Mathematical Fitting Research Articles

Research on collaborative reconstruction method of missing data and abnormal data in air handling units (AHU)system

The Air Handling Units (AHU), as critical components in building energy management, demand rigorous performance monitoring to ensure indoor comfort and energy efficiency. However, prolonged sensor operation often leads to malfunctions and measurement drifts due to insufficient maintenance, resulting in data gaps and anomalies. These issues pose significant challenges to system operational efficiency, occupant comfort, and energy consumption regulation. To address this dilemma, this paper innovatively leverages Bayesian inference techniques, developing a sophisticated likelihood function distance model. This model achieves precise imputation of missing data and effective rectification of anomalous data, thereby mitigating the issue of error accumulation associated with frequent reliance on historical data.Furthermore, the study exploits the intricate coupling relationships among multiple physical variables within the AHU systems to construct a comprehensive analytical model. This approach reduces the dependence on historical data for mathematical fitting and enhances the reliability of predicted data. Consequently, this paper presents an efficient methodology for handling missing and anomalous sensor data in AHU systems. Experimental results demonstrate that the relative error for reconstructing single-variable missing data remains below 7 %, while the relative error for reconstructing multi-variable missing data is even lower, at 3 %. These findings affirm the practical applicability of the methodology in calibrating anomalous sensor data within the building energy management domain.

An aluminum agglomeration model based on realistic pocket distribution via microcomputed tomography

The condensed combustion products (CCPs) resulted from aluminum agglomeration significantly affect the operation and safety of solid rocket motor, so it is essential to create a precise agglomeration model to predict the size of the CCPs of aluminized solid propellant. To accomplish this, high-precision microcomputed tomography (micro-CT) scanning was employed to obtain the quasi-three-dimensional structure of the propellant. The distribution of the ammonium perchlorate (AP) pockets was recognized via artificial intelligence (AI) method. The results revealed that the pocket size was mainly influenced by the AP grade. As the fraction of the coarse AP fraction declined from 43.1 % to 23.1 %, the average pocket diameter reduced from 388.91 to 68.23 μm. Size distribution predictions were subsequently performed for the agglomerations based on the pocket model theory. The equation relationship between agglomeration coefficient and propellant formulation was presented and corrected through mathematical fitting. The proposed agglomeration model was validated using the CCPs collection experiments of six aluminized propellants at 7 MPa. The agglomeration model produced an average particle size prediction error of <9.8 %, and the goodness of fit of the agglomerate distribution was >0.85. Subsequent analysis indicated that the agglomerate size mainly depended on the percentage of coarse AP, the burn rate, and the size distribution of raw aluminum particles. The present model is expected to offer a new way to achieve the accurate prediction of solid propellant agglomeration behaviors.

Fitting Quality of NMR Relaxation Data to Differentiate Asphalt Binders

Asphalt binder performance grades (PGs) are important metrics in designing pavements for effective transportation infrastructure. The PG system relies on the binder’s stiffness and is determined through energy- and time-intensive physical testing. Physical properties, like stiffness, can also be determined by spin–lattice NMR relaxometry, a non-destructive chemical method. NMR relaxometry can quantify the molecular mobility of materials by determining relaxation times from exponential decays of excited nuclear magnetization. While relaxation times have been used to determine physical properties of materials, a quantitative relation to the PG grades of asphalt binder is yet to be established. In this study, T1 NMR relaxation analyses were used to differentiate between solid asphalt binders and determine the fastest yet still-reliable method of modeling exponential decay data. Algorithms that fit exponential decay relaxation data using one, two, or three independent relaxation times were compared with a 128-coefficient discrete inverse Laplace transformation to determine the best mathematical fit for a comparative analysis. The number of data points was then reduced from 256 to 64 to 16 and finally to 8 data points on a relaxation curve to reduce the testing time and determine the minimum number of data points needed for comparison. Two batches of PG 64-22 asphalt binder, along with samples of PG 76-22 and 94-10 binders, were investigated. The best compromise between measuring time and data reliability was found by acquiring 64 data points and then using a biexponential model to fit the experimental data. The PG 64-22 sources provided similar results, indicating similar physical properties. The PG 64-22 and PG 76-22 binders could also be compared via monoexponential data fits, but the PG 94-10 samples required an additional relaxation parameter for comparison. To differentiate all three binder grades, the primary relaxation times, along with their relative ratios, were utilized.

Design and Management of Micro-Teaching Mode of Innovative Employment Education in Universities Driven by Big Data-Driven Approach

At present, the innovative employment education mode has been popularized in colleges and universities, and China has also begun to vigorously develop innovative employment education. According to the investigation, there are some disadvantages in the process of innovative employment education, which greatly hinder the teaching effect of innovative employment education. Based on the big data-driven method, this paper takes the micro-course education mode in innovative employment education as an example and makes a systematic study. This paper mainly analyzes three main indexes involved in innovative employment education. In this paper, three typical big data-driven methods are introduced, and the corresponding prediction and evaluation index values are predicted and analyzed. The analysis and prediction results show that the prediction effect based on extreme learning machine is the best. In addition, the results of mathematical fitting show that the corresponding predicted values show a good power function relationship at the personal level and the social level.

Grey-box solution for predicting thermo-mechanical response of rocks

Evaluating the thermo-mechanical response of rocks under high temperature treatments is crucial for various engineering geology projects. Current predictions of rock thermo-mechanical response rely on simplistic mathematical fittings treating temperature as a reduction factor, while existing machine learning algorithms often present practical challenges due to their black-box solutions. In this study, highly practical grey-box solutions, utilizing gene expression programming (GEP) are proposed for forecasting rock strength following high-temperature treatments. The dataset, comprising temperature, rock type, rock density, sample size, crack damage stress, confining pressure, and elastic modulus, serves as input parameters, with rock strength from triaxial compression tests as the output. Three grey-box solutions (mathematical formulations) based on distinct input parameter sets are proposed, all demonstrating excellent accuracy with high R2-values (R2 > 0.95) and low error values across both the training and testing phases. Feature importance analysis highlights crack damage stress, confining pressure, and elastic modulus as statistically significant parameters influencing the strength of rocks subjected to high temperatures. External validation of the proposed models indicates strong generalization capabilities, underscoring their ability to perform well beyond the training data. Furthermore, a monotonicity study demonstrates that the proposed models align with the expected physical processes. The proposed formulations offer valuable field implications, effectively addressing the limitations of labor-intensive and costly laboratory processes for evaluating rock thermo-mechanical responses.

Potential of digital autoradiography for characterization of uranium materials

This study evaluates the capabilities of a commercial digital autoradiography set-up in characterizing the spatial distribution of radioactivity in U-bearing materials. Two different imaging plates (IPs) from various manufacturers, as well as three read-out granularities (25 µm, 50 µm, and 100 µm) of a high-resolution IP scanner, were tested. A custom software, developed using Python, was used for processing of the image raw data obtained from the IP scanner. The software extracted 25 intensity profiles from each autoradiographic image, allowing for a detailed analysis of the data. By applying various mathematical fitting functions, important metrics such as edge width, amplitude of the flat top, and central core width of the intensity profiles were determined. This provided valuable insights into the interaction between the U samples and IPs, particularly for samples of different geometry and thickness. Comparisons were made between samples embedded in epoxy resin or modelling clay and non-embedded U specimens. The results highlighted the superior performance of epoxy embedding in the characterization of U-bearing materials. The variation in signal intensity between runs for individual samples reached up to 20 %, showing consistent behavior across all samples in each measurement. This suggests that the inconsistency in signal response during repetitive analysis is likely due to the IP scanner rather than the IP itself. By using the analytical method of global spatial autocorrelation (Moran’s I), we were able to effectively detect enrichment inhomogeneity within low enriched UO2 pellets. The Moran’s I value quantified the levels of inhomogeneity, providing a numerical measure that was not visually apparent from the digital autoradiographic image.

Shedding Light on Luminescence Lifetime Measurement and Associated Data Treatment

Luminescence lifetime is a crucial parameter in photophysical studies that bears essential physical and chemical information and that is used to quantify a variety of phenomena, from the determination of quenching mechanisms to temperature sensing and bioimaging. The current perception of lifetime measurement is that it is a trivial and fast experiment. However, despite this apparent simplicity, measuring luminescence decay and fitting the obtained data to a suitable model can be far more intricate. In this perspective, the influence of experimental parameters and fitting procedures on the determination of lifetimes are investigated and, through carefully chosen examples, it is shown that large variations, up to 10%, can be induced by varying parameters such as the data acquisition time, the baseline evaluation, or the mathematical fitting model. In order to present to a wider audience, detailed mathematical descriptions are kept out of the manuscript.

Prevention and control of Ebola virus transmission: mathematical modelling and data fitting.

The Ebola virus disease (EVD) has been endemic since 1976, and the case fatality rate is extremely high. EVD is spread by infected animals, symptomatic individuals, dead bodies, and contaminated environment. In this paper, we formulate an EVD model with four transmission modes and a time delay describing the incubation period. Through dynamical analysis, we verify the importance of blocking the infection source of infected animals. We get the basic reproduction number without considering the infection source of infected animals. And, it is proven that the model has a globally attractive disease-free equilibrium when the basic reproduction number is less than unity; the disease eventually becomes endemic when the basic reproduction number is greater than unity. Taking the EVD epidemic in Sierra Leone in 2014-2016 as an example, we complete the data fitting by combining the effect of the media to obtain the unknown parameters, the basic reproduction number and its time-varying reproduction number. It is shown by parameter sensitivity analysis that the contact rate and the removal rate of infected group have the greatest influence on the prevalence of the disease. And, the disease-controlling thresholds of these two parameters are obtained. In addition, according to the existing vaccination strategy, only the inoculation ratio in high-risk areas is greater than 0.4, the effective reproduction number can be less than unity. And, the earlier the vaccination time, the greater the inoculation ratio, and the faster the disease can be controlled.

Optimization of Extraction Conditions for Water-Soluble Polysaccharides from the Roots of Adenophora tetraphylla (Thunb.) Fisch. and Its Effects on Glucose Consumption on HepG2 Cells.

The root of Adenophora tetraphylla (Thunb.) Fisch. is a common Chinese materia medica and the polysaccharides which have been isolated from the plant are important active components for medicinal purposes. The objective of the current study was to optimize the extraction parameters and evaluate the glucose consumption activity for Adenophorae root polysaccharides (ARPs). The optimization of ARP extraction was evaluated with preliminary experiments and using response surface methodology (RSM). The conditions investigated were 35-45 °C extraction temperature, 20-30 (v/w) water-to-solid ratio, and 3-5 h extraction time. The antidiabetic effects of ARPs for the glucose consumption activity were evaluated in HepG2 cells. The statistical analyses of the experiments indicated that temperature, water-to-solid ratio, and extraction time significantly affected ARP yield (p < 0.01). The correlation analysis revealed that the experimental data were well-aligned with a quadratic polynomial model, as evidenced by the mathematical regression model's fit. The optimal conditions for maximum ARP yield were 45 °C extraction temperature and 28.47:1 (mL/g) water-to-solid ratio with a 4.60 h extraction time. Extracts from these conditions showed significant activity of promoting cell proliferation from 11.26% (p < 0.001) to 32.47% (p < 0.001) at a dose of 50 μg/mL to 800 μg/mL and increasing glucose consumption to 75.86% (p < 0.001) at 250 μg/mL on HepG2 cells. This study provides a sustainable alternative for the industry since it allowed simplified handling and a specific quantity of ARPs. Furthermore, ARPs might directly stimulate the glucose consumption in the liver and showed no cytotoxicity; therefore, ARPs probably could be taken as a potential natural source of antidiabetic materials.

Testing of spherical mirrors with extremely large R numbers using a quasi-autocollimation method.

Spherical mirrors with large R numbers have extreme advantages in optical systems with large apertures and long focus lengths for improving imaging resolution and field of view. Their manufacturing and testing accuracy directly affects the final wavefront aberration of the systems. However, due to the influence of airflow disturbance in the long optical path, testing large R number spherical mirrors with high precision is difficult for the direct testing method. In this paper, a quasi-autocollimation test (QACT) method is proposed based on the consistency and reverse compensation between sphere and paraboloid with large R numbers. In QACT, the length of the testing path is reduced to half, and the test sensitivity of the surface figure error is doubled. According to the Kolmogorov turbulence theory, the suppressed degree of QACT to airflow disturbance is quantitatively evaluated, and QACT can suppress the random error in test to 35%. A comparative experiment between direct test and QACT method is carried out on a ∅100 spherical mirror with 8-meter radius of curvature. Airflow disturbance in the testing environment is calculated by mathematical fitting and the repeated accuracy is improved from 4 nm to 1.4 nm in a single test using the QACT method, which is consistent with theoretical analysis. The research results will provide a new strategy for ultra-precision and efficiency tests of large R number spherical mirrors.

The eutrophication-related index of drinking water sources based on the oxidation-reduction potential

Eutrophication caused by excessive nitrogen and phosphorus is an important factor affecting water quality in drinking water sources. Convenient monitoring of eutrophication in water bodies can reduce the use of pesticides and reduce energy consumption, helping to promote ecological and economic development. This study examined the relationship between water eutrophication and the oxidation-reduction potential (ORP). The results showed that various parameters related to eutrophication, such as ammonia nitrogen, total nitrogen, total phosphorus, chlorophyll-a, and cyanobacteria, had correlations with ORP. There is a close relationship between eutrophication and the concentration of cyanobacteria. When cyanobacteria blooms occur in the drinking water source, it may contaminate the drinking water. Because the conventional eutrophication index does not include the concentration of cyanobacteria, principal component analysis (PCA) was utilized to comprehensively analyze these eutrophication-related parameters and obtain the eutrophication-related index, with the cumulative contribution of principal components reaching 81.8%. Different mathematical methods such as neural network model and mathematical fitting were used to study the relationship between ORP and the eutrophication-related index. A three-segment relationship between the ORP and the index was established. This three-stage relationship was confirmed in different reservoirs.

Comparison and analysis of goodness of fit and fitting formula between milk fat concentration and refractive index

Milk is considered to be one of the most perfect natural foods for human beings. The analysis of effective components and determination of important components in milk is an important practical work. Based on the previous measurement data of fat volume concentration and refractive index of milk in the market, this paper forms a fitting formula through mathematical fitting, which can solve the corresponding relationship between nonmeasurement points of milk concentration and refractive index. Because the actual measurement points are limited, its practical application is not convenient. However, fitting formulas can calculate the corresponding values of infinitely many points, which can be easily applied. However, judging from the goodness of fit of the fitting formula, a theoretically good fitting formula may produce underfitting and overfitting in practical application. Through the analysis of the first-order to sixth-order fitting formulas of milk concentration and refractive index, this paper tells us that the fitting formula with high goodness of fit is not necessarily a good formula. The specific problems should be analyzed in the application process to make the theory more consistent with the actual situation. From the calculation and analysis in this paper, it can be seen that the fitted sixth-order formula has the best effect when the fat volume concentration of milk is 0–10%. When considering a fat volume concentration of 0–34% in milk, the fitted second-order formula performs better.

Mathematical modeling of the drying and oil extraction processes of passion fruit seeds using fractional calculus

AbstractBACKGROUNDThis article aims to fit kinetic models of the passion fruit seed drying process, in addition to mathematical modeling using traditional models and fractional calculus of the extraction of lipids from the seeds.RESULTSRegarding the drying process, it was found that the model that best suited the two drying temperatures employed was the fractional order one.CONCLUSIONAnalysis showed that for both drying conditions the value of parameter α was greater than 1, indicating that the profile that occurs for the seeds is superdiffusion. Regarding the mathematical fits of oil extraction, it was found that the two models that presented the best fits for the lipid extraction kinetics were hyperbolic and fractional order. Regarding the fractional order model, as the value of parameter α was lower than 1, it can be seen that the process again does not follow Fick's law, and in this case a subdiffusion process occurs. © 2024 Society of Chemical Industry (SCI).

Machine learning-based model for the intelligent estimation of critical heat flux in nanofluids

The rising demand for advanced energy systems requires enhanced thermal management strategies to maximize resource utilization and productivity. This is quite an important industrial and academic trend as the efficiency of energy systems depends on the cooling systems. This study intends to address the critical need for efficient heat transfer mechanisms in industrial energy systems, particularly those relying on pool boiling conditions, by mainly focusing on Critical Heat Flux (CHF). In fact, CHF keeps a limit in thermal system design, beyond which the efficiency of the system drops. Recent research materials have highlighted nanofluids’ superior heat transfer properties over conventional pure fluids, like water, which makes them a considerable substitution for improving CHF in cooling systems. However, the broad variability in experimental outcomes challenges the development of a unified predictive model. Besides, Machine Learning (ML) based prediction has shown great accuracy for modeling of the designing parameters, including CHF. Utilizing ML algorithms—Cascade Forward Neural Network (CFNN), Extreme Gradient Boosting (XGBoost), Extra Tree, and Light Gradient Boosting Method (LightGBM)— four predictive models have been developed and the benchmark shows CFNN’s superior accuracy with an average goodness of fit of 89.32%, significantly higher than any available model in the literature. Also, the iterative stability analysis demonstrated that this model with a 0.0348 standard deviation and 0.0268 mean absolute deviation is the most stable and robust method that its performance minorly changes with input data. The novelty of the work mainly lies in the prediction of CHF with these advanced algorithm models to enhance the reliability and accuracy of CHF prediction for designing purposes, which are capable of considering many effective parameters into account with much higher accuracy than mathematical fittings. This study not only explains the complex interplay of nanofluid parameters affecting CHF but also offers practical implications for the design of more efficient thermal management systems, thereby contributing to the broader field of energy system enhancement through innovative cooling solutions.

Evaluating the biomolecular interaction between delamanid/formulations and human serum albumin by fluorescence, CD spectroscopy and SPR: Effects on protein conformation, kinetic and thermodynamic parameters

Delamanid is an anti-tuberculosis drug used for the treatment of drug-resistant tuberculosis. Since delamanid has a high protein bound potential, even patients with low albumin levels should experience high and rapid delamanid clearance. However, the interaction between delamanid and albumin should be better controlled to optimize drug efficacy. This study was designed to evaluate the binding characteristics of delamanid to human serum albumin (HSA) using various methods: fluorescence spectroscopy, circular dichroism (CD), surface plasmon resonance (SPR), and molecular docking simulation. The fluorescence emission band without any shift indicated the interaction was not affected by the polarity of the fluorophore microenvironment. The reduction of fluorescence intensity at 344 nm was proportional to the increment of delamanid concentration as a fluorescence quencher. UV-absorbance measurement at the maximum wavelength (λmax, 280 nm) was evaluated using inner filter effect correction. The HSA conformation change was explained by the intermolecular energy transfer between delamanid and HSA during complex formation. The study, which was conducted at temperatures of 298 K, 303 K, and 310 K, revealed a static quenching mechanism that correlated with a decreased of bimolecular quenching rate constant (kq) and binding constant (Ka) at increased temperatures. The Ka was 1.75–3.16 × 104 M−1 with a specific binding site with stoichiometry 1:1. The negative enthalpy change, negative entropy change, and negative Gibbs free energy change demonstrated an exothermic-spontaneous reaction while van der Waals forces and hydrogen bonds played a vital role in the binding. The molecular displacement approach and molecular docking confirmed that the binding occurred mainly in subdomain IIA, which is a hydrophobic pocket of HSA, with a theoretical binding free energy of −9.33 kcal/mol. SPR exhibited a real time negative sensorgram that resulted from deviation of the reflex angle due to ligand delamanid-HSA complex forming. The binding occurred spontaneously after delamanid was presented to the HSA surface. The SPR mathematical fitting model revealed that the association rate constant (kon) was 2.62 × 108 s−1M−1 and the dissociation rate constant (koff) was 5.65 × 10−3 s−1. The complexes were performed with an association constant (KA) of 4.64 × 1010 M−1 and the dissociation constant (KD) of 2.15 × 10−11 M. The binding constant indicated high binding affinity and high stability of the complex in an equilibrium. Modified CD spectra revealed that conformation of the HSA structure was altered by the presence of delamanid during preparation of the proliposomes that led to the reduction of secondary structure stabilization. This was indicated by the percentage decrease of α-helix. These findings are beneficial to understanding delamanid-HSA binding characteristics as well as the drug administration regimen.

Influence of design parameters on sustained drug release properties of 3D-printed theophylline tablets

The application of three-dimensional printing (3DP) in the pharmaceutical industry brings a broad spectrum of benefits to patients by addressing individual needs and improve treatment success. This study investigates the sustained release properties of 3DP tablets containing Theophylline (TPH), which is commonly used to treat respiratory diseases and recently having a comeback due to its potential in the treatment of conditions like Covid-19. Since TPH is a narrow therapeutic window (NTW) drug with serious side effects in the event of overdose, the release properties must be observed particularly closely. We employed a state-of-the-art single screw extrusion 3D printer, which is fed with granules containing the drug. By employing a Taguchi orthogonal array design of experiments (DOE), tablet design parameters and factor related process stability were sought to be evaluated fundamentally. Following this, examinations regarding tailored TPH dosages were undertaken and a relationship between the real printed dose of selected tablet designs and their sustained drug release was established. The release profiles were analyzed using different mathematical model fits and compared in terms of mean dissolution times (MDT). Finally, in-vivo/in-vitro correlation (IVIVC) and physiologically based pharmacokinetic (PBPK) modeling showed that a paradigm patient group could be covered with the dosage forms produced.

Prediction of Operational Lifetime of Perovskite Light Emitting Diodes by Machine Learning

Perovskite light‐emitting diodes (LEDs) with advantages of high electroluminescence efficiency at high brightness, good color purity, and tunable bandgap, are believed to have potential applications in the next generation display and lighting technologies. Due to the complex degradation process, mathematic models to describe the degradation process of perovskite LEDs are absent. In this work, it is found that the mathematical fitting methods which have been widely used to describe the decay trend of organic LEDs and quantum‐dot LEDs, are unable to accurately predict the lifetime of perovskite LEDs. Then an ensemble machine learning model is developed, which utilizes data augmentation technique to predict T50 of perovskite LEDs based on features before T80, achieving an accuracy of 0.995. Furthermore, the model can also accurately predict the T90 lifetime of quantum‐dot LEDs (QLEDs) using features before T98, suggesting it is a useful tool to efficiently evaluate LED lifetimes.

AI-driven battery ageing prediction with distributed renewable community and E-mobility energy sharing

Electrochemical battery storages play multiple functions in district energy systems, like peak shaving, load coverage, renewable penetration, load coverage, frequency regulation and short-term fast response. Battery cycling ageing will significantly affect the battery performance and the ignorance or inaccurate estimation on battery cycling ageing will lead to performance overestimation. However, current literature provides limited progress on these topics. In this study, a coastal district energy community is developed with district buildings, transportations, solar-wind systems, electrochemical battery storages, power grid and multi-directional power interactions. The ultimate target is to predict the dynamic state of health of various batteries with high accuracy and efficiency. In respect to frequent charging from intermittent renewables and discharging from stochastic demands and vehicle driving s, a series of cycling ageing models are developed, tested and compared, using mathematical fitting and machine learning approaches. Considering modelling complexity, time-consuming and product-dependent characteristic of mathematical models, machine learning-based regression learners are applied to firstly learn the underlying ageing mechanism, and then make accurate predictions. A top-down approach, following statistical analysis in training, cross-validation and prediction processes, is proposed for algorithm selection to accelerate the cycling ageing prediction. Results indicate that, during training and cross-validation processes, the final algorithm is identified as the exponential Gaussian Process Regression. Demonstration on battery cycling ageing verifies the feasibility and effectiveness in different battery categories and energy paradigms, so as to avoid techno-economic performance overestimation.

Correlation coefficient distribution and its application in the comparison of chemical data sets

This paper presents a comprehensive statistical framework in order to rigorously derive the correlation coefficient distribution between two independent chemical data sets. The novel approach not only allows for unequivocal interpretation of distribution parameters and confidence intervals but also the generalization of previous results for fixed size comparisons into the new and experimentally important case of variable dimension data assessments. Original theoretical results include an objective criterion (“number of nines”) for the coefficient of multiple determination in mathematical model fitting (e.g. calibration curve acceptance in validation protocols) and the requirement of a minimum correlation coefficient match of approximately 70% in variable size evaluations. Significance tests have been applied to the drug profile linkage of 532 real case cocaine samples seized by the National Police of Peru between the years of 2021 and 2022.

Experimental analysis and modeling of micro-texture and vickers hardness impact on polished stone value in high-friction aggregates

This article intends to study the influence of micro-texture and Vickers hardness on the Polished Stone Value (PSV) of four types of high friction aggregates (90# Bauxite, 75# Bauxite, Basalt, and Granite) during the long-term polishing process. For this purpose, profile roughness, Vickers hardness, and PSV were tested. The relationship between profile roughness, Vickers hardness, and PSV was analyzed with gray correlation analysis and mathematical fitting. The results show that arithmetic mean roughness (Ra) and maximum height (Rz) influenced PSV significantly while root mean square height (Rq), skewness (Rsk), kurtosis (Rku), and load length ratio (Rmr (c)) had a relatively weak effect. Because of the high correlation with PSV, Ra and Rz were chosen as indicators, and the relationship between variables (Ra, Rz) and PSV was established. There is a good linear relationship between the attenuation rate of Ra and Rz per polishing cycle (K1 and K2) and Vickers hardness. Finally, a model of estimation of the polished stone value of high friction aggregate based on micro-texture and Vickers hardness during the long-term polishing process is developed. Measuring the profile roughness and Vickers hardness to obtain Ra, Rz, and H correlation values and substituting them into the modeling equations in this paper can be used for optimal selection and life estimation of high friction aggregates, which belong to the raw materials, and the optimal selection of high friction aggregates will be helpful for the design of wear-resistant coatings, especially for high friction surface treatments.