• Korean Journal of Mathematics
• /
• v.30 no.1
• /
• pp.131-146
• /
• 2022

This is an expository article about the gradients in deep neural network. It is hard to find a place where gradients in a deep neural network are dealt in details in a systematic and mathematical way. We review and compute the gradients and Jacobians to derive formulas for gradients which appear in the backpropagation and implement them in vectorized forms in Python.

• Journal of the Chungcheong Mathematical Society
• /
• v.37 no.1
• /
• pp.41-55
• /
• 2024

The nonconvex and nonsmooth optimization problem has been widely applicable in image processing and machine learning. In this paper, we propose an extension of the proximal iteratively reweighted ℓ₁ algorithm for nonconvex and nonsmooth minmization problem. We assume the co-coerciveness of a term of objective function instead of Lipschitz gradient condition, which is generalized property of Lipschitz continuity. We prove the global convergence of the proposed algorithm. Numerical results show that the proposed algorithm converges faster than original proximal iteratively reweighed algorithm and existing algorithms.

• Journal of Mechanical Science and Technology
• /
• v.17 no.12
• /
• pp.2087-2098
• /
• 2003

The development of numerical mathematical model to calculate both the static and dynamic characteristics of a multi-shaft gas turbine consisting of a single combustion chamber, including advanced cycle components such as intercooler and regenerator is presented in this paper. The numerical mathematical model is based on the simplified assumptions that quasi-static characteristic of turbo-machine and injector is used, total pressure loss and heat transfer relation for static calculation neglecting fuel transport time delay can be employed. The supercharger power has a cubical relation to its rotating velocity. The accuracy of each calculation is confirmed by monitoring mass and energy balances with comparative calculations for different time steps of integration. The features of the studied gas turbine scheme are the starting device with compressed air volumes and injector's supercharging the air directly ahead of the combustion chamber.

• The Korean Journal of Applied Statistics
• /
• v.18 no.2
• /
• pp.421-434
• /
• 2005

Machine learning has been extensively studied in recent years as effective tools in pattern classification problem. Although there have been several approaches to machine learning, we focus on the mathematical programming (in particular, multi-objective and goal programming; MOP/GP) approaches in this paper. Among them, Support Vector Machine (SVM) is gaining much popularity recently. In pattern classification problem with two class sets, the idea is to find a maximal margin separating hyperplane which gives the greatest separation between the classes in a high dimensional feature space. However, the idea of maximal margin separation is not quite new: in 1960's the multi-surface method (MSM) was suggested by Mangasarian. In 1980's, linear classifiers using goal programming were developed extensively. This paper proposes a new family of SVM using MOP/GP techniques, and discusses its effectiveness throughout several numerical experiments.

• 제어로봇시스템학회:학술대회논문집
• /
• 1991.10b
• /
• pp.1904-1909
• /
• 1991

Software linear and exponential acceleration/deceleration algorithms for control of machine axes of motion in industrial robots and CNC machine tools are proposed. Typical hardware systems used to accelerate and decelerate axes of motion are mathematically analyzed. Discrete-time state equations are derived from the mathematical analyses for the development of software acceleration/deceleration algorithms. Synchronous control method of multiple axes of motion in industrial robots and CNC machine tools is shown to be easily obtained on the basis of the proposed acceleration/deceleration algorithms. The path error analyses are carried out for the case where the software linear and exponential acceleration/deceleration algorithms are applied to a circular interpolator. A motion control system based on a floating point digital signal processor (DSP) TMS 320C30 is developed in order to implement the proposed algorithms. Experimental results demonstrate that the developed algorithms and the motion control system are available for control of multiple axes and nonlinear motion composed of a combination of lines and circles which industrial robots and CNC machine tools require.

• Journal of Electrical Engineering and Technology
• /
• v.7 no.4
• /
• pp.530-537
• /
• 2012

In the recent past, genetic algorithm (GA) and evolutionary optimization scheme have become increasingly popular for the design of electromagnetic (EM) devices. However, the conventional GA suffers from computational drawback and parameter dependency when applied to a computationally expensive problem, such as practical EM optimization design. To overcome these issues, a hybrid optimization scheme using GA in conjunction with Kriging is proposed. The algorithm is validated by using two mathematical problems and by optimizing rotor structure of interior permanent magnet synchronous machine.

• IEMEK Journal of Embedded Systems and Applications
• /
• v.15 no.1
• /
• pp.1-8
• /
• 2020

A derivation method for a quantized gradient for machine learning on an embedded system is proposed, in this paper. The proposed differentiation method induces the quantized gradient vector to an objective function and provides that the validation of the directional derivation. Moreover, mathematical analysis shows that the sequence yielded by the learning equation based on the proposed quantization converges to the optimal point of the quantized objective function when the quantized parameter is sufficiently large. The simulation result shows that the optimization solver based on the proposed quantized method represents sufficient performance in comparison to the conventional method based on the floating-point system.

• International Journal of Automotive Technology
• /
• v.6 no.4
• /
• pp.391-402
• /
• 2005

Despite its superior braking performance to conventional vehicles on test tracks, the performance of the ABS-equipped car seems disappointing on real highway. The poor braking performance results from questionable design of the human-machine interface(HMI) of the brake system. Force-displacement relation at the brake pedal has a strong effect on the braking performance. Recently developed brake-by-wire (BBW) system may allow us to tailor the force feel at the brake pedal. This study aims at exploring analytical ways of designing human-machine interface of BBW system. In this paper, mathematical models of brake pedal feel for electro-hydraulic BBW (EH-BBW) system are developed, and the braking motion and the characteristics of the driver's leg action are modeled. Based on the dynamic characteristics of the brake pedal and the driver, two new HMI designs for EH-BBW system are proposed. In the designs, BBW system is modeled as a type of master-slave teleoperator. The effectiveness of the proposed designs is investigated using driving simulation.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2005.06a
• /
• pp.1901-1905
• /
• 2005

This Paper describes the mathematical modeling and control of the tension and the speed of moving Bio-wrap in a wrap winding machine. In winding process, important control specifications include the regulation of wrap tension and velocity. In this research, a tension and velocity model has been developed for winding processes. A prototype winding system has been constructed, and the controller has been implemented in a real time PC-based environment. The tension control system is modeled a MIMO of the two-input and four-output system. The performance of the modeled system has been evaluated via simulation using MATLAB and experiments.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 1995.10a
• /
• pp.1045-1049
• /
• 1995

This paper proposes the state-space model of the thermal behavior of the spindle system to establish dynamic mathematical model of thermal characteristics in machine tool spindle system. the model is derived form physical law of heat transfer and thermoelasticity and represents the thermal behavior induced by uneven thermal expansions whitin a bearing. The model, which is sucessfully validated for two typical configurations of high speed spindle assembles, provides a tool for understanding the basis mechanics of induced thermal expansion as a function of initial preload, spindle speed and housing cooling conditions.