• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.647-653
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• 2015

Extreme value theory concerns the distributional properties of the maximum of a random sample; subsequently, it has been significantly extended to stationary random sequences satisfying weak dependence restrictions. We focus on distributional mixing condition $D(u_n)$ and the Berman condition based on covariance among weak dependence restrictions. The former is assumed for general stationary sequences and the latter for stationary normal processes; however, both imply the same distributional limit of the maximum of the normal process. In this paper $D(u_n)$ condition is shown weaker than Berman's covariance condition. Examples are given where the Berman condition is satisfied but the distributional mixing is not.

• Proceedings of the Korean Society of Medical Physics Conference
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• 2002.09a
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• pp.341-344
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• 2002

Neurodegenerative disorders, like Alzheimer's disease, are often accompanied by reduced brain perfusion (cerebral blood flow). Using the intrinsic magnetic properties of water, arterial spin labeling magnetic resonance imaging (ASLMRI) can map brain perfusion without injection of radioactive tracers or contrast agents. However, accuracy in measuring perfusion with ASL-MRI can be limited because of contributions to the signal from stationary spins and because of signal modulations due to transient magnetic field effects. The goal was to optimize ASL-MRI for perfusion measurements in the aging human brain, including brains with Alzheimer's disease. A new ASL-MRI sequence was designed and evaluated on phantom and humans. Image texture analysis was performed to test quantitatively improvements. Compared to other ASL-MRI methods, the newly designed sequence provided improved signal to noise ratio improved signal uniformity across slices, and thus, increased measurement reliability. This new ASL-MRI sequence should therefore provide improved measurements of regional changes of brain perfusion in normal aging and neurodegenerative disorders.

• Industrial Engineering and Management Systems
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• v.12 no.1
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• pp.2-8
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• 2013

Uncertainty theory is a branch of mathematics based on normolity, duality, subadditivity and product axioms. Uncertain process is a sequence of uncertain variables indexed by time. Canonical Liu process is an uncertain process with stationary and independent increments. And the increments follow normal uncertainty distributions. Uncertain differential equation is a type of differential equation driven by the canonical Liu process. Stability analysis on uncertain differential equation is to investigate the qualitative properties, which is significant both in theory and application for uncertain differential equations. This paper aims to study stability properties of linear uncertain differential equations. First, the stability concepts are introduced. And then, several sufficient and necessary conditions of stability for linear uncertain differential equations are proposed. Besides, some examples are discussed.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.585-592
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• 2010

Let {$\varepsilon_i:-{\infty}$$\infty$} be a strictly stationary sequence of linearly positive quadrant dependent random variables and $\sum\limits\frac_{i=-{\infty}}^{\infty}|a_i|$<$\infty$. In this paper, we prove the precise asymptotics in the law of iterated logarithm for the moment convergence of moving-average process of the form $X_k=\sum\limits\frac_{i=-{\infty}}^{\infty}a_{i+k}{\varepsilon}_i,k{\geq}1$

• Journal of Korean Society of Industrial and Systems Engineering
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• v.44 no.2
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• pp.115-123
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• 2021

A lot of sensor and control signals is generated by an industrial controller and related internet-of-things in discrete manufacturing system. The acquired signals are such records indicating whether several process operations have been correctly conducted or not in the system, therefore they are usually composed of binary numbers. For example, once a certain sensor turns on, the corresponding value is changed from 0 to 1, and it means the process is finished the previous operation and ready to conduct next operation. If an actuator starts to move, the corresponding value is changed from 0 to 1 and it indicates the corresponding operation is been conducting. Because traditional fault detection approaches are generally conducted with analog sensor signals and the signals show stationary during normal operation states, it is not simple to identify whether the manufacturing process works properly via conventional fault detection methods. However, digital control signals collected from a programmable logic controller continuously vary during normal process operation in order to show inherent sequence information which indicates the conducting operation tasks. Therefore, in this research, it is proposed to a recurrent neural network-based fault detection approach for considering sequential patterns in normal states of the manufacturing process. Using the constructed long short-term memory based fault detection, it is possible to predict the next control signals and detect faulty states by compared the predicted and real control signals in real-time. We validated and verified the proposed fault detection methods using digital control signals which are collected from a laser marking process, and the method provide good detection performance only using binary values.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.263-275
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• 2010

Let {$X_n;n\;\geq\;1$} be a strictly stationary sequence of negatively associated random variables with mean zero and finite variance. Set $S_n\;=\;{\sum}^n_{k=1}X_k$, $M_n\;=\;max_{k{\leq}n}|S_k|$, $n\;{\geq}\;1$. Suppose $\sigma^2\;=\;EX^2_1+2{\sum}^\infty_{k=2}EX_1X_k$ (0 < $\sigma$ < $\infty$). We prove that for any b > -1/2, if $E|X|^{2+\delta}$(0<$\delta$$\leq$1), then $$lim\limits_{\varepsilon\searrow0}\varepsilon^{2b+1}\sum^{\infty}_{n=1}\frac{(loglogn)^{b-1/2}}{n^{3/2}logn}E\{M_n-\sigma\varepsilon\sqrt{2nloglogn}\}_+=\frac{2^{-1/2-b}{\sigma}E|N|^{2(b+1)}}{(b+1)(2b+1)}\sum^{\infty}_{k=0}\frac{(-1)^k}{(2k+1)^{2(b+1)}}$$ and for any b > -1/2, $$lim\limits_{\varepsilon\nearrow\infty}\varepsilon^{-2(b+1)}\sum^{\infty}_{n=1}\frac{(loglogn)^b}{n^{3/2}logn}E\{\sigma\varepsilon\sqrt{\frac{\pi^2n}{8loglogn}}-M_n\}_+=\frac{\Gamma(b+1/2)}{\sqrt{2}(b+1)}\sum^{\infty}_{k=0}\frac{(-1)^k}{(2k+1)^{2b+2'}}$$, where $\Gamma(\cdot)$ is the Gamma function and N stands for the standard normal random variable.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.2
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• pp.119-127
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• 2004

Butterfly valves are popularly used in service in the industrial and water works pipeline systems with large diameter because of its lightweight, simple structure and the rapidity of its manipulation. Sometimes cavitation can occur. resulting in noise, vibration and rapid deterioration of the valve trim, and do not allow further operation. Thus, the monitoring of cavitation is of economic interest and is very importance in industry. This paper proposes a condition monitoring scheme using statistical feature evaluation and support vector machine (SVM) to detect the cavitation conditions of butterfly valve which used as a flow control valve at the pumping stations. The stationary features of vibration signals are extracted from statistical moments. The SVMs are trained, and then classify normal and cavitation conditions of control valves. The SVMs with the reorganized feature vectors can distinguish the class of the untrained and untested data. The classification validity of this method is examined by various signals that are acquired from butterfly valves in the pumping stations and compared the classification success rate with those of self-organizing feature map neural network.