Gradient Optimizer Algorithm with Hybrid Deep Learning Based Failure Detection and Classification in the Industrial Environment

Failure detection is an essential task in industrial systems for preventing costly downtime and ensuring the seamlessoperation of the system. Current industrial processes are getting smarter with the emergence of Industry 4.0.Specifically, various modernized industrial processes have been equipped with quite a few sensors to collectprocess-based data to find faults arising or prevailing in processes along with monitoring the status of processes.Fault diagnosis of rotating machines serves a main role in the engineering field and industrial production. Dueto the disadvantages of existing fault, diagnosis approaches, which greatly depend on professional experienceand human knowledge, intellectual fault diagnosis based on deep learning (DL) has attracted the researcher’sinterest. DL reaches the desired fault classification and automatic feature learning. Therefore, this article designs a Gradient Optimizer Algorithm with Hybrid Deep Learning-based Failure Detection and Classification (GOAHDLFDC)in the industrial environment. The presented GOAHDL-FDC technique initially applies continuous wavelettransform (CWT) for preprocessing the actual vibrational signals of the rotating machinery. Next, the residualnetwork (ResNet18) model was exploited for the extraction of features from the vibration signals which are thenfed into theHDLmodel for automated fault detection. Finally, theGOA-based hyperparameter tuning is performedtoadjust the parameter valuesof theHDLmodel accurately.The experimental result analysis of the GOAHDL-FD Calgorithm takes place using a series of simulations and the experimentation outcomes highlight the better resultsof the GOAHDL-FDC technique under different aspects.

Fractional Gradient Descent RBFNN for Active Fault-Tolerant Control of Plant Protection UAVs

With the increasing prevalence of high-order systems in engineering applications, these systems often exhibitsignificant disturbances and can be challenging to model accurately. As a result, the active disturbance rejectioncontroller (ADRC) has been widely applied in various fields. However, in controlling plant protection unmannedaerial vehicles (UAVs), which are typically large and subject to significant disturbances, load disturbances andthe possibility of multiple actuator faults during pesticide spraying pose significant challenges. To address theseissues, this paper proposes a novel fault-tolerant control method that combines a radial basis function neuralnetwork (RBFNN) with a second-order ADRC and leverages a fractional gradient descent (FGD) algorithm.We integrate the plant protection UAV model’s uncertain parameters, load disturbance parameters, and actuatorfault parameters and utilize the RBFNN for system parameter identification. The resulting ADRC exhibits loaddisturbance suppression and fault tolerance capabilities, and our proposed active fault-tolerant control law hasLyapunov stability implications. Experimental results obtained using a multi-rotor fault-tolerant test platformdemonstrate that the proposed method outperforms other control strategies regarding load disturbance suppressionand fault-tolerant performance.

Improved gradient iterative algorithms for solving Lyapunov matrix equations

In this paper, an improved gradient iterative （GI） algorithm for solving the Lyapunov matrix equations is studied. Convergence of the improved method for any initial value is proved with some conditions. Compared with the GI algorithm, the improved algorithm reduces computational cost and storage. Finally, the algorithm is tested with GI several numerical examples.

HYBRID MULTI-OBJECTIVE GRADIENT ALGORITHM FOR INVERSE PLANNING OF IMRT

The intelligent optimization of a multi-objective evolutionary algorithm is combined with a gradient algorithm. The hybrid multi-objective gradient algorithm is framed by the real number. Test functions are used to analyze the efficiency of the algorithm. In the simulation case of the water phantom, the algorithm is applied to an inverse planning process of intensity modulated radiation treatment （IMRT）. The objective functions of planning target volume （PTV） and normal tissue （NT） are based on the average dose distribution. The obtained intensity profile shows that the hybrid multi-objective gradient algorithm saves the computational time and has good accuracy, thus meeting the requirements of practical applications.

ADAPTIVE EXPONENT SMOOTHING GRADIENT ALGORITHM

A new algorithm, called the adaptive exponent smoothing gradient algorithm (AESGA), is developed from Widrow′s LMS algorithm. It is based on the fact that LMS algorithm has properties of time delaying and low pass filtering. This paper shows that the algorithm, on the domain of {Ω 1:α∈(0,1)}×{Ω 2:β(0,∞)} , unbiasedly and asymptotically converges to the Winner solution when the signal is a stationary Gauss stochastic process. The convergent property and the performance misadjustment are analyzed in theory. And calculation method of the algorithm is also suggested. Numerical results given by computer simulations show that the algorithm is effective.

Improved preconditioned conjugate gradient algorithm and application in 3D inversion of gravity-gradiometry data

With the continuous development of full tensor gradiometer （FTG） measurement techniques, three-dimensional （3D） inversion of FTG data is becoming increasingly used in oil and gas exploration. In the fast processing and interpretation of large-scale high-precision data, the use of the graphics processing unit process unit （GPU） and preconditioning methods are very important in the data inversion. In this paper, an improved preconditioned conjugate gradient algorithm is proposed by combining the symmetric successive over-relaxation （SSOR） technique and the incomplete Choleksy decomposition conjugate gradient algorithm （ICCG）. Since preparing the preconditioner requires extra time, a parallel implement based on GPU is proposed. The improved method is then applied in the inversion of noise- contaminated synthetic data to prove its adaptability in the inversion of 3D FTG data. Results show that the parallel SSOR-ICCG algorithm based on NVIDIA Tesla C2050 GPU achieves a speedup of approximately 25 times that of a serial program using a 2.0 GHz Central Processing Unit （CPU）. Real airbome gravity-gradiometry data from Vinton salt dome （south- west Louisiana, USA） are also considered. Good results are obtained, which verifies the efficiency and feasibility of the proposed parallel method in fast inversion of 3D FTG data.

Comparison between iterative wavefront control algorithm and direct gradient wavefront control algorithm for adaptive optics system

Among all kinds of wavefront control algorithms in adaptive optics systems, the direct gradient wavefront control algorithm is the most widespread and common method. This control algorithm obtains the actuator voltages directly from wavefront slopes through pre-measuring the relational matrix between deformable mirror actuators and Hartmann wavefront sensor with perfect real-time characteristic and stability. However, with increasing the number of sub-apertures in wavefront sensor and deformable mirror actuators of adaptive optics systems, the matrix operation in direct gradient algorithm takes too much time, which becomes a major factor influencing control effect of adaptive optics systems. In this paper we apply an iterative wavefront control algorithm to high-resolution adaptive optics systems, in which the voltages of each actuator are obtained through iteration arithmetic, which gains great advantage in calculation and storage. For AO system with thousands of actuators, the computational complexity estimate is about O(n2) ～ O(n3) in direct gradient wavefront control algorithm, while the computational complexity estimate in iterative wavefront control algorithm is about O(n) ～(O(n)3/2), in which n is the number of actuators of AO system. And the more the numbers of sub-apertures and deformable mirror actuators, the more significant advantage the iterative wavefront control algorithm exhibits.

A Hybrid Conjugate Gradient Algorithm for Solving Relative Orientation of Big Rotation Angle Stereo Pair

The fast convergence without initial value dependence is the key to solving large angle relative orientation.Therefore,a hybrid conjugate gradient algorithm is proposed in this paper.The concrete process is:①stochastic hill climbing(SHC)algorithm is used to make a random disturbance to the given initial value of the relative orientation element,and the new value to guarantee the optimization direction is generated.②In local optimization,a super-linear convergent conjugate gradient method is used to replace the steepest descent method in relative orientation to improve its convergence rate.③The global convergence condition is that the calculation error is less than the prescribed limit error.The comparison experiment shows that the method proposed in this paper is independent of the initial value,and has higher accuracy and fewer iterations.

A Note on Global Convergence Result for Conjugate Gradient Methods

We extend a results presented by Y.F. Hu and C.Storey (1991) [1] on the global convergence result for conjugate gradient methods with different choices for the parameter β k . In this note, the conditions given on β k are milder than that used by Y.F. Hu and C. Storey.

Convergence of gradient method for Elman networks

The gradient method for training Elman networks with a finite training sample set is considered. Monotonicity of the error function in the iteration is shown. Weak and strong convergence results are proved, indicating that the gradient of the error function goes to zero and the weight sequence goes to a fixed point, respectively. A numerical example is given to support the theoretical findings.

Gradient Descent Algorithm for Small UAV Parameter Estimation System

A gradient descent algorithm with adjustable parameter for attitude estimation is developed,aiming at the attitude measurement for small unmanned aerial vehicle(UAV)in real-time flight conditions.The accelerometer and magnetometer are introduced to construct an error equation with the gyros,thus the drifting characteristics of gyroscope can be compensated by solving the error equation utilized by the gradient descent algorithm.Performance of the presented algorithm is evaluated using a self-proposed micro-electro-mechanical system(MEMS)based attitude heading reference system which is mounted on a tri-axis turntable.The on-ground,turntable and flight experiments indicate that the estimation attitude has a good accuracy.Also,the presented system is compared with an open-source flight control system which runs extended Kalman filter(EKF),and the results show that the attitude control system using the gradient descent method can estimate the attitudes for UAV effectively.

Auxiliary Model Based Multi-innovation Stochastic Gradient Identification Methods for Hammerstein Output-Error System

Special input signals identification method based on the auxiliary model based multi-innovation stochastic gradient algorithm for Hammerstein output-error system was proposed.The special input signals were used to realize the identification and separation of the Hammerstein model.As a result,the identification of the dynamic linear part can be separated from the static nonlinear elements without any redundant adjustable parameters.The auxiliary model based multi-innovation stochastic gradient algorithm was applied to identifying the serial link parameters of the Hammerstein model.The auxiliary model based multi-innovation stochastic gradient algorithm can avoid the influence of noise and improve the identification accuracy by changing the innovation length.The simulation results show the efficiency of the proposed method.

Gradient Gene Algorithm: a Fast Optimization Method to MST Problem

The extension of Minimum Spanning Tree(MST) problem is an NP hard problem which does not exit a polynomial time algorithm. In this paper, a fast optimization method on MST problem——the Gradient Gene Algorithm is introduced. Compared with other evolutionary algorithms on MST problem, it is more advanced: firstly, very simple and easy to realize; then, efficient and accurate; finally general on other combination optimization problems.

A UAV collaborative defense scheme driven by DDPG algorithm

The deep deterministic policy gradient(DDPG)algo-rithm is an off-policy method that combines two mainstream reinforcement learning methods based on value iteration and policy iteration.Using the DDPG algorithm,agents can explore and summarize the environment to achieve autonomous deci-sions in the continuous state space and action space.In this paper,a cooperative defense with DDPG via swarms of unmanned aerial vehicle(UAV)is developed and validated,which has shown promising practical value in the effect of defending.We solve the sparse rewards problem of reinforcement learning pair in a long-term task by building the reward function of UAV swarms and optimizing the learning process of artificial neural network based on the DDPG algorithm to reduce the vibration in the learning process.The experimental results show that the DDPG algorithm can guide the UAVs swarm to perform the defense task efficiently,meeting the requirements of a UAV swarm for non-centralization,autonomy,and promoting the intelligent development of UAVs swarm as well as the decision-making process.

A stochastic gradient-based two-step sparse identification algorithm for multivariate ARX systems

We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.

An Accelerated Proximal Gradient Algorithm for Hankel Tensor Completion

In this paper,an accelerated proximal gradient algorithm is proposed for Hankel tensor completion problems.In our method,the iterative completion tensors generated by the new algorithm keep Hankel structure based on projection on the Hankel tensor set.Moreover,due to the special properties of Hankel structure,using the fast singular value thresholding operator of the mode-s unfolding of a Hankel tensor can decrease the computational cost.Meanwhile,the convergence of the new algorithm is discussed under some reasonable conditions.Finally,the numerical experiments show the effectiveness of the proposed algorithm.

Multi-scale seismic full waveform inversion in the frequency-domain with a multi-grid method

Although full waveform inversion in the frequency domain can overcome the local minima problem in the time direction, such problem still exists in the space direction because of the media subsurface complexity. Based on the optimal steep descent methods, we present an algorithm which combines the preconditioned bi-conjugated gradient stable method and the multi-grid method to compute the wave propagation and the gradient space. The multiple scale prosperity of the waveform inversion and the multi-grid method can overcome the inverse problems local minima defect and accelerate convergence. The local inhomogeneous three-hole model simulated results and the Marmousi model certify the algorithm effectiveness.

Multi-channel blind deconvolution algorithm for multiple-input multiple-output DS/CDMA system

Direct sequence spread spectrum transmission can be realized at low SNR, and has low probabilityof detection. It is aly problem how to obtain the original users＇ signal in a non-cooperative context. In practicality, the DS/CDMA sources received are linear convolute mixing. A more complex multichannel blind deconvolution MBD algorithm is required to achieve better source separation. An improved MBD algorithm for separating linear convolved mixtures of signals in CDMA system is proposed. This algorithm is based on minimizing the average squared cross-output-channel-correlation. The mixture coefficients are totally unknown, while some knowledge about temporal model exists. Results show that the proposed algorithm can bring about the exactness and low computational complexity.

Preconditioned BiCGSTAB algorithm and its applications to eddy current solutions

A new favorable iterative algorithm named as PBiCGSTAB （preconditioned bi-conjugate gradient stabilized） algorithm is presented for solving large sparse complex systems. Based on the orthogonal list, the special technique of only storing non-zero elements is carried out. The incomplete LU factorization without fill-ins is adopted to reduce the condition number of the coefficient matrix. The BiCGSTAB algorithm is extended from the real system to the complex system and it is used to solve the preconditioned complex linear equations. The locked-rotor state of a single-sided linear induction machine is simulated by the software programmed with the finite element method and the PBiCGSTAB algorithm. Then the results are compared with those from the commercial software ANSYS, showing the validation of the proposed software. The iterative steps required for the proposed algorithm are reduced to about one-third, when compared to the BiCG method, therefore the algorithm is fast.

ADAPTIVE FUZZY CONTROL FOR ROBOT ARM MANIPULATOR WITH 5-DOF

To control the robot and track the designed trajectory with uncertain disturbances in a specified precision range, an adaptive fuzzy control scheme for the robot arm manipulator is discussed. The controller output error method （COEM） is used to design the adaptive fuzzy controller. A few or all of the parameters of the controller are adjusted by using the gradient descent algorithm to minimize the output error. COEM is adopted in the adaptive control system for the robot arm manipulator with 5-DOF. Simulation results show the effectiveness of the method and the real time adjustment of the parameters.