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.

Data-Driven Learning Control Algorithms for Unachievable Tracking Problems

For unachievable tracking problems, where the system output cannot precisely track a given reference, achieving the best possible approximation for the reference trajectory becomes the objective. This study aims to investigate solutions using the Ptype learning control scheme. Initially, we demonstrate the necessity of gradient information for achieving the best approximation.Subsequently, we propose an input-output-driven learning gain design to handle the imprecise gradients of a class of uncertain systems. However, it is discovered that the desired performance may not be attainable when faced with incomplete information.To address this issue, an extended iterative learning control scheme is introduced. In this scheme, the tracking errors are modified through output data sampling, which incorporates lowmemory footprints and offers flexibility in learning gain design.The input sequence is shown to converge towards the desired input, resulting in an output that is closest to the given reference in the least square sense. Numerical simulations are provided to validate the theoretical findings.

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.

Reduced projection augmented Lagrange bi-conjugate gradient method for contact and impact problems

Based on the numerical governing formulation and non-linear complementary conditions of contact and impact problems, a reduced projection augmented Lagrange bi- conjugate gradient method is proposed for contact and impact problems by translating non-linear complementary conditions into equivalent formulation of non-linear program- ming. For contact-impact problems, a larger time-step can be adopted arriving at numer- ical convergence compared with penalty method. By establishment of the impact-contact formulations which are equivalent with original non-linear complementary conditions, a reduced projection augmented Lagrange bi-conjugate gradient method is deduced to im- prove precision and efficiency of numerical solutions. A numerical example shows that the algorithm we suggested is valid and exact.

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.

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.

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.

Genetic Algorithm for the Thermal Stresses Optimum Design ofFunctionally Gradient Material Plate

Based on the thermal stress distribution for functionally gradient material (FGM) plates, a Genetic Algorithm (GA) method for the thermal stresses optimum design of FGM plate with computer technologies is given. The minimum thermal stresses combination distribution for FGM is obtained.

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.

The Irregular Weighted Wavelet Frame Conjugate Gradient Algorithm

The dropping off of data during information transmission and the storage device’s damage etc.often leads the sampled data to be non-uniform.The paper, based on the stability theory of irregular wavelet frame and the irregular weighted wavelet frame operator,proposed an irregular weighted wavelet fame conjugate gradient iterative algorithm for the reconstruction of non-uniformly sampling signal. Compared the experiment results with the iterative algorithm of the Ref.[5],the new algorithm has remarkable advantages in approximation error,running time and so on.

Space-borne antenna adaptive anti-jamming method based on gradient-genetic algorithm

A novel space-borne antenna adaptive anti-jamming method based on the genetic algorithm （GA）, which is combined with gradient-like reproduction operators is presented, to search for the best weight for pattern synthesis in radio frequency （RF）. Combined, the GA＇s the capability of the whole searching is, but not limited by selection of the initial parameter, with the gradient algorithm＇s advantage of fast searching. The proposed method requires a smaller sized initial population and lower computational complexity. Therefore, it is flexible to implement this method in the real-time systems. By using the proposed algorithm, the designer can efficiently control both main-lobe shaping and side-lobe level. Simulation results based on the spot survey data show that the algorithm proposed is efficient and feasible.

GENERALIZED CONJUGATE-GRADIENT ALGORITHM AND ITS APPLICATIONS TO SEISMIC TRACE INVERSION

１ＩＮＴＲＯＤＵＣＴＩＯＮＣｕｒｅｎｔｌｙ，ｓｅｉｓｍｉｃｔｒａｃｅｉｎｖｅｒｓｉｏｎｈａｓａｌｒｅａｄｙｂｅｅｎａｎｉｍｐｏｒｔａｎｔｗｏｒｋｉｎｓｅｉｓｍｉｃｄａｔａｐｒｏｃｅｓｓｉｎｇｆｏｒｍｅｔｉｃｕｌｏｕｓｏｉｌｇａｓｅｘｐｌｏｒａｔｉ...

TRANSFORM DOMAIN CONJUGATE GRADIENT ALGORITHM FOR ADAPTIVE FILTERING

This paper proposed a new normalized transform domain conjugate gradient algorithm (NT-CGA), which applies the data independent normalized orthogonal transform technique to approximately whiten the input signal and utilises the modified conjugate gradient method to perform sample-by-sample updating of the filter weights more efficiently. Simulation results illustrated that the proposed algorithm has the ability to provide a fast convergence speed and lower steady-error compared to that of traditional least mean square algorithm (LMSA), normalized transform domain least mean square algorithm (NT- LMSA), Quasi-Newton least mean square algorithm (Q-LMSA) and time domain conjugate gradient algorithm (TD-CGA) when the input signal is heavily coloured.

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.

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.

IMPROVEMENT OF PHASE GRADIENT AUTOFOCUS ALGORITHM

The phase error estimated by phase gradient autofocus(PGA) is not based on a finite order polynomial mode, so PGA has a good autofocus property for arbitrary order phase error and is fit for high resolution airborne SAR. But PGA has two shortcomings: first, it has a worse estimation property for fast changing phase error; second, there exists a section of linear phase in the phase error estimated by this algorithm. This paper introduces the idea of rank one phase estimate (ROPE) autofocus technique, and improves PGA. The improved PGA(IPGA) can successfully overcome both these shortcomings of PGA.

A Shifting Strategy for Electric Commercial Vehicles Considering Mass and Gradient Estimation

The extended Kalman filter (EKF) algorithm and acceleration sensor measurements were used to identify vehiclemass and road gradient in the work. Four different states of fixed mass, variable mass, fixed slope and variableslope were set to simulate real-time working conditions, respectively. A comprehensive electric commercial vehicleshifting strategy was formulated according to the identification results. The co-simulation results showed that,compared with the recursive least square (RLS) algorithm, the proposed algorithm could identify the real-timevehicle mass and road gradient quickly and accurately. The comprehensive shifting strategy formulated had thefollowing advantages, e.g., avoiding frequent shifting of vehicles up the hill, making full use ofmotor braking downthe hill, and improving the overall performance of vehicles.

Adaptive Matrix/Vector Gradient Algorithm for Design of IIR Filters and ARMA Models

This work describes a novel adaptive matrix/vector gradient (AMVG) algorithm for design of IIR filters and ARMA signal models. The AMVG algorithm can track to IIR filters and ARMA systems having poles also outside the unit circle. The time reversed filtering procedure was used to treat the unstable conditions. The SVD-based null space solution was used for the initialization of the AMVG algorithm. We demonstrate the feasibility of the method by designing a digital phase shifter, which adapts to complex frequency carriers in the presence of noise. We implement the half-sample delay filter and describe the envelope detector based on the Hilbert transform filter.