# Study of frequency characteristics of vehicle motions for the derivation of inherent jerk.

ABSTRACT

Jerk in a vehicle is a feel of user which appears due to sudden acceleration changes. The amplitude and frequency components of the jerk defines quality of an engine or an AMT calibration tuning. Traditional jerk evaluation methods use amplitude (peak) of the jerk as a performance index and its frequencies are either used as weighing factor with amplitude or not taken into account. A method is proposed in this paper to quantify and differentiate the non-acceptable level of jerk which is perceivable to human body.

Jerk is obtained by differentiating the acceleration data which contains the frequencies in the lower to higher range. Differentiation of such signal causes an amplification of undesired noise in both analog and digital circuits. This results in significant loss or disturbances in the useful data. In the process of filtering out such unwanted noise or signals, frequency characteristics of test data collected on vehicle in different driving conditions are analyzed for the identification of predominant frequencies. A Butterworth low pass filter is implemented for the analyzed cutoff frequency to remove the undesired signals from acceleration data thus ensuring analysis on actual jerk. This filter has the advantages of low order and higher attenuation of frequencies in pass band, improving the stability and accuracy of its response. The results are verified by carrying out subjective and objective assessment on test vehicle for perceivable jerk.

The present work derives comprehensive method which can differentiate desired and perceivable frequencies from the test data and quantifies the actual jerk.

CITATION: Deshmukh, A., Mulani, B., Jadhav, N., and Parihar, A., "Study of Frequency Characteristics of Vehicle Motions for the Derivation of Inherent Jerk," SAE Int. J. Passeng. Cars - Mech. Syst. 9(1):2016, doi:10.4271/2016-01-1681.

INTRODUCTION

Jerk is defined as rate of change of acceleration with respect to time, that is,

Jerk=da/dt

where a denotes vehicle acceleration and t denotes the time. When we are in a moving vehicle and feel a jolt or a sudden shock, we are actually experiencing change in vehicle acceleration, or the jerk, of a vehicle. Prolonged exposure to such jerk of a vehicle will lead to ride discomfort and even weaken the health of driver and passengers. The human body responds very quickly to rates of change in acceleration rather than the actual velocity of the vehicle. With the rate of change of acceleration, the forces upon the body change and if severe enough, the vehicle passengers or driver will start to become uncomfortable. Thus it is needed to be controlled in acceptable manner.

Jerk is commonly considered as an objective performance index of shift quality or ride quality [1]. Nowadays Jerk has attracted more attention in the area of vehicle design and control. The amplitude and frequency components of the jerk defines quality of an engine or an AMT calibration tuning. The acceleration data contains the frequencies in the lower to higher range. Differentiation of such data signal to obtain the jerk causes an amplification of undesired noise in both analog and digital circuits. This results in significant loss or disturbances in the useful data. To solve this problem, to measure the jerk without differentiation, different jerk sensors were proposed. But those sensors have their own drawbacks and restrictions of operations at lower frequencies and nonlinear phase distortions. This also leads to distortion in the output signal as input signal comprises of different frequency components.

Thus differentiating the acceleration signal remains the appropriate way to obtain the actual jerk. In the present work, we are analyzing the frequency characteristics of the different vehicle motions in all possible driving conditions. A method is proposed to quantify and differentiate perceivable frequencies from the test data and quantify the actual jerk.

FREQUENCY CHARACTERISTICS ANALYSIS OF VEHICLE MOTIONS

Jerk is the derivative of acceleration and acceleration is the derivative of velocity of vehicle. Therefore each of the three signals, velocity, acceleration and jerk comprises of same frequency components. Only the distribution of frequency components of those signals differs.

In order to study the frequency characteristics of the actual jerk, we can study the same for velocity and acceleration of the vehicle. We carried out the tests in different driving patterns to get the velocity and acceleration signals. Different test conditions are shown in table 1.

In different driving patterns, vehicle was driven considering different engine speed with different initial throttle conditions as mentioned in table 1. In addition to the conventional driving, haste starting, repeated shifting, part throttle driving conditions were carried out to find and analyze the actual jerk.

Accelerometer used for the longitudinal acceleration of the vehicle was MEMS (Micro Electronic Mechanical System) type. In most of the MEMS accelerometer polysilicon string is used to build mechanical structure. This mechanical system is designed to realize a variable capacitor. But it is very sensitive to the vibration arisen from the uneven road surface. This is the primary source of the noise which gets induced in the acceleration output. Thus to identify significant data, we found out the Fast Fourier Transform (FFT) of the acquired acceleration data. Figure 1 shows the original acceleration signal and figure 2 shows its Fast Fourier Transform.

From these figure we can see that low frequency signals are predominant in the acceleration data.

Similarly the velocity data was analyzed as shown in figure 3 and figure 4. From the frequency analysis of vehicle motions we found that vehicle and acceleration signals mainly comprise of low frequency components. From figure 2 and figure 4 it can be seen that the power spectral density decreases as the frequency goes on increasing. So we can conclude that the vehicle motions contain the significant data between 0 to 3Hz.

Hence acceleration data should be filtered out with a low pass filter of cutoff frequency 3Hz and differentiate it with respect to time to obtain the actual jerk.

DESIGN OF EVALUATION TECHNIQUE OF JERK

From the frequency characteristics analysis of vehicle motions it is clear that, desired acceleration data is present at lower frequencies and will be harmonics of fundamental stride frequencies, while higher frequency signal will be a noise signal. A low pass filter allows low frequencies to pass through the filter while blocking the higher frequency contents. The estimated cutoff frequency that separates desired signal contents and noise is determined.

The frequency response of the Butterworth filter is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Where N is the order and fic is the cutoff frequency of the filter. Sharp transition occurs at a cutoff frequency so that for all the frequencies below cutoff frequency, the response approaches to one. For all the frequencies above cutoff frequency, response of the filter approaches to zero. Sharper transition in the filter response occurs for higher orders. But higher order filters require more computation time.

Second order Butterworth filter is designed for the optimized filter response. For jerk evaluation, the accelerometer data is logged at 100Hz. The cutoff frequency is selected as 3Hz based on the above mentioned frequency characteristics analysis. The filter output was calculated by weighing the past raw data, the current raw data, and past filtered output using the filter coefficients as weighing terms. To calculate filter output coordinate X at sample n for input sequence Xi following filter function was implemented.

[X.sub.0](n) = [a.sub.0][X.sub.i](n) + [a.sub.1][X.sub.i](n - 1) + [a.sub.2][X.sub.i](n - 2) + [b.sub.0][X.sub.o](n - 1) + [b.sub.1][X.sub.o](n - 2)

In above equation, filter output for sample n is based on raw data input for sample n as well as the n-1 and n-2 samples. It is also weighted by filtered output of samples n-1 and n-2. The terms [a.sub.0], [a.sub.p] [a.sub.2] and [b.sub.0], [b.sub.1] are filter coefficients that are constants. These coefficient constants are based on the filter order, sampling frequency and cutoff frequency.

A ratio of sampling frequency [f.sub.s] to cutoff frequency [f.sub.c] is required to determine the filter coefficients. Correction factor C is applied to cutoff frequency for M number of passes to maintain it at specified level and is given as follows.

C = [([2.sup.1/M] - 1).sup.0.25] (1)

To calculate filter coefficient, radian cutoff frequency is determined from:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

Filter coefficient for second order Butterworth filter are given as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

For second order Butterworth filtering, there is a phase lag of 90[degrees] between input and output of the filter at cutoff frequency causing phase distortion. To cancel out this phase lag, the once-filtered data is filtered again in reverse direction of time. This introduces equal and opposite phase lead so that the net phase shift is zero. Due to this, the cutoff frequency of the filter will be as sharp as that for single filtering. The new cutoff frequency will be lower than that of the original cutoff frequency for single pass filter. Thus, the correction factor C, from equation (1) and equation (2), is applied to achieve the desired cutoff frequency for M number of passes for the filter.

This digital filter is implemented and acceleration data is filtered out to remove unwanted signals. Figure 5 shows the filter response for the input acceleration data. It can be seen that higher frequency noise in the acceleration data were removed and desired data obtained which was comparable with subjective assessment on vehicle

Actual jerk is calculated by the differentiation of the filtered acceleration data. The results are verified by carrying out subjective and objective assessment on test vehicle for perceivable jerk. Figure 6 and Figure 7 shows the actual jerk data evaluated from acceleration data without filter and acceleration data with filter respectively. Haste driving pattern is followed in this case with continuous gear shifting and emergency breakings. It can be seen that when the jerk is evaluated from acceleration data without filtering, noise is superimposed on the significant data. While jerk evaluated from filtered acceleration data with 3Hz cutoff frequency has greater significance with subjective assessment. Similar acceleration data is also filtered with different cutoff frequencies such as 5Hz, 7Hz, 10Hz and differentiated with respect to time to obtain jerk. Results show that jerk obtained with 3Hz filter cutoff frequency has significant data whereas data evaluated with other filter cutoff frequencies are almost corrupted by noise.

Figure 8 shows the jerk evaluation for drivability with part throttle condition. In this case, vehicle is made to run at engine speed of 2000RPM in 1st gear with 20% accelerator pedal throttle position. At this instance full accelerator pedal is pressed and drivability in this condition is analyzed. It can be seen from the graph that as soon as full accelerator pedal is pressed, a peak of the jerk is observed which is perceived by the driver also.

CONCLUSIONS

* Vehicle acceleration data should be filtered out with a low pass filter with cutoff frequency of 3Hz to evaluate actual jerk.

* The low pass Butterworth filtration derived has the advantages of low order and higher attenuation of frequencies in pass band, improving the stability and accuracy of its response.

* Phase distortion in the output of low pass filter needs to be removed by applying correction factor to the derived cutoff frequency.

REFERENCES

[1.] SAE of China International Federation of Automotive Engineering Societies Editors, "Chassis Systems and Integration Technology", Volume 10, Rev. 2012.

[2.] Doane James E., "Optimization Method For Estimating Subject Specific Lower Extremity Body Segment Parameter And Hip Center Locations From Walking Data", Rev. May 2008.

[3.] Winter David A., "Biomechanics and Motor Control Of Human Movement", Fourth Edition, Rev. 2009.

[4.] "Mechanical Vibration and Shock-Evaluation Of Human Exposure To Whole-Body Vibration, Part 1-General Requirements", International Standard ISO 2631-1, Second Edition, 1997-05-01

[5.] Alhussein Albarbar, Samir Mekid, Andrew Starr, Robert Pietruszkiewicz, "Suitability Of MEMS Accelerometers For Conditioning Monitoring: An Experimental Study", Sensors ISNN 1424-8220, Rev. 2008

[6.] Claudio Crivellaro, Donha Decio Crisol, "LQG/LTR Robust Semi-Active Suspension Control System Using Magneto-Rheological Dampers", ABCM Symposium Series In Mechatronics Vol. 5, Rev. 2012

[7.] HoberockL. L., "A Survey Of Longitudinal Acceleration Comfort Studies In Ground Transportation Vehicles", Research Report 40, Department of Transportation, Rev. July 1976

Akshay Deshmukh, Babalal Mulani, Narayan Jadhav, and Abhimanyu Singh Parihar

Tata Motors Ltd.

CONTACT INFORMATION

Akshay Rajendra Deshmukh

Assistant Manager

Engineering Research Centre

Tata Motors Ltd.

Pimpri, Pune, India

akshay.deshmukh@tatamotors.com

B. S. Mulani

Senior Manager

Engineering Research Centre, Tata Motors Ltd.

Pimpri, Pune, India

mulani.b@tatamotors.com

N. D. Jadhav

Assistant General Manager

Engineering Research Centre

Tata Motors Ltd

Pimpri, Pune, India

ndjadhav@tatamotors.com

Abhimanyu Singh Parihar

Assistant Manager

Engineering Research Centre

Tata Motors Ltd.

Pimpri, Pune, India

abhimanyu.parihar@tatamotors.com

Jerk in a vehicle is a feel of user which appears due to sudden acceleration changes. The amplitude and frequency components of the jerk defines quality of an engine or an AMT calibration tuning. Traditional jerk evaluation methods use amplitude (peak) of the jerk as a performance index and its frequencies are either used as weighing factor with amplitude or not taken into account. A method is proposed in this paper to quantify and differentiate the non-acceptable level of jerk which is perceivable to human body.

Jerk is obtained by differentiating the acceleration data which contains the frequencies in the lower to higher range. Differentiation of such signal causes an amplification of undesired noise in both analog and digital circuits. This results in significant loss or disturbances in the useful data. In the process of filtering out such unwanted noise or signals, frequency characteristics of test data collected on vehicle in different driving conditions are analyzed for the identification of predominant frequencies. A Butterworth low pass filter is implemented for the analyzed cutoff frequency to remove the undesired signals from acceleration data thus ensuring analysis on actual jerk. This filter has the advantages of low order and higher attenuation of frequencies in pass band, improving the stability and accuracy of its response. The results are verified by carrying out subjective and objective assessment on test vehicle for perceivable jerk.

The present work derives comprehensive method which can differentiate desired and perceivable frequencies from the test data and quantifies the actual jerk.

CITATION: Deshmukh, A., Mulani, B., Jadhav, N., and Parihar, A., "Study of Frequency Characteristics of Vehicle Motions for the Derivation of Inherent Jerk," SAE Int. J. Passeng. Cars - Mech. Syst. 9(1):2016, doi:10.4271/2016-01-1681.

INTRODUCTION

Jerk is defined as rate of change of acceleration with respect to time, that is,

Jerk=da/dt

where a denotes vehicle acceleration and t denotes the time. When we are in a moving vehicle and feel a jolt or a sudden shock, we are actually experiencing change in vehicle acceleration, or the jerk, of a vehicle. Prolonged exposure to such jerk of a vehicle will lead to ride discomfort and even weaken the health of driver and passengers. The human body responds very quickly to rates of change in acceleration rather than the actual velocity of the vehicle. With the rate of change of acceleration, the forces upon the body change and if severe enough, the vehicle passengers or driver will start to become uncomfortable. Thus it is needed to be controlled in acceptable manner.

Jerk is commonly considered as an objective performance index of shift quality or ride quality [1]. Nowadays Jerk has attracted more attention in the area of vehicle design and control. The amplitude and frequency components of the jerk defines quality of an engine or an AMT calibration tuning. The acceleration data contains the frequencies in the lower to higher range. Differentiation of such data signal to obtain the jerk causes an amplification of undesired noise in both analog and digital circuits. This results in significant loss or disturbances in the useful data. To solve this problem, to measure the jerk without differentiation, different jerk sensors were proposed. But those sensors have their own drawbacks and restrictions of operations at lower frequencies and nonlinear phase distortions. This also leads to distortion in the output signal as input signal comprises of different frequency components.

Thus differentiating the acceleration signal remains the appropriate way to obtain the actual jerk. In the present work, we are analyzing the frequency characteristics of the different vehicle motions in all possible driving conditions. A method is proposed to quantify and differentiate perceivable frequencies from the test data and quantify the actual jerk.

FREQUENCY CHARACTERISTICS ANALYSIS OF VEHICLE MOTIONS

Jerk is the derivative of acceleration and acceleration is the derivative of velocity of vehicle. Therefore each of the three signals, velocity, acceleration and jerk comprises of same frequency components. Only the distribution of frequency components of those signals differs.

In order to study the frequency characteristics of the actual jerk, we can study the same for velocity and acceleration of the vehicle. We carried out the tests in different driving patterns to get the velocity and acceleration signals. Different test conditions are shown in table 1.

In different driving patterns, vehicle was driven considering different engine speed with different initial throttle conditions as mentioned in table 1. In addition to the conventional driving, haste starting, repeated shifting, part throttle driving conditions were carried out to find and analyze the actual jerk.

Accelerometer used for the longitudinal acceleration of the vehicle was MEMS (Micro Electronic Mechanical System) type. In most of the MEMS accelerometer polysilicon string is used to build mechanical structure. This mechanical system is designed to realize a variable capacitor. But it is very sensitive to the vibration arisen from the uneven road surface. This is the primary source of the noise which gets induced in the acceleration output. Thus to identify significant data, we found out the Fast Fourier Transform (FFT) of the acquired acceleration data. Figure 1 shows the original acceleration signal and figure 2 shows its Fast Fourier Transform.

From these figure we can see that low frequency signals are predominant in the acceleration data.

Similarly the velocity data was analyzed as shown in figure 3 and figure 4. From the frequency analysis of vehicle motions we found that vehicle and acceleration signals mainly comprise of low frequency components. From figure 2 and figure 4 it can be seen that the power spectral density decreases as the frequency goes on increasing. So we can conclude that the vehicle motions contain the significant data between 0 to 3Hz.

Hence acceleration data should be filtered out with a low pass filter of cutoff frequency 3Hz and differentiate it with respect to time to obtain the actual jerk.

DESIGN OF EVALUATION TECHNIQUE OF JERK

From the frequency characteristics analysis of vehicle motions it is clear that, desired acceleration data is present at lower frequencies and will be harmonics of fundamental stride frequencies, while higher frequency signal will be a noise signal. A low pass filter allows low frequencies to pass through the filter while blocking the higher frequency contents. The estimated cutoff frequency that separates desired signal contents and noise is determined.

The frequency response of the Butterworth filter is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Where N is the order and fic is the cutoff frequency of the filter. Sharp transition occurs at a cutoff frequency so that for all the frequencies below cutoff frequency, the response approaches to one. For all the frequencies above cutoff frequency, response of the filter approaches to zero. Sharper transition in the filter response occurs for higher orders. But higher order filters require more computation time.

Second order Butterworth filter is designed for the optimized filter response. For jerk evaluation, the accelerometer data is logged at 100Hz. The cutoff frequency is selected as 3Hz based on the above mentioned frequency characteristics analysis. The filter output was calculated by weighing the past raw data, the current raw data, and past filtered output using the filter coefficients as weighing terms. To calculate filter output coordinate X at sample n for input sequence Xi following filter function was implemented.

[X.sub.0](n) = [a.sub.0][X.sub.i](n) + [a.sub.1][X.sub.i](n - 1) + [a.sub.2][X.sub.i](n - 2) + [b.sub.0][X.sub.o](n - 1) + [b.sub.1][X.sub.o](n - 2)

In above equation, filter output for sample n is based on raw data input for sample n as well as the n-1 and n-2 samples. It is also weighted by filtered output of samples n-1 and n-2. The terms [a.sub.0], [a.sub.p] [a.sub.2] and [b.sub.0], [b.sub.1] are filter coefficients that are constants. These coefficient constants are based on the filter order, sampling frequency and cutoff frequency.

A ratio of sampling frequency [f.sub.s] to cutoff frequency [f.sub.c] is required to determine the filter coefficients. Correction factor C is applied to cutoff frequency for M number of passes to maintain it at specified level and is given as follows.

C = [([2.sup.1/M] - 1).sup.0.25] (1)

To calculate filter coefficient, radian cutoff frequency is determined from:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

Filter coefficient for second order Butterworth filter are given as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

For second order Butterworth filtering, there is a phase lag of 90[degrees] between input and output of the filter at cutoff frequency causing phase distortion. To cancel out this phase lag, the once-filtered data is filtered again in reverse direction of time. This introduces equal and opposite phase lead so that the net phase shift is zero. Due to this, the cutoff frequency of the filter will be as sharp as that for single filtering. The new cutoff frequency will be lower than that of the original cutoff frequency for single pass filter. Thus, the correction factor C, from equation (1) and equation (2), is applied to achieve the desired cutoff frequency for M number of passes for the filter.

This digital filter is implemented and acceleration data is filtered out to remove unwanted signals. Figure 5 shows the filter response for the input acceleration data. It can be seen that higher frequency noise in the acceleration data were removed and desired data obtained which was comparable with subjective assessment on vehicle

Actual jerk is calculated by the differentiation of the filtered acceleration data. The results are verified by carrying out subjective and objective assessment on test vehicle for perceivable jerk. Figure 6 and Figure 7 shows the actual jerk data evaluated from acceleration data without filter and acceleration data with filter respectively. Haste driving pattern is followed in this case with continuous gear shifting and emergency breakings. It can be seen that when the jerk is evaluated from acceleration data without filtering, noise is superimposed on the significant data. While jerk evaluated from filtered acceleration data with 3Hz cutoff frequency has greater significance with subjective assessment. Similar acceleration data is also filtered with different cutoff frequencies such as 5Hz, 7Hz, 10Hz and differentiated with respect to time to obtain jerk. Results show that jerk obtained with 3Hz filter cutoff frequency has significant data whereas data evaluated with other filter cutoff frequencies are almost corrupted by noise.

Figure 8 shows the jerk evaluation for drivability with part throttle condition. In this case, vehicle is made to run at engine speed of 2000RPM in 1st gear with 20% accelerator pedal throttle position. At this instance full accelerator pedal is pressed and drivability in this condition is analyzed. It can be seen from the graph that as soon as full accelerator pedal is pressed, a peak of the jerk is observed which is perceived by the driver also.

CONCLUSIONS

* Vehicle acceleration data should be filtered out with a low pass filter with cutoff frequency of 3Hz to evaluate actual jerk.

* The low pass Butterworth filtration derived has the advantages of low order and higher attenuation of frequencies in pass band, improving the stability and accuracy of its response.

* Phase distortion in the output of low pass filter needs to be removed by applying correction factor to the derived cutoff frequency.

REFERENCES

[1.] SAE of China International Federation of Automotive Engineering Societies Editors, "Chassis Systems and Integration Technology", Volume 10, Rev. 2012.

[2.] Doane James E., "Optimization Method For Estimating Subject Specific Lower Extremity Body Segment Parameter And Hip Center Locations From Walking Data", Rev. May 2008.

[3.] Winter David A., "Biomechanics and Motor Control Of Human Movement", Fourth Edition, Rev. 2009.

[4.] "Mechanical Vibration and Shock-Evaluation Of Human Exposure To Whole-Body Vibration, Part 1-General Requirements", International Standard ISO 2631-1, Second Edition, 1997-05-01

[5.] Alhussein Albarbar, Samir Mekid, Andrew Starr, Robert Pietruszkiewicz, "Suitability Of MEMS Accelerometers For Conditioning Monitoring: An Experimental Study", Sensors ISNN 1424-8220, Rev. 2008

[6.] Claudio Crivellaro, Donha Decio Crisol, "LQG/LTR Robust Semi-Active Suspension Control System Using Magneto-Rheological Dampers", ABCM Symposium Series In Mechatronics Vol. 5, Rev. 2012

[7.] HoberockL. L., "A Survey Of Longitudinal Acceleration Comfort Studies In Ground Transportation Vehicles", Research Report 40, Department of Transportation, Rev. July 1976

Akshay Deshmukh, Babalal Mulani, Narayan Jadhav, and Abhimanyu Singh Parihar

Tata Motors Ltd.

CONTACT INFORMATION

Akshay Rajendra Deshmukh

Assistant Manager

Engineering Research Centre

Tata Motors Ltd.

Pimpri, Pune, India

akshay.deshmukh@tatamotors.com

B. S. Mulani

Senior Manager

Engineering Research Centre, Tata Motors Ltd.

Pimpri, Pune, India

mulani.b@tatamotors.com

N. D. Jadhav

Assistant General Manager

Engineering Research Centre

Tata Motors Ltd

Pimpri, Pune, India

ndjadhav@tatamotors.com

Abhimanyu Singh Parihar

Assistant Manager

Engineering Research Centre

Tata Motors Ltd.

Pimpri, Pune, India

abhimanyu.parihar@tatamotors.com

Table 1. Test Conditions description Parameters Description Vehicle Models Pickups Accelerator Throttle 0-100%, 20-80%, 25-100%, Position 50-100% Driving Patterns 1000RPM, 1250RPM, Speed (RPM) 1500RPM, 1750 RPM, 2000RPM Gear No 1,2,3,4,5,6 1) Data Acquisition System Instruments 2) MEMS Accelerometer 3) L350 Optical Sensor Location Straight High Speed Track

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Author: | Deshmukh, Akshay; Mulani, Babalal; Jadhav, Narayan; Parihar, Abhimanyu Singh |
---|---|

Publication: | SAE International Journal of Passenger Cars - Mechanical Systems |

Article Type: | Report |

Date: | Apr 1, 2016 |

Words: | 2193 |

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