High-precision wave height detection of triboelectric nanogenerator by using voltage waveforms and artificial neural network

Accurate monitoring of waves is vital in blue energy harvesting, weather forecasting, marine resource development, and natural disaster warning.^1–7 The extraction of high-precision wave spectrum information is crucial in the research on waves. Consequently, various wave spectrum sensors have been designed for accurate wave spectrum detection, such as wave buoys,⁸ photoelectric remote sensing,⁹ radar remote sensing,¹⁰ and capacitance-based wave height sensors.¹¹ However, some factors severely limit the applications of the aforementioned sensors in high-precision wave detection. The technology of wave buoys is mature, and many related products are available; however, small-amplitude wave measurements yield certain errors. When measuring small-amplitude waves, the measurement signal is weaker compared to the ambient noise in the environment due to the small amplitude of the waves. In addition, buoys are typically large, resulting in high usage and maintenance costs. In ocean-wave spectrum monitoring using radar remote sensing and photoelectric remote sensing technologies, which are based on the recurrent inversions and Fourier transforms of first signals, satisfying the requirement of high precision is difficult because of severe signal distortion encountered during signal processing.¹² Although capacitance-based liquid-level sensors exhibit excellent detection performance in wave spectrum monitoring, the long-term exposure to a humid environment substantially deteriorates their practicability. In particular, these sensors require external energy storage devices such as batteries; thus, the limited lifetime, non-negligible replacement costs, and environmental issues greatly limit their applicability. Therefore, a new sensor method that incurs low costs and is less susceptible to environmental factors is urgently required.

The triboelectric nanogenerator (TENG), as a novel type of energy harvester, has witnessed a tremendous technological evolution since it was proposed a decade ago.¹³ TENGs collect mechanical energy from the environment and convert it into electrical energy, such as wind energy¹⁴ and sea energy.¹⁵ In addition, TENGs can be used for the static and dynamic measurement of self-driven electronic products through open-circuit voltage and short-circuit current in the triboelectric signal, providing the prospect of omnidirectional application in self-powered sensing.^16,17 Due to the advantages of self-powering and high sensitivity, TENG-based ocean-wave spectrum sensors can be considered the next-generation ocean-wave spectrum sensor, replacing the conventional ones. Zhang et al. fabricated a self-powered, high-performance triboelectric ocean-wave spectrum sensor (TOSS) by using a tubular TENG and hollow ball buoy that can measure ocean surface water waves in any direction and eliminate the influence of seawater on the performance of the sensor.¹⁸ Wang et al. fabricated a highly sensitive wave sensor based on liquid–solid interfacing TENG made of copper electrodes covered by a polytetrafluoroethylene film with a microstructural surface that can sense wave heights on the millimeter scale.¹⁹ The aforementioned studies used a linear model for detecting waves on the ocean surface, relying on the expression of the operating voltage of the TENG. However, the voltage of the TENG is affected by the instability caused by wave motion; this may affect the measurement accuracy of the linear model. To solve these problems, researchers have turned their attention to machine learning algorithms, which allow computers to “learn” automatically, analyze data to obtain the law of mathematics, and then use the law to perform predictions on new samples, thus eliminating the effect of unstable factors on the prediction results.^20–23 Machine learning algorithms have the capability to identify complex relationships and patterns within data that may be difficult for humans to discern. They can learn from large amounts of data and extract meaningful insights, allowing for more accurate predictions and decisions. Tan et al. proposed a theoretical artificial intelligence (AI)-based modeling method for predicting the electrical performance of a rotating TENG whereby the optimal distribution of charge, voltage, and current are obtained and energy harvesting is realized.²⁴ Luo et al. designed a TENG-based wooden table and employed AI to achieve intelligent detection of a ball's landing point, speed, and motion trajectory.²⁵ Zhang et al. designed an AI toilet by using an array of triboelectric pressure sensors, providing a low-cost, easy-to-deploy approach; it utilizes the different pressure distributions of a user's sitting posture to obtain biometric information and uses deep learning to correctly identify up to six users with over 90% accuracy.²⁶ 

In this paper, we proposed a wave height detection method for TENG by using a multilayer perceptron (MLP) neural network, as shown in Fig. 1(a). We designed a TENG based on the contact-separation mode as a self-powered wave height sensor; the electrical signal from the TENG is used as the training object to realize wave height detection. The proposed MLP-based approach eliminates the influence of external factors on the sensor, thus allowing the sensor to maintain high measurement accuracy. Because the TENG can convert the mechanical signal of the wave into an electrical signal, wave height detection can be achieved without the need for additional power, thus providing a new method for future marine research.

The experimental platform included a data-generation system and a data-acquisition system. We used a six-DOF motion platform (LJ6D-C80–00) to simulate the motion of waves. The voltage was measured using an electrostatic meter (Keithley 6514). A computer was used as the data-acquisition system for collecting and saving data from the system software of the electrostatics meter. The voltage signal collected from the electrostatics meter (sampling rate: 100/s) was used for training. The MLP model was constructed using scikit-learn, and the experimental samples were trained and tested on an average-performance computer [CPU: Intel(R) Core(TM) i7–9700 3.00 GHz; GPU: NVIDIA GeForce GT 730].

The designed TENG consists of a pie iron, a Z-form triboelectric basic unit, and a spring structure. We used a laser cutter to cut a 2-mm-thick acrylic plate into three 6 × 6 cm² plates and spliced them with glue to form the basic frame of the TENG. Holes were punched in the corners of the square board, and acrylic tubes and springs were placed to form the support structure. A pie iron was placed at the top of the TENG to drive the movement of the triboelectric layer. Polytetrafluoroethylene (PTFE) film (80 μm) was selected as the triboelectric layer and was cut into 4 × 4 cm² and attached to the acrylic plate of the same size together with a conductive cloth. The materials used were commercial products without any surface treatment. Because the soft contact model can substantially improve the triboelectric efficiency, a sponge of the same size (4 × 4 cm²) was padded at the bottom.²⁷ 

The structure of the TENG is shown in Fig. 1(b). To effectively vary the voltage of the TENG with height, the TENG is composed of a pie iron, a Z-form triboelectric basic unit, and a spring structure. The basic unit comprises three joined acrylic plates. We used a polytetrafluoroethylene (PTFE) film as the triboelectric layer and a conductive cloth as the electrode, both of which are attached to the acrylic plates. The spring structure improves the output performance and stability of the TENG. The detailed fabrication process of the TENG is presented in Sec. II B. Triboelectrification and electrostatic induction are the two fundamental effects of a TENG. We operated the designed TENG in the contact-separation mode, which is beneficial for long-term operation. Electrons transferred and remained on the surface of the PTFE film due to their strong electron gain capacity under the frictional force between the conductive fabric and the PTFE film. The working mechanism of the TENG is depicted in Figs. 1(c) and 1(d). When the pie iron pressed the PTFE film against the conductive fabric, the negative charge on the PTFE film produced an electric potential difference between the two electrodes, driving free electrons to flow from the electrode without a PTFE film to another electrode. When the pie iron was raised, the separation between the two electrodes created a polar opposite electric potential difference, causing electrons to flow back. Thus, the mechanical energy of the wave motion was converted into electrical energy, and the wave heights were extracted using the output signal of the TENG. By analyzing the extracted wave heights, they were detected using a neural network model.

To realize wave height detection by using TENG, we constructed an experiment platform and collected 25 000 samples of voltage waveforms. By analyzing the correlation between the voltage of the TENG and the wave height, we developed a lightweight MLP prediction model that can quickly detect the wave height. In addition, we evaluated the quality of the model by using general evaluation indices, accuracy, and loss. Due to the interference of several external factors in the experiment, we verified the applicability of the MLP model in wave height prediction and eliminated the contingency. We performed data collection experiments several times and used multiple wave motion data sets as a single data unit for analyses. By setting fixed parameters, a six-degree-of-freedom (DOF) platform was used to simulate the wave motion, and the voltage of the TENG was collected using an electrostatic meter. By using the time coordinates as the reference system, the voltage values were compared with the actual wave height values at the same time point to establish the analysis data set. After establishing the data set, the linear regression prediction model and the MLP model were used to predict the dataset. Next, the wave heights predicted by the two models were compared with the actual wave heights. Finally, the prediction method with greater accuracy and generalization capability was determined based on the comparison results.

The relationship between the wave height and the operating voltage of the TENG is depicted in Fig. 2(a). The operating voltage waveform of the TENG was found to be similar to the wave motion. The typical capacitive behavior is displayed in the triboelectric waveform due to the usage of Keithley 6514 for voltage measurement in the experiment, with the measurement circuit connected to the internal capacitor of Keithley 6514. This situation is discussed in Ref. 28. Keithley 6514 is a high-precision resistance measurement instrument commonly used for measuring the resistance of resistors. However, it also has other functions, such as voltage measurement. When measuring voltage, the internal capacitor of the instrument affects the measurement results. When a voltage is applied to the capacitor, charge accumulates between the two plates of the capacitor. In the experiment, due to the connection between the circuit and the internal capacitor of Keithley 6514, the capacitor influences the accumulation and discharge of charges when the open-circuit voltage of the TENG is applied to the measurement circuit. Specifically, during the operation of the TENG, when two materials are rubbed together, charges transfer from one material to the other, resulting in voltage generation. This voltage is transmitted to the internal capacitor of Keithley 6514, which is connected to the measurement circuit, causing a gradual accumulation of charge in the capacitor. As the charge accumulates, the voltage across the capacitor increases until it reaches the open-circuit voltage of the TENG. This process conforms to the typical behavior of a capacitor, where the voltage across the capacitor is proportional to the amount of charge applied to it. When measuring voltage using Keithley 6514 due to the presence of internal capacitance in the instrument, a potential difference is generated when friction occurs between two objects and charge transfers from one object to another. In the initial stage, the potential difference rises rapidly as charge transfer progresses until the capacitor is fully charged. Once the capacitor is fully charged, the potential difference stabilizes, forming a plateau in the voltage.²⁸ As can be seen in Fig. 2(a), the operating voltage was not a smooth curve during the wave peaks and troughs; in addition, irregular fluctuations were observed because of the irregular vibration of the TENG when it fell to the trough of the wave. Similarly, irregular vibration occurred when the TENG rose to the wave crest. The details are shown in Figs. 2(c)–2(f). Figure 2(c) shows the operating voltage waveform of the TENG for a complete wave motion time in six randomly selected data sets at a wave amplitude of 35 mm. Due to the interference of external factors in the experimental environment, the working voltage of the TENG produced by wave motion with the same parameters differed; this can be clearly observed at the peak. Figure 2(d) shows the local magnification of the working voltage when the TENG rose to the wave peak at an amplitude of 35 mm. The difference in the working voltage of the TENG was more obvious at this moment. Furthermore, a small irregular trough was observed near the wave peak, as can be seen in Fig. 2(f).

Figure 3 shows the comparison between the predicted wave height and the actual wave height from the linear regression prediction model. The wave height amplitude was gradually decreased from 35 to 10 mm. The prediction accuracy of the linear regression model for the wave motion trajectory also decreases. For wave motion trajectories ranging from 0 to 35 mm, the predicted wave trajectory given by the linear regression model is the motion trajectory ranging from 4 to 35 mm. As the wave motion trajectory becomes smaller, the prediction error of the linear regression model increases. In the case of wave motion trajectories from 0 to 10 mm, the predicted wave motion trajectory value by the linear regression model is the wave motion trajectory ranging from 5 to 12 mm. Not only is the error rate of the peak wave height large, but the wave motion trajectory is also not a smooth curve. According to formula (1) of the linear regression prediction model, the predicted wave height value output by the linear regression prediction model is equal to the working voltage of the TENG multiplied by a weight coefficient W and added with a bias value. That is, the predicted value of the wave motion trajectory output by the linear regression prediction model is the working voltage waveform of the TENG. External forces that may affect the TENG during operation, as well as errors inherent in the device, accumulate into the linear regression prediction model, causing an impact on the wave motion trajectory. As shown in Table I, the error rate of the linear regression prediction model reached 64.6% in the group of 10 mm waves with the poorest model recognition rate, and the error rate also reached 16.2% in the group of 35 mm waves with the highest model recognition accuracy.

The main parameters of the linear regression prediction model are presented in Table I, where the amplitude corresponds to the maximum value of the wave height, the voltage variation is the difference between the maximum and minimum values of the operating voltage of the TENG during each wave motion, and the maximum error interval is the maximum difference between the predicted wave height value and the actual value of the linear regression prediction model in the interval near the peak.

As can be observed from Table I, a decrease in the amplitude led to a decrease in the total variation of the operating voltage of the TENG. A comparison between the predicted and actual values of the linear regression prediction model in Fig. 3 revealed that the error between the predicted and actual values increased as the wave height decreased. This is mainly because of two reasons. First, the error between the predicted and actual values of the model increased significantly as the wave height decreased. Second, as the wave height decreased, the operating voltage of the TENG decreased, and the overall effect of the error value of the operating voltage of the TENG on the linear regression prediction model increased. This is mainly because as the wave height of wave motion decreased, the waveform of the predicted value from the linear regression prediction model became increasingly similar to the waveform of the operating voltage of the TENG rather than the waveform of wave motion. Thus, the linear regression prediction model requires a sufficiently large change in the operating voltage of the TENG to achieve an accurate prediction of the wave height. A magnitude difference was observed between the operating voltage of the TENG and the wave height data; this affected the accuracy of the linear regression prediction model. Moreover, as the TENG operating voltage variation decreased, the overall effect of the TENG operating voltage error value on the linear regression prediction model increased, which indicates that the prediction model for wave height must possess a certain nonlinear fitting capability to eliminate the effect of the TENG operating voltage error.

Based on the analysis of the aforementioned linear regression model prediction results, for the data set used in this experiment, we eliminated the difference in the dimensions between the operating voltage of the TENG and the wave height to solve the problem of fluctuations near the inflection point of the wave motion. The structure of the MLP is illustrated in Fig. 4(a). We split a set of TENG voltages into data elements of 1 × 500 dimensions in time coordinates as input values. Similarly, we split the corresponding wave height into data elements of 1 × 500 dimensions as output values. To eliminate the influence of the dimensional difference between the input and output values on the accuracy of the model, all the input and output data were normalized using the data normalization in scikit-learn. The processed voltage data were fed into two fully connected (FC) layers (256 and 512 neurons in the first and second layers, respectively). The number of neurons in the output layer was the same as the number of labels, that is, there were 500 neurons for the operating voltage of the TENG and 500 neurons for the wave height. All wave motion parameters in this model were taken in the same amount. In contrast, during the actual operation of the TENG, the number of normal operating cases is much greater than that of abnormal ones. For wave motions with smaller amplitudes, as the amplitude decreased, the operating voltage variation of the TENG did not change considerably. In the training process, 20% of the samples were randomly selected as the validation set and were not used for training.

In this experiment, the errors in the working voltage of the TENG were within the interval between the highest peak and the lowest valley of the wave motion height. To eliminate the influence of these errors, the model introduces the ReLU activation function, which treats values less than 0 as zero, that is, the influence of the working voltage of the TENG within the error interval is reduced. Thus, the experimental appearance of the magnitude difference problem with the experimental numerical errors is resolved.

The training results for six wave heights obtained using the MLP neural network model are shown in Fig. 5. For all the training models, data normalization was performed to eliminate the dimension difference between the wave height and the operating voltage of the TENG; in addition, the ReLU activation function was used to enhance the nonlinear fitting ability of all the training models. Thus, the problem that the trend of the predicted wave height in the peak interval of wave motion does not match the actual changes in the linear regression prediction model was solved, and the problem of a large difference between the predicted wave height and the actual value at the lowest point of wave motion no longer occurred. This demonstrates the feasibility of ML-based TENG wave height measurement.

The main parameters of the MLP model with ReLU as the activation function are presented in Table II. Upon performing data normalization, the training error values of the model and the cumulative error values of the validation set were within the desired range with reduced wave height and reduced operating voltage of the TENG. In the validation session, we divided the validation set from the data set and used the voltage of the TENG as the input value of the MLP prediction model, and the wave height prediction value was obtained using the MLP prediction model. The numerical error between the wave height prediction value and the actual value of wave height yielded by the MLP prediction model was controlled within 0.3 mm, and the maximum model error rate of the prediction model was only 0.76% in the experimental groups ranging from 10 to 35 mm; thus, the MLP prediction model yielded an accuracy of over 99.24% in predicting the wave height by using the TENG working voltage.

In this study, the neural network method was employed for the first time in the field of wave height prediction by using the TENG operating voltage. The validation set errors in the range of amplitudes from 10 to 35 mm were controlled at 0.049% and 1.94%, respectively. The innovations and conclusions of this study are listed as follows:

1. The first wave motion prediction method based on voltage waveforms was proposed and employed for six waveforms.

2. The proposed model is a lightweight neural network with high accuracy and low time complexity with two FC layers. A data set of 30 sets of 1 × 500 voltage curves was trained in less than 15 s.

3. The model has strong learning ability and nonlinear fitting ability and can, thus, completely eliminate the influence of the error of the operating voltage of the TENG in the wave crest interval on the wave height prediction value. Wave height detection can also be performed well in the case of a small voltage change rate.

4. The higher the wave amplitude, the higher the operating voltage of the TENG, and the higher the model prediction accuracy.

5. Although the voltage waveforms of the TENG are similar for different wave heights, the model must be further studied for more complex wave motion scenarios in future work. The variation relationship between the voltage waveform and wave height was obtained experimentally; thus, there is a need to study the operating voltage of the TENG for more complex wave motion in practical application scenarios.

In conclusion, the proposed neural network model has good optimality for the operating voltage of the TENG. The findings presented in this paper provide a new approach for utilizing the working voltage of TENGs for wave height detection.

The supplementary material accompanying this manuscript consists of two parts, intended to provide comprehensive support and clarification of the research conducted. Supplementary Figure 1 includes actual photograph of the equipment used in our experiments. The images depict the appearance, structure, and components of the equipment, aiding readers in better understanding our experimental setup. Please refer to Supplementary Figure 1 for detailed information on the equipment photographs. Supplementary Video 2 comprises a video recording of the data collection process. This video showcases the steps and procedures involved in collecting data during our experiment. By viewing Supplementary Video 2, readers can gain a more visual understanding of our data collection methodology and operational procedures. Please consult Supplementary Material 2 to access the complete video of the data collection process.

This work was supported and funded by the National Key R&D Project from Ministry of Science and Technology (No. 2021YFA1201603) and National Natural Science Foundation of China (NNSFC) (Grant No. 22001102).

The authors have no conflicts to disclose.

Yuming Lai: Writing – original draft (equal). Jiahua Ma: Formal analysis (supporting). Honggui Wen: Methodology (supporting). Huilu Yao: Supervision (equal). Wenjuan Wei: Supervision (equal); Validation (equal). Lingyu Wan: Writing – review & editing (equal). Xiaodong Yang: Validation (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request. The data are not publicly available due to the project is still ongoing.