# Estimating Hardness of Cosmetic Cream Using Electro-Mechanical Impedance Sensing Technique
## 1 Introduction  
The hardness of cosmetics is a pivotal factor directly influencing consumer satisfaction. Specifically, the hardness of cosmetic products, including creams, balms, and lipsticks, holds significant sway over their efficacy. Consumer preferences are often centered around specific textures and consistencies, making the measurement of hardness essential for evaluating a product's alignment with these expectations. Consumer satisfaction is intricately linked to the sensory experience of using cosmetics, and a dissonance between a product's hardness and consumer expectations can lead to dissatisfaction and negative brand perceptions. The hardness of cosmetics serves as a key indicator of product quality, ensuring a consistent texture that delivers the desired feel and contributes significantly to a positive consumer experience [1, 2]. Moreover, the hardness of cosmetics plays a crucial role as an indicator of manufacturing quality control. Within the realm of cosmetic formulations, which encompass diverse ingredient combinations, hardness measurements are pivotal in optimizing formulations to achieve the desired properties, including texture, spreadability, and adhesion. Additionally, monitoring changes in the hardness of cosmetic products over time serves as an early warning for potential stability issues. Regular hardness assessments enable the proactive identification of problems, such as ingredient separation or degradation, allowing for preemptive measures before they compromise product performance [3]. The most common method to measure cosmetic hardness is penetration resistance testing using a texture analyzer. In this test method, the hardness of cosmetics is evaluated by calculating the stress, which is accomplished by dividing the load when the probe is inserted into the cosmetics at a certain depth and at a certain speed by the cross-sectional area of the probe. This test method has certain advantages, including test equipment that is compact and easy to operate. However, since this test method involves penetratingprobes into cosme, it destroys the internal structure of the cosmetics. Therefore, there are limitations in continuously measuring the hardness of cosmetics [4; 5]. In the construction field, penetration resistance tests, similar to the cosmetics hardness test method, are commonly used to evaluate the hardening properties of cementitious materials [6; 7]. Penetration resistance testing for cementitious materials uses the same sample to evaluate hardening over time. Penetration resistance values are measured by inserting the probe at a different location in the same sample [7]. However, the repeated penetration of the probe into different locations of the same sample can lead to a collapse of the internal structure, thereby affecting subsequent penetration. To overcome these limitations of destructive testing, various non-destructive tests have been proposed to evaluate the hardening of cementitious materials in the construction field [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. [PERSON] et al. have proposed an electro-mechanical impedance (EMI) sensing technique using a piezoelectric sensor as a non-destructive test to evaluate the hardening of cementitious materials [20; 21; 22; 23]. In studies by [PERSON] et al., a piezoelectric sensor was directly embedded in a cementitious material and the EMI signal of the piezoelectric sensor was measured continuously over time to evaluate the hardening properties of the cementitious material. The EMI signal of the piezoelectric sensor embedded in the cementitious material undergoes changes corresponding to variations in the rigidity of the cementitious material surrounding the sensor. This enables the determination of the degree of hardening of the cementitious material surrounding the piezoelectric sensor.