The rate of convergence on fractional power dissipative operator on some sobolev type spaces

In[3],Chen,Deng,Ding and Fan proved that the fractional power dissipative operator is bounded on Lebesgue spaces Lp(Rn),Hardy spaces Hp(Rn)and general mixed norm spaces,which implies almost everywhere convergence of such operator.In this paper,we study the rate of convergence on fractional power dissipative operator on some sobolev type spaces.

A Whale Optimization Algorithm with Distributed Collaboration and Reverse Learning Ability

Due to the development of digital transformation,intelligent algorithms are getting more and more attention.The whale optimization algorithm(WOA)is one of swarm intelligence optimization algorithms and is widely used to solve practical engineering optimization problems.However,with the increased dimensions,higher requirements are put forward for algorithm performance.The double population whale optimization algorithm with distributed collaboration and reverse learning ability(DCRWOA)is proposed to solve the slow convergence speed and unstable search accuracy of the WOA algorithm in optimization problems.In the DCRWOA algorithm,the novel double population search strategy is constructed.Meanwhile,the reverse learning strategy is adopted in the population search process to help individuals quickly jump out of the non-ideal search area.Numerical experi-ments are carried out using standard test functions with different dimensions(10,50,100,200).The optimization case of shield construction parameters is also used to test the practical application performance of the proposed algo-rithm.The results show that the DCRWOA algorithm has higher optimization accuracy and stability,and the convergence speed is significantly improved.Therefore,the proposed DCRWOA algorithm provides a better method for solving practical optimization problems.

Research on Narrowband Line Spectrum Noise Control Method Based on Nearest Neighbor Filter and BP Neural Network Feedback Mechanism

Thefilter-x least mean square(FxLMS)algorithm is widely used in active noise control(ANC)systems.However,because the algorithm is a feedback control algorithm based on the minimization of the error signal variance to update thefilter coefficients,it has a certain delay,usually has a slow convergence speed,and the system response time is long and easily affected by the learning rate leading to the lack of system stability,which often fails to achieve the desired control effect in practice.In this paper,we propose an active control algorithm with near-est-neighbor trap structure and neural network feedback mechanism to reduce the coefficient update time of the FxLMS algorithm and use the neural network feedback mechanism to realize the parameter update,which is called NNR-BPFxLMS algorithm.In the paper,the schematic diagram of the feedback control is given,and the performance of the algorithm is analyzed.Under various noise conditions,it is shown by simulation and experiment that the NNR-BPFxLMS algorithm has the following three advantages:in terms of performance,it has higher noise reduction under the same number of sampling points,i.e.,it has faster convergence speed,and by computer simulation and sound pipe experiment,for simple ideal line spectrum noise,compared with the convergence speed of NNR-BPFxLMS is improved by more than 95%compared with FxLMS algorithm,and the convergence speed of real noise is also improved by more than 70%.In terms of stability,NNR-BPFxLMS is insensitive to step size changes.In terms of tracking performance,its algorithm responds quickly to sudden changes in the noise spectrum and can cope with the complex control requirements of sudden changes in the noise spectrum.

An Adaptive Fruit Fly Optimization Algorithm for Optimization Problems

In this paper, we present a new fruit fly optimization algorithm with the adaptive step for solving unconstrained optimization problems, which is able to avoid the slow convergence and the tendency to fall into local optimum of the standard fruit fly optimization algorithm. By using the information of the iteration number and the maximum iteration number, the proposed algorithm uses the floor function to ensure that the fruit fly swarms adopt the large step search during the olfactory search stage which improves the search speed;in the visual search stage, the small step is used to effectively avoid local optimum. Finally, using commonly used benchmark testing functions, the proposed algorithm is compared with the standard fruit fly optimization algorithm with some fixed steps. The simulation experiment results show that the proposed algorithm can quickly approach the optimal solution in the olfactory search stage and accurately search in the visual search stage, demonstrating more effective performance.

Improved particle swarm optimization based on particles' explorative capability enhancement

Accelerating the convergence speed and avoiding the local optimal solution are two main goals of particle swarm optimization（PSO）. The very basic PSO model and some variants of PSO do not consider the enhancement of the explorative capability of each particle. Thus these methods have a slow convergence speed and may trap into a local optimal solution. To enhance the explorative capability of particles, a scheme called explorative capability enhancement in PSO（ECE-PSO） is proposed by introducing some virtual particles in random directions with random amplitude. The linearly decreasing method related to the maximum iteration and the nonlinearly decreasing method related to the fitness value of the globally best particle are employed to produce virtual particles. The above two methods are thoroughly compared with four representative advanced PSO variants on eight unimodal and multimodal benchmark problems. Experimental results indicate that the convergence speed and solution quality of ECE-PSO outperform the state-of-the-art PSO variants.

Effect of spatial spectrum overlap on Fourier ptychographic microscopy

Fourier ptychographic microscopy(FPM)is a newly developed imaging technique which stands out by virtue of its high-resolution and wide FOV.It improves a microscope's imaging perfor-mance beyond the diffraction limit of the employed optical components by illuminating the sample with oblique waves of different incident angles,similar to the concept of synthetic aperture.We propose to use an objective lens with high-NA to generate oblique illuminating waves in FPM.We demonstrate utilizing an objective lens with higher NA to iluminate the sample leads to better resolution by simulations,in which a resolution of 0.28 pum is achieved by using a high-NA illuminating objective lens(NA=1.49)and a low-NA collecting objective lens(NA=0.2)in coherent imaging(λ=488 nm).We then deeply study FPM's exact relevance of convergence speed to spatial spectrum overlap in frequency domain.The simulation results show that an overlap of about 60%is the optimal choice to acquire a high-quality recovery(520*520 pixels)with about 2 min's computing time.In addition,we testify the robustness of the algorithm of FPM to additive noises and its suitability for phase objects,which further proves FPM's potential application in biomedical imaging.

Collaborative beamforming based on directional perturbation using one bit feedback

A novel collaborative beamforming algorithm is proposed in a wireless communication system with multiple transmitters and one receiver. All transmitters take part in the collaboration and the weighted message is transmitted simultaneously. In order to maximize the beamforming gain, the transmitters use one bit feedback information to adjust the phase offset. It tracks the direction in which the signal strength at the receiver can increase. The directional search and perturbation theory is used to achieve the phase alignment. The feasibility of the proposed algorithm is proved both experimentally and theoretically. Simulation results show that the proposed algorithm can improve the convergent speed of the phase alignment.

Model free optimization of building cooling water systems with refined action space

Deep Q Network(DQN)is an efficient model-free optimization method,and has the potential to be used in building cooling water systems.However,due to the high dimension of actions,this method requires a complex neural network.Therefore,both the required number of training samples and the length of convergence period are barriers for real application.Furthermore,penalty function based exploration may lead to unsafe actions,causing the application of this optimization method even more difficult.To solve these problems,an approach to limit the action space within a safe area is proposed in this paper.First of all,the action space for cooling towers and pumps are separated into two sub-regions.Secondly,for each type of equipment,the action space is further divided into safe and unsafe regions.As a result,the convergence speed is significantly improved.Compared with the traditional DQN method in a simulation environment validated by real data,the proposed method is able to save the convergence time by 1 episode(one cooling season).The results in this paper suggest that,the proposed DQN method can achieve a much quicker learning speed without any undesired consequences,and therefore is more suitable to be used in projects without pre-learning stage.

Replica horizontal-shuffled iterative decoding of low-density parity-check codes

For practical considerations,it is essential to accelerate the convergence speed of the decoding algorithm used in an iterative decoding system. In this paper,replica versions of horizontal-shuffled decoding algorithms for low-density parity-check （LDPC） codes are proposed to improve the convergence speed of the original versions. The extrinsic information transfer （EXIT） chart technique is extended to the proposed algorithms to predict their convergence behavior. Both EXIT chart analysis and numerical results show that replica plain horizontal-shuffled （RPHS） decoding converges much faster than both plain horizontal-shuffled （PHS） decoding and the standard belief-propagation （BP） decoding. Furthermore,it is also revealed that replica group horizontal-shuffled （RGHS） decoding can increase the parallelism of RPHS decoding as well as preserve its high convergence speed if an equivalence condition is satisfied,and is thus suitable for hardware implementation.

Digital and analog hybrid control in adaptive interference cancellation system

The digital proportion control is introduced to improve the performance of the analog adaptive interference cancellation system （ICS）. For the high frequency parts of the signals after multiplier are not required,the sampling frequency need not satisfy the sampling theorem for high frequency. Because the sampling,calculation and output expend time in digital control,the ideal condition,delay condition and delay-wait condition are taken into account. Through analyzing the system model with three conditions,we gain the stable conditions of the system,the optimization step factors that can make the system converge fastest and the formulas of the interference cancellation ratios （ICRs）. One step convergence can be accomplished under ideal condition,whereas the system can not converge in one step under delay condition and delay-wait condition. The calculation results show the convergence speed of delay-wait condition is slower than that of delay condition. The ICR is improved with the increase of the step factor which is in stable bound,but the convergence speed is decreased if the step factor exceeds the optimization step factor. In order to avoid that confine,the method of amending the steady state weight to improve the ICR is proposed. The analyses are in agreement with the computer simulations.

Piecewise Linear Weighted Iterative Algorithm for Beam Alignment in Scanning Beam Interference Lithography

To obtain a good interference fringe contrast and high fidelity,an automated beam iterative alignment is achieved in scanning beam interference lithography(SBIL).To solve the problem of alignment failure caused by a large beam angle(or position)overshoot exceeding the detector range while also speeding up the convergence,a weighted iterative algorithm using a weight parameter that is changed linearly piecewise is proposed.The changes in the beam angle and position deviation during the alignment process based on different iterative algorithms are compared by experiment and simulation.The results show that the proposed iterative algorithm can be used to suppress the beam angle(or position)overshoot,avoiding alignment failure caused by over-ranging.In addition,the convergence speed can be effectively increased.The algorithm proposed can optimize the beam alignment process in SBIL.

Spherical harmonic series solution of fields excited by vertical electric dipole in earth-ionosphere cavity

The spherical harmonic series expression of electromagnetic fields excited by ELF/SLF vertical electric dipole in the spherical earth-ionosphere cavity is derived when the earth and ionosphere are regarded as non-ideal conductors.A method of speeding numerical convergence has been presented.The electromagnetic fields in the cavity are calculated by this algorithm,and the results show that the electromagnetic fields between the earth and the ionosphere are the sum of two traveling waves in the SLF band.Moreover,the results are in complete agreement with that of the well-known spherical second-order approximation in the SLF band.The electromagnetic fields in the cavity are a type of standing wave in the ELF band and the variation of the amplitude versus frequency coincides with Schumann’s resonance.