Unified Mathematical Model Research Articles

Cross-Track Illumination Correction for Hyperspectral Pushbroom Sensor Images Using Low-Rank and Sparse Representations

A hyperspectral pushbroom sensor scans objects line-by-line using a detector array, and a cross-track illumination error (CTIE) exists in the imagery acquired in this way. When the illumination of the individual cells of the detector is not aligned well, or if some of the cells are degraded or old, the acquired images will exhibit nonuniform illumination in the cross-track direction. As additive Gaussian noise is found widely in hyperspectral images (HSIs), we develop a unified mathematical model that describes the image formation process corrupted by the CTIE and additive Gaussian noise. The CTIE produced by line-by-line scanning is replicated and modeled as an offset term with the equivalent values in the direction of flight. The main contribution of this study is the development of a hyperspectral image cross-track illumination correction (HyCIC) method, which corrects the cross-track illumination using column (along-track) mean compensation with total variation and sparsity regularizations, and attenuates the Gaussian noise by using a form of low-rank constraint. The effectiveness of the proposed method is illustrated using semireal data and real HSIs. The performance of the proposed HyCIC is found to be better than other existing methods.

Mathematical model to assess energy consumption using water inflow-drainage system of iron-ore mines in terms of a stochastic process

Purpose is to develop a unified mathematical model to assess energy efficiency of a water inflow-drainage process as the real variant of stochastic method for water pumping from underground workings of iron-ore mines. Methods. The research process was based upon the methods of probability theory as well as stochastic modelling methods. The stochastic function integration has been reduced to summation of its ordinates and further transition to a proper boundary. Findings. A mathematical model of a water inflow-drainage system as a stochastic process has been developed in terms of input parameters of a standard operating iron-ore mine. The abovementioned has made it possible to assess realistically, substantiate, and obtain possibilities for a specific production facility as well as for generalization of the results involving determination of stochastic characteristics of drainage process. Originality. For the first time, a mathematical model of drainage from underground levels of iron-ore mines has been developed as a stochastic process. The process characteristics have been identified relying upon randomness of a water pumping technique. In contrast to the available settings, the new model parameters characterize their dispersion. Possibility to obtain complete characteristics of energy consumption has been obtained: for drainage; for water accumulation volume in underground water collectors; for water pumping from the specified mine depths over the specific period as random processes. A number of drainage features have been analyzed and differentiated being determined with the help of nor-mal law of water accumulation velocity in the underground water collectors in iron-ore mines. Practical implications. In terms of operating iron-ore mine, a generalized drainage mathematical model has been developed as a stochastic process using statistical data concerning water accumulation velocity in the underground water collectors. It has been proved that if the ordinates of water accumulation velocity in the underground water collectors obey the normal distribution law then it is expedient to characterize drainage as a stochastic process. The developed methods, studying drain-age as a stochastic process, help expand the research boundaries involving other auxiliary operations performed during underground mining of iron ore raw materials.

Study of Thixotropic Characteristics of a Kerosene Gel Propellant by Bayesian Optimization

The rheological behavior of gel propellants is crucial for their practical applications, especially in the rocket engine and ramjet fields. The thixotropic characteristics of gel propellants are an important component of their rheological properties and have a notable impact on their flow and injection process. However, most gel propellants contain rich, dynamic cross-linked network structures, which impart complex non-Newtonian fluid properties, and it is difficult to establish a unified mathematical model. In view of this, this study addresses the thixotropy of a prepared RP-3 kerosene gel and determines the mathematical model and model parameters describing its thixotropy. Experiments show that the kerosene gel exhibits shear-thinning properties as well as thixotropy. To describe the microstructural changes in the gel, three thixotropic constitutive models are introduced to analyze the rheological data, and the constitutive equation parameters are optimized. The three models are all structural dynamic models, which can be used to describe microstructural changes within the material. In addition, the fitting of the constitutive equation is a multiparameter optimization problem, and an appropriate optimization method must be used for parameter fitting. Therefore, the Bayesian optimization method combined with Gaussian process regression and the upper confidence bound (UCB) acquisition function is used in the multiparameter fitting of the constitutive models. Both experiments and numerical results show that the thixotropic model, which introduces a pre-factor with shear strain and assumes that the breakdown of the gel structure is related to energy dissipation rather than the shear rate, has a better fitting effect and prediction ability with regard to the gel. Combined with transient experiments at different shear rates, the model parameters of the constitutive law can be determined quickly by applying the Bayesian optimization method.

Fault feature extraction method for rolling bearing based on MVMD and complex Fourier transform

The vibration signals caused by rolling bearing defects in different directions may be different, and the fault diagnosis based on single channel vibration signals may be made incorrectly, and the observation results may be understood wrong. To avoid it, a new rolling bearing fault feature extraction method based on multivariate variational mode decomposition (MVMD) and complex Fourier transform (CFT) were proposed. First, the orthogonally sampled vibration signals were combined into a multivariate signal, and the multivariate signal was decomposed into several intrinsic mode functions (IMFs) using the MVMD. As per this method, a unified mathematical model was used to model vibration signals in two directions, ensuring that fault features were decomposed to the same level. Finally, the CFT was applied to fuse the envelope signals in two directions in order to obtain a clearer and comprehensive amplitude-frequency feature. Simulation and test results verify the feasibility and superiority of the proposed method.

Unified Power Quality Management for Traction Substation Groups Connected to Weak Power Grids

In remote areas, weak power grids, fewer grid access points, and power quality (PQ) problems dominated by excessive voltage unbalance (VU) and lower power factor (PF) have been prominent obstacles in single-phase 25 kV AC traction power supply systems. To achieve a long-distance power supply with a high PQ, a traction substation group connected to a weak remote power grid is introduced, where the electrical structure is composed of multiple slave traction substations using single-phase traction transformers (TTs), a master traction substation (MTS) using a combination of TTs and a power flow controller (PFC) adopting a modular multilevel converter (MMC). Then, a unified mathematical model of the proposed system suitable for different TT wiring types revealing the effect of asymmetrical grids on the PFC is established. The negative sequence current (NSC) caused by multiple traction stations at the point of common coupling (PCC) and the PF can be improved effectively based on power conservation theory. In addition, to reduce the compensation capacity, an optimization compensation strategy is proposed. Finally, the effectiveness of the proposed algorithm is verified by simulation and a case study. The installed capacity of the PFC is 18.5% lower than that of traditional compensation.

Unified Mathematical Model of Gear Train Analysis Based on State Space Method

The state space method of gear train analysis and the unified mathematical model of state space based gear train analysis are proposed in this paper. Firstly, the concept of basic gear train unit is defined, and the state transformation equation of basic gear train unit is established, which is applied to express the transformation rule of the basic gear train unit and the adjacency relationship between the units. Then, the gear train state space is formed based on the dual vectors including input state eigenvector and output state eigenvector, which describe the state characteristics of the gear train unit. The state space is established based on the mapping relationship among the input-output dual vectors, the state transformation matrix, and the gear train unit. Then the dual vector operation laws and mathematical operation methods in gear train state space are generated. Therefrom, a unified mathematical model based on the kinematic, statics, and structural characteristics of the gear train in the state space is established. Finally, the digital identification and automatic analysis of any complex gear train is realized. The fast comparison and analysis of a large number of gear train schemes is achievable in the scheme design stage.

Stem volume by height classes of immature, mature and overmature stands of the main forest-forming species of Ukraine

Generally, it is impossible to measure diameters and heights of all trees in a forest stand. Therefore, models of relationships between heights (h) and diameters (d) of trees are commonly used in practice for stem volume estimation. This study aimed at developing models of tree height-diameter (h-d) relationships as well as corresponding models of the tree stem volume for immature, mature and overmature stands of the main forest-forming species of Ukraine. This paper is a aggregation of long-term studies of the stem volume, which are based on the results of measuring about 10 thousand sample trees. Modelling of the tree height-diameter relationships was performed using relative height values. The methodology used in this study allowed generalising the measurements of sample trees collected in stands of various forest site types, productivity levels, and age categories. The average height of trees with a diameter of 24 cm was taken as the reference during modelling relative heights, while the diameter of 40 cm was chosen as the reference for overmature Scots pine stands. As a result, the parameters of a unified mathematical model of relative heights for immature, mature, and overmature stands of the main forest-forming tree species of Ukraine were established. Based on these models, height-diameter relationships in forest stands of different height classes were predicted. The authors demonstrated that the developed mathematical models substantially simplify the methodology of field work during timber surveys. The paper also presents models of the tree stem volume. These models predict the stem volume outside the bark based on diameters and heights of trees or using the developed models of h-d relationships. In this study, a unified system of mathematical models of stem volume by height classes were created for immature, mature, and overmature stands of the main forest-forming species of Ukraine. The results of the study are introduced to the National Forest Inventory of Ukraine for growing stock volume calculation at sample plot level using measurements of individual trees. The developed models can be used both by operation forestry (estimation of the timber volume during harvesting), and forest management (forecasting the future structure of forests and estimating the growing stock volume), as well as in the forest ecology

Effect of long-term acid attack on impermeability and microstructure of compacted cement-bound soils

ABSTRACT Compacted cement-bound soils (CCS) are widely used as leakage barriers around solid waste landfills and contaminated sites. However, a study of its long-term reliability in an acidic environment is relatively scarce. A 3-year-long experimental study on the changes in permeability coefficient and microstructure of CCS under acid attack was conducted, from which the following conclusions can be drawn: the permeability coefficient of CCS under weak acid (pH = 5.00) attack decreased progressively with time, from 4.90 × 10−8 cm/s at the beginning to 6.70 × 10−10 cm/s after 3 years. Under strongly acidic environments with pH values of 2.65 and 3.65, the permeability coefficients of CCS initially decreased and then increased with time, reaching 6.70 × 10−5 and 9.37 × 10−8 cm/s, respectively. The degradation effect of a weak acid (pH = 5.00) on the hydration products of cement was mild as a large amount of hydration products (e.g. C-S-H shaped in short fibrous) remained in the pores of CCS after 3 years of immersion. However, strong acid caused an obvious degradation effect on the hydration products, which almost disappeared after 3 years of immersion. Based on the study data, a unified mathematical model was developed to correlate the permeability coefficient of CCS, immersion time and acidic solution pH value. Furthermore, a quantitative expression function between the service life of CCS and solution pH value was established.

A unified model including non-Darcy flow and viscoelastic mechanisms in tight rocks

Tight porous media have extremely low porosities and permeabilities, which can induce low-fluid mobility and a significant non-Darcy flow phenomenon. We build a unified mathematical model considering the non-Darcy seepage and the viscoelasticity mechanism, which includes two new parameters related to the non-Darcy flow mechanism. We call this the non-Darcy viscoelastic (NDV) model. Numerical experiments reveal that the two parameters have significant effects on the dispersion and attenuation of the P and S waves. We find that the dispersion and attenuation of the waves depend on the initial amplitude. A comparison is conducted between experimental data for tight porous media in the low (seismic) frequency band and the numerical results of the NDV model. The comparison demonstrates that the NDV model can predict the velocity dispersion in tight oil and gas reservoirs more accurately.

Disentangling ERBB Signaling in Breast Cancer Subtypes-A Model-Based Analysis.

Simple SummaryBreast cancer subtypes are characterized by the expression and activity of estrogen-, progesterone- and HER2-receptors and differ by the treatment as well as patient prognosis. Tumors of the HER2-subtype overexpress this receptor and are successfully targeted with anti-HER2 therapies. We wanted to know if the HER2-receptor and the downstream signaling network act similarly also in the other subtypes and if this network could potentially be a therapeutic target beyond the HER2-positive subtype. To this end, we quantitatively assessed the wiring of signaling events in the individual subtypes to unravel the characteristics of HER-signaling. Our data along with a model-based analysis suggest that major parts of the intracellular signal transduction network are unchanged between the different breast cancer subtypes and that the clinical differences mostly come from the different levels at which these receptors are present in tumor cells as well as from the particular mutations that are present in individual tumors.Targeted therapies have shown striking success in the treatment of cancer over the last years. However, their specific effects on an individual tumor appear to be varying and difficult to predict. Using an integrative modeling approach that combines mechanistic and regression modeling, we gained insights into the response mechanisms of breast cancer cells due to different ligand–drug combinations. The multi-pathway model, capturing ERBB receptor signaling as well as downstream MAPK and PI3K pathways was calibrated on time-resolved data of the luminal breast cancer cell lines MCF7 and T47D across an array of four ligands and five drugs. The same model was then successfully applied to triple negative and HER2-positive breast cancer cell lines, requiring adjustments mostly for the respective receptor compositions within these cell lines. The additional relevance of cell-line-specific mutations in the MAPK and PI3K pathway components was identified via L1 regularization, where the impact of these mutations on pathway activation was uncovered. Finally, we predicted and experimentally validated the proliferation response of cells to drug co-treatments. We developed a unified mathematical model that can describe the ERBB receptor and downstream signaling in response to therapeutic drugs targeting this clinically relevant signaling network in cell line that represent three major subtypes of breast cancer. Our data and model suggest that alterations in this network could render anti-HER therapies relevant beyond the HER2-positive subtype.

Investigating the migration of immiscible contaminant fluid flow in homogeneous and heterogeneous aquifers with high-precision numerical simulations.

Numerical modeling of the migration of three-phase immiscible fluid flow in variably saturated zones is challenging due to the different behavior of the system between unsaturated and saturated zones. This behavior results in the use of different numerical methods for the numerical simulation of the fluid flow depending on whether it is in the unsaturated or saturated zones. This paper shows that using a high-resolution shock-capturing conservative method to resolve the nonlinear governing coupled partial differential equations of a three-phase immiscible fluid flow allows the numerical simulation of the system through both zones providing a unitary vision (and resolution) of the migration of an immiscible contaminant problem within a porous medium. In particular, using different initial scenarios (including impermeable “lenses” in heterogeneous aquifers), three-dimensional numerical simulation results are presented on the temporal evolution of the contaminant migration following the saturation profiles of the three-phases fluids flow in variably saturated zones. It is considered either light nonaqueous phase liquid with a density less than the water, or dense nonaqueous phase liquid, which has densities greater than the water initially released in unsaturated dry soil. Our study shows that the fate of the migration of immiscible contaminants in variably saturated zones can be accurately described, using a unique mathematical conservative model, with different evolution depending on the value of the system’s physical parameters, including the contaminant density, and accurately tracking the evolution of the sharp (shock) contaminant front.

Improved mathematical model of apparent permeability: A focused study on free and multilayer adsorptive phase flow

Apparent permeability is the quantification of gas transport in confined pore, which includes the pressure gradient-driven continuous flow (slip flow), the concentration gradient-driven molecular diffusion (Fick's diffusion, Knudsen diffusion) and the chemical gradient-driven surface diffusion. Molecular diffusion of free/adsorbed gas plays an important role in gas transfer, especially in nanopores. Most existing apparent permeability models simply define free gas diffusion as Knudsen diffusion, and surface diffusion as the diffusion of monolayer adsorbed molecules. However, the pore scale-dependent Knudsen diffusion, the molecular diffusion of free gas also includes the pore scale-independent Fick's diffusion. In addition, the empirical formula of surface diffusion coefficient derived from plug core diffusion experiment should be used cautiously, because there are other diffusion regimes involved in the diffusion process in multi-scale pores. In this work, the diffusion mechanisms of adsorbed/free gas were classified. A supercritical multilayer adsorption (SC-DA) model was obtained by fitting the adsorption data of homogeneous nano activated carbon, and the adsorption effect was applied to pore aperture change and surface diffusion, which is suitable for single/multilayer adsorption. Applying the improved surface diffusion flow and free gas diffusion flow into gas transport, a unified mathematical transport model was presented, from which the apparent permeability model was derived. Later, the improved model was verified using the experimental data from the micro-flow permeability of the nanofilms with regular size. Furthermore, the influence of each flow mechanism in nanopores was calculated and compared. The results showed that the gas transport in nanopores is dominated by molecular diffusion, but the contribution of surface diffusion in gas transfer is exaggerated if its diffusion coefficient is not chosen properly.

UPMaBoSS: A Novel Framework for Dynamic Cell Population Modeling.

Mathematical modeling aims at understanding the effects of biological perturbations, suggesting ways to intervene and to reestablish proper cell functioning in diseases such as cancer or in autoimmune disorders. This is a difficult task for obvious reasons: the level of details needed to describe the intra-cellular processes involved, the numerous interactions between cells and cell types, and the complex dynamical properties of such populations where cells die, divide and interact constantly, to cite a few. Another important difficulty comes from the spatial distribution of these cells, their diffusion and motility. All of these aspects cannot be easily resolved in a unique mathematical model or with a unique formalism. To cope with some of these issues, we introduce here a novel framework, UPMaBoSS (for Update Population MaBoSS), dedicated to modeling dynamic populations of interacting cells. We rely on the preexisting tool MaBoSS, which enables probabilistic simulations of cellular networks. A novel software layer is added to account for cell interactions and population dynamics, but without considering the spatial dimension. This modeling approach can be seen as an intermediate step towards more complex spatial descriptions. We illustrate our methodology by means of a case study dealing with TNF-induced cell death. Interestingly, the simulation of cell population dynamics with UPMaBoSS reveals a mechanism of resistance triggered by TNF treatment. Relatively easy to encode, UPMaBoSS simulations require only moderate computational power and execution time. To ease the reproduction of simulations, we provide several Jupyter notebooks that can be accessed within the CoLoMoTo Docker image, which contains all software and models used for this study.

A general mathematical model for the in vitro assembly dynamics of intermediate filament proteins

Intermediate filament (IF) proteins assemble into highly flexible filaments that organize into complex cytoplasmic networks: keratins in all types of epithelia, vimentin in endothelia, and desmin in muscle. Since IF elongation proceeds via end-to-end annealing of unit-length filaments and successively of progressively growing filaments, it is important to know how their remarkable flexibility, i.e., their persistence length lp, influences the assembly kinetics. In fact, their lp ranges between 0.3 μm (keratin K8/K18) and 1.0 μm (vimentin and desmin), and thus is orders of magnitude lower than that of microtubules and F-actin. Here, we present a unique mathematical model, which implements the semiflexible nature of the three IF types based on published semiflexible polymers theories and depends on a single free parameter k0. Calibrating this model to filament mean length dynamics of the three proteins, we demonstrate that the persistence length is indeed essential to accurately describe their assembly kinetics. Furthermore, we reveal that the difference in flexibility alone does not explain the significantly faster assembly rate of keratin filaments compared with that of vimentin. Likewise, desmin assembles approximately six times faster than vimentin, even though both their filaments exhibit the same lp value. These data strongly indicate that differences in their individual amino acid sequences significantly impact the assembly rates. Nevertheless, using a single k0 value for each of these three key representatives of the IF protein family, our advanced model does accurately describe the length distribution and mean length dynamics and provides effective filament assembly rates. It thus provides a tool for future investigations on the impact of posttranslational modifications or amino acid changes of IF proteins on assembly kinetics. This is an important issue, as the discovery of mutations in IF genes causing severe human disease, particularly for desmin and keratins, is steadily increasing.

Optimal Dispatch and Control Strategy of Integrated Energy System Considering Multiple P2H to Provide Integrated Demand Response

With the increase in multi-energy loads and renewable energy (RE) penetration, the valley-to-peak value of the electric-heat system is gradually increasing. Although the integrated energy system (IES) and power-to-hydrogen (P2H) technology are widely used to improve energy efficiency and promote the consumption of REs, the dispatch strategies for the IES with P2H to provide integrated demand response (IDR) are not investigated clearly. Thus, this paper presents an optimal dispatch strategy for the IES to provide IDR with multiple P2H technologies. Firstly, a unified mathematical model is built for describing multiple P2H technologies with joint consideration of start/shutdown and ramping constraints. Then, a bi-level P2H-coupled IDR dispatch model is built where the upper level is the IES model including P2H and hydrogen storages with consideration of electric/gas/thermal multi-energy coupling, and the lower level is a flexible user model including transferrable and reduced loads. The Karush–Kuhn–Tucker (KKT) condition and big M methods are used to reformulate the lower-level user model into several complementary relaxation constraints. Then, the whole model is transferred into a solvable single level and linearized model. Finally, the case study shows that the proposed method can improve system flexibility and effectively reduce load peak-to-valley difference. Besides, the addition of P2H and HS into the IES can further optimize the whole economic profits, energy efficiency, and ability to consume REs.

A Model for the Apparent Gas Permeability of Shale Matrix Organic Nanopore Considering Multiple Physical Phenomena

The flow of shale gas in nano scale pores is affected by multiple physical phenomena. At present, the influence of multiple physical phenomena on the transport mechanism of gas in nano-pores is not clear, and a unified mathematical model to describe these multiple physical phenomena is still not available. In this paper, an apparent permeability model was established, after comprehensively considering three gas flow mechanisms in shale matrix organic pores, including viscous slippage Flow, Knudsen diffusion and surface diffusion of adsorbed gas, and real gas effect and confinement effect, and at the same time considering the effects of matrix shrinkage, stress sensitivity, adsorption layer thinning, confinement effect and real gas effect on pore radius. The contribution of three flow mechanisms to apparent permeability under different pore pressure and pore size is analyzed. The effects of adsorption layer thinning, stress sensitivity, matrix shrinkage effect, real gas effect and confinement effect on apparent permeability were also systematically analyzed. The results show that the apparent permeability first decreases and then increases with the decrease of pore pressure. With the decrease of pore pressure, matrix shrinkage, Knudsen diffusion, slippage effect and surface diffusion effect increase gradually. These four effects will not only make up for the permeability loss caused by stress sensitivity and adsorption layer, but also significantly increase the permeability. With the decrease of pore radius, the contribution of slippage flow decreases, and the contributions of Knudsen diffusion and surface diffusion increase gradually. With the decrease of pore radius and the increase of pore pressure, the influence of real gas effect and confinement effect on permeability increases significantly. Considering real gas and confinement effect, the apparent permeability of pores with radius of 5 nm is increased by 13.2%, and the apparent permeability of pores with radius of 1 nm is increased by 61.3%. The apparent permeability model obtained in this paper can provide a theoretical basis for more accurate measurement of permeability of shale matrix and accurate evaluation of productivity of shale gas horizontal wells.

流体界面の一般化数理モデルの予混合火炎への適用

A unified mathematical model for fluid interface such as gas-liquid phase interface and chemical reaction surface is proposed as a viscosity solution of level-set equation, which is derived from conservative form of Allen-Cahn equation by phase field approach and is also related to an equation of arbitrary variable accompanied with order-parameter of the proposed level-set variable in the compressible fluid flow. This unified model is applied to flame approximations of pre-mixture combustion to investigate a relation between the conventional models, and is evaluated their model parameters by the machine learning using a solution of detailed chemical reaction calculation.

Age group and gender classification using convolutional neural networks with a fuzzy logic-based filter method for noise reduction

Biometry is the science that enables living things to be distinguished by examining their physical and behavioral characteristics. The facial recognition system (FCS) is a kind of biometric system. FCS provides a unique mathematical model by determining the distance between the cheekbones, chin, nose, eyes, jawline, and similar positions using the facial features of the persons. Determining the gender and age group of chosen persons’ from face images is the main purpose of this study. It is targeted to distinguish the gender of the person and to obtain information about the person is children or adults by making essential works on the images. Convolutional neural network (CNN) is one of the deep face recognition algorithms that widely used to recognize facial images. This study is suggested as a study that detects noise in images using the fuzzy logic-based filter method and classifies this cleared data by gender using the matrix completion and CNN. TensorFlow which is a machine learning library that used to train and tests deep learning methods is used for experiments. The customer photographs taken during using the system are transformed into a matrix expression through a system trained using this algorithm. The obtained results indicated that the offered technique detects age and gender with a 96% accuracy value and 1.145 seconds time.

Unsteady Transport Phenomena of Hybrid Al2O3-Cu/H2O Nanofluid Past a Shrinking Slender Cylinder

Theoretical investigations of unsteady boundary layer flow gain interest due to its relatability to practical settings. Thus, this study proposes a unique mathematical model of the unsteady flow and heat transfer in hybrid nanofluid past a permeable shrinking slender cylinder. The suitable form of similarity transformations is adapted to simplify the complex partial differential equations into a solvable form of ordinary differential equations. A built-in bvp4c function in MATLAB software is exercised to elucidate the numerical analysis for certain concerning parameters, including the unsteadiness and curvature parameters. The bvp4c procedure is excellent in providing more than one solution once sufficient predictions are visible. The present analysis further observed dual solutions that exist in the system of equations. Notable findings showed that by increasing the nanoparticles volume fraction, the skin friction coefficient increases in accordance with the heat transfer rate. In contrast, the decline of the unsteadiness parameter demonstrates a downward trend toward the heat transfer performance.

A Non-Dominated Genetic Algorithm Based on Decoding Rule of Heat Treatment Equipment Volume and Job Delivery Date

This paper investigated the flexible job-shop scheduling problem with the heat treatment process. To solve this problem, we built an unified mathematical model of the heat treatment process and machining process. Up to now, this problem has not been investigated much. Based on the features of this problem, we are intended to minimize Cmax, maximize the space utilization rate of heat treatment equipment, and minimize the total delay penalty to optimize the scheduling. By taking the dynamic process arrival under consideration, this paper proposed a set of decoding rules based on the heat treatment equipment volume and job delivery date to achieve a hybrid dynamic scheduling solution during one scheduling procedure. When the utilization rate of heat treatment equipment volume is maximized, and the job delivery date is taken under consideration, it is preferred to minimize the number of workpiece batches in the same job, and reduce the waiting time of the pending job. In combination with the improved adaptive non-dominated genetic algorithm, we worked out the solution. Furthermore, we verified the effectiveness of the proposed decoding rules and improved algorithm through algorithm comparison and calculation results. Finally, a software system for algorithm verification and algorithm comparison was developed to verify the validity of our proposed algorithm.