Nonlinear Fitting Function Research Articles

The rheological behavior characterization and prediction of cement concrete containing magnetite (Fe3O4) and/or carbon fiber

The effect of magnetite and carbon fiber (CF) on the rheological properties of concrete was investigated to reflect and affect its engineering performance development. The rheological parameters of concrete were measured. Next, a prediction model was established to predict the change tendency in the rheological properties of concrete. Then, the correlation between rheological and mechanical properties was investigated to explore the mechanism of rheological behavior on its engineering performance. The results showed that magnetite and CF had a significant effect on the rheological behavior of concrete. When the magnetite and CF contents were 50 % and 0.5 wt%, the yield stress and plastic viscosity of concrete increased by 210.77 % and 35.88 %, respectively, compared to the control group. The physical properties of the materials, their interaction with the cement matrix and their effect on the volume fraction of the concrete system are the main factors affecting the rheological properties of concrete. Meanwhile, the prediction model established by using the nonlinear surface fitting function could effectively predict the influence of materials on the rheological behavior of concrete. The R2 between the predicted and measured values of yield stress could be up to 0.99. However, under the condition of large magnetite and CF content, the aggregation effect of the materials had a certain influence on the plastic viscosity of the concrete, resulting in a certain deviation between the predicted and measured values, but the R2 could still be up to 0.89. It indicated that the prediction model had favorable reliability and accuracy. A strong correlation existed between the rheological parameters and mechanical strength of concrete. The effect of magnetite and CF on rheological properties of concrete promoted the internal microstructure characteristics optimization of concrete to affect its mechanical properties.

Experimental studied on suppressing vortex-induced vibration of closed-box girder bridges with various moveable guide vanes

A new moveable guide vane with the combination of the spring and guide vane was proposed to suppress the vortex-induced vibration (VIV) of closed-box girder bridges. This paper studies the influence of two important parameters (i.e., horizonal length and spring stiffness) of a moveable guide vane on controlling the VIV of a super long-span suspension bridge with closed-box girder by using VIV control tests. The VIV test of 1:50 scaled ratio of sectional model of the original closed-box girder under three wind attack angles were firstly conducted. The suppression ratios of vertical and torsional VIV displacements of the closed-box girder as well as the movement characteristics of moveable guide vane were then analyzed, respectively. The results show that the movable guide vane could significantly reduced the Root Mean Square (RMS) values of VIV displacement of the closed-box girder are after installing, especial for the torsional VIV displacement. A moveable guide vane with a relative smaller horizontal lengths or a relative larger spring stiffness could produce a better outcome of VIV control. The double VIV amplitude of the moveable guide vanes results in the energy dissipation of the closed-box girder in the lock-in VIV wind speed region, while the vertical displcement of the moveable guide vane are close to those of the closed-box girder in non-VIV wind speed region. Besides, the nonlinear exponential fitting function could effectively reflect the relationship among the wind speed, the VIV displacement of the MGV and the closed-box girder.

A multivariate nonlinear dynamic programming of female figures in Qing dynasty literature

Abstract To improve the recognition of female images in Qing Dynasty literature, this paper designs a multivariate nonlinear-based image dynamic programming model. Data-driven typical correlation analysis is used to extract the key controllable variables with the strongest correlation with female image features and use them as input variables for modeling so as to make the maximum correlation between different image features and improve the modeling efficiency. The nonlinear spatial state model is established by using the subspace identification method, and the female image planning model is substituted into the multivariate nonlinear analysis, and the parameters of the nonlinear fitting function about the image planning can be obtained. The simulation analysis of the image dynamic planning model based on multivariate nonlinearity is carried out, and the results show that the average annual failure time of the model designed in this paper is 12.6 hours, and the classification accuracy in female image classification is 96.3%, and the classification time is stable at 1.162 s. The results show that the multivariate nonlinear features of the model can carry out dynamic planning of female images in Qing dynasty literature and improve the classification of image feature recognition.

A machine learning model for fast approximation of free-surface Green's function and its application

In potential flow theory, the accurate and efficient calculation of free-surface Green's functions is essential for solving hydrodynamic issues. Given the impressive performance of machine learning methods in nonlinear function fitting, the present study utilizes an effective machine learning model called StripeGF for numerical approximation. In this model, equidistant horizontal datum lines are arranged in the computational domain away from the singularity, and Green's function and its derivatives on each line are fitted by a multi-layer perceptron (MLP) with a single input. Based on the first-order ordinary differential equation (ODE) that they satisfy, the fourth-order Runge-Kutta method is used to solve the Green's function and its derivatives between adjacent lines. In the domain nearing the singularity, a double-input MLP is applied. Use the Romberg quadrature to create a double-precision data set for training and validation, the numerical results demonstrate that StripeGF outperforms all 4 comparison methods in terms of efficiency and has accuracy of at least 4 digits in more than 99.9% of all zones. The boundary element program improved by StripeGF is verified in the hydrodynamic calculation of S175, showing good accuracy and reliability.

Nonlinear fitting based energetic material explosive shock wave pressure action evaluation model

There are many varieties of new developed energetic materials with different capabilities of shock wave pressure action. In order to effectively evaluate the explosive damage power of diverse energetic materials and to make the evaluation model universal, the TNT is used as the basic material, and the evaluation model of the explosive pressure action of energetic materials is established in this paper based on the nonlinear fitting method. Explosion tests of TNT with different charge quantities are carried out under the same test conditions, and the shock wave surface reflection pressure data at different proportional distances are obtained. The evaluation model between the peak pressure of the TNT shock wave and the proportional distances is constructed based on the explosion similarity ratio formula using the nonlinear fitting function. The prediction accuracy of the established model is verified by the typical TNT charge test, and the proposed model is applied to evaluate the explosive pressure effect of energetic materials. Experimental results show that the predication accuracy of the evaluation model for evaluating the explosion shock wave pressure action of energetic materials based on the nonlinear fitting method is higher than 86.5067%, which can meet the requirements of the engineering applications.

Genetic-simulated annealing optimization for surface wave inversion of shear-wave velocity profiles of geotechnical sites

A new hybrid genetic-simulated-annealing (GSA) optimization algorithm is introduced to solve the multivariable minimization problem for surface wave inversion. The algorithm is effective for both global and local searches due to its combination of the reproduction and selective generation schemes from genetic algorithms (GA) with the nonlinear scaling fitness function and perturbation scheme from simulated annealing (SA). The hybrid GSA algorithm can reduce the risk of a solution becoming trapped in a local minimum and improve global searching efficiency. A mathematical test function as well as surface wave examples are used to examine the advantages and performance of the GSA algorithm. Comparisons of GA, SA, and GSA inversion results demonstrates that GSA can yield the smallest uncertainty and greatest efficiency, and improve the statistical confidence of using surface wave testing for shear-wave velocity profiling.

Structural optimization of a latent heat storage unit with the fractal fin

The fractal structure was applied to the fin optimization of latent heat storage (LHS) technology based on the fractal principle. By numerical simulation, the performances of LHS units with fractal tree-shaped fins were compared with those with traditional plate fins, and the effects of fin structure parameters based on the fractal principle on heat storage and release performances were studied. The results show that the heat storage performance and heat release performance of LHS units with fractal tree-shaped fins are clearly improved, and the optimal fractal structure parameters allow the LHS units to achieve optimal performance. A nonlinear surface fitting function method was used to obtain the functional relation between the branching angle and length index and the heat storage time of the LHS unit. In fractal tree-shaped fins, the optimal length index is 1.141, the optimal width ratio is 1, and the branching angle is 73.55°. In comparison to the LHS unit with traditional plate fins, the LHS unit with the optimum fractal structure parameters has a 35.85% faster melting rate and a 63.39% faster heat release rate. The least entransy dissipation, least thermal resistance and best reversibility are all characteristics of the LHS unit with the optimal fractal structure parameters.

Optimum display luminance under a wide range of ambient light for cockpit displays.

The self-luminous cockpit displays need to be adaptive to a wide range of ambient light levels, which changes from very low illuminance to very high levels. Yet, current studies on evaluation and luminance setting of displays in bright surroundings are still limited. In this study, a three-dimensional visual ergonomic experiment was carried out to investigate how bright a cockpit display should be to meet aircrew operational requirements under different illuminance. A lab study with a within-subjects (N = 12) design was conducted in a simulated cockpit. According to the Weber-Fechner's Law, human observers evaluated five display luminance conditions (101, 101.5, 102, 102.5, 103 cd/m2) under five ambient illuminance conditions (10°, 101, 102, 103, 104 lx). Visual performance, visual fatigue and visual comfort were used as evaluation bases, which were measured by d2 task, subjective fatigue questionnaire and visual perception semantic scales. Nonlinear function fitting was used to calculate the optimal luminance under a certain illuminance. Finally, curvilinear regression was used to analyze the illuminance and its corresponding optimal luminance. Based on Silverstein luminance power function, a luminance adjustment model with the form of power function was obtained. The proposed three-dimensional model fits the experimental data well and is consistent with the existing studies. It can be regarded as a supplement and optimization of the previous model under high ambient illuminance. This study can contribute not only to the pleasing luminance setting of panel displays in aircraft cockpits but also to other self-luminous devices, such as tablet devices, outdoor monitoring equipment and advertising screens.

Sub-THz Small-Signal Equivalent Circuit Model and Parameter Extraction for 3 nm Gate-All-Around Nanosheet Transistor

This paper presents a novel RF small-signal equivalent circuit model and parameter extraction for 3 nm nanosheet gate-all-around field effect transistor (GAAFET). The extrinsic parasitic effect induced by ground-signal-ground (GSG) layout is evaluated by 3D full-wave electromagnetic simulation, and an improved five-step analytical parameter extraction method is proposed for such extrinsic GSG layout. The model parameters for the intrinsic device are analytically determined with the help of nonlinear rational function fitting. The accuracy of the proposed extraction method was confirmed via comparisons between device simulator and electromagnetic simulator with frequency responses up to 300 GHz. Excellent agreement is obtained between the simulated and modeled S-parameters, and the calculated error is lower than 2.689% for the extrinsic layout, and 0.897% for the intrinsic device in the whole frequency range among multi-bias points.

Nonlinear curve fitting-based fast robust MPC algorithm for nonlinear system

In the existing efficient robust model predictive control (ERMPC) algorithms (see e.g. [14,31,32]), through offline optimization and online lookup table calculation, a fixed state feedback control law or a linear interpolated control law is applied to a system when the system state lies between two adjacent polyhedrons, which undoubtedly will result in conservativeness of the controller. Faced with this issue, an improved ERMPC algorithm is proposed in this paper, which considers the nonlinearity between the state feedback control laws with respect to polyhedrons and the norm distance from system state to origin, and can provide continuously variable state feedback control law varying with the state. First, a set of polyhedral parameters and their corresponding state feedback control law sequences are obtained offline by solving a set of LMIs optimization problems. Next, for each state feedback control law sequence, a nonlinear fitting function is established offline between the state feedback control law and its serial number. Then a simplified lookup table is constructed offline to save memory space and shorten online computation time of the controller. According to the simplified lookup table and information of the norm distance from system state to origin, we online establish the coordinate of current state in the nonlinear fitting curve for getting current feedback control law, which changes continuously with the state. The proposed ERMPC algorithm is successfully applied to an actual fast-responding linear one stage inverted pendulum (LOSIP) system to verify its effectiveness.

Fitting Nonlinear Equations with the Levenberg–Marquardt Method on Google Earth Engine

Google Earth Engine (GEE) has been widely used to process geospatial data in recent years. Although the current GEE platform includes functions for fitting linear regression models, it does not have the function to fit nonlinear models, limiting the GEE platform’s capacity and application. To circumvent this limitation, this work proposes a general adaptation of the Levenberg–Marquardt (LM) method for fitting nonlinear models to a parallel processing framework and its integration into GEE. We compared two commonly used nonlinear fitting methods, the LM and nonlinear least square (NLS) methods. We found that the LM method was superior to the NLS method when we compared the convergence speed, initial value stability, and the accuracy of fitted parameters; therefore, we then applied the LM method to develop a nonlinear fitting function for the GEE platform. We further tested this function by fitting a double-logistic equation with the global leaf area index (LAI), normalized difference vegetation index (NDVI), and enhanced vegetation index (EVI) data to the GEE platform. We concluded that the nonlinear fitting function we developed for the GEE platform was fast, stable, and accurate in fitting double-logistic models with remote sensing data. Given the generality of the LM algorithm, we believe that the nonlinear function can also be used to fit other types of nonlinear equations with other sorts of datasets on the GEE platform.

Impact of Process Fluctuations on RF Small-Signal Parameter of Gate-All-Around Nanosheet Transistor Beyond 3 nm Node

In the present work, the variations of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RF</i> small-signal model parameters induced by the intrinsic process fluctuations are investigated in gate-all-around (GAA) nanosheet transistor beyond 3 nm node. With the help of nonlinear rational function fitting, the RF small-signal model parameters are first analytically extracted from the non-quasi-static (NQS) equivalent circuit. The impact of work-function variation (WFV), line edge roughness (LER), and gate edge roughness (GER) on small-signal model parameters are evaluated by 3-D TCAD simulation. Results demonstrate that the channel distribution resistance <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{\text {gdi}}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}_{\text {gsi}}$ </tex-math></inline-formula> are the most sensitive parameters to intrinsic process fluctuations. Furthermore, compared to LER and GER, WFV is found to have the dominated role in the variation of RF small-signal parameters, while LER and GER played a positive promotion role in aggravating the variation. The underlying physical mechanisms are discussed in detail.

Robust and accurate construction of the local volatility surface using the Black–Scholes equation

• We present an algorithm to reconstruct a local volatility (LV) function. • We reconstruct the local volatility surface using a nonlinear fitting function. • The results demonstrate the robustness and accuracy of the proposed algorithm. In this study, we develop a numerical method for the robust and accurate construction of a local volatility (LV) surface using the generalized Black–Scholes (BS) equation from the given option price data. The BS equation is a partial differential equation and has been used to model financial option pricing. Constant volatility was used in the classical BS model. However, it is well known that the constant volatility BS model is practically unsuitable because real financial market data demonstrate non-constant volatility behavior. The LV function is dependent on the asset prices and time. One of the difficulties in reconstructing an unknown LV surface is uniqueness. We extend a previous study of reconstructing time-dependent volatility, which is unique, to time- and space-dependent volatility surfaces. We propose an algorithm comprising four steps: the first step is estimating constant implied volatility; the second step is finding the influential region using the probability density function of a log-normal distribution; the third step is calculating the time-dependent volatility function; and the final step is reconstructing the LV surface. We use a finite difference method to numerically solve the BS model and a nonlinear fitting function to compute the LV surface. We perform computational experiments using synthetic and real market data. The numerical results demonstrate the robust and accurate construction of an unknown LV surface using the proposed method.

Multi-feature-scale fusion temporal convolution networks for metal temperature forecasting of ultra-supercritical coal-fired power plant reheater tubes

The ultra-supercritical coal-fired power plant has higher reheater steam temperatures. To reduce the possibility of overheating operation and decrease the explosion of reheater, the operating temperature of reheater should be accurately monitored in real-time. Through the real-time prediction of the temperature distribution of the reheater tube, the alarm threshold is set to prevent tube burst and other faults. To accurately predict the metal temperature of the reheater tube in real-time, a multi-feature-scale fusion temporal convolution network prediction model is proposed in this paper. The model has a strong ability of feature extraction and nonlinear function fitting, and can infinitely approximate the mapping relationship between input and output data. Innovative methods feature construction, spatial partition and feature fusion, are proposed to improve the accuracy. Original data are collected from one thermal power plant reheater in the Guangdong province of China. The multi-feature-scale fusion temporal convolution network is applied to study the real-life data from March 2020 to May 2020. Compared with 20 prediction models such as random forest, the proposed model has higher accuracy. The mean absolute percentage error result of the proposed model is smaller 0.16% than the second smallest model and 25.70% smaller than the largest model.

Belief-Rule-Base Inference Method Based on Gradient Descent With Momentum

The belief-rule-base (BRB) inference methodology using the evidential reasoning (ER) approach is widely used in different fields, such as fault diagnosis, system identification, and decision analysis. However, the calculation characteristic of the conventional rule activation weight makes the inference system have the rule zero activation problem. The difficulty of constructing partial derivatives restricts the optimization of parameters using the gradient method. Hence, this paper proposes a new belief rule structure and its gradient training method to solve the rule zero activation problem during the inference process and improve inference accuracy. The Gaussian function is applied to calculate the activation weight of the rule with the new structure. Its characteristics avoid the zero activation problem caused by the attribute reference value set in the original method. Based on the newly proposed method, the corresponding distance-sensitive parameter is set for each attribute, and the weight parameter of each rule is discarded. It simplifies the calculation of rule activation weights in the inference process and enables the partial derivatives of the parameters of the inference system to be easily constructed. In the parameter optimization, the momentum optimization gradient stochastic descent method is used to train the new BRB system, which improves the training speed and accuracy compared with the conventional methods. Experiments with nonlinear function fitting, oil pipeline leak detection, and classification of several public datasets are carried out to verify whether the new BRB system trained with momentum stochastic gradient descent (SGDM-BRB) has better performance than other conventional methods. The experimental results show that in the case of complete data, SGDM-BRB has higher accuracy and faster training speed than the conventional methods.

Fairness-Oriented Semichaotic Genetic Algorithm-Based Channel Assignment Technique for Node Starvation Problem in Wireless Mesh Networks.

Wireless mesh networks (WMNs) have emerged as a scalable, reliable, and agile wireless network that supports many types of innovative technologies such as the Internet of Things (IoT), Wireless Sensor Networks (WSN), and Internet of Vehicles (IoV). Due to the limited number of orthogonal channels, interference between channels adversely affects the fair distribution of bandwidth among mesh clients, causing node starvation in terms of insufficient bandwidth distribution, which impedes the adoption of WMN as an efficient access technology. Therefore, a fair channel assignment is crucial for the mesh clients to utilize the available resources. However, the node starvation problem due to unfair channel distribution has been vastly overlooked during channel assignment by the extant research. Instead, existing channel assignment algorithms equally distribute the interference reduction on the links to achieve fairness which neither guarantees a fair distribution of the network bandwidth nor eliminates node starvation. In addition, the metaheuristic-based solutions such as genetic algorithm, which is commonly used for WMN, use randomness in creating initial population and selecting the new generation usually leading the search to local minima. To this end, this study proposes a Fairness-Oriented Semichaotic Genetic Algorithm-Based Channel Assignment Technique (FA-SCGA-CAA) to solve node starvation problem in wireless mesh networks. FA-SCGA-CAA maximizes link fairness while minimizing link interference using a genetic algorithm (GA) with a novel nonlinear fairness-oriented fitness function. The primary chromosome with powerful genes is created based on multicriterion links ranking channel assignment algorithm. Such a chromosome was used with a proposed semichaotic technique to create a strong population that directs the search towards the global minima effectively and efficiently. The proposed semichaotic technique was also used during the mutation and parent selection of the new genes. Extensive experiments were conducted to evaluate the proposed algorithm. A comparison with related work shows that the proposed FA-SCGA-CAA reduced the potential node starvation by 22% and improved network capacity utilization by 23%. It can be concluded that the proposed FA-SCGA-CAA is reliable to maintain high node-level fairness while maximizing the utilization of the network resources, which is the ultimate goal of many wireless networks.

Ensemble-based method with combined fractional flow model for waterflooding optimization

Proxy models are widely used to estimate parameters such as interwell connectivity in the development and management of petroleum fields due to their low computational cost and not require prior knowledge of reservoir properties. In this work, we propose a proxy model to determine both oil and water production to maximize reservoir profitability. The approach uses production history and the Capacitance and Resistance Model based on Producer wells (CRMP), together with the combination of two fractional flow models, Koval [Cao (2014) Development of a Two-phase Flow Coupled Capacitance Resistance Model. PhD Dissertation, The University of Texas at Austin, USA] and Gentil [(2005) The use of Multilinear Regression Models in patterned waterfloods: physical meaning of the regression coefficient. Master’s Thesis, The University of Texas at Austin, USA]. The proposed combined fractional flow model is called Kogen. The combined fractional flow model can be formulated as a constrained nonlinear function fitting. The objective function to be minimized is a measure of the difference between calculated and observed Water cut (Wcut) values or Net Present Values (NPV). The constraint limits the difference in water cuts of the Koval and Gentil models at the time of transition between the two. The problem can be solved using the Sequential Quadratic Programming (SQP) algorithm. The parameters of the CRMP model are the connectivity between wells, time constant and productivity index. These parameters can be found using a Nonlinear Least Squares (NLS) algorithm. With these parameters, it is possible to predict the liquid rate of the wells. The Koval and Gentil models are used to calculate the Wcut in each producer well over the concession period which in turn allows to determine the accumulated oil and water productions. To verify the quality of Kogen model to forecast oil and water productions, we formulated an optimization problem to maximize the reservoir profitability where the objective function is the NPV. The design variables are the injector and producer well controls (liquid rate or bottom hole pressure). In this work the optimization problem is solved using a gradient-based method, SQP. Gradients are approximated using an ensemble-based method. To validate the proposed workflow, we used two realistic reservoirs models, Brush Canyon Outcrop and Brugge field. The results are shown into three stages. In the first stage, we analyze the ensemble size for the gradient computation. Second, we compare the solutions obtained with the three fractional flow models (Koval, Gentil and Kogen) with results achieved directly from the simulator. Third, we use the solutions calculated with the proxy models as starting points for a new high-fidelity optimization process, using exclusively the simulator to calculate the functions involved. This study shows that the proposed combined model, Kogen, consistently generated more accurate results. Also, CRMP/Kogen proxy model has demonstrated its applicability, especially when the available data for model construction is limited, always producing satisfactory results for production forecasting with low computational cost. In addition, it generates a good warm start for high fidelity optimization processes, decreasing the number of simulations by approximately 65%.

Extreme Learning Machine Based on Firefly Adaptive Flower Pollination Algorithm Optimization

Extreme learning machine (ELM) has aroused a lot of concern and discussion for its fast training speed and good generalization performance, and it has been used diffusely in both regression and classification problems. However, on account of the randomness of input parameters, it requires more hidden nodes to obtain the desired accuracy. In this paper, we come up with a firefly-based adaptive flower pollination algorithm (FA-FPA) to optimize the input weights and thresholds of the ELM algorithm. Nonlinear function fitting, iris classification and personal credit rating experiments show that the ELM with FA-FPA (FA-FPA-ELM) can obtain significantly better generalization performance (such as root mean square error, classification accuracy) than traditional ELM, ELM with firefly algorithm (FA-ELM), ELM with flower pollination algorithm (FPA-ELM), ELM with genetic algorithm (GA-ELM) and ELM with particle swarm optimization (PSO-ELM) algorithms.

A Novel Construction and Inference Methodology of Belief Rule Base

The belief rule base model performs well in continuous systems but not in piecewise systems, and it suffers from a combinatorial explosion when there are a large number of model input referential parameters, resulting in a slow model optimization speed. Aiming at these problems, we do the following things. Firstly, different from the existing methods that improve model performance by improving optimization algorithm, we propose a distributed belief rule base model construction and inference methodology, which reduces the algorithm complexity of model construction and inference and improves the model accuracy by dividing the model into several small and independent subsets of belief rule base. Then we prove that the distributed belief rule base model can reduce the optimization algorithm complexity by using this methodology optimizes all subsets in parallel and independently during model construction, and reduce the inference cost of inactivated rules by adopting a hierarchical inference methodology. Then we prove that the proposed distributed belief rule base model performs well on both continuous and piecewise systems; also, construction efficiency and inference accuracy using the same optimization algorithm are higher than those of the traditional belief rule base model through experiments of nonlinear continuous function fitting and binary piecewise function fitting. Finally, we improve that the proposed distributed belief rule base model has a noticeable performance advantage in complex environments compared to the traditional model through the network situation prediction experiment and point out that the distributed belief rule base model is suitable in applications that require high real-time performance and high accuracy.

Predicting of the Unit Grouting Quantity in Karst Curtain Grouting by the Water Permeability of Rock Strata

The prediction of the unit grouting quantity is one of the key points in the design and construction of karst curtain grouting. Because of the concealment and complexity of the karst curtain grouting project, there is no reliable solution to this problem. In this paper, based on the calculation method of water permeability in water-pressure test in grouting engineering, Poiseuille flow equation in fluid mechanics, and cubic law, the relationship between the unit grouting quantity and the water permeability of rock strata in karst curtain grouting is studied. It is found that there is a nonlinear positive correlation between the unit grouting quantity and the water permeability of rock strata in karst curtain grouting, which is in the form of power function. At the same time, the comprehensive coefficient of karst curtain grouting ( K ) is introduced to describe the quantitative relationship between the unit grouting quantity and the water permeability of rock strata. K is comprehensively characterized by three controlling factors, namely, the characteristics of slurry fluid, the characteristics of grouted rock strata, and the technical factors of grouting in karst curtain grouting. Based on this theoretical relationship, a method for predicting the unit grouting quantity in karst curtain grouting by the water permeability of rock strata is proposed in this paper. Finally, based on the typical example of karst curtain grouting project, through the field grouting test and nonlinear function fitting, the comprehensive coefficient of karst curtain grouting ( K ) is 24.37 in the area of strong karst development, and it is 16.51 in the area of weak karst development. The proposed method is applied to the prediction of the unit grouting quantity in the main project of karst curtain grouting, and the results verify the rationality and applicability of the method. This study has a certain reference value and guiding role in the design, construction, and theoretical research of karst curtain grouting.