• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1993.06a
• /
• pp.953-955
• /
• 1993

In this paper we propose a new stability theorem and a robust stability condition for linguistic fuzzy model systems in state space. First we define a stability in linear sense. After representing the fuzzy model by a system with disturbances, A necessary and sufficient condition for the stability is derived. This condition is proved to be a sufficient condition of the fuzzy model. The Q in the Lyapunov equation is iteratively adjusted by an gradient-based algorithm to improve its stability test. Finally, stability robustness bounds of a system having modeling error is derived. An example is also included to show that the stability test is powerful.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.1
• /
• pp.93-111
• /
• 2023

In this paper we study a nudging continuous data assimilation algorithm for the three-dimensional Leray-α model, where measurement errors are represented by stochastic noise. First, we show that the stochastic data assimilation equations are well-posed. Then we provide explicit conditions on the observation density (resolution) and the relaxation (nudging) parameter which guarantee explicit asymptotic bounds, as the time tends to infinity, on the error between the approximate solution and the actual solution which is corresponding to these measurements, in terms of the variance of the noise in the measurements.

• Korean Journal of Mathematics
• /
• v.31 no.1
• /
• pp.75-94
• /
• 2023

We aim in this article to establish variants of the Hadamard inequality for Caputo fractional derivatives. We present the Hadamard inequality for strongly (s, m)-convex functions which will provide refinements as well as generalizations of several such inequalities already exist in the literature. The error bounds of these inequalities are also given by applying some known identities. Moreover, various associated results are deduced.

• Journal of the Korean Society for Precision Engineering
• /
• v.12 no.10
• /
• pp.138-148
• /
• 1995

While Model-based Monitoring systems based on state observer theory have shown much promise in the laboratory, they have not been widely accepted by industry because, inpractice, these systems often have poor performance with respect to accuracy, band-width, reliability(false alarms), and robustness. In this paper, the linitations of the deterministic discrete-time state observer are investigated quantitatively from the machine monitoring viewpoint. The limitations in the transient and steady-state observer performance are quantified as estimation error bounds from which performance indices are selected. Each index represents the conditioning of the corresponding performance. By utilizing matrix norm theory, an unified main index is determined, that dominates all the indices. This index could from the basis for an observer design methodology that should improve the performance of model-based monitoring systems.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.33 no.3
• /
• pp.937-945
• /
• 2013

The accuracy of flood inundation maps is determined by the uncertainty propagated from all variables involved in the overall process including input data, model parameters and modeling approaches. This study investigated the uncertainty arising from key variables (flow condition and Manning's n) among model variables in flood inundation mapping for the Missouri River near Boonville, Missouri, USA. Methodology of this study involves the generalized likelihood uncertainty estimation (GLUE) to quantify the uncertainty bounds of flood inundation area. Uncertainty bounds in the GLUE procedure are evaluated by selecting two likelihood functions, which is two statistic (inverse of sum of squared error (1/SAE) and inverse of sum of absolute error (1/SSE)) based on an observed water surface elevation and simulated water surface elevations. The results from GLUE show that likelihood measure based on 1/SSE is more sensitive on observation than likelihood measure based on 1/SAE, and that the uncertainty propagated from two variables produces an uncertainty bound of about 2% in the inundation area compared to observed inundation. Based on the results obtained form this study, it is expected that this study will be useful to identify the characteristic of flood.

• Ocean and Polar Research
• /
• v.39 no.1
• /
• pp.13-21
• /
• 2017

Temporal changes in the number of zooplankton species are important information for understanding basic characteristics and species diversity in marine ecosystems. The aim of the present study was to estimate the optimal monitoring frequency (OMF) to guarantee and predict the minimum number of species occurrences for studies concerning marine ecosystems. The OMF is estimated using the temporal number of zooplankton species through bi-weekly monitoring of zooplankton species data according to operational taxonomic units in the Tongyoung coastal sea. The optimal model comprises two terms, a constant (optimal mean) and a cosine function with a one-year period. The confidence interval (CI) range of the model with monitoring frequency was estimated using a bootstrap method. The CI range was used as a reference to estimate the optimal monitoring frequency. In general, the minimum monitoring frequency (numbers per year) directly depends on the target (acceptable) estimation error. When the acceptable error (range of the CI) increases, the monitoring frequency decreases because the large acceptable error signals a rough estimation. If the acceptable error (unit: number value) of the number of the zooplankton species is set to 3, the minimum monitoring frequency (times per year) is 24. The residual distribution of the model followed a normal distribution. This model can be applied for the estimation of the minimal monitoring frequency that satisfies the target error bounds, as this model provides an estimation of the error of the zooplankton species numbers with monitoring frequencies.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.37 no.8C
• /
• pp.645-654
• /
• 2012

In this paper, we consider a two-way relay (TWR) system, where two user nodes exchange their information within two transmission phases, by the help of a relay node adopting physical layer network coding. In the system, two users transmit their binary phase shift keying symbols simultaneously in the first phase, and the relay node decodes the XORed version of two user data and broadcasts it back to two users in the second phase. The performance of the system is analyzed in terms of the average end-to-end symbol error probability in Nakagami-m fading channels, for which a tight upper bound is derived in a closed form to provide an accurate and handy estimate on the performance. The results show that our upper bounds are almost indistinguishable from simulation results for various channel and system configurations. In addition, the optimal relay location and power allocation for various conditions can be obtained quickly with our analysis.

• Nuclear Engineering and Technology
• /
• v.50 no.4
• /
• pp.589-598
• /
• 2018

To maintain safety and reliability of reactors, redundant sensors are usually used to measure critical variables and estimate their averaged time-dependency. Nonhealthy sensors can badly influence the estimation result of the process variable. Since online condition monitoring was introduced, the online cross-calibration method has been widely used to detect any anomaly of sensor readings among the redundant group. The cross-calibration method has four main averaging techniques: simple averaging, band averaging, weighted averaging, and parity space averaging (PSA). PSA is used to weigh redundant signals based on their error bounds and their band consistency. Using the consistency weighting factor (C), PSA assigns more weight to consistent signals that have shared bands, based on how many bands they share, and gives inconsistent signals of very low weight. In this article, three approaches are introduced for improving the PSA technique: the first is to add another consistency factor, so called trend consistency (TC), to include a consideration of the preserving of any characteristic edge that reflects the behavior of equipment/component measured by the process parameter; the second approach proposes replacing the error bound/accuracy based weighting factor ($W^a$) with a weighting factor based on the Euclidean distance ($W^d$), and the third approach proposes applying $W^d$, TC, and C, all together. Cold neutron source data sets of four redundant hydrogen pressure transmitters from a research reactor were used to perform the validation and verification. Results showed that the second and third modified approaches lead to reasonable improvement of the PSA technique. All approaches implemented in this study were similar in that they have the capability to (1) identify and isolate a drifted sensor that should undergo calibration, (2) identify a faulty sensor/s due to long and continuous missing data range, and (3) identify a healthy sensor.

• Convergence Security Journal
• /
• v.7 no.2
• /
• pp.17-25
• /
• 2007

In this paper, an algorithm that provisions proportional differentiation of packet delays is proposed with an objective for enhancing quality of service (QoS) in future packet networks. It features an adaptive scheme that adjusts the target delay every time slot to compensate the deviation from the target delay which is caused by the prediction error on the traffic to be arrived in the next time slot. It predicts the traffic to be arrived at the beginning of a time slot and measures the actual arrived traffic at the end of the time slot. The difference between them is utilized to the delay control operation for the next time slot to offset it. As it compensates the prediction error continuously, it shows superior adaptability to the bursty traffic as well as the exponential rate traffic. It is demonstrated through simulations that the algorithm meets the quantitative delay bounds and shows superiority to the traffic fluctuation in comparison with the conventional non-adaptive mechanism. The algorithm is implemented with VHDL on a Xilinx Spartan XC3S1500 FPGA and the performance is verified under the test board based on the XPC860P CPU.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.23 no.3
• /
• pp.205-214
• /
• 2011

Finite element grid refinements with different intensities having 14 K, 52 K and 211 K on the Yellow Sea (YS) have been constructed to make precise tidal simulations. In the meanwhile 57 K grid was made to the extended North Western Pacific (NWP) sea. Numerical simulation were done based on 32 parallel processors by using pADCIRC v 49.21 model. In the YS tidal simulation on YS-G52K and YS-G211K grid structure, KorBathy30s and ETOPO1 bathymetry data are used and 4 major tidal constituents are prescribed from FES2004. Computed results are in good agreement within 0.138 meter in RMS error for amplification and 14.80 degree of phase compared to observed tidal records. Similar error bounds are acquired in the extended NWP tidal simulation on NWP-G57K grid with 8 tidal constituent prescription on the open boundary.