# Analyzing the Nonlinear Performance of Miniature Loudspeakers in Consideration of the Creep Effect
## 3 Experimental Validation
### Results and Discussion  
The predicted and experimental displacement waveforms of the three samples are illustrated in Figure 5. The displacement waveforms predicted by the NL-C model align more closely with the measurement values than the NL-NC model, confirming that the NL-C model better reproduces the electrical dynamics of the miniature loudspeakers. This is primarily because music signals contain rich low-frequency components, leading to a prominent creep effect. The NL-NC model does not account for creep, causing discrepancies between the predicted and measured displacement waveforms. Figure 4: Setup for the experimental measurements of (**a**) displacement and (**b**) sound pressure level (SPL) and THD. Figure 5: Comparison of the predicted and measured displacement waveforms for Clip 01: (**a**) sample A, (**b**) sample B, and (**c**) sample C. A 100 ms window was selected to display the differences in waveforms. The stimulus length was 30 s.  
The root-mean-square error (RMSE) is a key quantitative indicator used to assess the average magnitude of the errors between predicted values and measured values. RMSE is defined as follows:  
\[\text{RMSE}=\sqrt{\frac{1}{N}\sum_{k=1}^{N}\left(x_{k,m}-x_{k,p}\right)^{2}}\,, \tag{15}\]  
where \(x\) represents the data under evaluation, \(N\) represents the numbers of data points, and the subscripts \(m\) and \(p\) indicate the measured and predicted values, respectively. The magnitude of RMSE is indicative of the discrepancy between the predicted and measured data. A lower RMSE value signifies a higher model accuracy and a closer alignment between the predicted and measured values. Table 2 displays the RMSE values for the displacement waveforms predicted using the two models across various frequency ranges. Overall, the NL-C model demonstrated better accuracy than the NL-NC model in both the low- and full-frequency ranges. In the low-frequency domain, where the disparity in RMSE between the two models was most pronounced, the NL-C model significantly outperformed the NL-NC model. However, in the high-frequency range, there was no noticeable difference in accuracy between the two models because the creep effect is negligible in this range. Thus, the NL-C model is more representative of actual loudspeaker behavior because it accounts for the creep effect, particularly at low frequencies. The predicted and measured THD and sound pressure level (SPL) values of the three samples are compared in Figure 6. The THD values predicted by both models were relatively consistent for all samples at frequencies beyond 500 Hz. However, at low frequencies, particularly those below 200 Hz, noticeable disparities emerged between the measured THD values and those predicted by the NL-NC model. The NL-NC model was inadequate for forecasting the substantial distortions observed at low frequencies. In contrast, the THD values predicted by the NL-C model corresponded well with the measurement values in nearly the entire frequency domain. In contrast to THD, the disparities in SPL were minimal, even at low frequencies. This can be attributed to the frequency response of the loudspeakers, which conforms to a high-pass model that results in minimal output at low frequencies. As a result, the variations caused by the creep effect are mitigated. Consequently, the differences in the predicted and measured SPL values were negligible for both models.