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Design of Experiments to Characterize and Predict Polymer Acoustic Properties (2021-US-EPO-866)

Valerie Rennoll, Johns Hopkins University, Johns Hopkins University
Ian McLane, Graduate student, Johns Hopkins University
Drew Grant, Graduate student, Johns Hopkins University
Mounya Elhilali, Professor, Johns Hopkins University

James West, Professor, Johns Hopkins University

 

Acoustic impedance and attenuation are important properties that impact sound propagation in underwater and medical applications.  To target specific acoustic properties, multiple polymers with a range of densities and stiffnesses can be used and then further tuned with the addition of dopants. Using an I-optimal design of experiments in JMP, the relationship between multiple fabrication and characterization conditions on the acoustic impedance and attenuation of polymers with nanoparticle dopants was explored. A total of 98 samples was fabricated and characterized with factors of polymer type (PDMS, ecoflex, and polyurethane), sample thickness, dopant density, dopant concentration, dopant size, and characterization frequency and temperature. The obtained statistical models specify the conditions necessary to match the polymers to acoustic impedances in the range of 1 to 2.2 MRayls, while minimizing or maximizing attenuation. Nine validation samples were fabricated to target five impedance values with minimum or maximum attenuations and demonstrated an average predicted error of 1.4% compared to the measured impedance values.  The model is used to construct sensors that are acoustically matched to materials such as human skin, wood, and water.

 

 

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Valerie Rennoll A major focus of the laboratory is developing new, flexible acoustic sensors for use on the body.
  Today I'll be discussing my research on using an optimal design of experiments to study the acoustic properties of several different polymer materials with added particles.
  The results of this experiment are used to develop an acoustic impedance matched sensor.
  And so acoustic impedance and attenuation are important material properties that impact sound propagation materials. Acoustic impedance is a function of its density in the speed of sound through the material.
  When sound travels from one material to another, differences in acoustic impedance cause energy to reflect at the boundary.
  This acoustic impedance mismatch between water and the air is why, if someone makes a sound underwater in a pool and you're standing at the side of that pool you won't be able to hear that sound.
  So these animations show how acoustic impedance impacts the transmission of body sounds.
  In this first figure you'll see that sound emitted from your body hits an interface between your skin and the air, causing most sound to be reflected back towards the body, due to the large impedance mismatch.
  The second figure shows how this effect is really amplified when a doctor listens to your...
  listens to your body using a stethoscop. The impedance mismatch leads to a small portion of the incident energy being transmitted to the stethoscope and also adds a path where airborne noise can really corrupt the signal.
  This third figure demonstrates our approach with impedance match sensor. The impedances are well matched so very little signal reflection occurs at the body sensor interface and airborne noise is passively reflected away from the sensor.
  Overall, by matching the acoustic impedance of the medium being monitored, a greater amount of sound can be captured. In order to do this, it must be understood how a polymer can be fabricated to target a specific acoustic impedance.
  So previous research had demonstrated that nanoparticles can be dispersed into a polymer matrix to control its acoustic impedance.
  However, existing research was limited in scope to basically exploring the design space, using a one factor at a time approach and focusing on a small subset of relevant factors.
  So we chose to expand on previous research by setting up an optimal design of experiments in JMP. The optimal design was ideal because we wanted to consider a mix of continuous, discrete, and categorical factors.
  So these two tables provide an overview of the factors and responses we included in the DOE.
  After a literature review to consider factors that should be studied, we chose to include seven total factors of polymer type; particle concentration, size, and density;
  sample thickness; and characterization frequency and temperature. As you can see in this third column, the factors typically included low, high, and center settings,
  although polymer type included four levels. The design was also set up to take into account factor restrictions, so certain polymer types couldn't be combined with the smallest particle size because it prevented the polymers curing.
  We studied four total responses, including density, speed of sound, acoustic impedance, and attenuation.
  The goal was to target a specific acoustic impedance value with minimum attenuation and just understand the factors that impact density in speed of sound.
  We aimed to estimate all mean effects, second order interactions, and quadratic terms to generate a model with high predictive accuracy. And to do this we settled on fabricating a total of 98 samples to have reasonable power to detect these effects.
  Materials were characterized using a through transmission technique in which the unknown acoustic properties of the material are obtained from comparison to a reference material, in this case water.
  A signal is sent from the transmitter to the receiver and the signal that's captured is compared when traveling through water alone, versus water and the sample.
  So within the design space we explored, we found...we measured a range of acoustic impedances depending on the polymer and added particle properties.
  We found that we could match the acoustic impedances of materials such as water, skin and wood.
  After collecting response data for each of the 98 samples, we compared various reduced candidate models, with the aim of obtaining the highest predictive accuracy
  with the fewest number of model coefficients. We used techniques such as backward selection and K fold cross validation
  to obtain possible models and then used a variety of assessment tools to choose the final model. We considered if there were outliers or influential points included in the data,
  if the errors were independent and normally distributed with constant variants and a mean of zero, and whether there was a significant lack of fit in the model.
  Overall, we found that the final chosen acoustic impedance model was an adequate fit for our purposes. This plot on the left
  shows the actual versus predicted plot, and you can see, the data fits really well along the diagonal line, meaning that the actual and predictive data are highly similar.
  And the residuals, as you can see, on this plot on the right, are normally distributed about zero with no distinct pattern.
  The final chosen model included significant factors of polymer type, dopant concentration and temperature. The model had an adjusted R squared value of .995 and a root mean square error of .02.
  So, because our main goal was to fabricate a polymer with a specific acoustic impedance and minimum attenuation, the prediction profiler was really helpful
  to reaching this goal. So in this video, you can see I'm demonstrating how the production profiler points out the conditions necessary to target an impedance value of 1.3MRayls with minimum attenuation.
  We used the prediction profiler to predict the conditions necessary to fabricate a total of nine polymers with impedance is of 1, 1.3, 1.6, 1.9, and 2.2 MRayls.
  The average error between the predicted and measured acoustic impedance values was only about 1.4%, a difference of around .05 MRayls.
  So, confident with the results from our DOE, we used the specific polymer fabrication conditions when putting together an impedance matched acoustic sensor, which I'll refer to as Hearo.
  In this image, you can see several Hearo devices with different target impedance values, depending on the target application of interest. We compare this impedance match device to a typical microphone and accelerometer using signal to noise ratio metrics.
  In these SNR figures, a higher value indicates greater correlation with the signal of interest and less correlation with airborne noise. So the overall signal metric is bound by taking the difference between
  the coherence with the simulator signal minus the coherence with the noise. You can see that Hearo in this sort of orangy color shows less coherence with the noise
  and greater coherence with the simulator signal, leading to an overall higher SNR metric compared to an accelerometer and microphone with a diaphragm.
  In these demonstrations, you can see that this leads to Hearo capturing a very clean signal from the body or instrument without picking up airborne noise. So this first video shows Hearo recording on heart and lung sounds in an at-home setting.
  And the second video shows Hearo recording the bells.
  So we really envision that this sensor could provide an improved way to monitor sounds from the body or instruments. Typical devices require costly noise suppression circuitry.
  So, in summary, we used a design of experiments in JMP to understand how multiple fabrication and characterization conditions impact the acoustic properties of polymers with added particles.
  The model obtained from the experiment demonstrated high predictive accuracy and was used in the design of an impedance matched acoustic sensor.
  The sensor demonstrates improved signal fidelity and noise reduction compared to existing sensors that are optimized for airborne sound pick up. Thank you for your attention, and please feel free to contact me with any questions.

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