## 1 Introduction  
The increase in global greenhouse gas emissions and the scarcity of petroleum fuels have prompted a search for clean and sustainable alternative energy sources. One of these is biodiesel, which has become the main fuel for the transport industry in several countries [1, 2]. Biodiesel is produced using the transesterification reactions of short-chain alcohols (methanol or ethanol) with oil-containing seeds, animal fats or recycled cooking oils [3, 4], catalyzed by acids, bases and enzymes. Acid and base catalysis can be homogeneous or multiphase [5]. Conventional homogeneous catalysis, especially base catalysis,greatly increases the reaction rate over slow acid catalysis, but the main disadvantage is the extra cost of catalyst removal. In contrast, multiphase catalysis simplifies the steps and requires no additional recovery of the catalyst after the reaction has taken place, as well as being a new development in production due to its reusability and the subsequent sustainability of the process [6]. The development of biocatalysts opens up another avenue for the industrial production of biodiesel, but even the most successful lipases are still in the early stages of industrial production [7]. It has several advantages over petroleum diesel due to its absence of sulfur-free and aromatic compounds, higher cetane number, and a higher flash point [8], as well as being biodegradable [9]. To promote the use of biodiesel, the European Union has implemented a policy requiring a 10% (\(v/v\)) proportion of biofuels in transportation fuels to replace fossil fuels [10]. In China, the national standard for \"B5 diesel\" requires the inclusion of 1-5% (\(v/v\)) BD100 biodiesel to be blended with diesel fuel, as well as the implementation of biodiesel in line with national standards of excise tax exemption and 70% of the value-added tax, which is a refundable policy [11]. Unfortunately, certain businessmen adulterate diesel fuel by adding cheap vegetable oils [12], kerosene [13] or low-grade oils instead of biodiesel for illicit profits. One of the most common methods of adulteration is the addition of vegetable oils to diesel fuel because of their excellent miscibility and similar molecular properties [14]. All research focusing on biodiesel adulteration of higher viscosity vegetable oils has showed that atomization and spraying were hindered at the fuel nozzles and also caused decreases in the engine power output and thermal efficiency, carbon deposition and other problems [15]. This not only leads to financial losses but also increases fuel consumption along with emissions of particulate and exhaust pollutants. It is crucial to establish dependable analytical techniques for ascertaining the quantity of biodiesel contained in diesel fuel blends that may contain vegetable oils. Various analytical approaches have been reported for identifying and quantifying biodiesel in diesel-biodesel blends, which include chromatographic techniques [16; 17; 18], infrared (IR) spectroscopy [19; 20], ultraviolet-visible (UV-Vis) spectroscopy [21; 22], fluorescence spectroscopy [23], and nuclear magnetic resonance (NMR) spectroscopy [24; 25; 26]. Gas chromatography (GC) and high-performance liquid chromatography (HPLC) have great advantages in determining the biodiesel content in biodiesel/diesel blends. In particular, GC is the standard method for determining the extent of conversion of feedstock to biodiesel with high accuracy and good reproducibility. However, the use of organic solvents in the operation is contrary to the concept of green chemistry, and the analyses are time-consuming and complex operations. Thus, there is a need for fast, efficient, non-destructive, and environmentally friendly techniques for the quantitative analysis of biodiesel. The application of chemometrics in combination with various spectroscopic techniques has been widely used for identifying and characterizing fuels or biofuels. For example, [PERSON] et al.