SOLUTIONS OF THE GENERALn－TH ORDER VARIABLE COEFFICIENTS LINEAR DIFFERENCE EQUATION

In this paper.variable operator and its product with shifting operator are studied.The product of power series of shifting operator with variable coefficient is defined andits convergence is proved under Mikusinski’s sequence convergence.After turning ageneral variable coefficient linear difference equation of order n into a set of operatorequations.we can obtain the solutions of the general n-th order variable coefficientlinear difference equation.

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.

Effect of some operational variables on bubble size in a pilot-scale mechanical flotation machine

This work aims to provide a relationship of how the key operational variables of frother type and impeller speed affect the size of bubble （D32）. The study was performed using pilot-scale equipment （0.8 m^3） that is up to two orders of magnitude larger than equipment used for studies performed to date by others, and incorporated the key process variables of frother type and impeller speed. The results show that each frother family exhibits a unique CCC95-HLB relationship dependent on n （number of C-atoms in alkyl group） and m （number of propylene oxide group）. Empirical models were developed to predict CCC95 from HLB associated with other two parameters a and ft. The impeller speed-bubble size tests show that D32 is unaffected by increased impeller tip speed across the range of 4.6 to 9.2 m/s （representing the industrial operating range）, although D32 starts to increase below 4.6 m/s. The finding is valid for both coalescing and non-coalescing conditions. The results suggest that the bubble size and bubble size distribution （BSD） being created do not change with increasing impeller speed in the quiescent zone of the flotation.

Deterministic Quantum Secure Direct Communication with Dense Coding and Continuous Variable Operations

We propose a deterministic quantum secure direct two check photon sequences are used to check the securities of the communication protocol by using dense coding. The channels between the message sender and the receiver. The continuous variable operations instead of the usual discrete unitary operations are performed on the travel photons so that the security of the present protocol can be enhanced. Therefore some specific attacks such as denial-of-service attack, intercept-measure-resend attack and invisible photon attack can be prevented in ideal quantum channel. In addition, the scheme is still secure in noise channel. Furthurmore, this protocol has the advantage of high capacity and can be realized in the experiment.

Assessment of the Influence of Torrefied Biomass Physical Characteristics, Design and Operating Variables on Gasification Efficiency

Gasification efficiency is an important factor that determines the actual technical operation as well as the economic viability of using a gasifier system for energy production. In this study, the impact of the physical properties of torrefied bagasse and the influence of gasifier design and operating variables were investigated in a computer simulated downdraft gasification system. Results obtained from the study indicated an interrelationship between feedstock characteristics, especially with regard to feed size, design variables such as throat angle and throat diameter as well as gasifier operating conditions such as temperature of input air and feed input. These variables influenced the efficiency of the gasification process of sugarcane bagasse because of increased enhancement of combustion zone reactions, which liberated huge amount of heat that led to a rise in the temperature of the gasification process. This condition also created increased tar cracking within the gasification system, contributing to reduction in the overall yield of tar.

Littlewood-Paley operators with variable kernels

In this paper we study a certain directional Hilbert transform and the boundedness on some mixed norm spaces. As one of applications, we prove the Lp-boundedness of the Littlewood-Paley operators with variable kernels. Our results are extensions of some known theorems.

Decentralized damage diagnostic technique for tall buildings using VARMAX model

Civil infrastructure,especially buildings,are becoming more slender,tall,and multipurpose,creating a need to continuously monitor their health to ensure the safety and security of human lives and assets.While the majority of structural health monitoring techniques use measurements from the entire structure,in this study,an output-only damage diagnostic technique using a decentralized concept(subdomain-based)for tall buildings and employing a vector form of the autoregressive moving average with exogenous input(VARMAX)model is proposed,which offers reduced instrumentation and data handling requirements.Unlike other decentralized approaches,this technique predicts more than one DOF at a time so the number of subdomains required for the diagnosis of the complete structure is minimized.The proposed subdomain-based damage diagnostic algorithm works with ambient loads and does not require any correlated numerical models since it is solely based on measured data.The proposed algorithm can identify the time instant of damage,spatial location(s)and characterize the damage intensity.Efforts have been made to account for confounding factors such as environmental and operational variabilities separate from measurement noise to avoid false positive alarms.The effectiveness of the proposed technique is illustrated using synthetic time history responses from a twenty-story framed structure under ambient loading and an experimental study on a ten-story framed structure.Both numerical and experimental investigations confirm the effectiveness of the method and its robustness to environmental/operational variabilities and measurement noise.

A novel fractional grey forecasting model with variable weighted buffer operator and its application in forecasting China's crude oil consumption

Oil is an important strategic material and civil energy.Accurate prediction of oil consumption can provide basis for relevant departments to reasonably arrange crude oil production,oil import and export,and optimize the allocation of social resources.Therefore,a new grey model FENBGM(1,1)is proposed to predict oil consumption in China.Firstly,the grey effect of the traditional GM(1,1)model was transformed into a quadratic equation.Four different parameters were introduced to improve the accuracy of the model,and the new initial conditions were designed by optimizing the initial values by weighted buffer operator.Combined with the reprocessing of the original data,the scheme eliminates the random disturbance effect,improves the stability of the system sequence,and can effectively extract the potential pattern of future development.Secondly,the cumulative order of the new model was optimized by fractional cumulative generation operation.At the same time,the smoothness rate quasi-smoothness condition was introduced to verify the stability of the model,and the particle swarm optimization algorithm(PSO)was used to search the optimal parameters of the model to enhance the adaptability of the model.Based on the above improvements,the new combination prediction model overcomes the limitation of the traditional grey model and obtains more accurate and robust prediction results.Then,taking the petroleum consumption of China's manufacturing industry and transportation,storage and postal industry as an example,this paper verifies the validity of FENBGM(1,1)model,analyzes and forecasts China's crude oil consumption with several commonly used forecasting models,and uses FENBGM(1,1)model to forecast China's oil consumption in the next four years.The results show that FENBGM(1,1)model performs best in all cases.Finally,based on the prediction results of FENBGM(1,1)model,some reasonable suggestions are put forward for China's oil consumption planning.

Component modeling and updating method of integrated energy systems based on knowledge distillation

Amid the backdrop of carbon neutrality, traditional energy production is transitioning towards integrated energy systems (IES), where model-based scheduling is key in scenarios with multiple uncertainties on both supply and demand sides. The development of artificial intelligence algorithms, has resolved issues related to model accuracy. However, under conditions of high proportion renewable energy integration, component load adjustments require increased flexibility, so the mathematical model of the component must adapt to constantly changing operating conditions. Therefore, the identification of operating condition changes and rapid model updating are pressing issues. This study proposes a modeling and updating method for IES components based on knowledge distillation. The core of this modeling method is the light weighting of the model, which is achieved through a knowledge distillation method, using a teacher-student mode to compress complex neural network models. The triggering of model updates is achieved through principal component analysis. The study also analyzes the impact of model errors caused by delayed model updates on the overall scheduling of IES. Case studies are conducted on critical components in IES, including coal-fired boilers and turbines. The results show that the time consumption for model updating is reduced by 76.67 % using the proposed method. Under changing conditions, compared with two traditional models, the average deviation of this method is reduced by 12.61 % and 3.49 %, respectively, thereby improving the model's adaptability. The necessity of updating the component model is further analyzed, as a 1.00 % mean squared error in the component model may lead to a power deviation of 0.075 MW. This method provides real-time, adaptable support for IES data modeling and updates.

Application of Transfer Learningin Mechanical Equipment Intelligent Diagnosis:Literature Review

Accelerating the process of intelligent manufacturing and the demand for new industrial productivity,the operating conditions of machinery and equipment have become ever more severe.As an important link to ensure the stable operation of the production process,the condition monitoring and fault diagnosis of equipment have become equally important.The fault diagnosis of equipment in actual production is often challenged by variable working conditions,large differences in data distribution,and lack of labeled samples,etc.Traditional fault diagnosis methods are often difficult to achieve ideal results in these complex environments.Transfer learning(TL)as an emerging technology can effectively utilize existing knowledge and data to improve the diagnostic performance.Firstly,this paper analyzes the trend of mechanical equipment fault diagnosis and explains the basic concept of TL.Then TL based on parameters,TL based on features,TL based on instances and domain adaptive(DA)methods are summarized and analyzed in terms of existing TL methods.Finally,the problems faced in the current TL research are summarized and the future development trend is pointed out.This review aims to help researchers in related fields understand the latest progress of TL and promote the application and development of TL in mechanical equipment diagnosis.

Existence results for degenerate p(x)-Laplace equations with Leray-Lions type operators

We show the existence and multiplicity of solutions to degenerate p(x)-Laplace equations with Leray-Lions type operators using direct methods and critical point theories in Calculus of Variations and prove the uniqueness and nonnegativeness of solutions when the principal operator is monotone and the nonlinearity is nonincreasing. Our operator is of the most general form containing all previous ones and we also weaken assumptions on the operator and the nonlinearity to get the above results. Moreover, we do not impose the restricted condition on p(x) and the uniform monotonicity of the operator to show the existence of three distinct solutions.

Ulam-Hyers stability and analytical approach for m-dimensional Caputo space-time variable fractional order advection-dispersion equation

This article introduces the computational analytical approach to solve the m-dimensional space-time variable Caputo fractional order advection–dispersion equation with the Dirichlet boundary using the two-step Adomian decomposition method and obtain the exact solution in just one iteration.Moreover,with the help of fixed point theory,we study the existence and uniqueness conditions for the positive solution and prove some new results.Also,obtain the Ulam–Hyers stabilities for the proposed problem.Two gen-eralized examples are considered to show the method’s applicability and compared with other existing numerical methods.The present method performs exceptionally well in terms of efficiency and simplicity.Further,we solved both examples using the two most well-known numerical methods and compared them with the TSADM solution.

Computational investigation of hydrodynamics,coal combustion and NOx emissions in a tangentially fired pulverized coal boiler at various loads

This work presents a computational investigation of hydrodynamics,coal combustion and NOx emissions in a tangentially fired pulverized coal boiler at different loads(630,440 and 300 MW;relative loads of 100%,70%and 48%)to clarify the effect of load change on the furnace processes.A computational fluids dynamics model was established;the flow field,temperature profile,species concentration and NOx emissions were predicted numerically;and the influence of burner tilt angles was evaluated.Simulation results indicate that a decrease in boiler load decreases the gas velocity,attenuates the airflow rotations,and increases the tangent circle size.The high-temperature zone and flame moved toward the side walls.Such behaviors impair air-fuel mixing,heat transfer and steady combustion in the furnace.In terms of species concentrations,a decrease in boiler load increased the O2 content,decreased the CO content,and decreased the char burnout rates only slightly.A change in boiler load from 630 to 440 and 300 MW increased the NOx emissions from 202 to 234 and 247 mg/m^(3),respectively.Burner tilt angles are important in coal combustion and NOx emissions.A burner angle of-15°favors heat transfer and low NOx emissions(<185 mg/m^(3))for the current tangentially fired boiler.

Orthogonal transformation operation theorem of a spatial universal uniform rotating magnetic field and its application in capsule endoscopy

According to the anti-phase sine current superposition theorem, the orientation, the magnetic flux density, the angular speed and the rotational direction of the spatial universal rotating magnetic field (SURMF) can be controlled within the tri-axial orthogonal square Helmholtz coils (TOSHC). Nevertheless, three coupling direction angles of the normal vector of the SURMF in the Descartes coordinate system cannot be separately controlled, thus the adjustment of the orientation of the SURMF is difficult and the flexibility of the robotic posture control is restricted. For the dimension reduction and the decoupling of control variables, the orthogonal transformation operation theorem of the SURMF is proposed based on two independent rotation angular variables, which employs azimuth and altitude angles as two variables of the three-phase sine current superposition formula derived by the orthogonal rotation inverse transformation. Then the unique control rules of the orientation and the rotational direction of the SURMF are generalized in each spatial quadrant, thus the scanning of the normal vector of the SURMF along the horizontal or vertical direction can be achieved through changing only one variable, which simplifies the control process of the orientation of the SURMF greatly. To validate its feasibility and maneuverability, experiments were conducted in the animal intestine utilizing the innovative dual hemisphere capsule robot (DHCR) with active and passive modes. It was demonstrated that the posture adjustment and the steering rolling locomotion of the DHCR can be realized through single variable control, thus the orthogonal transformation operation theorem makes the control of the orientation of the SURMF convenient and flexible significantly. This breakthrough will lay a foundation for the human-machine interaction control of the SURMF.