3D-Printed Sensors with Piezo-Actuators and Deep Learning for Biofuel Monitoring

1. Introduction

Three-dimensional (3D) printing enables cost-effective and highly precise sensor manufacturing, positioning it as a good alternative to traditional techniques like lithography and thin-film deposition. In this context, numerous studies have explored the application of 3D-printing technologies in the fabrication of piezoelectric sensors. For instance, in [1,2,3,4,5] they employed polyvinylidene fluoride (PVDF) polymers and their copolymers to develop piezoelectric devices for various sensing applications. These include pressure and force sensors tested under controlled laboratory conditions [1,3], acoustic receivers [4], flow sensors for deionized water, mimicking blood flow [2], and tactile sensors embedded in prosthetic hands capable of identifying object hardness [5]. In [6,7], the authors designed micromachined piezoelectric ultrasonic transducers (PMUTs) using PZT sheets mounted on titanium substrates. These were integrated with Helmholtz resonators featuring 3D-printed cavities of controllable volume to monitor human respiratory patterns. Additional approaches include the use of photopolymer resins mixed with PZT particles to fabricate ultrasonic wave sensors [8], and the development of piezoresistive MEMS accelerometers via 3D-printing for controlled experimental use [9].

A particularly active area of research involves 3D-printed sensors for liquid analysis [10,11,12,13,14]. These works leverage additive manufacturing to produce complete sensor assemblies, fluidic cavities, or microfluidic channels. Sensor modalities include substrate-integrated waveguide (SIW)-based designs [10,15,16], microwave resonators [11,13,14,17,18], parallel plate configurations [12], optical interferometers [19], and electromagnetic bandgap (EBG) microstrip sensors [20]. These systems enabled the differentiation of liquid compositions by measuring dielectric permittivity or transmission spectra. Applications span petroleum monitoring [18]; aqueous mixtures with water-ethanol blends [10,11,12,13,14] being the most notably but also solutions containing isopropanol [15], glucose [19], or potassium chloride [12]; toluene-methanol mixtures [20] and various pure chemicals [13,14,16,17,20]. All aforementioned studies used laboratory instrumentation in the measurement process.

Recent advancements have also integrated machine learning techniques with 3D-printed sensor systems. For example, in [21], the authors developed a deformation-sensitive sensor composed of graphene nanoparticles and carbon nanotubes, employing support vector machines (SVMs) to classify human motion and monitor exhalation; researchers in [22] applied neural networks to optimize the design of a 3D-printed accelerometer for human movement tracking, while in [23] they fabricated 3-axis force sensors and trained a support vector regression (SVR) model on simulated data to quantify forces in medical contexts; finally, the work in [24] combined multi-sensor 3D-printing with machine learning algorithms to predict behavioral impairment following alcohol consumption.

In previous studies [25,26], we introduced a 3D-printed sensing cell incorporating piezoelectric actuators, designed to vibrate at a specific resonance, and artificial intelligence (AI) techniques to characterize the physical properties of aqueous-glycerin solutions. In the present work, we propose an enhanced version of this type of sensor, designed to broaden its operational bandwidth and improve calibration and resolution results. Furthermore, we integrated the sensor into a microcontroller-based system equipped with convolutional neural networks (CNNs), targeting the application of biofuel monitoring. The development of such sensing platforms is particularly relevant given the increasing demand for fuels, their diverse applications, and the need to reduce emissions. Nevertheless, while biofuels are environmentally more favorable, they can lead to elevated emissions or suboptimal engine performance if their viscosity and density are not properly controlled [27,28,29,30]. Numerous studies have explored sensor technologies for monitoring the physical properties of fuels, biofuels and engine oils [29,30,31,32,33,34,35,36,37,38]. More recently, artificial intelligence has become a powerful complement to microsensor technologies, enabling advanced compositional analysis of fuel–lubricant and biofuel mixtures [39,40,41,42]. However, many of these approaches depend on costly instrumentation and complex electronics. To address this limitation, our recent work [43] presented a compact, integrated sensing device. While effective, that design employed a MEMS-based sensor which had higher manufacturing costs. In contrast, the present study focuses on a more cost-effective alternative without compromising performance.

The article is structured as follows: the “Materials and Methods section” details the sensor design, geometric parameters, simulation procedures, structural optimization criteria, complete device schematics, experimental methodology, the data processing techniques and the machine learning algorithms studied. The “Results” section presents optimal sensor geometries identified in real-world applications, experimental data captured with our system from biofuel monitoring, the architecture of the most effective AI models, and their precision obtained in calibration and drift experiments, as well as using dimensionality reduction, compared to the reference values. In the “Discussion”, we contextualize our findings within the existing literature and outline potential future research directions. Finally, we conclude with the key contributions and implications of this work.

2. Materials and Methods

2.1. Comparative Analysis of Sensor Structure and Actuator Layouts

The fundamental architecture of the developed sensor is illustrated in Figure 1. The device comprised two integrated components forming a unified system. The first part consisted of a semi-cylindrical container cell designed to hold the target liquid. This cell featured a vibrating membrane at its base and lateral connectors to facilitate fluid circulation. It was fabricated via stereolithography (SLA) 3D-printing technology [44] using a Formalbs® Form3 printer [44] and Rigid10K resin [45], a material validated in previous studies [25,26] for its mechanical robustness (Young’s modulus = 10 GPa). According to manufacturer specifications [45], this resin also demonstrates good chemical resistance against fuel exposure, exhibiting only a 0.1% weight increase after 24 hours when a sample structure is immersed in diesel. Key printing parameters including dimensional tolerance, resolution, printing speed, and ultraviolet (UV) light exposure duration were controlled throughout the manufacturing process.

The second component comprised the piezoelectric actuators. Commercially available PZT sheets (PIC255, type 5A modified lead zirconate titanate [46]), 100 microns thick, with top and bottom CuNi metallization, and a stiffness of 63 GPa, were manually sectioned and placed on the external surface of the cell membrane using a cyanoacrylate-based contact adhesive (Loctite® 401 [47]). This configuration ensured isolation of the piezoelectric ceramics from the diesel medium, preventing potential chemical degradation. The adhesive selection was validated by previous comparative studies, which revealed negligible performance variation across different cyanoacrylate formulations, attributed to the minimal adhesive layer thickness employed and its relatively low stiffness compared to other structural components of the sensor. Prior to adhesive application, the cell was subjected to an oxygen plasma treatment to improve surface wettability. This process was conducted for 2 minutes at 50 W plasma power and 0.2 mBar oxygen pressure within a vacuum chamber equipped with a radiofrequency plasma generator.

To establish electrical connectivity, 100 $\mu m$ Cu wires were soldered to each end of the piezoelectric patches. The opposite ends of the wires were connected to pins embedded in elastomeric plastic tubing for mechanical isolation. The integrity of the solder joints was verified by analyzing the impedance spectrum of the patches across a frequency range of 1 Hz to 1 MHz using an Agilent® 4294A impedance analyzer [48]. These elastomer-coated pins were subsequently inserted into the cell’s side connector protrusions, yielding a compact assembly and minimizing the influence of unwanted variable mechanical coupling caused by the introduction of the cell into a ZIF socket interface for electronic connection.

The optimization of piezoelectric patch configurations was assisted by finite element simulations in COMSOL® Multiphysics [49], enabling a comparative analysis of different actuator layouts based on their spectral response. In contrast, the design of the fluidic cell geometry was addressed experimentally due to the complexity of incorporating full three-dimensional fluid–structure interaction in the model. Multiple prototypes were fabricated and tested under controlled conditions, applying a performance metric focused on resonance amplitude, repeatability, and sensitivity to fluid changes to identify the most suitable sensor architecture.

The geometry and quantity of piezoelectric patches play a critical role in sensor design, as these components, being the most rigid elements, exert a dominant influence on the device’s response. Although simultaneous optimization of the host structure and patch geometry could be addressed as described in [50], this work focuses on a simpler approach: a computational evaluation comparing various actuator configurations to identify the optimal designs. To facilitate this analysis, a simplified cell model was developed using COMSOL. Mechanical and electrical boundary conditions were accurately defined, while non-essential geometric features such as side connectors were excluded due to their less impact on the sensor’s dynamic behavior. A mesh-convergence study was performed to ensure that the finite element results were independent of mesh density while maintaining computational efficiency. Additionally, as previously explained, fluid-structure interactions were omitted to streamline the simulation within a three-dimensional framework. Figure 2 illustrates the piezoelectric patch configurations analyzed through this approach. Performance assessment was based on the voltage amplitude spectrum within the operational frequency range of 1 kHz to 1 MHz. The optimization criterion aimed to maximize both the number and amplitude of resonance peaks in the spectra as these serve as sources of sensor data related to the target liquid [51]. Simulation results indicated that geometries 1 and 6–8 yielded suboptimal spectral profiles. Complementing this analysis, we conducted natural frequency simulations of the standard cell model either with a single piezoelectric sheet on its membrane or with two patches aligned along the vertical axis. In-plane stress values were averaged across all resulting modal shapes, yielding the distribution shown in Figure 3. We can observe that superposition of modes within this frequency range produced low-stress regions at the mid-width and mid-length of the structures, concentrating the effective action and sensing areas in the quadrants. As a result, structures such as 2-4 and 9-10 re-emerged (especially configurations 3, 9 and 10), further reinforcing the previous conclusions. Consequently, we concentrated the fabrication on configurations 2–4 and 9–10, which are also represented in the sensor schematic in Figure 1, with the possible cutouts of actuators highlighted by a black mesh in the plan view.

The other key component is the fluidic container. As previously outlined, one objective of this study was to develop a sensor capable of producing spectral responses characterized by a high number of resonances with high amplitude in a certain frequency range. However, these spectral features must also exhibit sensitivity to fluid changes, maintain repeatability across measurements to attain good resolution, and demonstrate recovery upon reintroduction of the reference fluid. To achieve this, we experimented with the geometric parameters of the fluidic cell depicted in Figure 1. Sensors were fabricated using parameter combinations within the ranges specified in Table 1. Iterative adjustments were made based on comparative performance, with superior parameter values informing the design of subsequent prototypes. This approach enabled progressive refinement of the sensor architecture.

The method for optimizing the cell structure consisted of the following experimental procedure. A sensor fabricated with a given set of geometric parameters was subjected to two fluids via a peristaltic pump: one comprising pure diesel fuel, and the other consisting of a 90:10 volumetric mixture of diesel and commercial sunflower oil. Starting with pure diesel, spectral data were acquired using an Analog Discovery 2 (AD) instrument [52] across a frequency range of 1 kHz to 1 MHz, discretized into 800 points. A sinusoidal input signal of 3.3 V was applied, preceded by a brief stabilization period to ensure fluid equilibrium. For each frequency point, measurements were performed over at least 10 signal periods and were averaged to enhance data robustness. Two spectra were recorded with a time interval of 5 minutes between successive acquisitions. Subsequently, the pure diesel was replaced with the adulterated mixture, using no further cleaning other than the entrainment effect of the new solution. The same measurement protocol was repeated, and finally, the system was flushed with pure diesel once more, and the measurement cycle was repeated. All measurements were conducted under static fluid conditions at room temperature (22±1ºC).

This experimental framework enabled the evaluation of three key performance metrics: sensitivity, reproducibility, and recovery. These were quantified as absolute differences between: spectra of different solutions ($sensitivity=|{\mathbf{s}}_j^i-{\mathbf{s}}_{j+1}^i|$); spectra of different consecutive measurements corresponding to the same solution ($resolution=|{\mathbf{s}}_j^i-{\mathbf{s}}_j^{i+1}|$); spectra of the same fluid measured before and after exposure to a different fluid ($recovery=|{\mathbf{s}}_j^i-{\mathbf{s}}_j^{\prime }i|$). The expression ${\mathbf{s}}_j^i$ denotes the spectrum corresponding to measurement $i\in \{1,2\}$ of liquid j (either pure diesel or the adulterated mixture). A higher sensitivity is desirable, indicating strong differentiation between fluid types, whereas elevated differentiation in resolution or recovery is undesirable, as it reflects inconsistency in repeated measurements of the same fluid.

Based on these definitions, to determine whether greater sensitivity `compensates’ for poorer resolution and recovery at each spectral point i, we propose the following equation. This formulation also serves as a dimensionality reduction strategy for subsequent analysis:

$$m_i={\left[{\displaystyle \frac{sensitivity}{\underset{diff}{max}(resolution,recovery)}}\right]}^p$$

(1)

where “max” denotes the greatest difference, corresponding to the worst result between resolution and recovery. To quantify the relative performance of each cell, two metrics are proposed: the first uses equation (1) to compute m over all points of the spectrum and $p=2$, while the second uses only the points where sensitivity compensates for resolution/recovery ($m>1$) and $p=1$. Then, in both cases, the mean value across all spectral points is calculated and the sensors with higher values of m are considered the best. The two approaches produced comparable results.

2.2. System Description and Calibration-Drift Experiments

This section presents the architecture of the measurement system designed to operate the sensors optimized using the method described in the preceding subsection, together with the experimental protocol implemented for calibration and drift assessment.

The best sensors were integrated into a measurement system analogous to that depicted in Figure 4, previously introduced in [51] for MEMS-based detection of adulterants in olive oil. In addition to the sensor element, the system comprised electronic interfacing circuits designed to operate with an ESP32-S3-DevKitC-1-N32R8V microcontroller [53]. Fluid samples were introduced into the sensor at maximum flow rate using a Gilson Minipuls 3 peristaltic pump [54]. A transistor-based circuit was employed to amplify the Pulse Width Modulation (PWM) signal generated by the microcontroller, which served to excite the sensor’s input actuator patch(es). The PWM frequency was swept from 10 kHz to 1 MHz, yielding 530 discrete frequency spectra. A variable frequency step was used to account for the microcontroller’s limited frequency resolution. The sensor’s output signal was further amplified via a bipolar junction transistor (BJT) biasing circuit incorporating emitter and collector feedback to improve DC stability at the operating point. This amplified signal was processed by an envelope detector, also implemented using a discrete transistor circuit, and captured via the microcontroller’s analog-to-digital converter (ADC). For each excitation frequency, 1000 output samples were acquired, each comprising 10 response periods. Averaging across these samples improved data robustness. All electronic components were powered using the 5 V supply provided by the microcontroller.

The measurement procedure was repeated for each of the biodiesel solutions listed in Table 2. These solutions were prepared by blending commercial diesel fuel with sunflower oil in proportions consistent with those reported in the literature and compliant with European regulatory standards [28]. The table contains the physical properties of the fluids, determined by averaging three measurements obtained using a commercial Anton Paar DMA4100M densitometer equipped with a Lovis module [55], maintained at 40ºC. Samples were introduced into the system in ascending order of viscosity. For each fluid, measurements were conducted under static conditions following a stabilization period of 5-15 minutes, and subsequently 33 spectra were collected over approximately 10 minutes. When changing the fluid, the sensor was flushed with the incoming fluid for 3 minutes without any additional cleaning protocol. All measurements were performed without active temperature control of the resonator; ambient temperature during the experiments was maintained at 23±1°C. Furthermore, the experiment was repeated using solutions $N_2$, $N_3$, $T_3$ and $T_4$ over a period of four days to assess whether spectral variations arising from temporal drift could be mitigated through data processing and AI techniques.

2.3. Deep Learning Algorithms Optimization

Following the acquisition of spectral data from all prepared solutions, machine learning models were constructed to establish predictive relationships between the spectra and the corresponding physical properties of the fluids. As demonstrated in our previous studies [26,43,51], convolutional neural networks exhibit strong performance in the analysis and interpretation of spectral signals. The procedures employed to identify network architectures best suited to our data, together with the spectral drift compensation and dimensionality reduction strategies implemented, are detailed below.

The first step involved defining the data sets and applying appropriate scaling. Mixtures labeled $N_1-N_5$ were designated as the training set, whereas mixtures labeled $T_1-T_6$ were reserved exclusively for testing and were not used during parameter optimization. Prior to training, the data were preprocessed using a scaling method based on the standard deviation. Following this process, optimization of the neural network architecture was undertaken. To identify the best network configurations that improve predictive accuracy, we applied a hyperparameter fine-tuning strategy analogous to that used in [43,51]. Specifically, we varied the number of convolutional layers (up to five), the number of filters, their size and stride. The tested parameter values are illustrated in Table 3, which summarizes the general architecture of the evaluated models. The filters and their associated parameters define distinct mechanisms for spectral feature extraction. The ReLU activation function was employed to facilitate gradient-based optimization via the Adam algorithm [56], which has proven effective in CNN training. Learning rates ranging from 0.01 to 0.001 were explored to minimize the mean squared error loss function. To control model complexity, we incorporated either high stride values or max-pooling layers, which perform local subsampling by selecting the maximum value within a defined neighborhood. Following the final convolutional block, an average pooling layer was applied to reduce dimensionality, thereby removing the need for a flattening operation and fully connected layers. This design choice is critical, as the latter approach introduces additional parameters and computational overhead, which are incompatible with the constraints of microcontroller deployment. The network ended with a single output neuron using a linear activation function to predict the target physical properties, such as viscosity or density. To identify the most effective model architecture, a comparative evaluation was conducted by quantifying the prediction error. This error was computed as the arithmetic mean of the absolute differences between the model-predicted values of viscosity or density and the corresponding reference values obtained from the commercial laboratory-grade viscometer. This approach enabled the selection of the network configuration that yielded the highest predictive accuracy. All models were implemented and trained using TensorFlow 2.17 [57].

The models were subsequently evaluated using data obtained from drift experiments. To simulate realistic operating conditions, liquid $T_3$ was selected as the reference fluid for measurements on different days. We employed this liquid as a reference because it constitutes a representative solution of the problem under study, namely biodiesels derived from mixtures of conventional diesel and sunflower oil, and it exhibits a comparatively low viscosity relative to other biofuels in our dataset, thereby enabling more efficient removal during the circulation of subsequent liquids to be measured. Following the measurement protocol described earlier, the mean spectrum was calculated from repeated measurements. The ratio between the average spectrum of the reference solution on the initial day (day 0) and that obtained on day n was then determined. This ratio defines a spectral factor ${\mathbf{r}}_n$, which encodes the relative variations in sensor response between day 0 and day n across all spectral components, each of which may evolve differently over time. The factor ${\mathbf{r}}_n$ was then employed to adjust the spectra of subsequent solutions. Specifically, the adjustment consisted of multiplying the measured spectrum of a given solution by ${\mathbf{r}}_n$, thereby approximating a transformation of the data from day n back to day 0. The corrected spectrum was then reintroduced as input to the trained machine learning models, yielding more accurate predictions of viscosity and density compared to unprocessed spectra. In this way, the operational lifespan of both the sensor and the overall system can be extended simply by using one single unique calibration solution as reference.

In addition, a dimensionality reduction study was conducted as follows. Using the equation (1) as a basis, the number of spectral points was progressively reduced, thereby decreasing measurement time while simultaneously evaluating the impact on neural network training and performance in both calibration and drift experiments.

It is important to note that the models were trained externally and subsequently deployed on the microcontroller via the TensorFlow Lite library, enabling a fully autonomous viscosity and density monitoring system. This machine learning framework not only enhanced system autonomy but also simplified the electronic requirements for signal processing, because any spurious effect originating from the parasitic elements of the resonator or the electronics remains constant across all measurements, so they can be learned and disregarded by the machine learning models.

3. Results

This section applies the previously defined performance metric to evaluate and compare 64 sensor geometries fabricated during the design refinement process. It presents representative examples illustrating how the criterion guided structural selection, summarizes the final geometric parameters, and discusses the influence of piezoelectric patch distribution and fluidic cell features on overall sensor performance.

In addition, we describe the outcomes of calibration and drift experiments performed with the optimized sensor integrated into the microcontroller-based system. These results include spectral measurements for all prepared solutions, the predictive performance of CNN models for viscosity and density estimation, and their comparison with laboratory references. The section also examines the correction of temporal drift and explores dimensionality reduction as a means to accelerate measurements while preserving accuracy and enabling efficient deployment on resource-constrained hardware.

3.1. Optimization of the Sensor Structure

As described in Section 2, we employed a systematic approach to refine the geometry of the liquid-containing cell, guided by equation 1 and the measurement protocol described in the corresponding subsection. According to this equation, spectral points yielding values greater than 1 are considered positive, as they indicate that the sensor’s sensitivity exceeds its limitations in resolution or recovery. Conversely, values below 1 are regarded as negative, since insufficient resolution or recovery cannot be distinguished from spectral variations induced by changes in the liquid. In total, 64 combinations of geometric parameters were designed, fabricated, and tested. Figure 5 illustrates the application of the optimization method to two representative geometries: one of larger dimensions without fins (left), and another of smaller scale incorporating membrane extensions (right). In the figure, green lines indicate cases where $m>1$, while red lines correspond to $m<1$, enabling refinement of the cell structure based on this criterion.

Following the structural refinement process, several conclusions could be drawn:

• In general, miniaturization of the cell, and consequently its patches, yielded improved m-metric values.
• When the cell membrane was fully covered by piezoelectric actuators, the addition of fins produced inferior results compared to an empty configuration. Conversely, when the actuators were reduced in size such that half of the membrane remained uncovered, the presence of fins substantially enhanced the m-metrics relative to a hollow cell.
• A comparable improvement was observed when the membrane thickness was reduced. However, combining fin addition with reduced membrane thickness led to overall poorer performance, as each factor independently increases variability in the printing process, and their simultaneous application amplifies this variability. Accordingly, a thicker membrane proved more suitable when fins were incorporated.
• The optimal fin configuration consisted of one fin per quadrant of the cell (i.e., a 2×2 array). Increasing the number of cilia along either axis degraded performance.
• A reduced arrangement (1×2) produced comparable results only when the cilia were positioned within quadrants.
• Complete coverage of the membrane with four piezoelectric patches significantly worsened the m-metric values, likely due to multiplied defects introduced during fabrication and gluing of the patches.

It should be emphasized that these conclusions are constrained by inherent imperfections in sensor fabrication. Manufacturing processes introduce additional sources of variability, including cell curing, resin evacuation, patch cutting, and non-uniform adhesion. Therefore, the findings presented here should be regarded as design guidelines rather than definitive optimization criteria.

Figure 6 presents the outcomes of these structural refinement techniques. Table 4 summarizes the geometric values obtained for this sensor. Regarding patch components, both vertical and horizontal divisions were observed, as described earlier. For the fluidic cell, a compact design incorporating four internal fins, one per rectangular quadrant, proved sufficient to achieve good results across the three defined metrics, while minimizing material requirements. Notably, alternative models based on this geometry, such as those with a 0.2 mm membrane or without fins, also performed well experimentally.

3.1.1. Calibration and Drift Experiments

The sensor depicted in Figure 6 was integrated into the microcontroller system illustrated in Figure 4. Subsequently, experiments were conducted to measure the solutions listed in Table 2, following the protocol described in subSection 2.2. A total of 363 spectra were acquired, as shown in Figure 7 (a). This figure demonstrates the capability of the proposed system to detect subtle variations in liquid properties.

Based on these data, convolutional neural networks were trained to predict viscosity and density using the optimization procedure explained in subSection 2.3. The solutions labeled N in Table 2 served as training data, while the remaining fluid measurements were reserved for testing, thereby assessing the model’s generalization performance. The optimal network architectures identified for both viscosity and density estimation followed the configuration shown in Figure 7 (b). This architecture comprised three convolutional layers with 8, 16, and 32 filters, respectively, each with a kernel size of 5 and a stride of 5, without intermediate max-pooling layers. The network concluded with a global average pooling layer and a dense output layer containing a single neuron, as detailed in the corresponding subsection. Training was performed with a batch size of 55 over 200 epochs.

Figure 8 (a) and (b) present the results obtained with our predictive models in comparison with the laboratory instrument. In Figure 8 (a), the red boxes denote viscosity predictions for the training solutions (N), the blue boxes correspond to the test solutions (T), and the green dots indicate the reference values measured with the commercial viscometer.

Similarly, Figure 8 (b) shows the density predictions, where the green boxes represent the training set, the orange boxes the test set, and the blue dots the reference measurements. For viscosity, the system successfully distinguishes between pure diesel and a mixture containing 1% sunflower oil; however, minor adulterations remain undetectable, as evidenced by the overlap of boxplot extremes. The density predictions are also very accurate. To further evaluate the system robustness, we repeated the measurement procedure described in subSection 2.2 for fluids $N_2$, $N_3$, $T_3$ and $T_4$ over four consecutive days. This experiment enabled the development of an algorithmic approach to extend sensor lifespan. Specifically, the previously trained models were combined with the drift correction method explained in subSection 2.3, yielding the results shown in Figure 8 (c) and (d). These figures compare predictions obtained from spectra recorded on day 0, corresponding to the initial measurement of the 11 solutions, with those derived from spectra collected on subsequent days. Spectral variations attributable to temporal drift were observed, underscoring the need for correction. Although prediction accuracy decreases over time, the integration of the models with the spectral transformation method still permits differentiation among most solutions. This demonstrates that simple algorithmic strategies can effectively mitigate drift effects and extend the operational lifetime of the sensing system, achieving accuracies sufficient for certain practical applications.

Table 5 and Table 6 report the mean errors associated with the viscosity and density models during the calibration experiment, whereas Table 7 and Table 8 present the corresponding results for the drift experiment. Consistent with previous studies [51], several metrics were employed to evaluate model performance: the absolute difference between predicted and reference values ($e(mPa·s)$ and $e(g/mL)$); the ratio between the mean error and the operating range (full-scale error, $e(\%FS)$); the relative deviation, defined as the mean difference normalized by the reference values ($e(\%RD)$); and the resolution error, quantified as the standard deviation across repeated measurements of the same solution ($e_{res}$). The tabulated results corroborate the conclusions observed in the graphics: both calibration and resolution errors are minimal, and when comparing drift experiment outcomes with those obtained on day 0, the errors increase slightly but remain within acceptable limits.

Finally, a dimensionality reduction analysis was performed using metric 1, using the new definition of resolution as the standard deviation, with the objective of reducing data acquisition time and thereby accelerating the estimation of fluid physical properties. To this end, progressively fewer spectral points were selected according to equation 1, and new convolutional neural networks were trained following the protocol described in subSection 2.3. The trained models were applied both to the calibration experiment and to the drift experiment. Table 9, Table 10, Table 11 and Table 12 summarize the errors obtained. The results indicate that performance remains comparable whether 530 or 103 spectral points are used, demonstrating that measurement time can be reduced with minimal impact on accuracy. Moreover, reducing the input dimensionality to 103 points lowered computational demands; that is, the optimal neural networks contained fewer parameters, improving their suitability for implementation in the limited memory of microcontrollers. Figure 9 presents the graphical results obtained with models trained on spectra of 103 points, confirming their strong overall performance when compared with models trained on spectra of 530 points (Figure 8).

4. Discussion

Using the error values reported in the tables of the previous section, the performance of the proposed device can be compared with that of other viscosity and density monitoring systems described in the literature [25,26,31,32,33,35,36,43]. The results of this comparison are presented in Table 13 and Table 14. For viscosity measurements, the proposed system achieves the second-best performance in the $e(mPa·s)$ and $e(\%FS)$ metrics, ranking only behind [43], while in the $e(\%RD)$ metric it occupies the third position (after [33] and [43]). In terms of density, the accuracy of our system consistently ranks third across the $e(g/mL)$, $e(\%FS)$ and $e(\%RD)$ metrics. With respect to resolution, the device ranks close to fourth, corresponding to the results reported by [43]. It should be emphasized that the studies compiled here are not restricted to fuels; they also encompass other types of liquids, whose interactions with the sensor material may yield either improved or diminished monitoring performance. A particularly relevant comparison can be observed in the tables, in the column corresponding to article [43]. In that case, the reported errors were obtained using a similar system configuration and a comparable set of biofuels but employing a MEMS sensor. The results were nearly identical to those presented here, although in that study it was possible to detect a 0.5% admixture of sunflower oil in diesel. These findings highlight that a sufficiently precise monitoring system can be realized using low-cost technologies, especially when combined with artificial intelligence, thereby achieving performance comparable to sensors fabricated with more expensive technologies.

Several avenues for future development and optimization of the proposed system can be identified. First, improvements in the manufacturing process are necessary. Two possible strategies may be considered: (i) laser-cutting the piezoelectric patches to improve reproducibility across samples, followed by bonding them to the fluidic cell using the printing resin itself; or (ii) incorporating piezoelectric particles directly into the plastic resins, thereby creating a uniformly sensitive fluidic cell throughout the structure. While both approaches could improve manufacturing reproducibility, the resolution of the 3D printer would remain a limiting factor. Another potential enhancement involves the use of specialized materials that exhibit reduced reactivity with fuels or other target liquids, thereby increasing sensor stability and durability. With respect to algorithmic improvements, equation 1 could be refined by incorporating drift experiment results into the denominator, thereby optimizing an additional critical aspect of sensor performance. Beyond this, more advanced correction techniques could be investigated and applied, potentially yielding superior data processing outcomes. Finally, for successful commercialization, these technical aspects must be complemented by the development of a comprehensive business plan. Such a plan should include detailed market research, regulatory compliance analysis, and brand development strategies to ensure the viability and competitiveness of the product.

5. Conclusions

In this work, we introduce a system that integrates 3D-printed fluidic cells and piezoelectric actuators with machine learning algorithms for the monitoring of liquids of industrial and environmental relevance. The transducer was structurally optimized using a novel metric that accounts for the multi-peak characteristics of the electromechanical response, as well as sensitivity, resolution, and regeneration capacity. Convolutional neural networks were employed and fine-tuned through hyperparameter optimization to improve accuracy in estimating fluid physical properties from spectral measurements. Both the sensor and the trained networks were implemented within a microcontroller-based platform with simple conditioning electronics. Calibration and resolution errors in viscosity and density estimation were small in comparison with reported values, reaching 0.99% and $1.48·{10}^{-2}$ mPa·s for viscosity, and 0.00485% and $1.9·{10}^{-4}$ g/mL for density. These precision levels enabled the detection of variations in biodiesel composition of less than 1%, based on viscosity and density measurements. Additional experiments addressing sensor temporal drift and dimensionality reduction further extended device lifespan and accelerated measurement speed. The results were benchmarked against comparable studies in the literature, demonstrating similar or superior performance in certain cases. While further improvements are possible, particularly through the automation of sensor fabrication, the present work provides effective solutions to challenges related to drift correction, geometric optimization, and data dimensionality reduction. The outcome is a low-cost, compact, portable, and precise sensing device capable of supporting biofuel quality assessment and adaptable to other industrial applications.