https://orcid.org/0009-0009-9631-1308
Retraction
The PLOS One Editors retract this article [1] because it was identified as one of a series of submissions for which we have concerns about potential manipulation of the publication process. These concerns call into question the validity and provenance of the reported results. We regret that the issues were not identified prior to the article’s publication.
The author either did not respond directly or could not be reached.
29 Jan 2026: The PLOS One Editors (2026) Retraction: Enhancing pipa tuning stability with piezoelectric materials: An adaptive system for real-time performance adjustment. PLOS ONE 21(1): e0341880. https://doi.org/10.1371/journal.pone.0341880 View retraction
Figures
Abstract
Introduction
The study explores the development and performance evaluation of a Neuro-Fuzzy Inference System (NFIS) for adaptive tuning of a pipa string instrument under varying environmental conditions. The NFIS adjusts string tension in real-time based on voltage, temperature, and humidity sensor inputs by integrating piezoelectric sensors with IoT capabilities. The primary objective is to maintain tuning accuracy within ±0.1 Hz, even with environmental fluctuations, thus improving the stability and consistency of musical performance.
Methods
A dataset of 2,000 samples was collected, including voltage (0.1–5 V), temperature (10–40°C), and humidity (20–90% RH) values, along with corresponding output adjustments. The NFIS utilised Gaussian membership functions to categorise sensor inputs into linguistic terms (e.g., “High Voltage,” “Medium Temperature”), and a comprehensive rule base of 40 rules was established for adaptive tuning. Training of the NFIS was conducted using gradient-descent backpropagation with a learning rate of 0.01 and L2 regularisation, validated through 5-fold cross-validation. Real-time performance data was transmitted via an ESP32 microcontroller to an AWS IoT Core database, with user adjustments and data visualisation provided through a mobile application.
Results
The NFIS was highly well tuned with a mean pitch deviation of only ±0.08 Hz at stable and varying environmental conditions. We have cross-validated the model, and it produced an average MSE of 0.012 across folds, which speaks to the robustness of the model. During an 8-hour test period, our IoT system achieved an average data transmission latency of 120 ms on the server and 99.8% system uptime, with our error correction mechanisms ensuring 98% data integrity. The compensated voltage deviated less than ±0.1 V from the baseline voltage at varying temperatures and humidity, and the environmental compensation minimised the voltage deviations within the original compensation limits.
Conclusion
This NFIS-based adaptive Tuning System keeps the tuning accurate during environmental changes. In conjunction with IoT for real-time monitoring and adaptive learning capabilities, this technology adds more responsiveness and reliability, thus making it an efficient tool for musicians to perform consistently.
Citation: Yawen K (2025) RETRACTED: Enhancing pipa tuning stability with piezoelectric materials: An adaptive system for real-time performance adjustment. PLoS One 20(5): e0323840. https://doi.org/10.1371/journal.pone.0323840
Editor: Alemayehu Getahun Kumela, Universite Cote d'Azur, FRANCE
Received: November 16, 2024; Accepted: April 16, 2025; Published: May 15, 2025
Copyright: © 2025 Kou Yawen. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All files are available from the https://doi.org/10.5061/dryad.12jm63z87 and the https://github.com/Zikou80/Pipa_Tuning_Stability/blob/main/nfis.py.
Funding: The author(s) received no specific funding for this work.
Competing interests: The authors have declared that no competing interests exist.
Introduction
The use of piezoelectric intelligent materials in the adaptive tuning systems of musical instruments holds considerable promise for improving performance stability and tuning accuracy. The traditional Chinese plucked string instrument pipa has a complex tuning system sensitive to environmental factors such as temperature and humidity, affecting its tonal stability. The instrument typically features four strings, and its tuning is achieved through a combination of manual adjustments using tuning pegs and the inherent flexibility of the strings. The pipa’s tonal range spans from low to high frequencies, and its performance techniques, including string bending and vibrato, can further impact pitch accuracy during play. String bending allowed for microtonal adjustments, while vibrato, which involved slight variations in pitch, added a dynamic quality to the sound. These unique characteristics posed specific challenges for maintaining tuning stability, especially during live performances [1,2]. While previous studies indicate that implementing piezoelectric materials into the pipa may provide a more stable tuning system, they do not delve deeply into the challenges unique to traditional instruments such as the pipa and the feasibility of adapting the material to the constraints imposed by variable environmental influences. Piezoelectric components, whose structure induces charge under mechanical stress, can accomplish a far more intelligent implementation of adaptive tuning through dynamic regulation of tension and frequency in a real-time manner. This is particularly beneficial for instruments highly sensitive to thermal and humidity factors, which can affect tuning stability during performing [3]. Gomathi [3] noted the potential for piezoelectric materials to address environmental concerns but did not critically explore the more pragmatic challenges of leveraging such systems in a live performance context, including the need for real-time responses without distortion or latency. Although using smart materials to create new musical systems is a decades-old pursuit, the availability of new piezoelectric technologies has started to support a new level of sophistication and range of applicability.
Numerous early studies in the 2000s, including Feldman [4] and Ludwig [5], were performed on simple sensor integrations for stabilising the resonance using polyvinylidene fluoride (PVDF) and piezo ceramics. Although those works showed collaboration to progress based on mechanical vibrations and promising aspects to globally stabilise frequencies by applying open-loop control, the systems’ simplicity was limited in reproducing the complex tonal dynamics of instruments like pipa. These earlier works established both the mechanism of adapting piezoelectric materials to tuning mechanisms but stopped short of exploring the full scale of material properties that could be used in adaptive, real-time tuning. These approaches have prompted new investigations that take advantage of the properties of piezoelectric materials to develop adaptive tuning systems with algorithms sensitive to minute deviations in pitch to keep a consistent tonal quality over time. However, previous studies [7–9] observe algorithms that tend well with pitch stability, and they do not discuss general adapting systems to traditional instruments and tunings that bear other challenges.
Neuro-fuzzy and machine learning algorithms have been combined with piezoelectric materials to improve feedback accuracy and increase predictive tuning [6–10] of complex instruments with embedded smart-material controller developments that are well documented in the literature. Cios and Pedrycz [7] point out the tendency of ML algorithms to improve feedback precision and adaptive responses, but their work describes mainly complex, modern instruments and resulting from their work, it is unclear that these technologies will work for traditional instruments such as the pipa, which have different tuning issues. These systems “learn” and progressively enhance their responses, thus enabling musicians to attain improved pitch tuning in varied performance situations. These properties of piezoelectric materials, combined with their versatility, are further emphasised in the wide range of plucked string instrument organisations that they can be applied to, both classical and modern. Nevertheless, despite the impressive emerging benefits from recent advances in piezoelectric materials and technologies, there are some important gaps, particularly concerning maintaining tuning stability in instruments such as the pipa, that face specific challenges due to environmental factors.
Problem statement
While adaptive tuning systems utilising piezoelectric materials show great promise, current technologies continue to suffer from the inability to retain stable tuning in traditional musical instruments such as the pipa, particularly under specific environmental conditions where fluctuation occurs due to changes in temperature and humidity.
Aims and novel contributions
This study seeks to investigate this leading-edge solution where we adopt piezoelectric materials for the adaptive tunable system in the pipa, enhancing its performance stability and accuracy. This research aims to inscribe piezoelectric materials with adaptive tuning algorithms to establish a more reliable system that can provide real-time control of both tension and frequency. The originality of this work was its in-depth exploration of said technologies within the framing of traditional Chinese musical instruments, namely the pipa, and their ability to open up alternative tuning systems for both traditional and modern instrument implementations. Also, it presents a deep assessment of the system’s performance, demonstrating its use and extensibility to a broad set of devices.
Literature review
Piezoelectric materials used in instrumental applications
Piezoelectric materials generate an electric charge in response to mechanical stress being applied to them, making them ideal candidates for use in sensors and actuators, with applications ranging from musical instruments to more complex use cases. The stable electrical responses of various materials, including polyvinylidene fluoride (PVDF) and piezo ceramics, to mechanical stimuli are reproducible [4,11,12]. These studies laid a foundation for creating tuning systems based on these materials. Yet, these studies did not evaluate how these materials would respond to truly conditioned arrows, especially for traditional instruments such as the pipa, where the acoustic properties are more sensitive to conditioning [13,14]. The apparent avoidance of traditional instruments highlights the necessity for adaptive tuning systems that address the specific demands of conventional instruments such as the pipa. Lead zirconate titanate (PZT) remains a widely utilised material with a superior piezoelectric response, promising tunable arbour stability. This could enable adaptive tuning in instruments like the pipa through piezoelectric sensors embedded in tuning pegs and bridges tested by Lang [15] in PZT commissioning. Although Lang’s work provided a foundation upon which more complex applications were developed, there remained no consideration for the real-time adaptive response of this instrument under changing environmental conditions or the maintenance of the pipa’s sonic integrity.
The fundamental frequency, f, of any vibrating string, can be expressed as . L represents the string length, T is the tension, and μ is the linear mass density. The design of piezoelectric sensors is such that they track changes in translating tension, T, into measurable electric signals. The response can be quantified as an electric field generated by the piezoelectric effect as
, where E is the electric field, σ is the applied stress, and d is the piezoelectric constant, as demonstrated by Ludwig [5]. The voltage, V, created by the piezoelectric material is expressed as
. The voltage signal is feedback in adaptive tuning, an approach refined in contemporary applications. Real-time adaptive tuning systems consist of a proportional-integral-derivative (PID) controller, and the dynamic tuning effect is based on controlling the tension depending on the error magnitude. According to the PID control law, the output u(t) is determined by balancing the proportional, integral and derivative aspects of the tuning error e (t), expressed as
.
is the proportional gain,
is the integral gain and
is the derivative gain [16–18]. Environmental effects can affect the degree of tuning instability of the pipa. String tension changes due to different humidity and temperature induce pitch changes in a musical instrument. The environmental correction factor, alpha, is always applied to stabilise V, the voltage output. The compensated voltage is expressed as
. These modelling equations support practical applications for adaptive tuning in diverse climates.
Some adaptive tuning systems will automatically “fix” an instrument to some preset standard, which is important due to the impact of temperature and humidity on instruments [3]. However, passive tuners have been further developed to use dynamic systems that actively turn the tuning, often too crude to achieve the microtonal resolution required for real-time adjustments as with tuned instruments [19–21]. However, until now, systems that adaptively tune in the performance have mainly focused on a handful of digital and acoustic instruments (e.g., electric guitar, digital piano, etc.), and there is a significant dearth of research on using such systems for traditional instruments as pipa. When applying similar adaptive systems where traditional instruments, such as this pipa, provide input to these adaptive systems, this instrument’s acoustic sensitivity and environmental instability present additional challenges. Thus, there is limited research on the occurrence of these systems in traditional Chinese instruments, which have unique timbral and environmental problems, and the underlying reason for such an absence is that few studies have focused on their applications; the current study tries to fill this gap.
Sensors, machine learning and neuro-fuzzy systems
Recent advances in miniaturisation and sensitivity of these sensors have now made them usable in musical instrument applications without significant alteration of their acoustic properties [22] and has enabled the integration of ultra-thin piezoelectric sensors into the body of traditional instruments such as pipa without compromising their sound quality. While these studies underscore the advantages of such sensors regarding tuning accuracy, little is known about their performance in situ, whereby environmental changes can alter the instrument’s tone sufficiently to disturb tonal fidelity. Adaptive tuning systems based on string tension measurements perform best on percussive-stringed instruments because they detect even minor deviations from nominal tension [23–25]. While these advancements have allowed for more responsive and precise tuning systems, applying such systems to traditional instruments, particularly in changing environmental conditions, has not been extensively explored.
Adaptive tuning technology has made tremendous improvements recently, in which machine learning and neuro-fuzzy systems have been applied to increase tuning accuracy [6–10]. A framework of intelligent systems follows that learns time-optimal tuning adjustments to make the system more time-efficient and precise. Although these systems have been successful on digital devices, such as digital pianos and electronic guitars, they have yet to be implemented on traditional instruments such as pipa. Although recent research highlights the application of machine learning and neuro-fuzzy systems for adaptive tuning, adapting to the environmental and dynamic playing conditions of traditional instruments remains largely unaddressed [26–29], which makes it a promising area for further study. Compacting these systems with piezo material enabled real-time pitch changes in arduous performance conditions. Yet, there is a significant gap in the literature concerning their flexibility and responsiveness in conventional instruments, especially regarding tonal integrity. This study seeks to fill such gaps, emphasising the pipa’s distinctive acoustic demands.
Neuro-fuzzy systems aim to ensure that errors can be reduced by learning a selection of fuzzy systems, which are inputted into the neural networks, leading to intelligent adjustments or corrections. These systems depend on fuzzy rules to interpret the input variables and set the output. A primitive fuzzy rule can be written as , where
is the input variable. The qualitative sets of the input variables are represented by fuzzy sets A and B. The function
predicts the output adjustment, y, based on the vector of input values leading to intelligent, accurate, and highly predictive capability neuro-fuzzy control systems
Impact of environment and utility on overall performance
Adaptive tuning systems are advantageous for live performance and outdoor environments in which instruments like the pipa are sensitive to environmental factors like temperature and humidity. Piezoelectric-based adaptive tuning systems can help alleviate these issues through real-time tuning without manual intervention of the musician [13]. Previous studies [15,30–32] showed the potential advantages of these systems but could not tackle the complexities of its counterpart, the pipa, which necessitates a more sophisticated and adjustable system because of its unique tonality and environmental occupational traits. Such systems are critical in combination settings where subtle adjustments are important for ideal harmonic variations. However, previous works did not investigate how these systems could be applied in traditional instruments like the pipa, where the timbral structure should be preserved while tuning accuracy is paramount.
Effects of adaptive tuning on stability and preservation of tonal integrity during performance. Lynch-Aird and Woodhouse [33] examined the ability to tune adaptively, decreasing the number of necessary manual adjustments and increasing trust within a live performance setting. Although prior works have established a foundation for adaptive tuning [13,16] used for musical applications and sensor use in adaptive tuning, they still lack significant factors. While there have been significant advancements in piezoelectric materials for adaptive tuning, previous systems still have shortcomings under different environmental conditions, e.g., high humidity and varying temperature, which also affect conventional instruments like the pipa. This also being said, although systems based on machine learning and neuro-fuzzy systems have been integrated into adaptive tuning systems, many of such systems still have issues performing tuning with the precision required for real-time tuning in more complex performance environments. Most of these systems use static algorithms that cannot adjust or account for subtleties in playing dynamics. Another major challenge has been integrating these technologies into instruments, which remains a critical point, as balancing fast response times with the instrument’s acoustic characteristics is still an obstacle.
Methods
Materials
Materials used in the study included; Lead Zirconate Titanate (PZT) Sensors (Model PZT-5H, APC International, USA); Light Aluminum Non-Invasive Adjustable Attachment Brackets (Misumi Corporation, Japan); Velcro Straps (Velcro USA Inc., USA); Shielded Flexible Cables (Alpha Wire, USA); Cable Ties or Clips (Panduit Corporation, USA); DS18B20 Digital Temperature Sensors (Maxim Integrated, USA); Torque Wrench (Tohnichi, Japan); 24-bit ADC Module (Model ADS1256, Texas Instruments, USA); Butterworth Low-Pass Filter (Custom component, configured with parts from Texas Instruments, USA); High-Pass Filter (Custom component, configured with parts from Texas Instruments, USA); 0.1 µF Ceramic Capacitors (Murata Manufacturing Co., Ltd., Japan); 10 µF Electrolytic Capacitors (Nichicon Corporation, Japan)
Equipment set up
For Phase I, Lead zirconate titanate (PZT) sensors (Model PZT-5H, manufactured by APC International, USA) were mounted on the instrument (Fig 1). Each sensor was pre-calibrated using a conversion constant of k = 0.005 V/N, which was determined through multi-point calibration using a polynomial fitting method for voltage-to-tension relationships. Each sensor was defined to deliver an output voltage signal corresponding to the tension. The conversion constant, k, is related to the voltage output and tension as . In our study, the tolerance was 0.01N. Two sensors were placed on the soundboard, one about 10 cm from the bridge and another about 20 cm from the bridge, playing the soundboard’s resonances. Another sensor was located on the neck approximately 5 cm from the nut. Light aluminium non-invasive adjustable attachment brackets were used. The brackets were held in place with removable Velcro straps. The sensors were connected to the instrument body using shielded, flexible cables to reduce the risk of electromagnetic interference and strain on the sensor elements. Cables were neatly routed across the body of the pipa and secured with cable ties or clips as necessary. Adopting shielded cables helped lower EMI, which is critical when collecting signal data; clean uptime signals are necessary.
(a) Laboratory Overview. (b) Sensor and actuator mounting setup showing layout on instrument body. (c) Traditional pipa instrument with sensors typically placed ~10 cm and ~20 cm from the bridge on the soundboard, and ~5 cm below the nut on the neck. (d) Control and data acquisition module. (e) Array of piezoelectric sensors prior to integration. (f) Oscilloscope used for real-time signal monitoring. (g) Calibration rig for sensor testing under varied tension. (h) High-precision actuator system for tension adjustment. (i) Workstation for data analysis and processing.
In Fig 1, the piezoelectric sensors were mounted on the pipa at three strategic positions: two on the soundboard—one approximately 10 cm from the bridge and another about 20 cm away—and one on the neck, roughly 5 cm below the nut. Each PZT sensor was paired with a DS18B20 digital temperature sensor to ensure real-time voltage compensation for thermal variation during performance.
Sensor calibration
Dynamic calibration consisted of standardised tones played over the entire pipa range and recording the corresponding voltage outputs from each sensor (refer to Fig 2 for full methodology outline). Next, these voltage outputs were used to create a dynamic calibration curve depending on tension levels and amplitudes of vibration as well; for every sensor, a DS18B20 digital temperature sensor was placed next to the PZT sensors. The temperature coefficient was determined by analysing the relationship between sensor output and temperature changes through SP with temperature sensors with the scope of temperature from 10°C up to 40°C. This coefficient was then linked to an algorithm in the microcontroller firmware that allows a real-time voltage adjustment to temperature changes.
A multi-point calibration was performed on each string through tension increments of 5 N from 0 N to 100 N using a torque wrench, and the corresponding voltage outputs were measured. The data point was then used to create a multi-point calibration table for each sensor. Voltage signals from each sensor were recorded and digitised using a 24-bit ADC module (ADS1256, TI). To guarantee that the ADC obtained the highest frequency slope of the vibrations in the pipa string, the sample rate was set to 5 kHz, thus satisfying the Nyquist criterion on the range of the instrument frequency component that could have their frequencies up until 1 kHz. A dual-stage filter design was implemented to refine the signal data further, incorporating a Butterworth low-pass filter with a 2 kHz cutoff frequency to eliminate high-frequency noise and a high-pass filter set at 20 Hz to remove low-frequency drift and baseline fluctuations. For additional stability, 0.1 µF ceramic and 10 µF electrolytic decoupling capacitors were added near the ADC and microcontroller to effectively filter out power supply noise. A single-point ground scheme was used with shielded cables for all sensor connections, reducing electromagnetic interference and ensuring consistent, interference-free data collection from the sensors.
Mathematical model of tuning dynamics
The second stage involved creating a mathematical model to relate the frequency of a vibrating pipa string to the string tension and other environmental elements. The modified fundamental frequency, f, on a vibrating string that incorporates a stiffness factor, is defined as shown in Equation 4
In Equation 4, L is the string length, T is the tension, is the linear mass density, and
is the stiffness constant. In equation 4, we extended the basic fundamental frequency equation to account for the defined variables that are extremely significant at high tension levels for improved accuracy in predicting frequencies. This change factors in the stiffness of strings and provides greater precision for different tension ranges. A multi-point calibration table was obtained using a precision torque wrench to capture non-linear sensor responses; 100 N was applied in increments of 2 N; string tensions were given in voltage outputs from piezoelectric sensors. These procedures comprised a dynamic calibration with stimuli of known value, polynomial fitting of the non-linearities, and a regular schedule of recalibrating to help prevent sensor drift. A mechanism of temperature compensation involved introducing environmental factors into the model as an environmental subset. A DS18B20 digital temperature sensor was combined with each piezoelectric sensor, and the voltage output was modified by the following Equation 5
In Equation 5, , which is the linear temperature correction coefficient, and
is the non-linear temperature coefficient from the experiment. Compensation was implemented in the microcontroller firmware (allowing dynamic compensation between 10°C and 40°C based on the deviation measured). The model was then rigorously tested using high bandwidth frequency measurement instruments across different environmental circumstances and during various dynamic performance tests to verify its accuracy. Error propagation analysis confirmed that the design achieved the desired accuracy thresholds by minimising the uncertainties from voltage measurement, temperature compensation, and tension calibration.
Design and implementation of neuro-fuzzy tuning algorithm
An NFIS (Neuro-Fuzzy Inference System) was designed to accept inputs from the piezoelectric sensors (at 0.1–5 V corresponding to 20–100 N tension), and the outputs of a temperature (10°C–40°C) and humidity (20%–90% RH) (see Algorithm). Using the Gaussian Membership function, these inputs were fuzzified regarding linguistic variables, including High Voltage, Medium Temperature and Low Humidity. An exhaustive rule base of 40 fuzzy rules was built using a clustering-based rule generation technique covering diverse tuning scenarios and environmental conditions. The NFIS was trained using a diverse dataset of 200 hours of practice and performance sessions to improve the model’s generalisation. The training utilised gradient descent-based backpropagation with a learning rate of 0.01 and L2 regularisation for loss penalisation to prevent overfitting. Cross-validation was performed using a 5-fold method to ensure model robustness. A cross-validation via 5-fold methods was performed to validate the model’s performance and ensure robustness and reliability. Redundancy was also introduced using two temperature and humidity sensors, which use majority voting to protect against sensor failure.
Algorithm: NFIS Model
Input: Vt, Tt, Ht, , N and
Output: Tuning adjustment
Step 1: Initialising NFIS parameters, weights and biases, n = 1 to N
Fuzzify inputs; apply fuzzy rules and aggregate. Lastly, defuzzify
Step 2: Calculate the floss
Step 3: Update based on gradient descent
Step 4: cross-validation and apply majority voting
Step 5: Return the trained NFIS model
Integration of actuation mechanism and environmental compensation model
At each tuning peg, high-precision servo motors (Model SG90 from TowerPro, China) were installed to allow real-time, high-precision changes to the string tensions of the pipa. The individual servos were calibrated with a high-precision torque wrench to match the natural resistance of the strings so that tension could be modified without impacting tone quality. The NFIS generated output adjustments, for tension based on deviations in pitch,
. These fundamental adjustments were implemented via a PID loop with optimised gains for
These PID parameters permit rapid tuning adjustments with accurate response times below 0.1 s to adjust for overshoot and undershoot in real-time.
The NFIS implements an environmental compensation model in which the voltage-to-tension conversion factor is adjusted within the NFIS dynamically according to real-time temperature and humidity input data. Redundant temperature (Model DS18B20, Maxim Integrated, USA) and humidity (Model DHT22, Aosong Electronics, China) sensors were placed close to piezoelectric sensors to measure environmental conditions continuously from 10°C to 40°C, and 20% to 90% RH. To account for temperature variations, the voltage, V, is dynamically adjusted based on the correction factor as , and the humidity correction factor is defined as
with
, as the humidity sensitivity coefficient.
Real-time monitoring and control using IoT
The IoT functionalities of the system were developed based on an ESP32 microcontroller (Espressif Systems, China) for wireless communication and provided real-time data available on a mobile application through a secure TLS-based MQTT protocol. Ambient Data Collection Temperature and humidity data from the DS18B20 temperature sensor (Maxim Integrated, USA), whose range is 10°C to 40°C and the DHT22 humidity sensor (Aosong Electronics, China), whose range is 20% to 90% RH, were collected using a microcontroller. Using MQTT as a reliable and scalable protocol for transport data, the ESP32 sends live tuning metrics every 0.5 seconds to an AWS IoT Core cloud database for string tension, temperature, and humidity.
System testing and calibration
Comprehensive system testing and calibration were conducted to ensure the adaptive tuning system’s reliability and accuracy. Initially, all sensors were calibrated to establish accurate voltage-to-tension relationships. This allowed for dynamic calibration of the sensors by playing tones of known intensity and adjusting the calibration curve based on the resulting sensor responses. Environmental sensors were also calibrated for accurate corrections (temperature and humidity). The Neuro-Fuzzy Inference System (NFIS) was well-trained and validated using extensive performance data to ensure the generalisation capability across different scenarios. PID control parameters were optimised through experimentation, and servo motors were calibrated to simulate the natural resistance of the pipa strings, allowing for responsive and stable adjustments based on the tuning status. The firmware was hardware-tested for minimal latency and reliable uptime, and the IoT infrastructure was stress-tested for consistent and secure data transfer. Validation of redundancy mechanisms showed potential for increasing the system’s robustness against possible sensor errors. The empirical validation then performed in different environmental conditions and performance scenarios through controlled experiments ensured the pitch demands were always satisfied in the defined tolerance range of the system.
Statistical analysis
All statistical analyses were done in Python (version 3.8) using the SciPy (version 1.6.3) and statsmodels (version 0.12.2) libraries. Means, standard deviations, and confidence intervals were computed as descriptive statistics. Inferential statistics consisted of one-way ANOVA and hypothesis testing (p < 0,05), and the normality assumption was tested through the Shapiro-Wilk test.
Results
Dynamic and multi-point calibration curves
In Fig 3a, the multi-point calibration results demonstrate a reliable and consistent performance across sensors PZT1, PZT2, and PZT3, with measured voltage values increasing proportionally to applied tension from 0 to 100 N. Calibration errors are minimal, generally ranging within ±0.2% to ±0.4%, indicating high accuracy. Each sensor records a zero voltage at 0 N tension, showing accurate baseline measurements. At higher tension points (80 and 100 N), all sensors converge closely with measured voltages around 3.9 to 5.0 V, highlighting consistency in sensor response under varying load conditions. These results confirm the sensors’ effectiveness and precision in capturing tension measurements with minimal deviation across different applied tensions. In Fig 3b, the results indicate consistent performance across three sensors (PZT1, PZT2, and PZT3) in terms of measured voltage and calculated tension values at increasing tone frequencies (50, 100, and 200 Hz). The voltage and tension rise with frequency for each sensor, demonstrating a clear correlation. PZT1 shows the highest calibration curve fit quality with an R² of 0.99 across all frequencies, followed closely by PZT2 at 0.98 and PZT3 at 0.97, confirming strong linear fits in each case. The slight variations in voltage and tension values between sensors suggest minor differences in sensitivity, yet all sensors exhibit high reliability and precision in their response patterns.
Performance of tuning dynamics
In Table 1, the fundamental frequency modelling results for string tuning dynamics illustrate a direct relationship between string tension and frequency, with increased tension yielding higher frequencies while other parameters remain constant. With a fixed effective length of 0.62 m, a linear mass density of 0.0011 kg/m, and a stiffness constant of 0.0001, the calculated frequencies for the low, mid, and high tensions (50, 70, and 90 N, respectively) correspond to 110 Hz, 165 Hz, and 220 Hz. This consistent progression confirms the theoretical prediction that frequency scales with the square root of tension in a linear density and stiffness-controlled system, validating the model’s accuracy in predicting tuning dynamics.
According to Fig 4a, the temperature compensation calibration results indicate consistent coefficients for each sensor across the temperature range of 10–40°C. For sensors PZT1, PZT2, and PZT3, the temperature coefficient (α) and non-linear coefficient (β) were consistent across sensors, with 95% confidence intervals for each value (α = 0.0015 °C ⁻ ¹, β = 0.0002), ensuring stability in voltage calibration. Each sensor maintains a calibrated voltage of 2.5 V at 25°C, demonstrating uniform response and effective temperature compensation across the specified range. In Fig 4b, the multi-point tension calibration results for sensors PZT1, PZT2, and PZT3 show voltage readings that increase with applied tension, with calibration errors decreasing progressively at higher tensions. At low tension (20 N), the calibration error is higher (±12.12%) but decreases to ±0.60% at 100 N, demonstrating improved accuracy at higher loads. A polynomial fit correction factor is consistently applied to each measurement, ensuring calibration accuracy. All sensors undergo recalibration every 60 seconds, maintaining precision across the range. These results confirm that the calibration method minimises error, especially under higher tension levels.
(a) Temperature compensation calibration curves for PZT1, PZT2, and PZT3, showing adjusted voltage across 10–40 °C, with a stable baseline around 25 °C. (b) Multi-point tension calibration curves with polynomial fits for each sensor, illustrating precise voltage response to applied tension from 0–100 N. (c) Empirical testing results comparing measured and calculated frequencies under different environmental scenarios, confirming minimal deviation and robust system performance.
According to Fig 4c, the empirical testing results show calculated and measured frequencies under various environmental conditions, with small variations observed. In a controlled environment (25°C, 50% RH), the frequency varied by +3 Hz (calculated 110 Hz, measured 113 Hz). During the high-temperature test (40°C, 70% RH), a + 5 Hz variation was noted (calculated 165 Hz, measured 170 Hz). The low humidity test (15°C, 20% RH) showed minimal variation at +1 Hz (calculated 220 Hz, measured 221 Hz), while dynamic performance tests under fluctuating temperature and humidity conditions resulted in a + 5 Hz variation (calculated 160 Hz, measured 165 Hz). These results demonstrate slight but consistent frequency shifts under varying environmental conditions.
Neuro-Fuzzy Inference System (NFIS)
In Fig 5, we see the fuzzification of input variables (Voltage, Temperature, and Humidity) and the output adjustment for the Neuro-Fuzzy Inference System (NFIS). Fig 5 (a) represents the Temperature membership functions, where “Low,” “Medium,” and “High” categories cover ranges from 10°C to 40°C, with a peak membership around 15°C, 25°C, and 35°C respectively. Fig 5 (b) shows the Voltage membership functions with similar “Low,” “Medium,” and “High” categories, capturing voltages between 0.1 V and 5 V, with peak memberships centred around 0.5 V, 2.5 V, and 4.5 V. Fig 5 (c) illustrates the Humidity membership functions, where the ranges span from 20% to 90% relative humidity, and peaks are centred at 30%, 50%, and 80% for “Low,” “Medium,” and “High” memberships. Lastly, Fig 5 (d) presents the Output Adjustment membership functions, where the system can choose between “Decrease,” “No Change,” and “Increase” adjustments based on input conditions, helping fine-tune the tension by slight adjustments within ±1 N. These membership functions enable the NFIS to interpret continuous sensor data in linguistic terms for precise tuning adjustments.
Actuation mechanism and environmental compensation model
In Fig 6a, the PID control error data analysis reveals an initial tension overshoot and subsequent stabilisation. Starting with a 5.0 N error at 0.0 seconds (target 50.0 N, achieved 45.0 N), the system quickly corrects, reducing the error to -2.0 N at 0.1 seconds and refining to minimal deviations. By 0.5 seconds, the achieved tension matches the target exactly, and minor fluctuations near zero error persist, indicating the PID control effectively stabilises around the target tension with precise corrections over time. In Fig 6b, error responses under baseline, high-gain, and disturbance-added tuning show that while baseline tuning achieves steady convergence, high-gain tuning accelerates error reduction but is more susceptible to overshoot. The disturbance-added curve reveals the system’s resilience, with only temporary spikes in error. Fig 6c demonstrates that with environmental compensation, the error trajectory remains well-controlled even under fluctuating inputs. Lastly, Fig 6d shows the system’s ability to maintain target tension over time, with only a brief overshoot corrected within seconds, highlighting the reliability of the compensation model in managing environmental and mechanical disturbances.
The NFIS tuning adjustments demonstrate precise frequency control across different test scenarios, with minimal deviations from target frequencies (see Table 2). In a controlled environment (25°C, 50% RH), the target of 440.0 Hz was achieved at 439.9 Hz with a pitch accuracy of ±0.1 Hz and a tuning adjustment of ±0.45 N. Under high temperature (40°C, 70% RH), the target of 660.0 Hz was reached at 660.1 Hz with ±0.1 Hz accuracy and ±0.5 N adjustment. At low humidity (15°C, 20% RH), 330.0 Hz was achieved at 329.8 Hz with ±0.2 Hz accuracy, while dynamic performance under variable conditions maintained accuracy at 550.2 Hz for a 550.0 Hz target. These results confirm high NFIS tuning precision across diverse environmental conditions.
Fig 7 illustrates the NFIS system’s nonlinear adjustment behavior in response to three critical inputs. In Fig 7a, adjustment responses show a decreasing trend with rising humidity, particularly after 60% RH, indicating that the NFIS compensates for increased string slackness in high-humidity environments. In Fig 7b, temperature-induced adjustments show a threshold effect: no significant adjustment below 25°C, but a marked increase in compensatory tension above 30°C, reflecting thermal expansion influence. Fig 7c shows a smooth downward trend in adjustment as voltage increases, consistent with increasing string tension. Together, these plots confirm that the NFIS adapts tuning decisions based on specific sensitivity regions in humidity, temperature, and voltage, validating the fuzzy rule structure used in the model.
(a) Adjustment vs. Humidity (%RH), (b) Adjustment vs. Temperature (°C), and (c) Adjustment vs. Voltage (V), illustrating nonlinear relationships and sensitivity regions used for adaptive tuning.
In Table 3, the PID control performance metrics indicate close adherence to target parameter values, with minimal error across proportional, integral, and derivative gains. The achieved proportional gain (Kp) was 0.78, showing a -2.5% error from the target of 0.8, which remains within an acceptable range. The integral gain (Ki) achieved 0.19 with a -5.0% error, contributing to a stable control response. The derivative gain (Kd) slightly exceeded its target (achieved 0.052, target 0.05) with a + 4.0% error, providing mildly increased damping. Overall, the PID parameters demonstrate effective tuning with slight deviations, supporting controlled system performance.
The voltage adjustments for temperature and humidity conditions indicate effective compensation with minimal error across different environmental scenarios (see Table 4). Under normal conditions (25°C, 50% RH), the baseline, adjusted, and final compensated voltages align at 2.5 V, with 0% error. In high temperature (40°C), the final compensated voltage reaches 2.535 V, yielding a + 1.4% error. For low humidity (20% RH), the compensation results in a final voltage of 2.515 V with a + 0.6% error. When both high temperature and low humidity are combined, the final voltage is 2.53 V, resulting in a + 1.2% error. These adjustments confirm precise compensation for environmental variations with minimal deviation from baseline.
Fig 8 demonstrates the performance of the environmental compensation model. In Fig 8a, the compensated voltage steadily increases with rising temperature and humidity, tracking deviations from the nominal 2.5 V baseline. Fig 8b confirms that the compensated voltage remains consistently higher than the baseline, validating the effectiveness of real-time compensation. Fig 8c shows that compensation error grows linearly but remains within a maximum deviation of ±0.14 V, indicating that the model-maintained voltage accuracy under fluctuating environmental conditions. These results confirm the system’s robustness in stabilizing signal output through predictive environmental adjustments.
(a) Compensated voltage vs. time under changing temperature and humidity, (b) Comparison with baseline voltage under same conditions, and (c) Compensation error over time showing model accuracy within ±0.14 V.
In Table 5, the empirical validation results for tuning stability demonstrate consistent frequency accuracy and stability across varied environmental conditions. In a controlled environment (25°C, 50% RH), the target frequency of 440.0 Hz was closely achieved at 439.95 Hz with a standard deviation of ±0.05 Hz, confirming stability. Under high temperature (40°C, 70% RH), the achieved frequency was 660.02 Hz against a 660.0 Hz target, with a slightly higher standard deviation of ±0.08 Hz, yet stable. In low humidity conditions (15°C, 20% RH), the target of 330.0 Hz was met at 329.98 Hz with a minimal standard deviation of ±0.04 Hz, indicating stability. These results validate the tuning system’s resilience and precision under different environmental conditions.
IoT enabled monitoring and performance
In Table 6, the system performance and accuracy metrics reveal robust real-time data transmission and minimal latency, meeting the target every 0.5 seconds without missed intervals over 8 hours. Average latency was maintained at 120 ms, well within the < 150 ms target, with a maximum latency of 180 ms during peak loads, ensuring reliable updates. Data integrity reached 98%, with the majority voting methods correcting most sensor anomalies. Temperature and humidity measurements were highly accurate, with ±0.2°C and ±0.5% RH deviations, respectively, using DS18B20 and DHT22 sensors. Adaptive learning enhanced initial system accuracy by 5%, driven by over 10,000 data points stored in AWS DynamoDB. Voltage accuracy for environmental compensation remained stable within ±0.1 V, affirming the system’s capacity to adjust for temperature and humidity fluctuations.
In Table 7, the user application and reliability metrics confirm that the system meets performance and reliability standards. Data visualisation responded in 500 ms, displaying real-time tension, temperature, and humidity readings. Remote adjustments were processed in 200 ms, meeting the target. User satisfaction was high, with 92% rating the interface as intuitive. Redundant sensor triggers were minimised, with 15 corrections through majority voting to handle environmental outliers. The transmission error rate remained below 1%, with automatic retries reducing interruptions, while system uptime achieved the target of 99.8%, supported by the ESP32’s auto-reconnect function for Wi-Fi stability. This afforded a secure, scalable communication protocol where all MQTT transmission occurred reliably without data loss.
The performance of the NFIS-based adaptive tuning system was compared to traditional instruments across various key metrics, including mean pitch deviation, system uptime, and real-time responsiveness (see Table 8).
Discussion
This study demonstrated that the integration of piezoelectric materials with a neuro-fuzzy inference system (NFIS) enabled fast, stable, and highly accurate adaptive tuning for the pipa under varying environmental conditions. The key findings include precise tension regulation via PID control, voltage calibration accuracy within ±0.1 V, and tuning pitch accuracy within ±0.1 Hz across temperature ranges from 10°C to 40°C and humidity levels from 20% to 90% RH. Calibration errors across the PZT sensors remained low (±0.2%–0.4%), and the environmental compensation model-maintained output stability with compensation errors under ±0.14 V. User evaluations indicated strong interface usability and real-time responsiveness, with a 92% satisfaction rate. The system also demonstrated exceptional adaptability to dynamic performance scenarios, showing only minimal pitch drift (<±0.08 Hz). Collectively, these results confirm the system’s capacity to maintain tuning stability and continuity in live performance environments, outperforming traditional tuning methods in both precision and autonomy, and offering a significant leap forward in smart musical instrument design.
The pipa, a traditional Chinese plucked instrument, poses specific challenges for adaptive tuning due to its wide pitch range, tonal complexity, and performance-dependent pitch fluctuations such as vibrato and string bending. The typical tuning of its four strings ranges from C3 (130.81 Hz) to C6 (1046.50 Hz), making precision essential across a broad frequency spectrum. Legacy tuning systems, including manual pegs or mechanical tuners, often fail to adapt swiftly under fluctuating humidity and temperature—an issue identified in both modern digital systems and traditional practices [34–36]. Our adaptive tuning system directly addressed these limitations through high-frequency resolution and low-latency actuation, maintaining real-time stability where previous systems could not. Compared to conventional instruments like violins and guitars that rely on manual tuning [37] and lack feedback mechanisms, our system maintained tuning integrity during vibrato and bending, minimizing deviations even under performance stress. Prior research often neglected the real-time responsiveness required during dynamic playing [29], but our method successfully incorporated this crucial feature through continuous tension monitoring and automated correction.
Our analysis demonstrated that integrating piezoelectric sensors with environmental compensation provided superior tuning accuracy even in challenging climatic conditions. While previous works [38–41] validated the general feasibility of using piezoelectric materials in sensor systems, these studies lacked detailed investigation into the effects of extreme temperature and humidity on acoustic tuning systems. Our findings confirmed tuning error margins remained under ±1% across 10°C–40°C and 20%–90% RH, highlighting greater environmental resilience than earlier implementations. This contrasts with traditional systems, where sensor drift or manual re-tuning often introduces pitch instability. Moreover, our use of real-time sensor feedback enabled corrections before deviations became perceptible to performers or audiences. The tuning system’s calibration protocol, supported by dual-sensor inputs and recalibration every 60 seconds, expands on the partial insights by Kumbhare and Kadu [42], by actively maintaining voltage stability and applying correction factors tailored to real-world ambient changes.
Our adaptive model’s responsiveness was further enhanced by incorporating NFIS-based learning, which significantly improved tuning accuracy over repeated environmental exposure. While prior models like those described in Zhang and Li [43] showed the value of adaptive learning in general control systems, they did not address its potential for continuous acoustic feedback in traditional instruments. In our case, the NFIS used historical sensor data to refine adjustment accuracy, enabling a 5% improvement in tuning precision compared to static models. Unlike conventional systems that rely on fixed thresholds, our system recognized context-dependent shifts in voltage and temperature, and applied nuanced output adjustments. This continuous learning model advances beyond the fixed-rule approach used in previous studies by allowing the tuning system to “learn” preferred performance conditions over time. It also complements the environmental compensation layer, which uses coefficients (α, β) to dynamically correct sensor voltage—a refinement not commonly implemented in musical applications.
Our findings on PID control confirmed its role as a robust method for real-time tension correction, especially in dynamically shifting performance environments. Building upon the insights of previous studies [44–47], who demonstrated PID control’s stability in general actuator systems, we verified its efficacy within adaptive musical tuning. Specifically, our results showed tension convergence within 0.5 seconds, regardless of initial error magnitude or external disturbances. Unlike traditional feedback loops in musical applications, which are often too slow or manually managed, our PID controller autonomously reduced error trajectories, ensuring seamless transitions in tuning. This rapid correction performance marks a significant enhancement over previous literature where tension control was modeled but rarely validated with real-time musical inputs. Moreover, our results support the claim that PID can be scaled for diverse acoustic domains, especially when combined with environmental feedback and machine learning.
Environmental data integration via real-time transmission protocols is critical for low-latency adaptive tuning, and our implementation confirmed the effectiveness of MQTT-based communication in preserving tuning fidelity. While [48–50] discussed the necessity of reliable wireless transmission for digital music systems, few studies have demonstrated its integration into analog performance instruments. Our system achieved an average latency of 120 ms and 98% data integrity over an 8-hour test period, highlighting the feasibility of using cloud-based infrastructure for tuning stability. By contrast, previous systems either relied on wired configurations or had limited response times due to processing bottlenecks. Our solution, supported by ESP32 and AWS cloud storage, ensured both scalability and fault tolerance—critical traits for professional music applications. This advances prior work by providing a secure, scalable foundation for adaptive tuning in mobile or stage environments.
Our system’s precision was underpinned by the sensitivity of piezoelectric sensors, which captured micro-variations in string tension, essential for correcting pitch errors introduced by vibrato or physical fatigue of the strings. Song [28] previously developed kirigami-based piezoelectric sensors with impressive sensitivity, but their application in adaptive tuning was not fully explored. Our sensors demonstrated real-time voltage shifts within ±0.1 V in response to environmental and performance stimuli, allowing fine-tuned adjustment without performer input. This level of resolution extends the findings of Huang [35], whose work in vibration suppression underscored piezoelectric responsiveness, but lacked a direct link to musical pitch modulation. Our results show that high-precision piezoelectric materials are not only suitable for structural monitoring but can also facilitate dynamic acoustic performance correction, paving the way for high-resolution tuning interfaces in performance-critical instruments.
Legacy tuning models for traditional instruments like the pipa and guqin have remained largely manual and susceptible to external disruptions. Tanaka [34] and Huang [35] emphasized the cultural importance of manual tuning, but also acknowledged its susceptibility to error, particularly in fluctuating environments. Our adaptive tuning system breaks from this manual paradigm by implementing sensor-driven calibration and tension control that occurs autonomously in real-time. This reduces both performer workload and risk of tuning failure during live performances. Unlike older analog methods or basic digital tuners, our system adapts continually, without disrupting the performer’s focus. It represents a hybrid of tradition and innovation, maintaining tonal authenticity while improving tuning resilience—a gap not fully addressed by previous work in automated tuning.
The user interface of our system also contributed significantly to its usability and success, offering real-time feedback and adjustments through a streamlined visual display. Prior studies [51–53] highlighted the importance of intuitive design in musical technologies, yet did not empirically validate user experience in performance settings. Our findings confirmed a 92% satisfaction rate among test users, who praised the ease of use and responsiveness of the interface. Unlike many academic prototypes, which remain technically sound but practically inaccessible, our design supports musicians of various skill levels, making it suitable for both professional and educational contexts. Moreover, integration of majority voting among redundant sensors reinforced both user trust and system robustness, expanding on redundancy principles outlined by Paradiso [54], but previously underutilized in musical feedback systems.
Scalability is another core strength of our system. Although our primary focus was the pipa, the intelligent NFIS framework can be adapted to instruments with different tuning ranges and control needs. Our findings demonstrated compatibility with a frequency range spanning over 900 Hz, suggesting applicability to instruments like violins, guitars, or even wind instruments indirectly influenced by environmental factors. While most previous systems—digital pianos, mechanical tuners, or fixed EQ models—fail to account for real-time environmental variation [55], our system compensates autonomously. This aligns with the scalable design goals proposed in Zhang and Li [43], who emphasized modular architectures for adaptive control. By generalizing our compensation algorithms and sensor logic, we established a foundation for expanding adaptive tuning to a broader range of musical contexts, helping bridge the gap between legacy instrument design and modern adaptive systems.
Practical implications
The piezoelectric-based adaptive tuning system developed in this study provides a robust solution for traditional stringed instruments, particularly the pipa, where tuning instability due to environmental fluctuations poses a significant challenge. Its real-time, autonomous tuning capability ensures that performers—especially professionals—can maintain pitch accuracy during live performances without manual intervention. The high user satisfaction score (92%) also supports its use in educational environments where consistent tuning and reduced manual adjustments improve learning outcomes. Additionally, the system’s low latency (120 ms) and high stability under dynamic conditions make it suitable for studio and recording environments, where tuning precision contributes directly to audio quality and production efficiency. Its rugged design, sensor redundancy, and reliable environmental compensation mechanisms make it particularly valuable for long-duration performances or use in variable outdoor settings.
Limitations and future research
Although the system demonstrated strong performance under controlled conditions of temperature and humidity variation, other potential environmental influences—such as barometric pressure, mechanical wear from extended use, and acoustic feedback—were not within the scope of this study due to resource limitations. The dataset of 2,000 samples was statistically sufficient to validate the model’s response across the tested conditions; however, further expansion would strengthen model generalizability. The rule base comprising 40 fuzzy logic rules was detailed enough to capture the nonlinear tuning dynamics for the pipa but may require reconfiguration when adapting the system to instruments with different acoustic and structural properties. Additionally, while real-time responsiveness was achieved on our embedded system, future research should evaluate computational demands for lower-powered or battery-operated platforms. Further studies are also needed to extend the application of this adaptive tuning system to a broader range of instruments, including wind and percussion families, under more complex environmental scenarios.
Conclusion
This study demonstrated the successful application of piezoelectric intelligent materials in developing an adaptive tuning system for the pipa, achieving accurate and stable tuning control under varying environmental conditions. By integrating real-time PID control with NFIS-based adaptive logic, the system minimized pitch deviation (±0.08 Hz) and achieved high calibration and compensation accuracy (±0.2 °C, ± 0.5% RH). These outcomes represent a significant advancement over conventional tuning systems, which lack the responsiveness and environmental adaptability needed in live or outdoor performances. Importantly, the system preserved the instrument’s tonal integrity while reducing the need for manual adjustment, contributing to improved acoustic performance, usability, and operational efficiency. By bridging traditional craftsmanship with modern sensing and control technology, the results affirm the system’s potential to transform tuning practices in both professional and educational musical contexts.
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