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Estimating the performance of heavy impact sound insulation using empirical approaches
Estimating the performance of heavy impact sound insulation using empirical approaches
Cho, Jongwoo; Lee, Hyun-Soo; Park, Moonseo; Song, Kwonsik; Kim, Jaegon; Kwon, Nahyun
2021-05-04 00:00:00
JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 2021, VOL. 20, NO. 3, 298–313 https://doi.org/10.1080/13467581.2020.1786390 CONSTRUCTION MANAGEMENT Estimating the performance of heavy impact sound insulation using empirical approaches a b c d e f Jongwoo Cho , Hyun-Soo Lee , Moonseo Park , Kwonsik Song , Jaegon Kim and Nahyun Kwon a b Department of Architecture and Architectural Engineering, Seoul National University, Seoul, Republic of Korea; Dept. Of Architecture and Architectural Engineering, Institute of Construction and Environmental Engineering, Seoul National University, Seoul, Republic of Korea; Department of Architecture and Architectural Engineering, Institute of Construction and Environmental Engineering, Seoul National University, Seoul, Republic of Korea; Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, MI, e f USA; Department of Architecture and Architectural Engineering, Seoul National Univ., Seoul, Republic of Korea; Department of Architecture and Architectural Engineering, Hanyang University, Ansan, Republic of Korea ABSTRACT ARTICLE HISTORY Received 28 October 2019 With an increasing demand for quieter residential environments, impact sound insulation for Accepted 29 May 2020 floating floors is gaining importance. However, existing methods for estimating the perfor- mance of heavy impact sound insulation are limited by their inability to comprehensively KEYWORDS analyze various types of floating floors, as well as difficulties mathematically determining the Sound insulation; floating input force of the reference source for heavy impacts. To overcome these limitations, this study floor; empirical modeling; proposes empirical models for estimating the sound insulation performance of floating floors multivariate regression; under heavy impacts. The proposed models are then validated; the model with the highest principal component regression accuracy exhibits an average estimation error of 2.73 dB at 50–630 Hz. The proposed models exhibit better accuracies than existing analytical models for frequencies below 100 Hz, where the estimation errors of the analytical models were large. Thus, the proposed models may help reduce errors in analytical estimates or when estimating a single numerical quantity for sound insulation rating during the design stage of multifamily housing. 1. Introduction cause a number of noise-related problems in high occupancy areas with multifamily housing (e.g., apart- The acoustic performance of residential buildings has ment buildings) as they are inevitably transmitted recently become a prominent issue due to recognition through the floors and walls (Eom and Paek 2009; of the adverse effects of noise on the health and lives Kim et al. 2009; K-eco 2018; Ho and Yoon 2019). Such of residents (e.g., speech interference, hearing impair- sounds are generally termed neighbor noise. ment, sleep disturbance, annoyance) (Berglund, According to the World Health Organization, neighbor Lindvall, and Schwela 1999; Secchi et al. 2016; Schiavi noise is the second major cause of noise annoyance 2018; NECRC 2016; Haron, Yahya, and Mohamad 2009; after road traffic in many European countries (WHO- Kwon et al. 2018). Specifically, floor impact sounds CONTACT Nahyun Kwon nhkwon78@naver.com Department of Architecture and Architectural Engineering, Hanyang University, Ansan, Republic of Korea © 2020 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the Architectural Institute of Japan, Architectural Institute of Korea and Architectural Society of China. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 299 Europe 2004). Moreover, the noise dispute resolution Grimwood 1997). Heavy impact sounds are authority (K-eco) in Korea, where approximately 75.7% a particular cause of nuisance for residents, especially of the population lives in multifamily housing, received in dwellings where people do not wear hard-heeled an average of 22,099 acoustic discomfort consultations shoes (K-eco 2018,Inoue, Yasuoka, and Tachibana pertaining to neighbor noise over the past five years 2000, Schoenwald, Zeitler, and Nightingale 2011, Oh (2014–2018); approximately 82.8% of all acoustic 2014). To quantify the poor sound insulation caused annoyance cases stemmed from floor impacts (e.g., by heavy impacts, the International Organization for footsteps, children running/jumping, and moving fur- Standardization (ISO) provides two reference impact niture) (K-eco 2018,Statistics Korea 2018). Therefore, sources as a tool for evaluating sound insulation floor impact noise should be effectively managed in performance: a tapping machine and a rubber ball residential buildings with shared floors and walls. (ISO 10140-3 2010; ISO 10140-5 2010; ISO 16283-2 As a way to manage floor impact sounds in multi- 2018). The tapping machine consists of five equally family housing, floating floor structures are widely spaced hammers that generate a series of constant used (Kim et al. 2009; Vér 1971; Cremer, Heckl, and impacts, which allows the accurate measurement of Petersson 2005; Park et al. 2015). Floating floors, continuous signals. However, the tapping machine, which comprise rigid walking surfaces decoupled which is acoustically equivalent to walking with hard- from the surrounding structure by resilient layers, heeled shoes, cannot adequately reflect the charac- have high potential for reducing disturbances due to teristics of heavy impacts (Schoenwald, Zeitler, and impact noises in dwellings (Schiavi 2018; Caniato et al. Nightingale 2011). On the contrary, the rubber ball, 2017). Accordingly, considerable attention has been which takes the form of a silicone rubber spherical given to estimating the impact sound insulation per- shell, is more appropriate for representing heavy formance of floating floors (Vér 1971; Gerretsen 1999; impacts because the sound response induced by its Stewart and Craik 2000; Schiavi, Belli, and Russo 2005; impact corresponds relatively well to that of an adult e Sousa and Gibbs 2014). These studies have primarily jumping (Tachibana and Tanaka 1996; Inoue, aimed to derive estimation models based on the the- Yasuoka, and Tachibana 2000). Nevertheless, the oretical analysis of sound transmission when a certain input force of the rubber ball approach is inadequate impact is input into a given system (i.e., a schematic for the analytical estimation of sound insulation per- model reflecting the shape of the floating floor). In formance because the rubber ball generates a single previous theoretical studies, experiments were per- free-fall impact and the measurement of such formed to verify the accuracy of the estimated insula- a transient impact is typically based on the maximum tion performance of floating floors (Mak and Wang value over a short time period (Hopkins 2014). To 2015). Floating floors can be categorized into three overcome these limitations, many studies have ana- types based on the connection state between the lyzed the deformation and impact force spectrum of walking surface and the base slab (Hopkins 2014; the rubber ball approach (Park, Jeon, and Park 2010) Rindel 2018). For floor types in which the walking sur- and performed mathematical modeling of the rubber face covers the entire base via resilient layers, the ball impacting a rigid surface (Schoenwald, Zeitler, insulation performance is considerably influenced by and Nightingale 2011). Despite these efforts, there the mass of the walking surface and the dynamic stiff - are still limitations to estimating the sound insulation ness of the resilient material (Gerretsen 1999; Schiavi, performance of floating floors due to the unique Belli, and Russo 2005; e Sousa and Gibbs 2014; Schiavi characteristics of the rubber ball (Robinson and et al. 2007; e Sousa and Gibbs 2011). However, for Hopkins 2015). other floor types, the estimation accuracy is poor for Therefore, this research aims to develop empirical practical applications, even when more factors are models for estimating the sound insulation perfor- considered (e.g., the quasi-longitudinal phase velocity, mance of various types of floating floor upon heavy loss factor, or surface area of the subsystem) (Vér 1971; impacts. One of the advantages of an empirical meth- Stewart and Craik 2000; Hopkins 2014; Dickow, odology, which derives models from observations or Brunskog, and Ohlrich 2013). experiments, is that it can provide convincing solutions Notably, previous analytical approaches for esti- even when the causal relationships among variables mating sound insulation performance are limited are ambiguous (Flood and Issa 2009). Accordingly, this because the input force is merely assumed as the advantage eliminates the need for impact force calcu- impact of a tapping machine. Footsteps, which are lations and allows the assessment of various types of the main cause of complaints regarding sound insu- floating floor during the model development process. lation in multifamily housings, can be categorized as However, adequate explanatory variables that suffi - either light impacts (e.g., those produced by foot- ciently explain the comprehensive estimation models steps in hard-heeled shoes) or heavy impacts (e.g., should be carefully considered. Hence, this research those generated by barefoot walking or running and utilizes several superficial variables as input variables jumping) (Hopkins 2014; Tachibana and Tanaka 1996; (e.g., surface density, structure thickness, contact area 300 J. CHO ET AL. on the walking/resilient layer, etc.) that can be com- base slab. Many researchers (Schiavi 2018; Kim et al. monly derived from each type of floor during the 2009; Gerretsen 1999; e Sousa and Gibbs 2014, 2011; design phase. This approach enables more flexibility Cho 2013) have limited the scope of their investiga- when optimizing sound insulation structures due to its tions to Type C floating floors because they do not compatibility and applicability; however, validation is contain any bars or coupling, unlike the other two required to confirm the effectiveness of the developed types. Due to its simple composition, analytical estima- models. tion models are relatively well established for this floor The steps performed in this study are as follows. (1) type based on sound and vibration transmission Preliminary research is conducted on floating floor theories. types, their impact on sound insulation performance, Based on the results of Cremer et al. (Cremer, Heckl, and the reference impact sources used as a premise for and Petersson 2005), the improvement in the sound the estimation in order to determine the limitations of pressure level, Δ L, of a Type C floor under tapping conventional approaches. (2) Considering the charac- machine impacts can be obtained using Equation (1): teristics of three types of floating floor and the vari- Δ L ¼ 40lg ðdBÞ; (1) ables used in analytical estimation approaches, explanatory variables are selected for empirical estima- where f is the octave or 1/3-octave band center fre- tion modeling. Simultaneously, a total of 45 sample quency (unit: Hz) to be observed and f is the reso- floating floors are prepared to collect data related to 0 nance frequency of the system (Hz), which is each variable. Subsequently, the sound reduction level dominated by the mass per unit area of the walking of each sample floor is measured using the rubber ball surface (ρ , unit: kg=m ) and the dynamic stiffness per method. Based on the measured values and the expla- 0 3 natory variables derived from the sample floating unit area of the resilient layer (s , unit: MN=m Þ. sffiffiffiffiffi floors, several estimation models are proposed 1 s through empirical approaches such as multivariate f ¼ ðHzÞ: (2) 2π ρ regression and principal component regression. (3) s Additional experiments are conducted using Equations (1 and 2) indicate that such a structure is a validation sample to compare the estimation error usually effective at high-frequency bands, but the between the developed models. Based on the expla- sound reduction decreases toward lower frequencies natory variables derived from the validation sample, (Gudmundsson 1984). In contrast to Type C, Types the estimation results of each developed model are A and B require structural coupling. Thus, many factors obtained. Then, the applicability of the developed affect the sound insulation performance and it is diffi - models is validated through an analysis of the absolute cult to estimate Δ L. In the case of Type A, an approx- differences and absolute error rate (AER) in the esti- imate estimation equation for Δ L under tapping mated and measured results. machine impacts can be derived using the statistical energy analysis model proposed by Vér (Vér 1971) (Equation 3): 2. Related works 2 3 2:3ρ c h η S ω L1 1 1 s1 1 2.1. Estimating sound insulation performance Δ L � 10lg ðdBÞ (3) Nk according to floating floor type where N is the number of mounts, k is the dynamic According to the classification of Hopkins (Hopkins stiffness of each resilient mount (N/m), the subscript 1 2014) and Rindel (Rindel 2018), the shapes of walking represents the properties of subsystem 1, which repre- surfaces that can float on base slabs were divided into sents a Type A floating structure, ρ is the mass per three main types, as shown in Figure 1. For the first unit area (=surface density, kg/m ), c is the quasi- type, labeled “A”, the walking surface and base are longitudinal phase velocity (m/s), h is the plate thick- connected via resilient materials at individual points. ness, η is the loss factor, S is the area (m ), and ω is the This form resembles what is often called a raised floor angular frequency ( ¼ 2πf ). consisting of pedestals and panels KS F 4760(2008). For Although some researchers (Hopkins 2014; the second type, labeled “B,” the walking surface is Maysenhölder and Horvatic 1998; Rindel 1994) have coupled along lines. For the third type, labeled “C,” evaluated c and η for homogenous materials by the walking surface continuously covers the entire assuming a finite plate, these values are difficult to determine in the design stage because they differ according to the material composition and shape of the floating structure. Thus, in addition to the relatively large number of variables, this aspect hinders the accuracy of Δ Lestimates for this floor type (Rindel Figure 1. Conceptual types of floating floor. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 301 2018). Furthermore, in the case of Type B, it is more a rubber ball transiently contacts a solid surface is difficult to estimate and generalize Δ L using a similar difficult to determine mathematically as the rubber approach to that of Vér (Vér 1971) because of the joint ball does not generate a constant impact over a long complexity and variety (Stewart and Craik 2000). Thus, period. Therefore, the observation involves measuring the ability of analytical approaches to estimate the the maximum sound pressure level within a short time sound insulation performance of floating floors is hin- period of 25 ms (Hopkins 2014). Some researchers have dered as their joint complexity increases. Moreover, modeled the force spectrum by considering morpho- because the estimation methods proposed in previous logical changes (Schoenwald, Zeitler, and Nightingale studies are based on floor type, they cannot provide 2011) or using observational approaches (Park, Jeon, the information required to select suitable sound man- and Park 2010). The force characteristics are modeled agement methods during the design stage. Therefore, to predict the sound insulation performance of the an estimation model that can comprehensively com- structure by using the force as the input parameter of pare the performance of different floor types is an analytical model. By employing this method, required to aid decision-making. Robinson and Hopkins (Robinson and Hopkins 2015) estimated the sound pressure level when a rubber ball impacted a homogeneous structure. However, the lim- itation of this approach is that it cannot be used to 2.2. Reference sources for heavy impacts evaluate the sound insulation performance of floating floors because they are commonly composed of het- The analytical models discussed above are commonly erogeneous materials. Some important studies on the derived using the impact force of the tapping machine sound insulation performance of floating floors are as an input variable. A tapping machine generates con- summarized in Table 1. In contrast to these studies, tinuous impacts by dropping five steel hammers the approach proposed in this study estimates the through an electrically operated lifting shaft from improvement in the sound pressure level (Δ L) under a height of 4 cm (ISO 10140-3 2010; ISO 10140-5 2010). rubber ball impacts for a diverse range of floating floor Its force spectrum is constant in intervals of 10 Hz and types utilizing the empirical methodologies described resembles a human wearing hard-heeled shoes walking in Section 2.3. on a heavy concrete floor. Tapping machines have com- monly been used due to the convenience of signal processing (e.g., averaging and normalization), which 2.3. Empirical modeling methodologies stems from their signal characteristics (Schoenwald, Zeitler, and Nightingale 2011). However, the sounds Mathematical models can be simply classified into generated by barefoot impacts or jumping children either empirical or analytical models. An empirical peak in the low-frequency range, unlike those of the model is developed based on the observed responses tapping machine, and are dominated by floor-structure of a specific system. In contrast, a model derived by vibration characteristics (Inoue, Yasuoka, and Tachibana considering the fundamental laws or principles that 2000). Therefore, to represent the sound characteristics govern the system is called an analytical model of such impacts, a rubber ball has been suggested as an (Flood and Issa 2009). Although empirical models do alternative. In this method, a hollow spherical shell not provide sufficient explanations of their outputs, composed of 30-mm-thick silicone rubber with an exter- they can help to yield appropriate solutions for areas nal diameter of 180 mm is dropped from a height of 1 m in which relevant input variables have not been com- (Tachibana and Tanaka 1996). prehensively established (Flood and Issa 2009). After As the forces of heavy impacts tend to be concen- reviewing the studies mentioned in Table 1, it is clear trated in the low-frequency band, Sousa and Gibbs (e that it is still difficult to determine the input variables Sousa and Gibbs 2014, 2011) investigated the para- (e.g., impact force of the rubber ball and variables meters influencing low-frequency impact sounds related to floating floor composition) required to under in-situ conditions for Type C floating floors. model heavy impact sound insulation using analytical These parameters included descriptions of the sur- approaches. Thus, empirical modeling is applied in this rounding elements rather than the floating floor, study to estimate the sound insulation performance of such as the material properties of the base slab, walk- floating floors. Regression analysis and principal com- ing surface dimensions, and edge conditions, in order ponent regression (PCR) are the primary to reduce the prediction uncertainty at low frequen- methodologies. cies. Some researchers (Kim et al. 2009; Park et al. 2015) Regression analysis, which is a widely used empiri- also used rubber balls as reference impact sources in cal modeling approach, attempts to model the rela- their experiments. These works also focused on resili- tionship between explanatory and response variables ent materials and their composites for Type C floors. by fitting a linear equation to the observed data. An However, compared with the force generated by approach using two or more explanatory variables is a tapping machine, the force produced when termed multivariate regression (MR) (Pires et al. 2008). 302 J. CHO ET AL. Table 1. Literature review on impact sound insulation of floating floors. Estimating Reference Subject Authors Research contents Highlighted factors methods impact structure machine Gerretsen (1999) Validation of Cremer’s ΔL estimation model through the Material properties Analytical Tapping properties of various materials Type C floating floor Schiavi et al. (2007) Research on the change in acoustic performance of Material properties Analytical Tapping machine resilient materials under floating floors over time (resilient layer) Type C floating floor Vér (1971) Derivation of the ΔL estimation model for point- Estimation model Analytical Tapping machine supported floating floors based on analytical development approach Type A floating floor Rindel (1994) Research on the phase velocity of various concrete Material properties – – Type A floating affecting the vibration transmission floor Stewart and Craik (2000) Research on ΔL estimation for batten-supported floating Vibration Analytical Tapping machine floor based on proposed wave transmission model transmission modeling Type B floating floor Inoue et al. (2000) Development of a rubber ball as a standard impact Reference impact – Rubber – source representing heavy impact source ball development Schoenwald et al. (2011) Research on modeling the time-depending impact force Impact force – Rubber – of rubber balls considering their deformation of spectrum ball shape modeling Robinson and Hopkins Research on estimation of sound pressure level upon Validation of Analytical Rubber Homogenous (2015) transient rubber ball impact in homogenous structure analytical ball concrete estimation structure Kim et al. (2009) Research on the relation between the dynamic stiffness Material properties Empirical Bang machine and the heavy impact sound pressure level (resilient layer) Type C floating floor Cho (2013) Research on sound pressure level comparisons between Observation focused Analytical Bang machine analytical estimates and in situ measurements on 63 Hz octave band Type C floating floor Principal component analysis (PCA) is a powerful multi- Equation (5), the standardized PCR equation for esti- variate technique not only for analyzing the structures mating the response variable, y, using the selected PCs of variables or compressing data sets while preserving and their regression coefficients is important information but also for dealing with the X y ¼ B PC (5) j j multicollinearity problem which causes inappropriate j¼1 regression estimates in MR (Abdi and Williams 2010; where ^ y is the estimated PCR value, B is the jth stan- Rencher 2002). PCA is a mathematical method that dardized partial regression coefficient of PC , and P is utilizes orthogonal linear transformation to convert the selected number of PCs. Consequently, the final correlated variables into a set of uncorrelated variables form of this PCR process resembles a general linear (Ji, Park, and Lee 2012). Gathering the highly correlated regression (Li et al. 2015). variances of the given data set, PCA creates new vari- ables called principal components (PCs) that are ortho- gonal and uncorrelated. As shown in Equation (4), PC , 3. Model for estimating heavy impact sound one of the created PCs, is presented as a linear function insulation performance of all standardized original variables X : This study developed empirical models for estimating PC ¼ c X (4) the improvement in sound pressure level (Δ L) achieved j ij i i¼1 by floating floors under rubber ball impacts. The model Here, c is the eigenvector corresponding to the jth PC development process consists of (1) data collection ij and ith explanatory variable (Li et al. 2015). In PCA, the and (2) empirical modeling (Figure 2). In the data first PC (PC ) demonstrates the greatest variance in the collection phase, the explanatory variables for the data. Also, the contribution of converted PCs for the empirical modeling are selected, including the vari- original variance can be prioritized by the subscript ables whose correlation to Δ L has been verified analy- values of the PCs. (Kwan 2008). tically in previous research (Vér 1971; Cremer, Heckl, PCR, which is used in this research as an empirical and Petersson 2005; Stewart and Craik 2000; Schiavi, modeling technique, utilizes the PCs selected through Belli, and Russo 2005). Then, data for the explanatory PCA as explanatory variables in MR; that is, this and response variable Δ L are collected for different approach is a combination of PCA and MR (Pires et al. floating floor samples. In the empirical modeling 2008). PCR establishes the relationship between the phase, correlations between the quantitative explana- output variable, y, and the selected PCs derived from tory variables are examined because their multicolli- the standardized input variables X . As shown in nearity can lead to an adverse effect on estimation i JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 303 are the structure thickness, h, the contact surface area of the walking layer, S , the contact surface area of top the resilient layer per unit area, S , and the ratio bottom between the two contact surface areas, C . These ratio variables can be expressed in values per unit area. As the floor type affects the sound insulation performance (Vér 1971; Cremer, Heckl, and Petersson 2005; Stewart and Craik 2000; Hopkins 2014), it is assumed that the four variables are also correlated to Δ L; however, the estimation results of an empirical model using these variables must be further validated. Figure 4 illustrates the four variables in detail, using Type B as an example. If the middle part with an area of 0:4� 3 m is in contact with a total walking surface area of 6 m , S is 0.2. Similarly, if the bottom of the top middle part has an area of 0:45� 2 m , S bottom becomes 0:9� 6 ¼ 0:15, where C is 0:2� 0:15 ratio � Figure 2. Framework of empirical sound insulation estimation 1:3 (i.e., S /S ). If the same walking surface is top bottom model for heavy impact. supported by nine pedestals which have the same top and bottom side area of 0.06 (i.e., the middle part of Type A in Figure 3), S and S are equally accuracy. Next, the estimation models are developed top bottom ð0:06� 9Þ� 6 ¼ 0:09, where C is 1. If the walking using two different empirical approaches (MR and PCR) ratio surface is directly supported by a resilient layer (i.e., because the performance of empirical approaches var- Type C), S ; S , and C become 1. Also, the ies depending on the data characteristics. top bottom ratio vertical form information of floating floors is expressed by h, the height from the upper side of the resilient 3.1. Data collection layer to the walking surface. Table 2 summarizes the explanatory variables used in the empirical modeling. 3.1.1. Explanatory variable selection A floating floor commonly has a resilient layer and a walking surface on the base slab. Because types of 3.1.2. Data acquisition floating floor are distinguished by the connection state To obtain data corresponding to the selected explana- of the middle part between the resilient layer and the tory variables, floating floor samples were prepared by walking surface, the variables used in the estimations varying the three components. First, the three sample should be able to explain the information regarding (1) floor types include raised floors using cement panels the connection state of the floor, (2) the damping with a joint compound (i.e., Type A), battens/joists properties of the resilient layer, and (3) the physical incorporating polypropylene (i.e., Type B), and form of the walking surface, as shown in Figure 3. a continuous layer of cement boards (i.e., Type C). Therefore, for MR modeling, one qualitative variable Second, the resilient layer of samples consists of either (i.e., the floor type) and two quantitative variables (i.e., a 12-mm-thick layer of polyurethane (PU), a 24-mm- the surface density of the walking surface ρ and the thick PU layer, or a 24-mm-thick ethylene-vinyl acetate dynamic stiffness of the resilient layer ðs )) are used as compound. The purpose of changing the resilient layer 0 0 explanatory variables to estimate Δ L considering the is to obtain several different s values. Thus, the s analytical equations (Equations (1–3)). For PCR model- values of each resilient layer are measured according ing, the floor type variable is substituted for four quan- to ISO 9052–1 (ISO 9052-1 1989). Finally, the walking titative variables because the purpose of PCR is to surface of samples consists of five thicknesses of propose empirical estimation models that are univer- sally applicable regardless of the floor type. The four variables that contain information regarding the con- nection state and are identifiable in the design stage Figure 4. Derivation of explanatory variables describing mid- Figure 3. Factors that distinguish the type of floating floors. dle-part connection state. 304 J. CHO ET AL. Table 2. Configuration of variables for empirical ΔL Estimation Model. Notation Unit Description Applied approach Explanatory variables - - Floating floor type (qualitative) MR ρ kg/m Surface density MR, PCR 0 3 s MN/m Dynamic stiffness of the resilient layers MR, PCR h m Structure thickness PCR S m Contact area on the walking layer (per unit area) PCR top S m Contact area on the resilient layer (per unit area) PCR bottom C - S /S PCR ratio top bottom cement board by varying the number of 12-mm-thick edges of the installed samples. To avoid measuring cement board stacks from zero to eight. Each cement outliers that can occur when the microphone is too board has a mass of 16.3 kg/m . Therefore, the total close to the room edge, the microphones were sample size is 45 (composition of three floor types � installed at four evenly distributed measurement three resilient layers � five walking surfaces). For each points located 0.7 m from the receiving room wall at of these samples, the variables presented in Section a height of 1 m. When using a rubber ball as the impact 3.1.1 are derived and used to develop the estimation source, the measured fast time-weighted maximum models. Figure 5 illustrates different floating floor sam- sound pressure level, L , is generally in the fre- i;Fmax ples depending on the substructure shape, resilient quency range of 50–630 Hz (ISO 10140-3 2010; ISO layer, and laminated mass. 16283-2 2018). The sound pressure level for each To obtain the response variable data, Δ L, impact was obtained from microphone positions M1– 2:5� 2:5-m-dimension floating floor samples with M4, as illustrated in Figure 6. The measurements each detail level element of the three components obtained from each microphone through a 1/3 octave illustrated in Figure 5 were sequentially installed in band filter were then averaged using Equation (6): the center of impact source room of an experimental 1 n laboratory and impacted by a rubber ball. Figure 6 L =10 Fmax;k L ¼ 10 lg 10 ðdBÞ: (6) i;Fmax k¼1 shows laboratory specifications with the sample instal- lation location, its impact positions in the source room, In addition, for each L value of the 1/3-octave i;Fmax and the microphone positions in the receiving room. band, the response variable is Δ L for the floating floors The samples were constructed by placing a resilient when exposed to the impact of the rubber ball: layer first, substructure on it, and laminating several cement boards over the substructure. The laboratory, Δ L ¼ L L ðdBÞ (7) slab specimen which has a 210-mm-thick concrete base slab, is a two- story reinforced concrete structure; its second floor Here, L is the value of L when the bare slab of slab i;Fmax was used as the impact source room, and the first the impact source room is impacted by the ball and floor was used as the receiving room. To reflect the L is the value of L when the impact source specimen i;Fmax general characteristics of multifamily housing in Korea, room slab is impacted with a given sample installed. the base slab thickness of the laboratory was set con- Consequently, the measurement dataset for each sidering the floor thickness guidelines for multifamily impact consists of 12 Δ L values in the 50–630 Hz fre- housing structures in Korea (MOLIT 2013). quency band, expressed as Δ L , Δ L ;��� ; Δ L . 50 63 630 As shown in Figure 6, five evenly distributed impact positions were employed, with one point near the center and the other four points 0.5 m from the Figure 6. Laboratory specifications, with impact and micro- Figure 5. Description of sample structures. phone positions. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 305 most distinctive results. As presented in Figure 7(a), 3.1.3. Measurement results the average Δ L is largest for Type A and smallest for As described above, each sample was impacted at five points, and each impact provided Δ L values in Type C over almost the entire observed frequency range (i.e., Type C shows the least improvement in the 50–630 Hz frequency range. For a more precise the sound pressure level). The sound insulation investigation of Δ L differences according to the effects of the floating floor types can, therefore, be respective detail levels illustrated in Figure 5, the Δ L measurements obtained from common detail ranked in descending order as follows: Type A > B > C. Type C shows a significant difference to the other levels were clustered and averaged. Figure 7 types in that the noise is somewhat amplified in the shows the mean measured values of the respective levels within the observed frequency range at 95% 50–80 Hz band. However, according to Figure 7(b), there is no notable difference in the average value confidence intervals. In other words, the black rec- of Δ L due to the change of resilient material when tangular points in Figure 7(a) represent the averages of measured Δ L obtained from samples compared to the differences caused by a change in the floor type or walking surface. This result could with “Type A” as a common denominator; this be misunderstood as indicating that the damping of group consists of 15 samples containing each one of three different levels of resilient layers and five an impact force has no effect on the sound control. different levels of stacked boards, respectively. Thus, more detailed analysis of this result will be addressed in Section 5. In Figure 7(c), Δ L seems to As can be deduced from Equation (1), Δ L tends improve as the mass of the walking surface to increase as the observation frequency increases. Among the three graphs in Figure 7, and Figure 7 increases. In a series of experiments, the number of stacked boards ( ¼ N) was controlled at regular (a), which compares the structure type, shows the intervals, but the reduction effect due to the increase in ρ seemed to decrease gradually. This result implies that the relationship between ρ and Δ L is not linear. Therefore, considering the results shown in Figure 7(c) and Equations. (1 and 2), it seems appropriate to apply logarithmic transforma- tion to the explanatory variables in the empirical modeling. 3.2. Empirical modeling 3.2.1. Multicollinearity between explanatory variables Although the explanatory variables in Table 2 are com- mon elements of the three floor types, it is unreason- able to regard them as mutually exclusive. Accordingly, it is necessary to confirm the correlations among them prior to deriving the estimation models based on the collected data. If the correlation is significant and high, the linear model derived from the regression analysis cannot provide appropriate estimates. Thus, a correlation analysis matrix for the explanatory vari- ables is presented in Figure 8. The correlation calcula- tions and subsequent model development were performed using the R language and environment (R Core Team 2019). When the six variables were sepa- rated into three categories; that is, rigid body traits (ρ , h), connection states (S , S , C ), and resi- top bottom ratio lient properties (sÞ, remarkably high correlations were found within each category. With a large frame, there was almost no correlation between the resilient prop- erties and those in the other two categories; however, the rigid body traits and connection states exhibited Figure 7. Comparison of measured ΔL: (a) the comparing close correlations. These results imply that the multi- result focusing on the type of floating floors, (b) the compar- collinearity problem cannot be avoided if all explana- ing result focusing on resilient layers, (c) the comparing result tory variables are applied to the MR. Thus, the focusing on the stacked cement boards. 306 J. CHO ET AL. Figure 8. Correlation matrix of quantitative explanatory variables. influence of multicollinearity should be minimized through variable extraction or suppression methods (Li et al. 2015). The following two sections describe the generation of empirical models using these two approaches. Figure 9. Regression equations and graphs for relation between ∆ L–s , – s (Type A). ’ ’ 3.2.2. Multivariate regression In regression analysis, one of the fundamental empiri- cal modeling approaches, the simplest method of minimizing the influence of multicollinearity is to use only those variables exhibiting no correlation (Rencher 2002). As shown in Figure 8, ρ and s are not signifi - cantly correlated. Furthermore, considering Equation (2) regarding Type C floors, which are not coupled to the surrounding structure, it is expected that a highly appropriate linear equation could be derived from these two variables. For the other floor types, these two variables can also be regarded as significant expla- natory variables for estimating Δ L under heavy impacts. In addition, considering the measurement results and the fact that the response variable Δ L was obtained in units of decibels, a logarithmic transforma- 0 0 tion was applied for the quantitative variables s and s . Therefore, the regression equations for each type were first derived using the qualitative variable; i.e., the floating floor types, in addition to the two logarithmi- cally transformed quantitative variables. In total, 12 multivariate regressions were performed to construct a model to estimate Δ Lof each 1/3 octave band fre- quency. As qualitative data were applied as explana- tory variables in the multivariate regression, corresponding to three different structure types, three regression equations were derived from each regression analysis. In this research, the derived set of regression equations in the 50–630 Hz frequency range Figure 10. Regression equations and graphs for relation is termed the MR model. Figures 9–11 show the MR between ∆ L–ρ , – s (Type B). s JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 307 3.2.3. Derivation of PCR models To derive a more generally applicable model than pre- vious MR models, another empirical modeling process was performed. Instead of variable extraction, another way to derive an estimation model that minimizes the influence of multicollinearity is to suppress the variable (Li et al. 2015). This involves using PCs obtained through PCA that have orthogonal and uncorrelated relationships as the explanatory variables. PCA is a process of deriving new variables through the var- iance of data with different units. For unit unification, Figure 11. Regression equations and graphs for relation 0 normalization is required. The PCA results of the log- between ∆ L–ρ , – s (Type C). transformed and normalized variables are presented in Table 3, which also lists the eigenvectors and cumula- tive variances of the PCs. results, which illustrate the relationships among ρ , S , On closer examination of the PCA results, PC3 is and Δ L for each frequency band and their regression 0 0 mainly dominated by S , whereas S has a dominant equations for Type A, B and C floors, respectively. influence on PC4 via the C . It is particularly note- ratio In the regression results for the 50-Hz frequency worthy that PC4 contains a large volume of informa- band, it is difficult to judge whether the results are tion about the ratio of the connection between the significant due to the low coefficient of determination top and bottom surfaces. In addition, PC1 and PC2 (R = 0.37). However, the results for other frequency account for 0.67 of the total dataset variances, with bands are applicable because they have R values of PC3 and PC4 accounting for 0.17 and 0.15, respec- 0.67–0.8, exceeding the permissible threshold of 0.6 tively. To construct PCR models, the number of PCs to (Rencher 2002). According to Equations (2 and 3), ∆L be used as explanatory variables must be deter- should have a positive correlation with ρ and mined. According to the cumulative variance shown a negative correlation with S . Indeed, the MR model in Table 3, as PC1–PC3 account for 84% of the total showed that ∆L and ρ were positively correlated variance, it is reasonable to construct a model only across all frequency bands. The improvement in ρ using these three variables. However, by including decreased gradually when it exceeded a certain level. PC4 in the PCR modeling, one can account for 99% Of course, this aspect may have been amplified of the total variance of the dataset. Consequently, it is because this relationship was assumed to follow necessary to compare models that include PC4 with a logarithmic model. However, contrary to expecta- models that do not. The sets of equations derived tions, the Δ L S relationship was found to vary from the two different PCR processes according to between negative and positive correlations depending the number of explanatory variables are termed PCR3 on the frequency band. Besides, the significance level and PCR4 models. These two PCR models and their (p-value) of S xceeded 0.05 in the 80, 315, and 630 Hz coefficients of determination are compared in frequency bands of the MR model. This indicates that S Table 4. does not have a statistically significant effect on Δ L. For Similar to the results of the previously investigated the results that do not fit with the sound transmission MR model, the signs of the regression coefficient of the theories, additional analysis is provided in Section 5. PCs that contain large amounts of information regard- In a comparison of the three types of prediction sur- ing S (i.e., PC3 and PC4) vary between positive and face based on the smallest ρ values (i.e., 40 kg/m ) negative depending on the frequency range. illustrated in Figures 9–11, Type A shows positive values Comparing the average R values of each model, the of ∆L in the 63–160 Hz frequency range (Figure 9). In values decrease in the order of MR (0.71) > PCR4 (0.67) contrast, Type B is possible to amplify the heavy impact > PCR3 (0.66), but the difference between PCR4 and sound at 63 Hz, as the prediction shows a negative value (Figure 10), and Type C can cause amplification through- out the 63–160 Hz frequency range (Figure 11). In the Table 3. Eigenvectors and cumulative variance of PCs. 200–315 Hz range, ∆L of Type A is predicted over 10 dB. Explanatory variable PC1 PC2 PC3 PC4 PC5 PC6 Type B is expected to show slightly better sound insula- ρ 0.32 0.68 −0.14 0.03 −0.65 −0.00 h 0.52 0.36 −0.23 0.26 0.69 0.00 tion performance than Type C, and Type C will start to S −0.55 0.26 −0.30 0.25 0.08 0.69 top show a sound insulation effect without amplification S −0.56 0.34 −0.20 0.11 0.13 −0.71 bottom from this frequency range based on the ρ of 40 kg/ C 0.13 −0.45 −0.44 0.70 −0.28 −0.14 s ratio s 0.07 −0.16 −0.78 −0.61 0.00 −0.00 m . Also, the difference between predicted ∆L of three % cumulative 0.41 0.67 0.84 0.99 1.000 1.000 types appears to decrease from the observation range variance over 400 Hz. Values in bold indicate the most influence variables for each PC. 308 J. CHO ET AL. Table 4. Comparison of PCR models. PCR3 (explanatory variables: PC1–PC3) PCR4 (explanatory variables: PC1–PC4) 2 2 Estimation model R Estimation model R ΔL 8:6þ 3:6PC þ 1:2PC 2:5PC 0.33 5:2þ 4:1PC 1:4PC þ 2:2:PC 0.34 2 3 1 3 4 ΔL 9:8þ 8:5PC þ 3:2PC þ 0:7PC 0.64 5:9þ 9:0PC þ 2:6PC þ 2:0PC þ 2:2PC 0.64 1 2 3 1 2 3 4 ΔL 8:7þ 9:8PC þ 4:2PC þ 0:4PC 0.73 10:0þ 9:7PC þ 4:3PC þ 0:8PC þ 0:7PC 0.73 1 2 3 1 2 3 4 ΔL 2:8þ 7:1PC þ 7:9PC 6:0PC 0.69 1:4þ 6:5PC þ 8:4PC 4:6PC þ 2:8PC 0.70 1 2 3 1 2 3 4 ΔL 3:5þ 8:0PC þ 9:9PC 2:1PC 0.71 5:7þ 8:0PC þ 9:9PC 1:6PC þ 1:2PC 0.71 1 2 3 1 2 3 4 ΔL 8:1þ 7:8PC þ 8:9PC þ 3:2PC 0.72 4:5þ 6:9PC þ 9:9PC þ 1:4PC 3:4PC 0.73 1 2 3 1 2 3 4 ΔL 2:1þ 6:8PC þ 7:6PC 0:3PC 0.66 6:9þ 6:6PC þ 7:8PC þ 1:1:PC þ 2:7PC 0.67 1 2 3 1 2 3 4 ΔL 4:5þ 5:2PC þ 6:8PC þ 2:8PC 0.65 3:7þ 5:1PC þ 6:9PC þ 2:5PC þ 0:5PC 0.65 1 2 3 1 2 3 4 ΔL 0:4þ 6:2PC þ 7:0PC þ 3:1PC 0.63 4:3þ 6:3PC þ 6:8PC þ 3:5PC 2:9PC 0.64 315 1 2 3 1 2 3 4 ΔL 1:7þ 8:0PC þ 8:7Pc þ 2:1PC 0.79 6:9þ 8:1PC þ 8:4PC þ 2:9PC þ 3:4PC 0.79 400 1 2 3 1 2 3 4 ΔL 3:1þ 8:1PC þ 10:6PC þ 2:1PC 0.72 6:8þ 8:3PC þ 10:3PC þ 3:2PC þ 2:3PC 0.73 500 1 2 3 1 3 3 4 ΔL 1:9þ 7:6PC þ 12:6PC 1:0PC 0.63 10:3þ 7:7PC þ 12:4PC 0:9PC 5:2PC 0.65 630 1 2 3 1 2 3 4 PCR3 is not significant. It is not sufficient to discuss the objective analysis of the estimation results (Ji, merits of these models based on the analysis pre- Park, and Lee 2012; Kwon et al. 2017, 2019a). sented thus far; therefore, comparison and validation Thus, the estimates were expressed as L specimen of the estimation performance of the models are using Equation (7) even though the three models assessed using additional experimental data. estimated Δ L for a clearer observation of the sound improvement effect. The AER was calculated using Equation (8): 4. Model validation � � � � L L A E � � Model validation was conducted focusing on type AERð%Þ ¼ � 100 (8) � � A expected to improve sound insulation most, consider- ing the estimation result derived from proposed models. where L and L denote the actual and estimated A E To improve their practical applicability, single-layer L . Larger AER values indicate greater estimation specimen panels were manufactured for the model validation. errors and reduced accuracy. Table 5 presents the The panels were designed to satisfy two requirements. The first requirement was that ρ should not cause sound amplification throughout the observed fre- quency range when the resilient material exhibits the medium level of s used in the data collection phase. Accordingly, ρ was set to be greater than 80 kg/m based on the regression equations in Figure 9. The second requirement was that the panel size should consider the manual workability according to the deter- mined value of ρ . Thus, the size was adjusted to 400 mm� 400 mm so as not to exceed a weight of 15 kg per panel. Panels of this size are smaller than the panels of the Type A substructure (500 mm� 500 mm) used in the data collection phase but have larger values of ρ . The manufactured panels were applied to the Type A shape and employed for collection of the valida- tion data. Because of their size difference, these panels required more pedestals for support, which generated slight differences in the connection state as well as in the rigid body traits. The section drawing and explana- tory variables of the validation sample are provided in Figure 12. The sound pressure level of the installed sample condition (L ) was measured using the same specimen procedure and environment described in 3.1.2. The data from the five impact positions were also aver- aged using Equation (6). Simultaneously, based on the explanatory variables, L was estimated specimen using the three developed empirical models. As in Figure 12. The section drawing and specifications of validation several other studies, the AER was used for an sample. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 309 Table 5. Absolute differences and AER between measurements and estimates. Estimated value (dB) Absolute difference (dB) Absolute error rate (%) Frequency (Hz) Actual value MR PCR3 PCR4 MR PCR3 PCR4 MR PCR3 PCR4 50 Hz 64.59 65.72 62.95 63.20 1.13 1.64 1.39 1.75% 2.54% 2.15% 63 Hz 60.78 56.89 57.88 58.21 3.90 2.91 2.57 6.41% 4.78% 4.23% 80 Hz 60.83 61.18 62.70 62.62 0.34 1.86 1.79 0.56% 3.06% 2.94% 100 Hz 55.56 61.21 63.10 62.59 5.65 7.54 7.03 10.17% 13.57% 12.66% 125 Hz 58.73 58.69 60.47 60.38 0.04 1.74 1.65 0.07% 2.96% 2.81% 160 Hz 52.01 50.40 53.18 52.58 1.62 1.17 0.57 3.11% 2.24% 1.09% 200 Hz 44.56 45.76 48.09 47.84 1.20 3.53 3.28 2.69% 7.92% 7.36% 250 Hz 46.76 44.71 46.23 46.19 2.05 0.53 0.57 4.37% 1.12% 1.22% 315 Hz 40.02 40.66 42.29 42.31 0.63 2.27 2.29 1.58% 5.66% 5.71% 400 Hz 33.35 37.17 38.63 38.70 3.82 5.28 5.35 11.45% 15.84% 16.04% 500 Hz 28.49 32.73 33.71 33.88 4.24 5.22 5.39 14.88% 18.33% 18.91% 630 Hz 22.46 30.61 31.37 31.29 8.15 8.92 8.84 36.30% 39.70% 39.36% Mean 2.73 3.55 3.39 7.78% 9.81% 9.54% differences and AERs between the actual and esti- as an explanatory variable in the experiments according mated values for each model. to the results of previous studies, which indicated that The mean absolute differences and AERs Δ L under tapping machine impacts is negatively corre- between the measurements and estimates obtained lated with s (Gudmundsson 1984); however, resilient using the three models were 2.73 dB and 7.78% for materials with extremely low values of s were excluded MR, 3.55 dB and 9.81% for PCR3, and 3.39 dB and from the investigation as such materials can cause dis- 9.54% for PCR4. A comparison of the models shows comfort on the sensation of hardness while walking that the MR model had the smallest estimation (AURUM 2013, Matsuda and Shimizu 2017). However, errors. The error of the PCR4 estimate was slightly previous experimental data regarding the relationship lower than that of the PCR3 estimate, and PCR3 between heavy impact sound insulation performance 0 0 showed the largest estimation errors. Looking clo- and s (Kim et al. 2009) indicate that s does not exhibit sely at the absolute differences and AERs across the a significant effect in the range over 10 MN/m . observation frequency bands, all models showed Therefore, to derive an empirical model that accurately differences of over 8.15 dB and AERs of more than reflects the influence of s , more observation data corre- 36.3% at the 630-Hz octave band; this represents sponding to very low values of s should be included in a limitation of the models in terms of their estima- the empirical modeling. tion capabilities. On the other hand, all models demonstrated very good estimation capabilities, with absolute differences and AERs not exceeding 5.2. Coefficients of determination and validation 4 dB and 7% in the range of 0–315 Hz, respectively. results of developed models However, the absolute difference and AER of MR, The mean coefficients of determination of the three PCR3, and PCR4 in the 100-Hz range were 5.65 dB proposed models were 0.74 (MR), 0.69 (PCR3), and 0.7 (10.17%), 7.54 dB (13.57%), and 7.03 dB (12.66%), (PCR4), except at 50 Hz. The difference between the R respectively; this indicates limited accuracy com- values of the MR and PCR models can be explained by pared to the other frequency bands. This result is the fact that not all variables related to sound trans- attributed to the stack of cement boards causing mission are included in these models. The explanatory excessive resonance during the experiments in the variables in the PCR models can be considered as the data collection phase. results obtained by substituting the qualitative vari- able in the MR model (i.e., the floating floor type) 5. Discussion with other quantitative variables describing the con- nection state. Accordingly, the variables added to the 5.1. Experimental results from data collection PCR model may not fully describe the information phase expressed by the floating floor type. Nevertheless, R As shown in Figure 7(b), no significant Δ L improvement and the estimation accuracy were slightly improved by was obtained in the experiments by varying the resilient adding PC4 to the PCR model. Thus, the C ; i.e., the ratio 3 0 layers in the range from 29.2 to 51.6 MN/m of s . dominant quantity contained in PC4, is useful for Consequently, the proposed empirical estimation mod- explaining the sound insulation characteristics of float - els are robust against the influence of the dynamic ing floors and increasing the estimation accuracy. As stiffness of the resilient material s . This characteristic PCR modeling is relatively free from multicollinearity can be used to differentiate heavy impact sound insula- problems, it is possible to improve the estimation tion from light impact sound insulation. s was selected accuracy by adding related explanatory variables. 310 J. CHO ET AL. Thus, including variables in PCR or other empirical relatively low-frequency domain where the force of modeling processes that are difficult to include in heavy impact source concentrated. Also, under the analytical models but that contain relevant informa- condition that ρ and s are the same, the expected tion (e.g. variables regarding constituent materials) is sound insulation performance is estimated to be in the expected to improve the estimation accuracy. following order: Type A > B > C. In this respect, the In terms of the model validation results, the results validation of derived models was conducted first for showed slight differences of 5 dB below 500 Hz; that is, Type A which is expected to show good sound insula- the difference that is difficult to be easily perceived by tion performance, to consider the applicability. people. The errors also seem to be acceptable when For scientific investigation, sound pressure level compared with the predictions of other studies using measurements provide values that are frequency empirical approaches (Kwon et al. 2017, 2019b). dependent. However, to evaluate the sound insulation Further, the validation experiment was planned such effect more intuitively in practical applications, the that amplification would not occur anywhere in the acoustic performance is generally expressed by con- observed frequency band, and the results confirmed verting the frequency-dependent value into a single this. However, the proposed models tended to under- numerical quantity (ISO 717-2 2013; KS F 2863-2 2007). estimate the sound insulation performance of the By converting the estimates and measurements listed floating floors in the higher frequency range, resulting in Table 5 using the standard method, the single in estimation errors of 8.15–8.92 dB at 630 Hz. The fact numerical quantities L of the three models are i;Fmax;AW that the proposed models themselves were developed calculated as 43 dBA (actual), 44 dBA (MR), 45 dBA to be robust against variations in s could be one of the (PCR3), and 45 dBA (PCR4). Based on this result, the causes of this phenomenon. In contrast, approximately differences between the proposed models are not 10 dB of estimation errors were observed below 100 Hz more than 2 dBA. The L calculation is largely i;Fmax;AW in a previous study, which estimated the sound pres- dominated by the value in the frequency band in sure level when a homogenous bare slab was which the sound pressure level is high. Accordingly, impacted by a rubber ball using an analytical approach the error is reduced when converting to the value used (Robinson and Hopkins 2015). This accuracy level does for rating because the impact force of the rubber ball is not differ substantially from that of the estimation concentrated at low frequencies, where the proposed results obtained for tapping machine impacts using models exhibit better estimation accuracy. Therefore, analytical approaches (Hopkins 2014). According to even though the proposed models show low accuracy comparisons with analytical models, the three pro- in some frequency ranges, they can be used to pre- posed models yielded competitive estimates in the cisely estimate L and provide construction i;Fmax;AW low-frequency range below 100 Hz, where the estima- managers or designers with useful information regard- tion accuracy of the analytical models is low. In addi- ing the expected acoustic performance of residential tion, their estimates are relatively inaccurate in the buildings during the design stage. Moreover, it is range above 400 Hz, where estimates by the analytical appropriate to use the MR model first due to its higher model become more accurate. In other words, empiri- accuracy. cally and analytically derived models exhibit good esti- mation accuracy in opposing frequency ranges. Just as analytical models are considered useful despite the 6. Conclusions error of approximately 10 dB in a specific frequency Despite the recent increase in demand for quieter range, the three proposed models were confirmed to residential environments, the available techniques for be sufficiently useful and to have good accuracy in the estimating the sound insulation performance in resi- following order: MR > PCR4 > PCR3. According to pre- dential buildings remain limited. This limitation vious experimental results (Mak and Wang 2015; includes estimation of sound insulation performance Ohlrich 2011), the inevitable omission of cross- under the impact of a rubber ball representing bare- coupling in analytical estimation modeling could foot impacts or children jumping. Mathematical deter- cause the estimates to deviate at low frequencies. mination of the impact force of the rubber ball has Therefore, future research regarding the complemen- obstacles for solving the problem through analytical tary use of the two approaches is necessary to improve approaches. Therefore, the objective of this research estimation accuracy. was to empirically estimate the sound insulation per- formance of floating floors under rubber ball impacts. 5.3. Applicability of developed models To consider the various types of floating floors, three empirical models (MR, PCR3, and PCR4) were derived According to the collected data in 3.1.3 and the esti- using information that can be easily obtained during mation result based on empirically derived models in the design stage by referring to previous analytical 3.2, the difference in sound insulation depending on modeling literature. the form of floating floors appears large in the JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 311 The model validation was focused on Type A which is Disclosure statement expected to show the most improvement. It revealed No potential conflict of interest was reported by the authors. that the MR model, which was the most accurate of the proposed models, showed an average estimation devia- tion of 2.73 dB at 50–630 Hz. The proposed models Funding showed relatively precise estimation abilities at low fre- This work was supported by the National Research quencies but were slightly inaccurate at 400–630 Hz. This Foundation of Korea [2017R1A2B2007050]. is in contrast to other analytically derived estimation models, which have low accuracy below 100 Hz. Thus, it is expected that these empirical estimation methodol- Notes on contributors ogies may help reduce the estimation error caused by Jongwoo Cho is a PhD candidate at the Department of the omission of cross-coupling from more widely Architecture of Seoul National University. He received a accepted analytical modeling methods. Moreover, from bachelor’s degree from Hanyang University School of a practical viewpoint, a single numerical quantity for Architecture in 2011. In 2015, he graduated master’s course for construction management in 2015 at SNU. His main rating sound insulation performance can be obtained research area is construction engineering and management by estimating Δ L with the proposed models using the including sound insulation methods and built environment. specifications of floating floors as input variables and Hyun-Soo Lee received bachelor’s degree in 1983 and mas- adding this estimated attenuation value to the sound ter’s degree in 1985 at the Department of Architecture of pressure level of the base structure. As the proposed Seoul National University. He has studied Construction models have high accuracy in the low-frequency range, Engineering & Management at the University of Michigan where the impact force of the rubber ball is concen- since 1988 and finished doctor’s degree in 1992. And he trated, they show better accuracy at estimating this worked for the Dept. of Architecture Engineering in Inha University as a professor. Since 1997, he has been working single numerical quantity. Therefore, when considering as a professor at the Department of Architecture and the acoustic performance of concrete residential build- Architectural Engineering of Seoul National University. His ings, construction managers or architectural designers major research area is Construction Engineering and can use these empirically derived models to compare the Management. single numerical quantity of various sound management Moonseo Park got into Department of Architecture of Seoul methods during the design stage. As such, this research National University in 1985, completed the courses for a contributes to noise management research by present- bachelor’s degree in 1989, and graduated master’s course ing a method for estimating sound insulation perfor- for City Planning at SNU in 1992. In 1998-2001, he received mance using an empirical approach. master’s degree and doctor’s degree for Project Management in MIT. After graduation, he worked for the The observed limitation in the proposed models at Dept. of Building in National University of Singapore as an high frequencies may be because of the lack of data for assistant professor. Since 2005 he has been working as a resilient layers with low dynamic stiffnesses. Moreover, professor at the Department of Architectural Engineering of different surrounding structures (e.g., modular or CLT Seoul National University. Currently, his major research area housings), junction conditions or the complex consti- is systematic approach for construction, knowledge-based construction etc. tuent materials of floating floors may not have been adequately considered. Thus, the MR model is the Kwonsik Song received his PhD in 2017 in Construction most accurate of the proposed models at present; Engineering and Management from Seoul National University, South Korea. He earned his MS degree in however, if these factors are considered, and relevant Construction Engineering and Management from Seoul data is collected in future research, PCR modeling, National University in 2013 and BA in Architectural which boasts improved accuracy due to the addition Engineering from Sejong University in 2010. His research of relevant variables, may be more promising than MR, focuses on smart and connected communities, human-build- which only uses qualitative variables. Otherwise, other ing interaction, and energy-efficient buildings. He is a research associate in the Department of Civil and empirical methodologies free from the multicollinear- Environmental Engineering at the University of Michigan ity problem offer a more precise estimation of sound and a research professor at Kyungpook National University. insulation performance under heavy impacts. Jaegon Kim received a bachelor’s degree in Architecture from Wonkwang University in 2001. In 2012, he got a mas- ter’s degree in construction management from Seoul Acknowlegments National University and continues his research at SNU as a Ph.D student. This work was supported by the National ResearchFoundation of Korea (NRF) grant funded by Korea Nahyun Kwon got a bachelor’s degree in Architecture from government (MSIT) [2017R1A2B2007050] and Institute of Hanyang University in 2010 and then graduated a master’s Construction and Environmental Engineering at course for Construction Management at Seoul National Seoul National University. The authors wish to express their University in 2014. In 2018, he received a doctor’s degree gratitude for the support. for Construction Engineering and Management at Seoul 312 J. CHO ET AL. National University. After the graduation, he has worked for Ho, S. W., and S.-J. Yoon. 2019. “Experimental Evaluation of Hanyang University ERICA campus as a post-doctoral Reinforced Concrete Slab Reinforced by Composite Mortar researcher. 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