrier/backfill,the retaining structures as well as the geological barrier.Thus,it is essential to well understand the hydro-mechanical behaviours of these bentonite-based materials.This review paper presents the recent advances of knowledge on MX80 bentonite-based materials,in terms of water retention properties,hydraulic behaviour and mechanical behaviour.Emphasis is put on the effect of technological voids and the role of the dry density of bentonite.The swelling anisotropy is also discussed based on the results from swelling tests with measurements of both axial and radial swelling pressures on a sand-bentonite mixture compacted at different densities.Microstructure observation was used to help the interpretation of macroscopic hydromechanical behaviour.Also,the evolution of soil microstructure thus the soil density over time is discussed based on the results from mock-up tests.This evolution is essential for understanding the longterm hydro-mechanical behaviour of the engineered barrier/backfill.

Design and performance analysis of adaptive ordered LDPC coded OFDM system

A novel adaptive ordered LDPC （low-density parity-check） coded OFDM （orthogonal frequency-division multiplexing） transmission technique is proposed to exploit different error probabilities of irregular LDPC coded bits in OFDM systems. Assuming that the CSI （channel state information） is known at the transmitter, the irregular LDPC coded bits are ordered according to their degrees and then allocated into subcarriers adaptively. Bits with higher degrees are allocated into less attenuated subcarriers and bits with lower degrees are allocated into deep attenuated subcarriers. Quantization on CSI feedback can be applied to minimize the signaling overhead. Performance of this strategy is analyzed by density evolution and numerical simulation. Simulation results show that about a 1 to 1.5 dB gain in terms of SNR （ signal to noise ratio） can be achieved over frequency-selective fading channels compared to conventional LDPC coded OFDM systems without ordering, and the proposed scheme is robust to CSI quantization.

Extreme value distribution and reliability of nonlinear stochastic structures

A new approach to evaluate the extreme value distribution （EVD） of the response and reliability of general multi-DOF nonlinear stochastic structures is proposed. The approach is based on the recently developed probability density evolution method, which enables the instantaneous probability density functions of the stochastic responses to be captured. In the proposed method, a virtual stochastic process is first constructed to satisfy the condition that the extreme value of the response equals the value of the constructed process at a certain instant of time. The probability density evolution method is then applied to evaluate the instantaneous probability density function of the response, yielding the EVD. The reliability is therefore available through a simple integration over the safe domain. A numerical algorithm is developed using the Number Theoretical Method to select the discretized representative points. Further, a hyper-ball is imposed to sieve the points from the preceding point set in the hypercube. In the numerical examples, the EVD of random variables is evaluated and compared with the analytical solution. A frame structure is analyzed to capture the EVD of the response and the dynamic reliability. The investigations indicate that the proposed approach provides reasonable accuracy and efficiency.

Probabilistic model and analysis of coupled train-ballasted track-subgrade system with uncertain structural parameters

Random dynamic responses caused by the uncertainty of structural parameters of the coupled train-ballasted track-subgrade system under train loading can pose safety concerns to the train operation.This paper introduced a computational model for analyzing probabilistic dynamic responses of three-dimensional(3D)coupled train-ballasted track-subgrade system(TBTSS),where the coupling effects of uncertain rail irregularities,stiffness and damping properties of ballast and subgrade layers were simultaneously considered.The number theoretical method(NTM)was employed to design discrete points for the multi-dimensional stochastic parameters.The time-histories of stochastic dynamic vibrations of the TBSS with systematically uncertain structural parameters were calculated accurately and efficiently by employing the probability density evolution method(PDEM).The model-predicted results were consistent with those by the Monte Carlo simulation method.A sensitivity study was performed to assess the relative importance of those uncertain structural parameters,based on which a case study was presented to explore the stochastic probability evolution mechanism of such train-ballasted track-subgrade system.

Pilot Domain NOMA for Grant-Free Massive Random Access in Massive MIMO Marine Communication System

We propose a pilot domain non-orthogonal multiple access(NOMA)for uplink massive devices grant-free random access scenarios in massive multiple-input multiple-output(MIMO)maritime communication systems.These scenarios are characterized by numerous devices with sporadic access behavior,and therefore only a subset of them are active.Due to massive potential devices in the network,it is infeasible to assign a unique orthogonal pilot to each device in advance.In such scenarios,pilot decontamination is a crucial problem.In this paper,the devices are randomly assigned non-orthogonal pilots which are constructed by a linear combination of some orthogonal pilots.We show that a bipartite graph can conveniently describe the interference cancellation(IC)processes of pilot decontamination.High spectrum efficiency(SE)and low outage probability can be obtained by selecting the numbers of orthogonal pilots according to the given probability distribution.Numerical evaluatioDs show that the proposed pilot domain NOMA decreases the outage probability from 20%to 2 e-12 at the SE of 4 bits/s/Hz for a single device,compared to the conventional method of slotted ALOHA with 1024 antennas at the BS,or increases the spectrum efficiency from 1.2 bits/s/Hz to 4 bit/s/Hz at the outage probability of2 e-12 in contrast with the Welch bound equality(WBE)non-orthogonal pilots.

Serviceability evaluation of water supply networks under seismic loads utilizing their operational physical mechanism

The serviceability of water supply networks(WSNs)under seismic loads has significant importance for estimating the probable losses and the impact of diminished functionality on affected communities.The innovation presented in this paper is suggesting a new strategy to evaluate the seismic serviceability of WSNs,utilizing their operational physical mechanism.On one hand,this method can obtain the seismic serviceability of each node as well as entire WSNs.On the other hand,this method can dynamically reflect the propagation of randomness from ground motions to WSNs.First,a finite element model is established to capture the seismic response of buried pipe networks,and a leakage model is suggested to obtain the leakage area of WSNs.Second,the transient flow analysis of WSNs with or without leakage is derived to obtain dynamic water flow and pressure.Third,the seismic serviceability of WSNs is analyzed based on the probability density evolution method(PDEM).Finally,the seismic serviceability of a real WSN in Mianzhu city is assessed to illustrate the method.The case study shows that randomness from the ground motions can obviously affect the leakage state and the probability density of the nodal head during earthquakes.