Temporally Preserving Latent Variable Models:Offline and Online Training for Reconstruction and Interpretation of Fault Data for Gearbox Condition Monitoring

Latent variable models can effectively determine the condition of essential rotating machinery without needing labeled data.These models analyze vibration data via an unsupervised learning strategy.Temporal preservation is necessary to obtain an informative latent manifold for the fault diagnosis task.In a temporalpreserving context,two approaches exist to develop a condition-monitoring methodology:offline and online.For latent variable models,the available training modes are not different.While many traditional methods use offline training,online training can dynamically adjust the latent manifold,possibly leading to better fault signature extraction from the vibration data.This study explores online training using temporal-preserving latent variable models.Within online training,there are two main methods:one focuses on reconstructing data and the other on interpreting the data components.Both are considered to evaluate how they diagnose faults over time.Using two experimental datasets,the study confirms that models from both training modes can detect changes in machinery health and identify faults even under varying conditions.Importantly,the complementarity of offline and online models is emphasized,reassuring their versatility in fault diagnostics.Understanding the implications of the training approach and the available model formulations is crucial for further research in latent variable modelbased fault diagnostics.

Feature Extraction Method Based on Pseudo-Wigner-Ville Distribution for Rotational Machinery in Variable Operating Conditions

In the case of fault diagnosis for roller bearings, the conventional diagnosis approaches by using the time interval of energy impacts in time-frequency distribution or the pass-frequencies are based on the assumption that machinery operates under a constant rotational speed. However, when the rotational speed varies in the broader range, the pass-frequencies vary with the change of rotational speed and bearing faults cannot be identified by the interval of impacts. Researches related to automatic diagnosis for rotational machinery in variable operating conditions were quite few. A novel automatic feature extraction method is proposed based on a pseudo-Wigner-Ville distribution （PWVD） and an extraction of symptom parameter （SP）. An extraction method for instantaneous feature spectrum is presented using the relative crossing information （RCI） and sequential inference approach, by which the feature spectrum from time-frequency distribution can be automatically, sequentially extracted. The SPs are considered in the frequency domain using the extracted feature spectrum to identify among the conditions of a machine. A method to obtain the synthetic symptom parameter is also proposed by the least squares mapping （LSM） technique for increasing the diagnosis sensitivity of SP. Practical examples of diagnosis for bearings are given in order to verify the effectiveness of the proposed method. The verification results show that the features of bearing faults, such as the outer-race, inner-race and roller element defects have been effectively extracted, and the proposed method can be used for condition diagnosis of a machine under the variable rotational speed.

GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS

A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.

Establishment of Dynamic Model for Axle Box Bearing of High-Speed Trains Under Variable Speed Conditions

In this study,a dynamic model for the bearing rotor system of a high-speed train under variable speed conditions is established.In contrast to previous studies,the contact stress is simplifed in the proposed model and the compensation balance excitation caused by the rotor mass eccentricity considered.The angle iteration method is used to overcome the challenge posed by the inability to determine the roller space position during bearing rotation.The simulation results show that the model accurately describes the dynamics of bearings under varying speed profles that contain acceleration,deceleration,and speed oscillation stages.The order ratio spectrum of the bearing vibration signal indicates that both the single and multiple frequencies in the simulation results are consistent with the theoretical results.Experiments on bearings with outer and inner ring faults under various operating conditions are performed to verify the developed model.

The Condenser Performance Test and Thermal Performance Analysis of Variable Conditions in TQNPC

Condenser is one of the important auxiliary equipments in nuclear power plants. The thermal efficiency of the entire unit was depended on the condenser performance. Cleanliness factor and condenser corrected pressure are the two most important evaluation indexes. The definition and derivation of these two evaluation indexes were elaborated and clarified in this paper. And the condenser performance at variable conditions was analyzed. The seawater temperature, pipe plugging rate and seawater volume rate effect on unit output was calculated. The calculation method was simple, which can provide reference guidance for similar power plant.

Classification random forest with exact conditioning for spatial prediction of categorical variables

Machine learning methods are increasingly used for spatially predicting a categorical target variable when spatially exhaustive predictor variables are available within the study region.Even though these methods exhibit competitive spatial prediction performance,they do not exactly honor the categorical target variable's observed values at sampling locations by construction.On the other side,competitor geostatistical methods perfectly match the categorical target variable's observed values at sampling locations by essence.In many geoscience applications,it is often desirable to perfectly match the observed values of the categorical target variable at sampling locations,especially when the categorical target variable's measurements can be reasonably considered error-free.This paper addresses the problem of exact conditioning of machine learning methods for the spatial prediction of categorical variables.It introduces a classification random forest-based approach in which the categorical target variable is exactly conditioned to the data,thus having the exact conditioning property like competitor geostatistical methods.The proposed method extends a previous work dedicated to continuous target variables by using an implicit representation of the categorical target variable.The basic idea consists of transforming the ensemble of classification tree predictors'(categorical)resulting from the traditional classification random forest into an ensemble of signed distances(continuous)associated with each category of the categorical target variable.Then,an orthogonal representation of the ensemble of signed distances is created through the principal component analysis,thus allowing to reformulate the exact conditioning problem as a system of linear inequalities on principal component scores.Then,the sampling of new principal component scores ensuring the data's exact conditioning is performed via randomized quadratic programming.The resulting conditional signed distances are turned out into an ensemble of categorical outputs,which perfectly honor the categorical target variable's observed values at sampling locations.Then,the majority vote is used to aggregate the ensemble of categorical outputs.The effectiveness of the proposed method is illustrated on a simulated dataset for which ground-truth is available and showcased on a real-world dataset,including geochemical data.A comparison with geostatistical and traditional machine learning methods show that the proposed technique can perfectly match the categorical target variable's observed values at sampling locations while maintaining competitive out-of-sample predictive performance.

Necessary Conditions and Situational Variables of Payments for Ecosystem Services

Clarifying the necessary conditions for the emergence of payments for ecosystem services (PES) and the situational variables that affect PES is the basis for their interpretation, prediction, and selection. This article proposes an analytical framework for the emergence of PES and argues that the key to determining whether PES can occur and whether a selected PES program is appropriate is to evaluate the net gain. When payers anticipate that a PES program will provide a satisfactory number of ES and a net gain over the opportunity cost and will cover all costs, it is assumed that the program will be implemented. When it is difficult to accurately evaluate the net gain of PES, the situational variables that affect the costs and benefits need to be examined. The group characteristics, ES characteristics, spatial and temporal contacts between the suppliers and demanders, correlation with private goods and additionality are important situational variables that affect the emergence and choice of PES.

Research on the dynamic response of connecting rod bearing bush wear of reciprocating machine under variable working conditions

As a type of reciprocating machine, the reciprocating compressor has a compact structure and many excitation sources.Once the small end bearing of the connecting rod is worn, it is easy to cause the sintering of the bearing and the abnormal vibration of the body.Based on the characteristics of poor lubrication state and complex force of connecting rod small head bearing, a mixed lubrication model considering oil groove feed was established, and the dynamic simulation of the reciprocating compressor model with lubricated bearings was carried out;considering different speeds and gas load conditions, the law of the impact of the eigenvalues changing with working conditions was explored.The fault simulation experiment was carried out by selecting representative working conditions, which verified the correctness of the simulation method.The study found that two contact collisions between the pin and the bearing bush occurred in one cycle, the collision impact was more severe under the wear fault, and the existence of the gap made the dynamic response more sensitive to the change of working conditions.This research provides ideas for the location and feature extraction of fault symptom signal angular segments in the process of complex measured signal processing.

Some Necessary and Sufficient Condition of Multivariate Random Variable Satisfy Normal Distribution

In this paper,we extended some results of article[1],obtain some sufficient and necessary condition which multivariate random variable satisfy normal distribution.

Determination of Dynamic Load Condition of Aircraft Carrier based on Multivariable Distribution of Flight Parameters

In order to solve the design problem of dynamic load of a carrier-based aircraft,according to the relevant criteria of national military standards,eight key flight parameters of the dynamic load conditions for the aircraft carrier were selected.Based on the multivariable distribution data of landing flight parameters obtained from flight test,the distribution form and range limitation of each flight parameter were determined by using the probability distribution of each flight parameter and the spatial relationship among variables.Furthermore,100000 sets of data were constructed to simulate the landing condition of aircraft in the form of random number.After the envelope is screened by multivariable joint probability distribution,the boundary conditions were compared and merged,and finally the dynamic load conditions were obtained.In this paper,a set of dynamic load condition design method based on the aircraft requirements is constructed,which systematically covers all kinds of situations that occur in the process of aircraft landing,and improves the conventional design process of aircraft dynamic load.

Performance analysis of continuous-variable measurement-device-independent quantum key distribution under diverse weather conditions

The effects of weather conditions are ubiquitous in practical wireless quantum communication links.Here in this work,the performances of atmospheric continuous-variable measurement-device-independent quantum key distribution(CV-MDI-QKD)under diverse weather conditions are analyzed quantitatively.According to the Mie scattering theory and atmospheric CV-MDI-QKD model,we numerically simulate the relationship between performance of CV-MDI-QKD and the rainy and foggy conditions,aiming to get close to the actual combat environment in the future.The results show that both rain and fog will degrade the performance of the CV-MDI-QKD protocol.Under the rainy condition,the larger the raindrop diameter,the more obvious the extinction effect is and the lower the secret key rate accordingly.In addition,we find that the secret key rate decreases with the increase of spot deflection distance and the fluctuation of deflection.Under the foggy condition,the results illustrate that the transmittance decreases with the increase of droplet radius or deflection distance,which eventually yields the decrease in the secret key rate.Besides,in both weather conditions,the increase of transmission distance also leads the secret key rate to deteriorate.Our work can provide a foundation for evaluating the performance evaluation and successfully implementing the atmospheric CV-MDI-QKD in the future field operation environment under different weather conditions.

Existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p(x)-Laplacian with Neumann Boundary Condition

We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.

GLOBAL CONVERGENCE OF A CLASS OF OPTIMALLY CONDITIONED SSVM METHODS

This paper explores the convergence of a class of optimally conditioned self scaling variable metric (OCSSVM) methods for unconstrained optimization. We show that this class of methods with Wolfe line search are globally convergent for general convex functions.

PROPER CONDITIONS OF MESHING FOR Hy-Vo SILENT CHAIN AND SPROCKET

Proper meshing of Hy-Vo silent chain and sprocket is important for realizing the transmission of the silent chain with more efficiency and less noise. Based on the study of the meshing theory of the Hy-Vo silent chain with the sprocket and the roll cutting machining principle of the sprocket with the hob, the proper conditions of the meshing for the Hy-Vo silent chain and the sprocket are put forward with the variable pitch characteristic of the Hy-Vo silent chain taken into consideration, and the proper meshing design method on the condition that the value of the link tooth pressure angle is unequal to the value of the sprocket tooth pressure angle is studied. Experiments show that this new design method is feasible. In addition, the design of the pitch, the sprocket tooth pressure angle and the fillet radius of the sprocket addendum circle are studied. It is crucial for guiding the design of the hob which cuts the Hy-Vo silent chain sprocket.

The derivative-dependent functional variable separation for the evolution equations

This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt = A（u, ux）uxx＋B（u, ux, ut） which admits the derivative- dependent functional separable solutions （DDFSSs）. We also extend the concept of the DDFSS to cover other variable separation approaches.

A Trend towards a Stable Warm and Windless State of the Surface Weather Conditions in Northern and Northeastern China during 1961–2014

This study investigates the trends in the mean state and the day-to-day variability （DDV） of the surface weather conditions over northern and northeastern China （NNEC） during 1961-2014 using CN05.1 observational data. In this study, we show that the surface temperature （wind speed） has increased （decreased） over NNEC and that the DDV of the surface temperatures and wind speeds has decreased, indicating a trend towards a stable warm and windless state of the surface weather conditions over NNEC. This finding implies a trend towards more persistent hot and windless episodes, which threaten human health and aggravate environmental problems. The trends are also examined in reanalysis data. Both the ERA-40 and the NCEP data show an increasing （decreasing） trend in the mean state of the surface temperatures （wind speeds）. However, the reanalysis data show a consistent decreasing trend in the DDV of the surface weather conditions only in the spring. The underlying reason for the decreased DDV of the surface weather conditions is further analyzed, focusing on the spring season. Essentially, the decreased DDV of the surface weather conditions can be attributed to a decrease in synoptic-scale wave activity, which is caused by a decrease in the baroclinic instability. There is a contrasting change in the baroclinic instability over East Asia, showing a decreasing （increasing） trend north （south） of 40°N. This contrasting change in the baroclinic instability is primarily caused by a tropospheric cooling zone over East Asia at approximately 40°N, which influences the meridional temperature gradient over East Asia.

Functional Variable Separation for Extended Nonlinear Elliptic Equations

This paper is devoted to the study of functional variable separation for extended nonlinear elliptic equations. By applying the functional variable separation approach to extended nonlinear elliptic equations via the generalized conditional symmetry, we obtain complete classification of those equations which admit functional separable solutions （FSSs） and construct some exact FSSs to the resulting equations.

Hypersingular parameterized Marcinkiewicz integrals with variable kernels on Sobolev and Hardy-Sobolev spaces

Let α≥ 0 and 0 〈 ρ ≤ n/2, the boundedness of hypersingular parameterized Marcinkiewicz integrals μΩ,α^ρ with variable kernels on Sobolev spaces Lα^ρ and HardySobolev spaces Hα^ρ is established.

Extension of Variable Separable Solutions for Nonlinear Evolution Equations

We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.

Acoustic finite-difference modeling beyond conventional Courant-Friedrichs-Lewy stability limit:Approach based on variable-length temporal and spatial operators

Conventional finite-difference(FD)methods cannot model acoustic wave propagation beyond Courant-Friedrichs-Lewy(CFL)numbers 0.707 and 0.577 for two-dimensional(2D)and three-dimensional(3D)equal spacing cases,respectively,thereby limiting time step selection.Based on the definition of temporal and spatial FD operators,we propose a variable-length temporal and spatial operator strategy to model wave propagation beyond those CFL numbers while preserving accuracy.First,to simulate wave propagation beyond the conventional CFL stability limit,the lengths of the temporal operators are modified to exceed the lengths of the spatial operators for high-velocity zones.Second,to preserve the modeling accuracy,the velocity-dependent lengths of the temporal and spatial operators are adaptively varied.The maximum CFL numbers for the proposed method can reach 1.25 and 1.0 in high velocity contrast 2D and 3D simulation examples,respectively.We demonstrate the effectiveness of our method by modeling wave propagation in simple and complex media.