Appropriate usage of multi-layered OTPA to identify intensive meas- uring part among sequential parts Ryusei Yanagita 1 Junji Yoshida 1 Osaka Institute of Technology 5-16-1 Omiya, Asahi-ku, Osaka-city, Osaka, 535-8585, Japan

ABSTRACT Conducting effective countermeasure to the vehicle interior noise is important for compatible with the other vehicle performances such as light weight. Operational transfer path analysis (OTPA) was proposed to identify high contributing parts (OTPA reference model) and vibration behaviors (OTPA principal component model) to the interior noise with small man-hours. By using this method, we can determine which parts should be measured intensively. In case we apply the method to a vehicle body panel, the method tells us suitable measuring part of the body panel at the target frequency band. However, if the body panel is excited by a forced vibration from the suspension, we had better to apply countermeasure to the suspension. Then in this study, we applied the OTPA several times to identify which sequential parts from frame, body to interior noise makes the large noise using a sim- ple plate model. In the analysis, both OTPA models (reference model and principal component model) were applied at various part and considered appropriate procedure of OTPA to obtain useful infor- mation for finding out the modification target part accurately. Through the verification test, the ef- fectiveness of the proposed procedure was confirmed. 1. INTRODUCTION

Conducting effective countermeasure to vehicle interior noise is important for compatible with the other vehicle performance such as light weight. Then, operational transfer path analysis (OTPA) has been proposed to identify high contributing parts to the interior noise. In the original OTPA (OTPA reference model) was developed to identify high contributing points such as engine mount attachment points 1, 4-8 . In addition, OTPA principal component (PC) model was recently proposed to obtain high contributing vibration behaviors such as body panels to know important vibration mode of the target structure 2 . Through these methods, we can understand which parts and vibration behaviors should be measured intensively. Furthermore, for estimating the high contributing part in complex system such as frame, body and cabin in vehicle, repeating OTPA procedure sequentially was demonstrated 8 . However, an appropriate combination of these OTPA methods to obtain useful information has not proposed yet. Then in this study, we applied both OTPA reference and principal component models to simple plate model and considered an effective analysis procedure to determine important parts and vibration behaviors accurately for effective countermeasure.

1 junji.yoshida@oit.ac.jp

worm 2022

2. OPERATIONAL TRANSFER PATH ANALYSIS (OTPA) REFERENCE AND PRINCI- PAL MODEL

In OTPA, transfer function of each reference point to the response point is calculated by applying principal component regression method using only simultaneously measured reference and response signals at the operational condition as shown in Figure 1. Contribution of each reference point to the response point is obtained by multiplying each reference signal with the transfer function.

Figure 1: Calculation procedure of Operational TPA.

Firstly, reference and response signals are measured at the operational condition and frequency analysis is carried out to the measured signals by applying FFT repeatedly. Secondly, PC analysis is applied to the reference signal matrix [ A in ] by singular value decomposition (SVD) as shown in Equation 1. And correlated components among reference signals are extracted to obtain principal component (PC) matrix [ T ] by using matrix [ V ] as shown in Equation 2.

[𝐴 in ] = [𝑈][𝑆][𝑉] 𝑇 (1)

[𝑇] = [𝐴 in ][𝑉] = [𝑈][𝑆] (2) Here, [ V ] is the coefficient matrix to transpose the reference matrix [ A in ] to the PC matrix [ T ]. And regression coefficient (PC transfer function) [ B ] of each PC to the response signal to transpose the PC matrix [ T ] to the response signal matrix [ A out ] is obtained by multiple regression analysis as shown in Equations 3 and 4.

[𝐴 out ] = [𝑇][𝐵] (3)

[𝐵] = ([𝑇] 𝑇 [𝑇] −1 )[𝑇] 𝑇 [𝐴 out ] (4)

Transfer function [ H A ] from reference signal to response signal is calculated by multiplying the coefficient matrix [ V ] with the regression coefficient [ B ] as shown in Equation 5.

[𝐻 A ] = [𝑉]([𝑇] 𝑇 [𝑇] −1 )[𝑇] 𝑇 [𝐴 out ] (5)

As the result, we can obtain contributions of reference and principal component to response signal by using [ H A ] and [ B ] as shown in Equations 6 and 7.

[𝐴 contribution ] = [𝐴 in ][𝐻 A ] (6)

[𝑇 contribution ] = [𝑇][𝐵] (7)

In the principal component model, reference signals are also re-generated by multiplying PC matrix [ T ] with the inverse (transpose) matrix of unitary matrix [ V ] as shown in Equation 8.

[𝐴 in ] = [𝑇][𝑉] −1 (8)

The response signals obtained in Equation 8 have phase and amplitude. Hence, the vibraion behavior composing each principal component (principal component mode) can be expressed by using these information 2 . Therefore, the PC mode related to high contributing PC to the response point becomes the high contributing PC mode and the mode is the target mode for effective countermeausre to the response.

3. CONSIDERATION OF EFFECTIVE SEQUENTIAL OTPA APPLICATION

Here, we consider effective procedure to find out the high contributing part among sequential system in the road noise transmission from frame, body to cabin as follows.

3.1. Stepwise Application of Reference and Principal Component Model Road noise is transmitted from tire, suspension, frame, body, and cabin in general. In this study, we focused on the frame, body and cabin characteristics as the evaluation target of OTPA application for the road noise. Here, OTPA is applied several times between body to cabin (response point) and frame to body to find out the intensive measuring part. At first, OTPA PC model is applied to obtain the body panel high contributing vibration behavior to the interior noise as shown in Figure 2 (Step 1). After that, OTPA reference model is applied for focusing on important input point of transfer parts between the high contributing body vibration behavior and the frame reference (input) points (Step 2) as previous study 3 . Nevertheless, in Step 2, if the reference point (input point) of the frame does not vibrate largely but the frame global vibration behavior is the main factor to increase the body vibration, applying OTPA reference model might be inappropriate way and we may not identify important measuring part. Then as the additional application, OTPA PC model is again applied in this study between frame and body as shown in Figure 2 and attempt to extract not only high contributing input parts but the high contributing vibration behavior of the frame to the body response for identifying which system should be measured. And finally, we consider which procedure is the best to obtain important information easily for more effective countermeasure.

PC - Reference model Response : High contributing Body PC

PC model Response : SPL Reference : Body PC

Reference : Frame Mounts

PC model Response : SPL Reference : Body PC

PC - Reference model Response : High contributing Body PC

PC - PC model Response : High contributing Body PC

Reference : Frame Mounts

Reference : Frame PC

Response points (Body PC)

Response point (SPL)

Response points (Body PC)

Figure 2: Procedure of sequential OTPA application in previous and present studies.

Reference points (Frame PC)

Reference points (Frame mounts)

Reference points (Body PC)

3.2. Operational Test Here, OTPA reference and PC models were applied several times to a simple plate model, and we considered which procedure is the best way to obtain important information easily for more effective countermeasure.

3.2.1. Experimental outline For the operational test, a simple plate model was prepared as shown in Figure 3 (a). This simple model consisted of body panel, four rubber bush mounts, and frame. The length, width and height of

a model was 320 × 200 × 30 mm, and the thickness of body panel, frame and material were 1 mm, 2 mm and Aluminum, respectively.

(a) Simple plate model (b) Input points

Figure 3: Experiment model and condition.

In this operational test, four electrical magnetic exiters (Modalshop: K2007E01) were put under the upper plate imitating body panel in Figure 3 (a) to give random input signals for 30 s. As the response point signal, sound pressure was recorded by microphone set above 50 mm at center of body panel imitating interior noise as shown in Figure 3 (b). As the reference points, acceleration signals were measured at 15 points on the body panel as shown in Figure 4 (a) for the first OTPA application and the vibraiton signals at 12 points on the frame were also used as the reference signals in the second OTPA as shown in Figure 4 (b). Four of them (black circles) were used in the OTPA reference model between frame and body and all points (red points) were used for the OTPA PC model. In the measurements, each reference signal was measured simultaneously with the response point signal.

(a) Body reference points (b) Frame reference points

Figure 4: Measurement points for Operational TPA.

3.2.2. Response sound pressure level As the first step, we obtained the sound pressure level at the response point recoded at the operational test and the PC contribution of body panel to the response point was calculated as shown in Figure 5.

Figure 5: Sound pressure level at the response point and the PC1 contribution.

As shown in the figure, the response point sound pressure level (pink curve) was found to have several peaks and PC1 contribution of the body (black curve) was observed to be almost same with the actual measured response level. Hence, PC1 contribution was found to have the dominant contribution to the response signal. Then, we focused on the PC1 at 240 Hz as the evaluation target for the further analysis.

3.2.3. Obtaining high contributing body PC characteristics In the previous part, we obtained high contributing pricipal component of body to the response. Subsequently, we evaluated the body PC1 level and the transefer function to understand which made the PC1 contribution peak at around 240 Hz. Figure 6 shows the PC1 contribution, transfer function, and PC1 level, respectively.

Figure 6: PC1 contribution, transfer function and level from body to radiated noise.

As shown in the figure, the SPL peak were observed to be made by the PC itself at the target frequency because PC1 had the similar peak with the contribution. This indicates that the response point noise was increased by the vibration characteristic of the body plate structure at the frequency. Hence, the high contributing PC1 mode was obtained using Equation 8. Figure 7 shows the high contributing body PC1 vibration behavior (high contributing body PC mode) at 240 Hz extracted by the PC contribution analysis.

Figure 7: High contributing body PC mode at 240 Hz.

As shown in Figure 7, the high contributing body PC mode was observed to be third bending mode. On the other hand, it had better to know what made the large body vibration behavior (resonance of body itself or the large vibration from frame reference points) for the effective countermeasure. Then, we applied OTPA reference model as the second OTPA application to estimate the main factor increasing the body vibration as follows.

3.2.4. Obtaining reference point contribution of the frame input points to body PC1 As the second step, we applied OTPA reference model between body PC1 and the frame reference points where four rubber bushes attachment points (black circles in Figure 4 (b)) and obtained each reference point contribution. Figure 8 shows the calculated frame reference point contribution to body PC1, transfer function and reference point acceleration, respectively ．

Figure 8: Contribution, transfer function, and acceleration from frame mounts

to body PC1 by OTPA reference model.

As shown in the figure, all frame reference point acceleration were observed to have vibration acceleration peaks. Hence, the high contributing body panel vibration (PC1) at around 240 Hz were estimated to be increased by the frame reference point vibration. However, all reference point acceleration level were similar and determining unique frame reference point for intensive countemeasure was difficult.

3.2.5. Obtaining high contributing PC of frame to body PC1 Then, OTPA PC model was again applied between body PC1 (response) and the frame acceleration signals as the third step. For applying OTPA PC model to frame, we increased the number of frame reference points from 4 to 12 (all red points in Figure 4 (b)). And we attempted to understand the main factor of the high contributing body vibration (PC1) at around 240 Hz again. Figure 9 (a), (b), (c) shows the PC1 contribution, the PC1 transfer function and the PC1 of the frame, respectively.

Figure 9: Contribution, transfer function of PC1 and PC1 level from frame PC

to body PC1 by OTPA principal component model.

As shown in this figure, PC1 contribution of frame was almost same with the high contributing body PC1 level at around 240 Hz. In addition, the frame PC1 contribution were significantly larger

than the other PC contribution by comparing with the reference point contribution distribution as shown in Figure 8 (a). Furthermore, the PC1 contribution peak was observed to be made by frame PC1. This means that the high contributing body vibration behavior was excited mainly by the entire vibration characteristic of the frame structure. Figure 10 shows the frame PC1 vibration behavior (high contributing frame PC mode) at 240 Hz extracted by the PC contribution analysis.

Figure 10: High contributing frame PC mode at 240 Hz.

As shown in Figure 10, the high contributing frame PC mode had two large vibration amplitude points at around the center of the frame. According to the these analytical results, we could estimate whether the body vibration (PC1) to the sound at around 240 Hz were increased by body side or frame side by applying OTPA reference and PC model sequentially. For the verification of the estimated factor, we actually applied countermeasure to the high contributing frame PC mode in the next section.

4. VERIFICATION OF THE ANALYTICAL RESULTS

In the previous sections, we applied OTPA several times to find out the main factors increasing the radiated noise (response point signal) at the target frequency of 240 Hz. The analytical result of OTPA using frame input point in the OTPA reference model indicated all reference points (input points of frame) had similar vibration peak and determing intensive measuring input point was hard. On the other hand, the OTPA PC model between body and frame indicated that the frame PC1 was dominant to the body vibration. Then, we performed two countermeasure instances considering these analytical results to verify which method could indicate useful information for effective radiated noise reduction. As the countermeasure to the frame reference points, small 25 g weight was added at the four frame reference points (Total 100 g) and the radiated noise was measured. Furthermore, as the countermeasure instance to the frame high contributing PC1 mode as shown in Figure 10, 50 g weight was added at around the center of the both side frame (Total 100 g), and the radiated noise was measured again for the comparison of the noise. Figure 11 shows the comparison of the sound pressure level among original (without weight), countermeasure 1 (with weight at all reference points) and countermeasure 2 (with weight at side frame center). Black, light green, pink curves show the SPL of original condition (without weight), countermeasure 1 and countermeasure 2, respectively.

Figure 11: SPL comparison of before and after countermeasure in two way.

As shown in Figure 11, the SPL at around 240 Hz was almost same between original and countermeasure 1. This indicates that adding weight to all frame input points was not appropriate way to decrease response level and the application of OTPA reference model between body and frame was not suitable method in this case. On the other hand, the response level at 240 Hz was observed to be reduced largely in the countermeasure 2. This shows that the intensive countemeasure to the high contribuitng frame PC1 mode could decrease the response level significantly. These results reveals that the proposed method utilizing an additional application of OTPA PC model is better way

to identify the key points which should be measured intensively for more effective reduction of the sound presssure level at the response point.

5. SUMMARY

In this study, we considered an appropriate analysis procedure of OTPA reference and PC models in sequential OTPA application to identify important countermeasure part by operational test using simple plate model. At first, OTPA principal component (PC) model was applied between SPL at response point and vibration at the body panel (reference point) to obtain the body panel high contributing vibration behavior to the response SPL. As a result, the SPL at 240 Hz, where the level was large, was found to be affected largely by the body PC1 vibration behavior and the high contributing PC1 body mode was obtained. Subsequently, OTPA reference model was applied between the body PC1 and the frame four reference points to determine which reference point increased the body PC1 at the target frequency of 240 Hz for the further analysis. However, determining measuring reference points into four points was difficult because all frame reference points had similar vibration peaks at around the frequency. Then, OTPA PC model was again applied between the body PC1 and the vibration signals at a lot of frame reference points. The result indicated that the frame PC1 vibration was dominant to the high contributing body PC1 and the frame high contributing PC1 vibration behavior was clearly identified. As the verification of the proposed method using sequential OTPA PC model application, countermeasure was performed by adding mass to the large amplitude points of the frame PC1 vibration behavior. And the response point SPL could be decreased significantly and the reduction level was much larger than the countermeasure by reference model. From these results, the effectiveness of the sequential application of OTPA PC model was clarified to identify intensive measuring parts and points. 6. REFERENCES

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