## 6 Sensor Data Acquisition and Collection  
### Sensor Data Acquisition by AE  
One part of the service (shown in Figure 1) is the support for sensor data acquisition, relating to the identification of a sensor function for each individual QTSS solution as defined in Equation (1). The design goal is to effectively manage and treat the measurement uncertainty caused by the inherent variations in sensed design, printed electronics, and intra-socket interactions. Due to the operational complexity, we opt for a data-centric approach to this task. In particular, a specific variant of deep learning neural networks, referred to as Autoencoder (AE), is used to capture the functional relation between the sensor signal data (i.e., voltage) and the possible source dynamic load conditions (i.e., measured pressure). Such a data-driven approach to sensor calibration, as mentioned before, is motivated by the unique variation of specific contact surfaces among measurement points (e.g., varying curvatures of the intra-socket regions), as well as the inherent performance uncertainty of specific printed electronics (e.g., exhibiting drift, hysteresis, and repeatability). To this end, all deep-learning neural network-based methods could in fact be useful by providing support for encoding the expected nonlinear transformations, while filtering the undesired operational disturbances or uncertainties. The main reason for choosing AE over other deep-learning neural network-based methods is due to its transparency in terms of its  
Figure 6: The physical prototyping and dynamic testing: (**a**) The shell mold casting process of silicone stump. (**b**) The physical test-rig with the femur-stump assembly and prosthetic socket mounted on the Stewart manipulator. (**c**) The sensors deployed inside the socket for measurement of dynamic pressure load conditions. support for an explicit intermediate latent space representation. Such an intermediate representation is useful not only for justifying the robustness of a calibrated sensor function regarding its dynamic operational ranges, but also for compressing raw sensor data for effective storage and transmission. AE has a feed-forward structure with two neural networks. The design is characterized by the following parameters:  
\[\textbf{Autoencoder}:Q=(\mathcal{I},\hat{\mathcal{I}},H,\mathcal{F},\mathcal{G}) \tag{3}\]  
where \(\mathcal{I}\) refers to the input data and \(\hat{\mathcal{I}}\) refers to the output data; \(\mathcal{F}\) is the encoder function, \(\mathcal{F}:\mathcal{I}\to H\); \(H\) represents the latent variables in the AE; and \(\mathcal{G}\) is the decoder function, \(\mathcal{G}:H\rightarrow\hat{\mathcal{I}}\). Autoencoders are trained to minimize reconstruction errors: \(\mathcal{F},\mathcal{G}=\operatorname*{arg\,min}_{\mathcal{F},\mathcal{G}} \|\mathcal{I}-\mathcal{I}\|^{2}\). The training and usage AE as a sensor function is given in Algorithm 1. In our case, the training data for AE are generated by deploying the sensors within socket and then subjecting it to some well-defined reference cyclic pressure loads (i.e., the ground truth data). Since the AE design is trained with reference cyclic pressure loads, the outputs recover such load conditions, while removing all measurement uncertainties during the same intra-socket operational conditions. During the training phase, it is also possible to compare directly the outputs with the reference inputs in the manner of supervised learning. Gaussian noises can also be added to the inputs during training or calibration for improving the robustness of sensing. ```
Result:\(Calibration\ results\ (pressure)\ \hat{\mathcal{I}}\), Loss Input: Train signals (voltage) \(\mathcal{I}_{train}\), test data \(\mathcal{I}_{test}\), Ground truth for trainset \(\mathcal{I}_{ground}\).