• Communications for Statistical Applications and Methods
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• v.31 no.2
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• pp.179-189
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• 2024

In multivariate regression with a high-dimensional response Y ∈ ℝ^r and a relatively low-dimensional predictor X ∈ ℝ^p (where r ≥ 2), the statistical analysis of such data presents significant challenges due to the exponential increase in the number of parameters as the dimension of the response grows. Most existing dimension reduction techniques primarily focus on reducing the dimension of the predictors (X), not the dimension of the response variable (Y). Yoo and Cook (2008) introduced a response dimension reduction method that preserves information about the conditional mean E(Y | X). Building upon this foundational work, Yoo (2018) proposed two semi-parametric methods, principal response reduction (PRR) and principal fitted response reduction (PFRR), then expanded these methods to unstructured principal fitted response reduction (UPFRR) (Yoo, 2019). This paper reviews these four response dimension reduction methodologies mentioned above. In addition, it introduces the implementation of the mbrdr package in R. The mbrdr is a unique tool in the R community, as it is specifically designed for response dimension reduction, setting it apart from existing dimension reduction packages that focus solely on predictors.

• Communications for Statistical Applications and Methods
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• v.31 no.2
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• pp.191-202
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• 2024

The goal of this paper is to show how multivariate regression analysis with high-dimensional responses is facilitated by the response dimension reduction. Multivariate regression, characterized by multi-dimensional response variables, is increasingly prevalent across diverse fields such as repeated measures, longitudinal studies, and functional data analysis. One of the key challenges in analyzing such data is managing the response dimensions, which can complicate the analysis due to an exponential increase in the number of parameters. Although response dimension reduction methods are developed, there is no practically useful illustration for various types of data such as so-called large p-small n data. This paper aims to fill this gap by showcasing how response dimension reduction can enhance the analysis of high-dimensional response data, thereby providing significant assistance to statistical practitioners and contributing to advancements in multiple scientific domains.

• Steel and Composite Structures
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• v.11 no.4
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• pp.273-290
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• 2011

In current ductility-based earthquake-resistant design, the estimation of design forces continues to be carried out with the application of response modification factors on elastic design spectra. It is well-known that the response modification factor (R) takes into account the force reduction, strength, redundancy, and damping of structural systems. The key components of the response modification factor (R) are force reduction ($R_{\mu}$) and strength ($R_S$) factors. However, the response modification and strength factors for structural systems presented in design codes were based on professional judgment and experiences. A numerical study has been accomplished to evaluate force reduction, strength, and response modification factors for special steel moment resisting frames. A total of 72 prototype steel frames were designed based on the recommendations given in the AISC Seismic Provisions and UBC Codes. Number of stories, soil profiles, seismic zone factors, framing systems, and failure mechanisms were considered as the design parameters that influence the response. The effects of the design parameters on force reduction ($R_{\mu}$), strength ($R_S$), and response modification (R) factors were studied. Based on the analysis results, these factors for special steel moment resisting frames are evaluated.

• Communications for Statistical Applications and Methods
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• v.26 no.5
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• pp.519-526
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• 2019

Response dimension reduction in a sufficient dimension reduction (SDR) context has been widely ignored until Yoo and Cook (Computational Statistics and Data Analysis, 53, 334-343, 2008) founded theories for it and developed an estimation approach. Recent research in SDR shows that a semi-parametric approach can outperform conventional non-parametric SDR methods. Yoo (Statistics: A Journal of Theoretical and Applied Statistics, 52, 409-425, 2018) developed a semi-parametric approach for response reduction in Yoo and Cook (2008) context, and Yoo (Journal of the Korean Statistical Society, 2019) completes the semi-parametric approach by proposing an unstructured method. This paper theoretically discusses and provides insightful remarks on three versions of semi-parametric approaches that can be useful for statistical practitioners. It is also possible to avoid numerical instability by presenting the results for an orthogonal transformation of the response variables.

• Journal of Electrical Engineering and Technology
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• v.8 no.6
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• pp.1296-1304
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• 2013

This study performed an analysis on power demand reduction effects exhibited by demand response programs, which are advanced from traditional demand-side management programs, in the smart grid environment. The target demand response systems for the analysis included incentive-based load control systems (2 month-ahead demand control system, 1~5 days ahead demand control system, and demand bidding system), which are currently implemented in Korea, and price-based demand response systems (mainly critical peak pricing system or real-time pricing system, currently not implemented, but representative demand response systems). Firstly, the status of the above systems at home and abroad was briefly examined. Next, energy saving effects and peak demand reduction effects of implementing the critical peak or real-time pricing systems, which are price-based demand response systems, and the existing incentive-based load control systems were estimated.

• Structural Engineering and Mechanics
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• v.62 no.2
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• pp.209-224
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• 2017

Elevated water tanks are considered as important structures due to its post-earthquake requirements. Elevated water tank on reinforced concrete frame staging is widely used in India. Different response reduction factors depending on ductility of frame members are used in seismic design of frame staging. The study on appropriateness of response reduction factor for reinforced concrete tank staging is sparse in literature. In the present paper a systematic study on estimation of key components of response reduction factors is presented. By considering the various combinations of tank capacity, height of staging, seismic design level and design response reduction factors, forty-eight analytical models are developed and designed using relevant Indian codes. The minimum specified design cross section of column as per Indian code is found to be sufficient to accommodate the design steel. The strength factor and ductility factor are estimated using results of nonlinear static pushover analysis. It was observed that for seismic design category 'high' the strength factor has lesser contribution than ductility factor, whereas, opposite trend is observed for seismic design category 'low'. Further, the effects of staging height and tank capacity on strength and ductility factors for two different seismic design categories are studied. For both seismic design categories, the response reduction factors obtained from the nonlinear static analysis is higher than the code specified response reduction factors. The minimum dimension restriction of column is observed as key parameter in achieving the desired performance of the elevated water tank on frame staging.

• Earthquakes and Structures
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• v.14 no.6
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• pp.537-549
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• 2018

Using vertical links in eccentric braced frames is one of the best passive structural control approaches due to its effectiveness and practicality advantages. However, in spite of the subject importance there are limited studies which evaluate the seismic reliability and response reduction factor (R-factor) in this system. Therefore, the present study has been conducted to improve the current understanding about failure mechanism in the structural systems equipped with vertical links. For this purpose, following definition of demand and capacity response reduction factors, these parameters are computed for three different buildings (4, 8 and 12 stories) equipped with this system. In this regards, pushover and incremental dynamic analysis have been employed, and seismic reliability as well as multi-level response reduction factor according to the seismic demand and capacity of the frames have been derived. Based on the results, this system demonstrates high ductility and seismic energy dissipation capacity, and using the response reduction factor as high as 8 also provides acceptable reliability for the frame in the moderate and high earthquake intensities. This system can be used in original buildings as lateral load resisting system in addition to seismic rehabilitation of the existing buildings.

• The Korean Journal of Applied Statistics
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• v.34 no.4
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• pp.659-669
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• 2021

Multivariate regression often appears in longitudinal or functional data analysis. Since multivariate regression involves multi-dimensional response variables, it is more strongly affected by the so-called curse of dimension that univariate regression. To overcome this issue, Yoo (2018) and Yoo (2019a) proposed three model-based response dimension reduction methodologies. According to various numerical studies in Yoo (2019a), the default method suggested in Yoo (2019a) is least sensitive to the simulated models, but it is not the best one. To release this issue, the paper proposes an selection algorithm by comparing the other two methods with the default one. This approach is called principal selected response reduction. Various simulation studies show that the proposed method provides more accurate estimation results than the default one by Yoo (2019a), and it confirms practical and empirical usefulness of the propose method over the default one by Yoo (2019a).

• International Journal of Control, Automation, and Systems
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• v.2 no.4
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• pp.516-522
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• 2004

In this paper we investigate the properties of a generalized impulse response Gramian. The recursive relationship satisfied by the family of Gramians is established. It is shown that the generalized impulse response Gramian contains information on the characteristic polynomial of a linear time-invariant continuous system. The results are applied to model reduction problem.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2009.04a
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• pp.135-138
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• 2009

Most of the studies use model order reduction for low frequency (LF) response analysis due to their high computational efficiency. In LF response analysis, one of model order reduction, algebraic substructuring (AS) retains all LF modes when using the modal superposition. However, in mid-frequency (MF) response analysis, the LF modes make very little contribution and also increase the number of retained modes, which leads to loss of computational efficiency. Therefore, MF response analysis should consider low truncated modes to improve the computational efficiency. The current work is focused on improving the computational efficiency using a AS and a frequency sweep algorithm. Finite element simulation for a MEMS resonator array showed that the performance of the presented method is superior to a conventional method.