Fermentation of organic compounds is a vital biochemical process with significant applications in food industry, biofuel generation, and biotechnology [1]. It involves the microbial metabolism of organic substrates such as carbohydrates into simpler compounds like alcohols, organic acids, and gases facilitated by bacteria, yeast, and fungi [1]. Detecting the fermentation endpoint is essential to ensure optimal yield, quality, and process efficiency [1]. For example, in the fermentation of Soybean into acetic acid, the process occurs in two stages [1, 2]: the first is the hydrolysis of Soybean proteins and carbohydrates into simpler sugars and amino acids, followed by the oxidation of ethanol to acetic acid by acetic acid bacteria (AAB) such as acetobacter species. Accurate endpoint detection is crucial to prevent over-oxidation which could degrade acetic acid into carbon dioxide and water, compromising both quality and yield [2]. Advanced analytical techniques, including pH monitoring, gas chromatography, and high-performance liquid chromatography are commonly used to determine the fermentation endpoint and maintain the desired acetic acid concentration. Research emphasizes the importance of controlling factors like temperature, oxygen levels, and microbial activity to optimize the process [2, 3]. Beyond enhancing the nutritional profile of Soy-based products, Soybean fermentation for acetic acid production also yields valuable ingredients for the food industry such as vinegar and condiments, showcasing the broader economic and nutritional significance of fermentation [2, 3].

From an economic perspective, the production of acetic acid from Soybean’s fermentation is highly valuable due to its applications in food, pharmaceuticals, and chemicals. This process is cost-effective compared to synthetic production as it utilizes natural source, thus reducing the energy consumption and production costs. The growing demand of acetic acid produced through natural sources has further boosted its market value. The global acetic acid market, valued at over $10 billion in 2022, is projected to grow, driven by its use in food processing, textiles, and biodegradable plastics [4]. Fermentation supports sustainability and creates economic opportunities for agricultural communities by utilizing local raw materials.

Determining the fermentation endpoint in Soybean processing is crucial for ensuring the product quality, maximizing yield, and avoiding over-fermentation which can result in unwanted byproducts. A range of traditional analytical techniques are utilized to identify when fermentation is complete. These methods include pH monitoring [5], gas chromatography (GC) [6], high-performance liquid chromatography (HPLC) [7], and Fourier transform infrared (FTIR) spectroscopy [8]. Analytical methods for fermentation endpoint detection often suffer from limitations such as time consuming sample preparation, high operational costs, potential contamination risks, and need for specialized equipment and expertise. Non-destructive, real-time, and online techniques for fermentation endpoint detection are essential to overcome the limitations of traditional analytical methods ensuring continuous monitoring and improved process efficiency. Various real-time techniques have been proposed to monitor the fermentation endpoint in different organic compounds. For example, monitoring the fermentation in dairy products using fluorescence spectroscopy [5], ultrasonic sensor [9], infrared light backscatter sensor [10], near-infrared (NIR) spectroscopy [11], monitoring the fermentation process in ethanol using viable cell sensor [12], monitoring the fermentation in yeast using software controlled automatic real-time biosensor [13], monitoring the fermentation process in Soybean using miniature fiber NIR spectrometer [14], monitoring the fermentation process in wine with benchtop 1H NMR spectroscopy [15] and NIR spectroscopy [16], and monitoring the fermentation process in black tea using an electronic tongue [17]. The literature review has been further elaborated in Table 1 by comparing the important achievements of past studies with proposed work.

We introduce a novel non-destructive approach for real-time detection of the Soybean fermentation endpoint using a P d -coated FBG stress sensor. This method detects fermentation completion by tracking the Bragg wavelength shift caused by stress in the P d -coated FBG sensor due to P d coating expansion upon P d H x formation after H 2 absorption which is a key fermentation byproduct. The sensor is analytically designed and validated using OptiSystem simulation tool having a wavelength sensitivity of 61.6 p.m./MPa. This pioneering work establishes a new pathway for real-time monitoring of fermentation processes involving H 2 production.

To accurately model the fermentation process of Soybean and explain the working principle of the proposed method, it is important to estimate the total yield of H 2 released as byproduct during fermentation process and the amount of stress induced on the P d -coated FBG sensor by volume expansion of the P d coating due to the formation of P d H x after absorption of H 2 , where x is the ratio of Hydrogen to Palladium. The fermentation of Soybean involves microbial activity that degrades organic compounds, resulting in the production of H 2 alongside other byproducts such as organic acids and carbon dioxide C O 2 . The fermentation process of soybean can be expressed by following chemical equation [18]. C 6 H 12 O 6 + 2 H 2 O → 2 CH 3 COOH + 2 CO 2 + 4 H 2 (1)

The Equation 1 illustrates the fermentation process of Glucose ( C 6 H 12 O 6 ) which is considered as a primary component in Soybean, into acetic acid ( C H 3 C O O H ) , C O 2 , and H 2 . From this equation, it is evident that 1 mol of C 6 H 12 O 6 produces 4 mol of H 2 . Therefore, the total mass of H 2 produced per kg of C 6 H 12 O 6 can be calculated by following steps. Molecular weight of  C 6 H 12 O 6 = 80   g/mol Molecular weight of  H 2 = 2   g/mol Mass of  4 H 2 = 4 × 2 = 8  g

Thus, 180 g of C 6 H 12 O 6 (1 mol) yields 8 g of H 2 . The mass of H 2 produced per kg of C 6 H 12 O 6 is calculated as. 8  g 180  g × 1000 = 44.49  g

Therefore, 1 kg of C 6 H 12 O 6 produces approximately 44.49 g of H 2 . As we have considered 5 kg Soybean in this research, therefore 222.5 g ( ≈ 2.5 m 3 ) of H 2 gas is produced as byproduct during the fermentation process. To calculate the volume of H 2 generated during fermentation at STP, we use the ideal gas law. At STP, the molar volume of an ideal gas is 22 L/mol. The molar mass of H 2 is 2 g/mol, so for 222.5 g of H 2 , the number of moles is calculated as: Number of moles = Mass Molar mass = 222.5   g 2   g/mol = 111.25   mol .

Using the molar volume of an ideal gas at STP, the volume of H 2 gas is: Volume = Number of moles × Molar volume = 111.25   mol × 22.4   L/mol = 2492   L .

Converting liters to cubic meters (since 1   m 3 = 1000   L ), the volume of H 2 generated at STP is: Volume = 2492   L 1000 = 2.492   m 3 .

To determine the stress induced in P d -coated FBG sensor when exposed to 222.5 g of H 2 , first we need to consider the H 2 absorption in P d coating, saturation limit of P d H x formation, and stress-strain relationship. Then we shall be able to calculate the shift in Bragg wavelength of FBG stress sensor.

The analytical model of the P d -coated FBG stress sensor that is developed in the last section produces a Bragg wavelength shift of 24.2 nm is analyzed using OptiSystem simulation tool. Table 2 compares the parameters used in the analytical model with those employed in OptiSystem for design analysis. Using the parameters of the OptiSystem model, a shift of 24.5 nm in Bragg wavelength is achieved which is comparable to the analytical model making the assumption reasonable.

Figure 2 shows the block diagram of the simulation setup designed in OptiSystem to detect the fermentation endpoint of Soybean. A white light source (WLS) with a power spectral density (PSD) and center wavelength of −60 dBm/Hz and 1,551 nm, respectively is used to illuminate the FBG stress sensor. Figure 3 illustrates the spectrum of WLS. The WLS model used in OptiSystem generates noise bins or sampled signals at the output according to the following mathematical expression. E x t E y t = x x t + j y x t x y t + j y y t ⋅ P 4 (6) In Equation 6, E is the optical field and P is average power. In the above equation, a Gaussian distribution has been assumed to describe the probability density function (PDF) for the real and imaginary parts of the optical field components E x and E y . A broadband light source is essential for FBG sensors because it provides a wide spectral range to accurately track the shifts in Bragg wavelength caused by external perturbations [21]. Unlike narrowband lasers that require fast scanning to avoid missing signal detection, WLS enables high-resolution detection of small wavelength changes which are critical for real-time monitoring in applications like P d -coated FBG stress sensor [21]. Additionally, broadband light sources support multiplexing of multiple FBGs on a single fiber, making it ideal for scalable industrial systems. Its stable and noise-resistant output ensures reliable measurement of stress-induced shifts which are vital for precise fermentation endpoint detection [21]. In practical scenario, the P d -coated FBG stress sensor will be placed inside the fermentation container holding 5 kg of Soybean with a suitable microbial culture to initiate the fermentation process. The temperature, humidity, and pressure inside the container is controlled to ensure optimal fermentation conditions. The P d layer serves as the active sensing material, absorbing H 2 molecules released during fermentation. Upon absorption, P d undergoes a phase transition to P d H x , leading to volumetric expansion which induces mechanical strain inside the FBG sensor. This strain modifies the grating period of the FBG, causing a Bragg wavelength shift which serves as an indicator of the fermentation endpoint. In OptiSystem, this process is realized using the numerical values of stress calculated in Section 3 to create the corresponding shift in Bragg wavelength of stress sensor. The optical signal reflected from the FBG stress sensor at a shifted Bragg wavelength corresponding to the applied stress, is split into two parts using a 20:80 power splitter (PS) attached to the sensor’s reflection port (RP). The 20% output of the PS is sent to an optical spectrum analyzer (OSA) for analysis of the results while the 80% output is connected to the alarm system (AS) for annunciation of the fermentation endpoint. Similarly, the transmitted spectrum is directed to another OSA via the transmission port (TP) for analysis. The important simulation parameters used in this work are described in Table 3.

Figure 4 illustrates the induced stress due to formation of P d H x after absorbing H 2 by P d -coated FBG sensor versus wavelength shift. It is clear that wavelength sensitivity of 61.6 p.m./MPa has been achieved. A linear relationship between the wavelength shift and induced stress can be observed. The reason of linear relationship between the wavelength shift and the stress shown in Figure 4 is attributed to the fundamental principle of opto-mechanical coupling as expressed in Equation 5. We acknowledge that practical scenarios may introduce noise and nonlinearities due to thermal fluctuations, mechanical vibrations, material hysteresis, and deformations in the P d coating which can affect wavelength shift and resolution. However, the reported sensitivity threshold of 61.6 p.m./MPa sets a floor for the FBG interrogators. Figure 5a shows the transmission spectra of the FBG sensor for stress values of 0 MPa and 393.44 MPa obtained by connecting the OSA to TP of FBG stress sensor as illustrated in Figure 2. Similarly, Figure 5b shows the reflection spectra of FBG the sensor for stress values of 0 MPa and 393.44 MPa indicating the onset and endpoint of fermentation process, respectively. Reflection spectra is obtained by connecting the OSA with 20% output of the PS, that is connected with RP of the FBG stress sensor as shown in Figure 2. Assuming the fermentation starts at time t o , the transmission dip and the reflection peak of the transmitted and reflected optical signals, respectively equal to the initial Bragg wavelength of P d -coated FBG sensor which is 1,550 nm, as shown in Figure 5 corresponding to the absence of detectable H 2 . As fermentation process progresses, microbial activity produces H 2 which is absorbed by the P d coating forming P d H x . This induces stress in the P d -coated FBG stress sensor, linearly shifting the Bragg wavelength of reflected optical signal. Similarly, the fermentation endpoint is achieved at time t e . Consequently, the absorption of H 2 in P d coating saturates and any excess H 2 will not contribute to further stress development. The transmission dip and reflection peak of transmitted and reflected optical signals equal to 1,574.5 nm. A maximum shift of 24.5 nm in Bragg wavelength corresponding to a stress of 393.44 MPa is induced in FBG sensor indicating the fermentation endpoint.

In this study, we demonstrated a non-destructive and real-time method for detecting the fermentation endpoint of Soybeans using a P d -coated fiber Bragg grating stress sensor. The method relies on monitoring the shift in the Bragg wavelength, which is caused by the stress induced in the P d -coated FBG sensor due to the volume expansion of the Palladium layer upon the formation of Palladium Hydride after absorbing Hydrogen gas released as a byproduct during the fermentation of Soybeans. The P d -coated fiber Bragg grating sensor was analytically designed and its performance was analyzed using the OptiSystem simulation tool, achieving a wavelength sensitivity of 61.6 p.m./MPa. The results demonstrate that the proposed method provides a reliable, straightforward, and efficient solution for real-time monitoring and detection of the fermentation endpoint of various organic compounds that release Hydrogen gas as a byproduct. This approach holds significant potential for applications in food processing, biotechnology, and industrial fermentation processes.