381 research outputs found
Dimension reduction for Gaussian process emulation: an application to the influence of bathymetry on tsunami heights
High accuracy complex computer models, or simulators, require large resources
in time and memory to produce realistic results. Statistical emulators are
computationally cheap approximations of such simulators. They can be built to
replace simulators for various purposes, such as the propagation of
uncertainties from inputs to outputs or the calibration of some internal
parameters against observations. However, when the input space is of high
dimension, the construction of an emulator can become prohibitively expensive.
In this paper, we introduce a joint framework merging emulation with dimension
reduction in order to overcome this hurdle. The gradient-based kernel dimension
reduction technique is chosen due to its ability to drastically decrease
dimensionality with little loss in information. The Gaussian process emulation
technique is combined with this dimension reduction approach. Our proposed
approach provides an answer to the dimension reduction issue in emulation for a
wide range of simulation problems that cannot be tackled using existing
methods. The efficiency and accuracy of the proposed framework is demonstrated
theoretically, and compared with other methods on an elliptic partial
differential equation (PDE) problem. We finally present a realistic application
to tsunami modeling. The uncertainties in the bathymetry (seafloor elevation)
are modeled as high-dimensional realizations of a spatial process using a
geostatistical approach. Our dimension-reduced emulation enables us to compute
the impact of these uncertainties on resulting possible tsunami wave heights
near-shore and on-shore. We observe a significant increase in the spread of
uncertainties in the tsunami heights due to the contribution of the bathymetry
uncertainties. These results highlight the need to include the effect of
uncertainties in the bathymetry in tsunami early warnings and risk assessments.Comment: 26 pages, 8 figures, 2 table
Regularized System Identification
This open access book provides a comprehensive treatment of recent developments in kernel-based identification that are of interest to anyone engaged in learning dynamic systems from data. The reader is led step by step into understanding of a novel paradigm that leverages the power of machine learning without losing sight of the system-theoretical principles of black-box identification. The authorsโ reformulation of the identification problem in the light of regularization theory not only offers new insight on classical questions, but paves the way to new and powerful algorithms for a variety of linear and nonlinear problems. Regression methods such as regularization networks and support vector machines are the basis of techniques that extend the function-estimation problem to the estimation of dynamic models. Many examples, also from real-world applications, illustrate the comparative advantages of the new nonparametric approach with respect to classic parametric prediction error methods. The challenges it addresses lie at the intersection of several disciplines so Regularized System Identification will be of interest to a variety of researchers and practitioners in the areas of control systems, machine learning, statistics, and data science. This is an open access book
Penalized Likelihood and Bayesian Function Selection in Regression Models
Challenging research in various fields has driven a wide range of
methodological advances in variable selection for regression models with
high-dimensional predictors. In comparison, selection of nonlinear functions in
models with additive predictors has been considered only more recently. Several
competing suggestions have been developed at about the same time and often do
not refer to each other. This article provides a state-of-the-art review on
function selection, focusing on penalized likelihood and Bayesian concepts,
relating various approaches to each other in a unified framework. In an
empirical comparison, also including boosting, we evaluate several methods
through applications to simulated and real data, thereby providing some
guidance on their performance in practice
Learning from data: Plant breeding applications of machine learning
Increasingly, new sources of data are being incorporated into plant breeding pipelines. Enormous amounts of data from field phenomics and genotyping technologies places data mining and analysis into a completely different level that is challenging from practical and theoretical standpoints. Intelligent decision-making relies on our capability of extracting from data useful information that may help us to achieve our goals more efficiently. Many plant breeders, agronomists and geneticists perform analyses without knowing relevant underlying assumptions, strengths or pitfalls of the employed methods. The study endeavors to assess statistical learning properties and plant breeding applications of supervised and unsupervised machine learning techniques. A soybean nested association panel (aka. SoyNAM) was the base-population for experiments designed in situ and in silico. We used mixed models and Markov random fields to evaluate phenotypic-genotypic-environmental associations among traits and learning properties of genome-wide prediction methods. Alternative methods for analyses were proposed
๋ง๋ฅด์ฝํ ๋๋ค ํ๋ ํ์ต ๋ฐ ์ถ๋ก ๊ณผ ๊ทธ๋ํ ๋ผ์๋ฅผ ํ์ฉํ ๊ณต์ ์ด์ ๊ฐ์ง ๋ฐ ์ง๋จ ๋ฐฉ๋ฒ๋ก
ํ์๋
ผ๋ฌธ (๋ฐ์ฌ)-- ์์ธ๋ํ๊ต ๋ํ์ : ๊ณต๊ณผ๋ํ ํํ์๋ฌผ๊ณตํ๋ถ, 2019. 2. ์ด์๋ณด.Fault detection and diagnosis (FDD) is an essential part of safe plant operation. Fault detection refers to the process of detecting the occurrence of a fault quickly and accurately, and representative methods include the use of principal component analysis (PCA), and autoencoders (AE). Fault diagnosis is the process of isolating the root cause node of the fault, then determining the fault propagation path to identify the characteristic of the fault. Among the various methods, data-driven methods are the most widely-used, due to their applicability and good performance compared to analytical and knowledge-based methods. Although many studies have been conducted regarding FDD, no methodology for conducting every step of FDD exists, where the fault is effectively detected and diagnosed. Moreover, existing methods have limited applicability and show limited performance. Previous fault detection methods show loss of variable characteristics in dimensionality reduction methods and have large computational loads, leading to poor performance for complex faults. Likewise, preceding fault diagnosis methods show inaccurate fault isolation results, and biased fault propagation path analysis as a consequence of implementing knowledge-based characteristics for construction of digraphs of process variable relationships. Thus a comprehensive methodology for FDD which shows good performance for complex faults and variable relationships, is required.
In this study, an efficient and effective comprehensive FDD methodology based on Markov random fields (MRF) modelling is proposed. MRFs provide an effective means for modelling complex variable relationships, and allows efficient computation of marginal probability of the process variables, leading to good performance regarding FDD.
First, a fault detection framework for process variables, integrating the MRF modelling and structure learning with iterative graphical lasso is proposed. Graphical lasso is an algorithm for learning the structure of MRFs, and is applicable to large variable sets since it approximates the MRF structure by assuming the relationships between variables to be Gaussian. By iteratively applying the graphical lasso to monitored variables, the variable set is subdivided into smaller groups, and consequently the computational cost of MRF inference is mitigated allowing efficient fault detection. After variable groups are obtained through iterative graphical lasso, they are subject to the MRF monitoring framework that is proposed in this work. The framework obtains the monitoring statistics by calculating the probability density of the variable groups through kernel density estimation, and the monitoring limits are obtained separately for each group by using a false alarm rate of 5%.
Second, a fault isolation and propagation path analysis methodology is proposed, where the conditional marginal probability of each variable is computed via inference, then is used to calculate the conditional contribution of individual variables during the occurrence of a fault. Using the kernel belief propagation (KBP) algorithm, which is an algorithm for learning and inferencing MRFs comprising continuous variables, the parameters of MRF are trained using normal process data, then the individual conditional contribution of each variable is calculated for every sample of the fault process data. By analyzing the magnitude and reaction speed of the conditional contribution of individual variables, the root fault node can be isolated and the fault propagation path can be determined effectively.
Finally, the proposed methodology is verified by applying it to the well-known Tennessee Eastman process (TEP) model. Since the TEP has been used as a benchmark process over the past years for verifying various FDD methods, it serves the purpose of performance comparison. Also, since it consists of multiple units and has complex variable relationships such as recycle loops, it is suitable for verifying the performance of the proposed methodology. Application results show that the proposed methodology performs better compared to state-of-the-art FDD algorithms, in terms of both fault detection and diagnosis. Fault detection results showed that all 28 faults designed inside the TEP model were detected with a fault detection accuracy of over 95%, which is higher than any other previously proposed fault detection method. Also, the method showed good fault isolation and propagation path analysis results, where the root-cause node for every fault was detected correctly, and the characteristics of the initiated faults were identified through fault propagation path analysis.๊ณต์ ์ด์์ ๊ฐ์ง ๋ฐ ์ง๋จ ์์คํ
์ ์์ ํ ๊ณต์ ์ด์์ ํ์์ ์ธ ๋ถ๋ถ์ด๋ค. ์ด์ ๊ฐ์ง๋ ์ด์์ด ๋ฐ์ํ์ ๊ฒฝ์ฐ ์ฆ๊ฐ์ ์ผ๋ก ์ด๋ฅผ ์ ํํ๊ฒ ๊ฐ์งํ๋ ํ๋ก์ธ์ค๋ฅผ ์๋ฏธํ๋ฉฐ, ๋ํ์ ์ธ ๋ฐฉ๋ฒ์ผ๋ก๋ ์ฃผ์ฑ๋ถ ๋ถ์ ๋ฐ ์คํ ์ธ์ฝ๋๋ฅผ ํ์ฉํ ๊ฐ์ง ๋ฐฉ๋ฒ๋ก ์ด ์๋ค. ์ด์ ์ง๋จ์ ๊ฒฐํจ์ ๊ทผ๋ณธ ์์ธ์ด ๋๋ ๋
ธ๋๋ฅผ ๊ฒฉ๋ฆฌํ๊ณ , ์ด์์ ์ ํ ๊ฒฝ๋ก๋ฅผ ํ์งํ์ฌ ์ด์์ ํน์ฑ์ ์๋ณํ๋ ํ๋ก์ธ์ค์ด๋ค. ๊ณต์ ์ด์์ ๊ฐ์ง ๋ฐ ์ง๋จ ๋ฐฉ๋ฒ๋ก ์๋ ๋ชจ๋ธ ๋ถ์ ๋ฐฉ๋ฒ๋ก , ์ง์ ๊ธฐ๋ฐ ๋ฐฉ๋ฒ๋ก ๋ฑ์ ๋ค์ํ ๋ฐฉ๋ฒ๋ก ์ด ์์ง๋ง, ๊ณต์ ์ ๋ํ ์ ์ฉ ๊ฐ๋ฅ์ฑ๊ณผ ์ฑ๋ฅ ์ธก๋ฉด์์ ๊ฐ์ฅ ์ ์ฉํ๋ค๊ณ ์๋ ค์ ธ ์๋ ๋ฐ์ดํฐ ๊ธฐ๋ฐ ๋ฐฉ๋ฒ๋ก ์ด ๋๋ฆฌ ํ์ฉ๋๊ณ ์๋ค. ๊ณต์ ์ด์์ ๊ฐ์ง ๋ฐ ์ง๋จ์ ๋ํ ๋ฐ์ดํฐ ๊ธฐ๋ฐ ๋ฐฉ๋ฒ๋ก ์ ๋ค๋ฐฉ๋ฉด์ผ๋ก ์ฐ๊ตฌ๋์ด ์์ง๋ง, ์ด์ ๊ฐ์ง ๋ฐ ์ง๋จ์ ๋ชจ๋ ํจ๊ณผ์ ์ผ๋ก ์ํํ ์ ์๋ ๋ฐฉ๋ฒ๋ก ์ ์์์ ๋ถ๊ณผํ๋ฉฐ, ์กด์ฌํ๊ณ ์๋ ๋ฐฉ๋ฒ๋ก ๋ค ์ญ์ ๋ ๋ถ์ผ ๋ชจ๋์์ ์ข์ ์ฑ๋ฅ์ ๋ณด์ฌ์ฃผ๊ณ ์๋ ๊ฒฝ์ฐ๋ ์๋ค. ์ด๋ ๊ธฐ์กด ๋ฐฉ๋ฒ๋ก ๋ค์ ์ ์ฉ ๊ฐ๋ฅ์ฑ์ด ์ ํ๋์ด ์์ผ๋ฉฐ ๊ณต์ ์ ์ ์ฉ์ ์ ํ๋ ์ฑ๋ฅ์ ๋ณด์ฌ์ฃผ๊ธฐ ๋๋ฌธ์ด๋ค. ์ด์ ๊ฐ์ง์ ๊ฒฝ์ฐ, ๋์ฉ๋์ ๋ฐ์ดํฐ๋ฅผ ์ฒ๋ฆฌํ ๋ ๋ฐ์ํ๋ ๊ณผ๋ถํ๋ก ์ธํ ๊ฐ์ง ๋ฅ๋ ฅ์ ์ ํ, ์ฐจ์ ์ถ์ ๋ฐฉ๋ฒ๋ก ๋ค์ ์ฌ์ฉํ ์ ์ด์ ๋ฐ๋ฅธ ๋ณ์ ํน์ฑ ๋ฐ์์ ๋ถ์ ํ์ฑ, ๊ทธ๋ฆฌ๊ณ ์ถ์๋ ์ฐจ์์์์ ๊ณ์ฐ์ผ๋ก ์ธํ์ฌ ๋ณตํฉ์ ์ธ ํํ์ ์ด์์ ๊ฐ์งํด ๋ด์ง ๋ชปํ๋ ๋ฌธ์ ๋ฑ์ด ์๋ค. ์ด์ ์ง๋จ์ ๊ฒฝ์ฐ ์ด์์ ์์ธ์ด ๋๋ ๋
ธ๋์ ๊ฒฉ๋ฆฌ ๋ฐ ์ด์ ์ ํ ๊ฒฝ๋ก์ ๋ํ ๋ถ์์ด ๋ถ์ ํํ ๊ฒฝ์ฐ๊ฐ ๋ง์๋ฐ, ์ด๋ ์ฐจ์ ์ถ์๋ก ์ธํ์ฌ ๊ณต์ ๋ณ์์ ํน์ฑ์ด ์์ค๋๋ ์ฑ์ง์ด ์๊ณ , ๋ฐฉํฅ์ฑ ๊ทธ๋ํ๋ฅผ ํ์ฉํ ์ ๊ณต์ ์ ๋ํ ์ ํ ์ง์์ ์ ์ฉํจ์ผ๋ก์จ ํธํฅ๋ ์ด์ ์ง๋จ ๊ฒฐ๊ณผ๊ฐ ๋ํ๋๋ ๊ฒฝ์ฐ๋ค์ด ๋ฐ์ํ๊ธฐ ๋๋ฌธ์ด๋ค. ๊ธฐ์กด ๋ฐฉ๋ฒ๋ก ๋ค์ ๋ํ ์ด๋ฌํ ํ๊ณ์ ๋ค์ ๊ณ ๋ คํด ๋ดค์๋, ๋ณ์ ๊ฐ๊ฐ์ ํน์ฑ์ด ์์ค๋์ง ์๋๋กํ์ฌ ํจ๊ณผ์ ์ผ๋ก ์ด์์ ๋ํ ๊ฐ์ง์ ์ง๋จ์ ๋ชจ๋ ์ํํด ๋ผ ์ ์์ผ๋ฉด์๋, ๊ณ์ฐ์์ ํจ์จ์ฑ์ ๊ฐ์ถ, ์ด์ ๊ฐ์ง ๋ฐ ์ง๋จ์ ๋ํ ํตํฉ๋ ๋ฐฉ๋ฒ๋ก ์ ๊ฐ๋ฐ์ด ์๊ธํ๋ค๊ณ ํ ์ ์๋ค.
๋ณธ ์ฐ๊ตฌ์์๋ ๋ง๋ฅด์ฝํ ๋๋ค ํ๋ ๋ชจ๋ธ๋ง๊ณผ ๊ทธ๋ํ ๋ผ์๋ฅผ ๊ธฐ๋ฐ์ผ๋กํ์ฌ, ์ด์์ ๋ํ ๊ฐ์ง ๋ฐ ์ง๋จ์ ๋ชจ๋ ์ํํด ๋ผ ์ ์๋ ํตํฉ์ ์ธ ๊ณต์ ๋ชจ๋ํฐ๋ง ๋ฐฉ๋ฒ๋ก ์ ์ ์ํ๋ค. ๋ง๋ฅด์ฝํ ๋๋ค ํ๋๋ ๋น์ ํ์ ์ด๊ณ ๋น์ ๊ท์ ์ธ ๋ณ์ ๊ด๊ณ๋ฅผ ํจ๊ณผ์ ์ผ๋ก ๋ชจ๋ธ๋งํ ์ ์๊ฒ ํด์ฃผ๊ณ , ์ด์ ๋ฐ์ ์ํฉ์์์ ๋ชจ๋ํฐ๋ง ํต๊ณ๊ฐ ๊ณ์ฐ์์ ๊ฐ ๋ณ์์ ํน์ฑ์ ๋ฐ์ํ์ฌ ํ๋ฅ ๊ณ์ฐ์ ํด ๋ผ ์ ์๊ธฐ ๋๋ฌธ์ ํจ๊ณผ์ ์ธ ์ด์ ๊ฐ์ง ๋ฐ ์ง๋จ ์๋จ์ด ๋๋ค. ๊ธฐ๋ณธ์ ์ผ๋ก ๋ง๋ฅด์ฝํ ๋๋ค ํ๋๋ ํ๋ฅ ๊ฐ ๊ณ์ฐ์์ ๋ถํ๊ฐ ํฌ์ง๋ง, ๋ณธ ์ฐ๊ตฌ์์๋ ๊ทธ๋ํ ๋ผ์ ๋ฐฉ๋ฒ๋ก ์ ์ถ๊ฐ์ ์ผ๋ก ํจ๊ป ํ์ฉํ์ฌ ๊ณ์ฐ ์์ ๋ถํ๋ฅผ ์ค์ด๊ณ ํจ์จ์ ์ผ๋ก ์ด์ ๊ฐ์ง ๋ฐ ์ง๋จ์ ํด๋ผ ์ ์๋๋ก ํ์๋ค. ๋ณธ ์ฐ๊ตฌ์์ ์ ์๋ ๋ด์ฉ๋ค์ ๋ค์๊ณผ ๊ฐ๋ค.
์ฒซ์งธ, ๊ณต์ ๋ณ์๋ฅผ ๋ง๋ฅด์ฝํ ๋๋ค ํ๋ ํํ๋ก ๋ชจ๋ธ๋งํ๊ณ , ๊ทธ๋ํ ๋ผ์๋ฅผ ํ์ฉํด ๋ง๋ฅด์ฝํ ๋๋ค ํ๋์ ๊ตฌ์กฐ๋ฅผ ์ป์ ์ ์๋ ๋ฐฉ๋ฒ๋ก ์ ์ ์ํ์๋ค. ๊ทธ๋ํ ๋ผ์๋ ๋ง๋ฅด์ฝํ ๋๋ค ํ๋์ ๊ตฌ์กฐ๋ฅผ ํ์
ํ๊ธฐ ์ํ ๋ฐฉ๋ฒ๋ก ์ธ๋ฐ, ๋ณ์ ๊ฐ์ ๊ด๊ณ๋ฅผ ๊ฐ์ฐ์ค ํจ์์ ํํ๋ก ๊ฐ์ ํ๊ธฐ ๋๋ฌธ์ ๋ค๋ณ์ ์์คํ
์์๋ ํจ์จ์ ์ผ๋ก ๊ทธ๋ํ ๊ตฌ์กฐ๋ฅผ ํ์
ํ ์ ์๋๋ก ํด์ค๋ค. ๋ณธ ์ฐ๊ตฌ์์๋ ๋ฐ๋ณต์ ๊ทธ๋ํ ๋ผ์๋ฅผ ์ ์ํ์ฌ ๋ชจ๋ ๊ณต์ ๋ณ์๋ค์ด ์๊ด๊ด๊ณ๊ฐ ๋์ ๋ณ์ ์ง๋จ์ผ๋ก ๋ฌถ์ผ ์ ์๋๋ก ํ์๋ค. ์ด๋ฅผ ํ์ฉํ๋ฉด ์ ์ฒด ๊ณต์ ๋ณ์ ์ง๋จ์ ๋ค์์ ์์ง๋จ์ผ๋ก ๋ถ๋ฅํ๊ณ ๊ฐ๊ฐ์ ๋ํ ๊ทธ๋ํ ๊ตฌ์กฐ๋ฅผ ํ์
ํ ์ ์๊ฒ ๋๋๋ฐ, ํฌ๊ฒ ๋ ๊ฐ์ง์ ํจ๊ณผ๋ฅผ ์ป์ ์ ์๋ค. ์ฐ์ ์ ์ผ๋ก ๋ง๋ฅด์ฝํ ๋๋ค ํ๋ ํ๋ฅ ๊ณ์ฐ์ ๋์์ด ๋๋ ๋ณ์์ ๊ฐ์๋ฅผ ์ค์ฌ์ค์ผ๋ก์จ ๊ณ์ฐ ๋ถํ๋ฅผ ์ค์ด๊ณ ํจ์จ์ ์ธ ์ด์ ๊ฐ์ง๊ฐ ์ด๋ฃจ์ด์ง ์ ์๋๋ก ํ๋ค. ๋ํ ์๊ด๊ด๊ณ๊ฐ ๋์ ์ง๋จ๋ผ๋ฆฌ ๋ฌถ์ฌ์ ๋ชจ๋ธ๋ง ๋ ๊ทธ๋ํ๋ฅผ ํ์ฉํ์ฌ ์ด์์ ์ง๋จ ๊ณผ์ ์์ ๊ณต์ ๋ณ์ ๊ฐ์ ๊ด๊ณ ํ์
๋ฐ ์ ํ ๊ฒฝ๋ก ๋ถ์์ ์ฉ์ดํ๋๋ก ํด์ค๋ค.
๋ ๋ฒ์งธ๋ก, ๋ง๋ฅด์ฝํ ๋๋ค ํ๋์ ํ๋ฅ ์ถ๋ก ์ ๊ธฐ๋ฐ์ผ๋ก ํ์ฌ ํจ๊ณผ์ ์ผ๋ก ์ด์ ๊ฐ์ง๊ฐ ์ด๋ฃจ์ด์ง ์ ์๋๋ก ํ๋ ๋ฐฉ๋ฒ๋ก ์ ์ ์ํ์๋ค. ๋ฐ๋ณต์ ๊ทธ๋ํ ๋ผ์๋ฅผ ํตํด ์ป์ด์ง ๋ค์์ ๋ณ์ ์์ง๋จ์ ๋ํ์ฌ ๊ฐ๊ฐ ํ๋ฅ ์ถ๋ก ์ ์ ์ฉํ์ฌ ์ด์ ๊ฐ์ง๋ฅผ ์งํํ๊ฒ ๋๋๋ฐ, ์ ์๋ ๋ฐฉ๋ฒ๋ก ์์๋ ์ปค๋ ๋ฐ๋ ์ถ์ ๋ฐฉ๋ฒ๋ก ์ ํ์ฉํ์๋ค. ์ ์ ๋ฐ์ดํฐ๋ฅผ ํ์ฉํ์ฌ ๊ฐ ๋ณ์๋ค์ ๋ํ ์ปค๋ ๋ฐ๋์ ๋์ญํญ์ ํ์ตํ๊ณ , ์ด์ ๋ฐ์ดํฐ๊ฐ ๋ฐ์ํ ์ ์ด๋ฅผ ํ์ฉํ ์ปค๋ ๋ฐ๋ ์ถ์ ๋ฒ์ ์ฌ์ฉํ์ฌ ์ด์๊ฐ์ ํต๊ณ์น๋ฅผ ๊ณ์ฐํ๊ฒ ๋๋ค. ์ด๋ ํ์ ์ง๋จ์จ์ 5%๋ก ๊ฐ์ ํ์ฌ ๊ฐ๊ฐ์ ์์ง๋จ์ ๋ํ ๊ณต์ ๊ฐ์ง ๊ธฐ์ค์ ์ ์ค์ ํ์๊ณ , ์ด์๊ฐ์ ํต๊ณ์น๊ฐ ๊ณต์ ๊ฐ์ ๊ธฐ์ค์ ๋ณด๋ค ๋ฎ๊ฒ ๋ ๊ฒฝ์ฐ ์ด์์ด ๊ฐ์ง๋๋ค.
์ธ ๋ฒ์งธ๋ก, ์ด์ ๋ฐ์ ์ ์์ธ์ด ๋๋ ๋ณ์์ ๊ฒฉ๋ฆฌ ๋ฐ ์ด์ ์ ํ ๊ฒฝ๋ก ๋ถ์์ ํจ๊ณผ์ ์ผ๋ก ์ํํ ์ ์๋ ๋ฐฉ๋ฒ๋ก ์ ์ ์ํ์๋ค. ์ ์๋ ๋ฐฉ๋ฒ๋ก ์์๋ ๋ง๋ฅด์ฝํ ๋๋ค ํ๋์ ํ๋ฅ ์ถ๋ก ๊ณผ์ ์ ํ์ฉํ์ฌ ์ด์ ๋ฐ์ ์ ๊ฐ ๋ณ์์ ์กฐ๊ฑด๋ถ ํ๊ณ ํ๋ฅ ์ ๊ณ์ฐํ๊ณ , ์ด๋ฅผ ํ์ฉํด ์๋กญ๊ฒ ์ ์๋ ์กฐ๊ฑด๋ถ ๊ธฐ์ฌ๋ ๊ฐ์ ๊ณ์ฐํ์ฌ, ์ด์์ ๋ํ ๊ฐ ๋ณ์์ ๊ธฐ์ฌ๋๋ฅผ ํ์
ํ ์ ์๋๋ก ํ๋ค. ์ด ๊ณผ์ ์์๋ ์ปค๋ ์ ๋ขฐ๋ ์ ํ ๋ฐฉ๋ฒ๋ก ์ด ์ฌ์ฉ๋๋๋ฐ, ์ด๋ ์ฐ์ ๋ณ์๋ฅผ ๊ฐ์ง๋ ๋ง๋ฅด์ฝํ ๋๋ค ํ๋์ ๋ํ์ฌ ํ๋ฅ ์ถ๋ก ์ ์ํํ ์ ์๋๋ก ํ๋ ๋ฐฉ๋ฒ๋ก ์ด๋ค. ์ปค๋ ์ ๋ขฐ๋ ์ ํ๋ฒ์ ์ฌ์ฉํ๋ฉด ์ ์ ์ํ์ ๊ณต์ ๋ฐ์ดํฐ๋ฅผ ํ์ฉํ์ฌ ๋ง๋ฅด์ฝํ ๋๋ค ํ๋๋ฅผ ๊ตฌ์ฑํ๋ ํ๋ผ๋ฏธํฐ ๊ฐ๋ค์ ํ์ตํ๊ณ , ์ด์ ๋ฐ์์ ์ด์ ๋ฐ์ดํฐ์ ๋ํ์ฌ ๊ฐ ๋ณ์์ ์กฐ๊ฑด๋ถ ๊ธฐ์ฌ๋ ๊ฐ์ ๊ณ์ฐํ ์ ์๊ฒ ๋๋ค. ์ด ๋ ๊ณ์ฐ๋ ์กฐ๊ฑด๋ถ ๊ธฐ์ฌ๋ ๊ฐ์ ํฌ๊ธฐ์, ์ด์ ๋ฐ์ ์ดํ ๊ฐ ๋ณ์์ ์กฐ๊ฑด๋ถ ๊ธฐ์ฌ๋ ๊ฐ์ ๋ณํ ๋ฐ์ ์๋๋ฅผ ์ข
ํฉ์ ์ผ๋ก ํ๋จํ์ฌ, ์ด์์ ์์ธ ๋ณ์์ ๋ํ ๊ฒฉ๋ฆฌ์ ์ด์ ์ ํ ๊ฒฝ๋ก ๋ถ์์ ํจ๊ณผ์ ์ผ๋ก ์ํํ ์ ์๊ฒ ๋๋ค.
๋ณธ ์ฐ๊ตฌ์์๋ ์ ์๋ ์ด์ ๊ฐ์ง ๋ฐ ์ง๋จ ๋ฐฉ๋ฒ๋ก ์ ์ฑ๋ฅ์ ๊ฒ์ฆํ๊ธฐ ์ํ์ฌ ํ
๋ค์ ์ด์คํธ๋ง ๊ณต์ ๋ชจ๋ธ์ ์ด๋ฅผ ์ ์ฉํ๊ณ ๊ฒฐ๊ณผ๋ฅผ ๋ถ์ํ์๋ค. ํ
๋ค์ ์ด์คํธ๋ง ๊ณต์ ์ ์๋
๊ฐ ๊ณต์ ๊ฐ์ ๋ฐฉ๋ฒ๋ก ์ ๊ฒ์ฆํ๊ธฐ ์ํ ๋ฒค์น๋งํฌ ๊ณต์ ์ผ๋ก ๋๋ฆฌ ์ฌ์ฉ๋์ด ์๊ธฐ ๋๋ฌธ์, ์ ์๋ ๋ฐฉ๋ฒ๋ก ์ ์ด์ ์ ์ฉํด ๋ด์ผ๋ก์จ ๋ค๋ฅธ ๊ณต์ ๊ฐ์ ๋ฐฉ๋ฒ๋ก ๋ค๊ณผ์ ์ฑ๋ฅ์ ๋น๊ตํด ๋ณผ ์ ์์๋ค. ๋ํ ๋ค์์ ๋จ์ ๊ณต์ ์ ํฌํจํ๊ณ ์๊ณ , ์ํ์ ์ธ ๋ณ์ ๊ด๊ณ ์ญ์ ํฌํจํ๊ณ ์๊ธฐ ๋๋ฌธ์ ์ ์๋ ๋ฐฉ๋ฒ๋ก ์ ์ฑ๋ฅ์ ์ํํด ๋ณด๊ธฐ์ ์ ํฉํ๋ค. ํ
๋ค์ ์ด์คํธ๋ง ๊ณต์ ๋ด๋ถ์๋ 28๊ฐ ์ข
๋ฅ์ ์ด์์ด ํ๋ก๊ทธ๋จ ์์ ๋ด์ฅ๋์ด ์๋๋ฐ, ์ ์๋ ๊ณต์ ๊ฐ์ง ๋ฐฉ๋ฒ๋ก ์ ์ ์ฉํ ๊ฒฐ๊ณผ ๋ชจ๋ ์ด์์ ๋ํ์ฌ 96% ์ด์์ ๋์ ์ด์ ๊ฐ์ง์จ์ ๋ํ๋ด์๋ค. ์ด๋ ๊ธฐ์กด์ ์ ์๋ ๊ณต์ ๊ฐ์ ๋ฐฉ๋ฒ๋ก ๋ค์ ๋นํ์ฌ ์๋ฑํ ๋์ ์์น์๋ค. ๋ํ ์ด์ ์ง๋จ ์ฑ๋ฅ์ ๋ถ์ํด ๋ณธ ๊ฒฐ๊ณผ, ๋ชจ๋ ์ด์์ ๋ํ์ฌ ์์ธ์ด ๋๋ ๋
ธ๋๋ฅผ ํจ๊ณผ์ ์ผ๋ก ํ์
ํ ์ ์์๊ณ , ์ด์ ์ ํ ๊ฒฝ๋ก ์ญ์ ์ ํํ๊ฒ ํ์งํ์ฌ ๊ธฐ์กด ๋ฐฉ๋ฒ๋ก ๋ค๊ณผ๋ ์ฐจ๋ณํ๋ ์ฑ๋ฅ์ ๋ํ๋ด์๋ค. ์ ์๋ ๋ฐฉ๋ฒ๋ก ์ ํ
๋ค์ ์ด์คํธ๋ง ๊ณต์ ์ ์ ์ฉํด ๋ด์ผ๋ก์จ, ๋ณธ ์ฐ๊ตฌ ๋ด์ฉ์ด ๊ณต์ ์ด์์ ๊ฐ์ง ๋ฐ ์ง๋จ์ ๋ํ ํตํฉ์ ์ธ ๋ฐฉ๋ฒ๋ก ์ค์์ ๊ฐ์ฅ ์ฐ์ํ ์ฑ๋ฅ์ ๋ํ๋ด๋ ๊ฒ์ ํ์ธํ ์ ์์๋ค.Contents
Abstract i
Contents iv
List of Tables vii
List of Figures ix
1 Introduction 1
1.1 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Markov Random Fields Modelling, Graphical Lasso, and Optimal Structure Learning 10
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Markov Random Fields . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Graphical Lasso . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4 MRF Modelling & Structure Learning . . . . . . . . . . . . . . . . . 19
2.4.1 MRF modelling in process systems . . . . . . . . . . . . . . 19
2.4.2 Structure learning using iterative graphical lasso . . . . . . . 20
2.5 Application of Iterative Graphical Lasso on the TEP . . . . . . . . . . 24
3 Efficient Process Monitoring via the Integrated Use of Markov Random
Fields Learning and the Graphical Lasso 31
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 MRF Monitoring Integrated with Graphical Lasso . . . . . . . . . . . 35
3.2.1 Step 1: Iterative graphical lasso . . . . . . . . . . . . . . . . 36
3.2.2 Step 2: MRF monitoring . . . . . . . . . . . . . . . . . . . . 36
3.3 Implementation of Glasso-MRF monitoring to the Tennessee Eastman
process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.1 Tennessee Eastman process . . . . . . . . . . . . . . . . . . 41
3.3.2 Glasso-MRF monitoring on TEP . . . . . . . . . . . . . . . . 48
3.3.3 Fault detection accuracy comparison with other monitoring
techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.3.4 Fault detection speed & fault propagation . . . . . . . . . . . 95
4 Process Fault Diagnosis via Markov Random Fields Learning and Inference 101
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.2.1 Probabilistic graphical models & Markov random fields . . . 106
4.2.2 Kernel belief propagation . . . . . . . . . . . . . . . . . . . . 107
4.3 Fault Diagnosis via MRF Modeling . . . . . . . . . . . . . . . . . . 113
4.3.1 MRF structure learning via graphical lasso . . . . . . . . . . 116
4.3.2 Kernel belief propagation - bandwidth selection . . . . . . . . 116
4.3.3 Conditional contribution evaluation . . . . . . . . . . . . . . 117
4.4 Application Results & Discussion . . . . . . . . . . . . . . . . . . . 118
4.4.1 Two tank process . . . . . . . . . . . . . . . . . . . . . . . . 119
4.4.2 Tennessee Eastman process . . . . . . . . . . . . . . . . . . 137
5 Concluding Remarks 152
Bibliography 157
Nomenclature 169
Abstract (In Korean) 170Docto
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