Multistage Model Research Articles

Waiting times in a branching process model of colorectal cancer initiation

We study a multi-stage model for the development of colorectal cancer from initially healthy tissue. The model incorporates a complex sequence of driver gene alterations, some of which result in immediate growth advantage, while others have initially neutral effects. We derive analytic estimates for the sizes of premalignant subpopulations, and use these results to compute the waiting times to premalignant and malignant genotypes. This work contributes to the quantitative understanding of colorectal tumor evolution and the lifetime risk of colorectal cancer.

Manpower scheduling of hospital call center: a multi-objective multi-stage optimization approach

This research investigates the solution approach for scheduling staff in a call center to determine the appropriate staff schedules in order to minimize workforce costs while meeting the target level of service quality. In this regard, a multi-objective multi-stage integer mathematical model is developed to determine the optimal schedules for the staff. The first objective aims to minimize the maximum understaffing, and the second objective minimizes the weighted sum of understaffing and overstaffing to create a balance between these two conflicting objectives. The first stage of the model is devoted to full-time (FT) and part-time (PT) staff scheduling, and the second stage of the model determines the schedules for the Per Diem staff (referred to as PRNs in this study). This model considers several constraints and aspects of the problem that include employees’ days off, lunch breaks, preferences, etc. The lexicographic method and weighted sum approach are used to solve the models. Results show that the optimal schedules obtained from the models outperform the current practice of the call center and significantly reduce the maximum/total sum of overstaffing and understaffing over the planning horizon.

Risk aware decomposition of online scheduling for large flexible consumers considering the age of information

The stability and security of the power system is significantly influenced by large electricity consumers, especially those with flexible demand, whose electricity purchase scheduling has been extensively studied. However, the high penetration of renewable energy and various widespread distributed storage systems have increased uncertainty of the power system, making it difficult to plan effective day-ahead electricity purchase for major electrical consumers. Online scheduling is therefore required so that the surplus can be sold to and the insufficient can be purchased from the real-time market at the lowest electricity cost. To this end, we formulate a multi-stage online scheduling model for large power consumers with flexible demand. To improve the efficiency of online scheduling, we decompose the problem into multiple single-stage sub-problems. Aimed at each single-stage scheduling, an online algorithm is designed to ensure the performance of optimal scheduling strategies maintains at a level comparable to the offline fixed strategies obtained from an oracle who has complete knowledge of the problem’s settings. We prove that our proposed online energy schedule algorithm is able to achieve O(T) regret bound for the single-stage online scheduling problem. To further highlight the significance of data and improve the multi-stage performance of our online scheduling algorithm, we also involve the notion of age of information combined with regret bound to help determine the optimal interval length.

Logistic cost analysis for 3D printing construction projects using a multi-stage network-based approach

Construction 3D printing (3DP) could make supply chains more cost-effective, shorter, and less wasteful; however, many questions are raised regarding equipment and material supply. This paper develops a construction 3DP multi-stage network-based logistics cost assessment model for materials, equipment and waste flows of low-story building construction that supports: (1) a 3DP project logistics network evaluation; (2) a 3DP project feasibility analysis by comparing various 3DP logistic scenarios with traditional construction; and (3) determination of suitable logistics strategies for a 3DP project. A node approach for the logistics systems analysis and a two-type costing approach are employed for model development, the feasibility and practicality of which are demonstrated through case studies. Results show that the dominant logistics cost category for 3DP is transportation, the attentive consideration of which allows the feasibility of a construction 3DP project. As a further step, a 3DP capability map should be developed for 3DP market expansion and transportation reduction.

Predicting fine-scale daily NO2 over Mexico city using an ensemble modeling approach

In recent years, there has been growing interest in developing air pollution prediction models to reduce exposure measurement error in epidemiologic studies. However, efforts for localized, fine-scale prediction models have been predominantly focused in the United States and Europe. Furthermore, the availability of new satellite instruments such as the TROPOsopheric Monitoring Instrument (TROPOMI) provides novel opportunities for modeling efforts. We estimated daily ground-level nitrogen dioxide (NO2) concentrations in the Mexico City Metropolitan Area at 1-km2 grids from 2005 to 2019 using a four-stage approach. In stage 1 (imputation stage), we imputed missing satellite NO2 column measurements from the Ozone Monitoring Instrument (OMI) and TROPOMI using the random forest (RF) approach. In stage 2 (calibration stage), we calibrated the association of column NO2 to ground-level NO2 using ground monitors and meteorological features using RF and extreme gradient boosting (XGBoost) models. In stage 3 (prediction stage), we predicted the stage 2 model over each 1-km2 grid in our study area, then ensembled the results using a generalized additive model (GAM). In stage 4 (residual stage), we used XGBoost to model the local component at the 200-m2 scale. The cross-validated R2 of the RF and XGBoost models in stage 2 were 0.75 and 0.86 respectively, and 0.87 for the ensembled GAM. Cross-validated root-mean-squared error (RMSE) of the GAM was 3.95 μg/m3. Using novel approaches and newly available remote sensing data, our multi-stage model presented high cross-validated fits and reconstructs fine-scale NO2 estimates for further epidemiologic studies in Mexico City.

Multi-stage dynamic evolution of green financial system from the perspective of bilateral moral hazard

In order to improve the regulatory efficiency of the government in the construction process of the green financial system, the multi-stage dynamic evolution game model of green financial system from the perspective of bilateral moral risk is constructed and analyzed. It is found that cost-controllable and profitable collaborative innovation are the fundamental to realize the sustainable cooperation of green innovation between financial institutions and carbon emission enterprises. The introduction of reward and punishment mechanism and transfer payment mechanism for government is conducive to promoting the willingness of financial institutions and carbon emission enterprises to cooperate in green innovation. However, with the increase of appeal willingness of carbon emission enterprises and the cost reduction of appeal, although the risk of illegal arbitrage of financial institutions can be curbed to a certain extent, there is a risk of deterioration in the collaborative relationship between financial institutions and carbon emission enterprises.

Optimizing subsidy strategies of the ride-sourcing platform under government regulation

Under governmental regulation of ride-sourcing platforms, subsidies on passengers and drivers have become an effective incentive to coordinate supply and demand. To achieve the optimization goal of both growth and savings, platforms need to know the impact of the two subsidies on coordinating the supply and demand and what amount of the subsidy is appropriate. This paper formulates a multi-stage game-theoretic model to reveal the coupling game among heterogeneous passengers, heterogeneous drivers, and the ride-sourcing platform in the on-demand ride services market regulated by the government. In this model, passengers with heterogeneous willingness to pay have heterogeneous coupon costs, while drivers are divided into part-time drivers and full-time drivers. We analyze the endogenous influence of platform subsidy strategies on drivers' and passengers' decision-making during surge and regular periods. Numerical experiments are conducted to illustrate the response curves to platform subsidies. The analytical and numerical results show that when the subsidy on passengers is moderate, the rapid demand growth during the regular period can be achieved. Precise subsidies on part-time drivers can achieve the same effect as subsidizing both part-time and full-time drivers, which increases supply and generates higher profits at a lower subsidy cost. Platform subsidies benefit the platform, passengers, and drivers, but may increase driving fatigue. When the subsidy budget is limited, the platform should prioritize subsidizing passengers before providing subsidies for drivers during the surge period. Finally, we discuss the impacts of governmental regulation on different stakeholders. This research gains insights into optimizing subsidy strategies of the ride-sourcing platform under government regulation and budget constraint, and the results provide suggestions for the platform and support government decision-making.

Determining susceptible body parts of construction workers due to occupational injuries using inclusive modelling

Despite significant progress has been made in safety management practices, construction industry still accounts for a substantial number of occupational accidents leading to injuries in different body parts of construction workers. In this vein, detecting the most susceptible body parts of construction workers by using only pre-accident information is of particular importance by means of performance augmentation using advanced modelling techniques as it helps safety managers orchestrate the most relevant and adequate mitigation measures. The central focus of this study is to identify the susceptible body parts of construction workers proactively and propose measures specific to the corresponding body parts. Hence, this study aims to develop a machine learning (ML)-based novel inclusive multi-stage ensemble model that identifies the most vulnerable body parts of construction workers using a national dataset recorded in Turkey. Findings illustrate that incorporating ensemble modelling approach into predictions enhanced accuracies and the ensemble random forest (RF) model reinforced with principal component analysis (PCA) yielded the best performance. Results further highlight that number of workers in the company, working days of the worker, and age of the worker are the most influential attributes in the susceptibility of body parts. A utilization plan is developed based on the analysis results, which can be run monthly on construction sites to identify the most vulnerable body parts of construction workers. Overall, this study is expected to contribute to the development of more robust safety management applications by allowing safety managers to evaluate susceptible body parts of construction workers prior to accidents.

On the study of multistage stochastic vector quasi-variational problems

This paper focuses on the study of multistage stochastic vector generalized quasi-variational inequalities with a variable ordering structure. The proposed multistage stochastic vector quasi-variational problems are defined in a suitable functional setting relative to a finite set of final possible states and certain information fields; these formulations are a multicriteria extension of the multistage stochastic variational inequalities. A relevant aspect of these problems is the presence of the nonanticipativity constraints on the variables of the problem; stage by stage, these constraints impose the measurability with respect to the information field at that stage. Without requiring any assumption of monotonicity, we prove some existence results by using a nonlinear scalarization technique. On this basis, we analyze multistage stochastic vector Nash equilibrium problems: as an example, we focus on a suitable multistage stochastic bicriteria Cournot oligopolistic model.

Reduced-Sensor-Based Multistage Model Reference Adaptive Control of PV-Fed PMSM Drive for Water Pump

Typically, photovoltaic (PV) array fed permanent magnet (PM) synchronous motor based water pumping system uses a current sensor to realize maximum power point tracking (MPPT) of PV array, and an encoder to obtain rotor speed. These sensors reduce reliability and increases cost of system. Besides, they are sensitive to both the temperature and electromagnetic noise. This necessitates the elimination of both the PV current sensor and encoder from the system. Thus, first, a multistage model reference adaptive control (MS-MRAC) for encoderless operation of system is presented in this article. The MS-MRAC is a three-stage structure wherein motor speed is estimated by first-stage, while resistance and PM flux linkages are estimated by the remaining two stages. Thus, the MS-MRAC is independent of motor parameters like resistance and PM flux linkages unlike conventional MRAC. Then, the motor speed as estimated by MS-MRAC is used to estimate PV array power, which along with PV voltage is used to realize MPPT, thereby eliminating PV current sensor. The effectiveness of presented control technique is shown through simulated results followed by their experimental validation under different operating scenarios.

A Comparative Study of Single and Multi-Stage Forecasting Algorithms for the Prediction of Electricity Consumption Using a UK-National Health Service (NHS) Hospital Dataset

Accurately looking into the future was a significantly major challenge prior to the era of big data, but with rapid advancements in the Internet of Things (IoT), Artificial Intelligence (AI), and the data availability around us, this has become relatively easier. Nevertheless, in order to ensure high-accuracy forecasting, it is crucial to consider suitable algorithms and the impact of the extracted features. This paper presents a framework to evaluate a total of nine forecasting algorithms categorised into single and multistage models, constructed from the Prophet, Support Vector Regression (SVR), Long Short-Term Memory (LSTM), and the Least Absolute Shrinkage and Selection Operator (LASSO) approaches, applied to an electricity demand dataset from an NHS hospital. The aim is to see such techniques widely used in accurately predicting energy consumption, limiting the negative impacts of future waste on energy, and making a contribution towards the 2050 net zero carbon target. The proposed method accounts for patterns in demand and temperature to accurately forecast consumption. The Coefficient of Determination (R2), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE) were used to evaluate the algorithms’ performance. The results show the superiority of the Long Short-Term Memory (LSTM) model and the multistage Facebook Prophet model, with R2 values of 87.20% and 68.06%, respectively.

Optimal defense strategy for AC/DC hybrid power grid cascading failures based on game theory and deep reinforcement learning

This paper proposes a two-person multi-stage zero-sum game model considering the confrontation between cascading failures and control strategies in an AC/DC hybrid system to solve the blocking problem of DC systems caused by successive failures at the receiving end of an AC/DC system. A game model is established between an attacker (power grid failure) and a defender (dispatch side). From the attacker’s perspective, this study mainly investigates the problem of system line failures caused by AC or DC blockages. From the perspective of dispatch-side defense, the multiple-feed short-circuit ratio constraint method, output adjustment measures of the energy storage system, sensitivity control, and distance third-segment protection adjustment are used as strategies to reduce system losses. Using as many line return data as possible as samples, the deep Q-network (DQN), a deep reinforcement learning algorithm, is used to obtain the Nash equilibrium of the game model. The corresponding optimal dispatch and defense strategies are also obtained while obtaining the optimal sequence of tripping failures for AC/DC hybrid system cascading failures. Using the improved IEEE 39-node system as an example, the simulation results verify the appropriateness of the two-stage dynamic zero-sum game model to schedule online defense strategies and the effectiveness and superiority of the energy storage system participating in defense adjustment.

Machine Learning-Aided Remote Monitoring of NOx Emissions from Heavy-Duty Diesel Vehicles Based on OBD Data Streams

Most of the current, popular approaches to monitoring real driving NOx emissions are based on direct measurement. However, due to the uncertainty of sensor-based measurements, such methods cannot always be used to accurately screen out the malfunctions of an emission control system. In this paper, a random forest (RF) model which extracts information from on-board diagnostics (OBD) data streams transmitted by a remote emission management vehicle terminal (REMVT) is proposed to provide a specific emission method for the online screening of high NOx emissions. First, two particular forms of modeling, random forest and logistic regression (LR), are laid out as representatives of nonparametric models and specified linear models. These two models were trained, validated and compared using OBD data collected from three China-VI heavy-duty diesel vehicles (HDDVs). The results show that as a data-driven, highly adaptive and robust learning method, the RF model can more accurately identify an abnormal emission state. Finally, a further validation was conducted, in which another China-VI HDDV was tested in two typical states, including a fault state and a normal state. The results indicated that the RF model could clearly distinguish the out-of-control emission condition from the normal operation state. The outcome of this research verifies the feasibility of using a machine learning model to process remote OBD data on HD vehicles and to identify high emissions in the case of an in-use fleet. On this basis, more sophisticated combined models and multi-stage models could be developed.

Analysis and Study on Chemical Composition of Ancient Glass Products

Based on the artificial neural network, K-Means clustering and decision tree algorithm, this paper constructs a variety of models to study the relevant factors of the surface weathering of glass relics and the changes of various chemical components.In this paper, the statistical results are obtained by processing the data with glass type, texture and color respectively, and chi square test is carried out with weathering type respectively. At the same time, a logical regression classification model is established to analyze the relationship. Secondly, the data are divided into four groups based on the glass type and weathering degree, and the statistical rules are obtained by analyzing the average, median, maximum, minimum and change degree of each group of data. Finally, a multi-stage weathering backtracking model is built based on multihead self-attention to predict the chemical composition content of the detection point before weathering. The accuracy of the test is 99%, and the effect is good.

Influence of Molecular Weight on the Nucleation and Growth of Different Crystal Forms in Isotactic Polypropylene: In Situ Synchrotron Microfocus X-Ray Scattering Combined with Fast-Scanning Chip Calorimetry Investigations

The molecular weight (Mw)-dependent formation of mesophase and the α phase of isotactic polypropylene (iPP) was explored by utilizing in situ synchrotron microfocus X-ray scattering measurements combined with a portable fast-scanning chip calorimetry (FSC) technique. A phase diagram illustrating the relationship between the lamellar long spacing (dac) and crystallization as well as melting temperatures of three iPP samples with different molecular weights suggests that a common crystallization line was shared by the mesophase of all three samples, whereas three different crystallization lines were observed for these iPP samples. Furthermore, unlike in the case of the α phase where the melting lines were significantly different from their crystallization lines, the melting line of the mesophase was found to overlap with its crystallization line. The results indicate that the crystallization of the α phase satisfied the multistage crystallization model in which an intermediate layer is suggested to be generated prior to the formation of native crystallites. The Mw-independent formation of the mesophase demonstrated that the nucleus size did not rely on the Mw of iPP because the final sizes of the mesophase were close to the initial nuclei sizes. The larger difference of the lamellar long spacing presented in the α phase of iPP with different Mw indicated that the growth from nuclei to crystallites was significantly influenced by the Mw.

Multistage carcinogenesis: Impact of age, genetic, and environmental factors on the incidence of malignant mesothelioma

The current paradigm of carcinogenesis as a cellular evolutionary process driven by mutations of a few critical driver genes has immediate logical implications for the epidemiology of cancer. These include the impact of age on cancer risk, the role played by inherited tumor predisposition syndromes, and the interaction of genetics and environmental exposures on cancer risk. In this paper, we explore the following logical epidemiological consequences of carcinogenesis as a clonal process of mutation accumulation, with special emphasis on asbestos-related cancers, specifically malignant mesothelioma:1 All cancers, including mesothelioma, can and do occur spontaneously, i.e., in the absence of exposure to any environmental carcinogens. 2. Age is an important determinant of cancer risk, with or without exposure to environmental carcinogens. 3. Genetic tumor predisposition syndromes, such as the BAP1 syndrome, increase enormously the risk of cancer even in the absence of exposure to environmental carcinogens. We illustrate these concepts by applying a multistage clonal expansion model to U.S. Surveillance, Epidemiology, and End Results cancer registry data for pleural and peritoneal malignant mesotheliomas in 1975–2018.

A hybrid method for cutting tool RUL prediction based on CNN and multistage Wiener process using small sample data

Based on the multistage and nonlinear characteristics of cutting tool wear, a hybrid method for cutting tool remaining useful life (RUL) prediction based on convolutional neural network (CNN) and multistage Wiener process using small sample data is proposed in this paper. First, wavelet transform is used to analyse the vibration data collected for cutting tools in the time–frequency domain to obtain an initial image data set. A CCVAE (conditional variational autoencoder with CNN) network is built to expand the initial data set and solve the problem of unbalanced data in different stages of cutting tool wear. The expanded data is used as the input of the CNN to monitor the tool wear state and amount of wear. Then, a nonlinear multistage Wiener process is established to describe the cutting tool wear degradation process and achieve accurate RUL prediction for the cutting tool. Specifically, a nonlinear Wiener process model corresponding to different degradation stages based on the change points between the cutting tool wear states output by the CNN is established. Maximum likelihood estimation and Bayesian methods are used to estimate and update the parameters, respectively, and the RUL value and corresponding probability density function (PDF) are obtained under different wear conditions. Finally, through experimental research and comparative analysis, it is found that the multistage nonlinear Wiener model accurately simulates cutting tool wear degradation, which verifies the feasibility and performance of the method proposed in this paper.

CT-GAN: A conditional Generative Adversarial Network of transformer architecture for text-to-image

How to generate an image from a text description is an imaginative and challenging task. This study proposes a conditional generative adversarial network (GAN) of transformer architecture for text-to-image tasks called CT-GAN by employing the GAN generator based on transformer architecture. We also propose a filtering module suitable for non-end-to-end multi-stage models. This module can screen out the good images generated in the previous stage and allows only the good images to participate in the generation of the later stage. This method significantly improves the quality of the generated images. Furthermore, we designed a generator and discriminator based on symmetry. In the generator, we propose a shift self-attention technology to establish information communication between grids, reduce boundary loss, and improve image quality. We established two modes of local and global discriminations based on the grid, which can balance the performance of the generator and discriminator, improve the training stability, and accelerate the model convergence. We conducted several experiments on the widely used conditional datasets (CUB and COCO) and unconditional datasets (CelebA and LSUN church). The experimental results show that the proposed CT-GAN is superior to the most advanced convolution model in generating diversity and semantic consistency. Codes are available at: https://github.com/Jwtcode/CT-GAN.

Application of the multi-stage centrifugal compressor 1D loss model in the adiabatic compressed air energy storage

A compressor is the core equipment used to convert and store energy in an adiabatic compressed air energy storage system. However, existing compressor models cannot be used for design and detailed loss analyses, which in turn makes simulations of the energy storage process inadequate. In response to this problem, a 1D loss model was developed and applied to an adiabatic compressed air energy storage system to realize compressor design and simulate the compression process. In the design section, based on the 1D loss model and novel optimization algorithms for the stage distribution and single-stage compressor design, we achieved detailed geometric dimensioning of every single-stage compressor and analyzed the energy loss distribution in each representative single-stage compressor. In the simulation session, we generated performance maps of the single-stage and multi-stage compressors under both speed and variable inlet guide vane regulations. Furthermore, the performance maps were combined with heat exchanger and air storage tank models to simulate the entire energy-storage process. The results show that through variable inlet guide vane regulation, the adiabatic compressed air energy storage system has good flexibility to meet different demands under fluctuating renewable energy flows.

A novel stochastic programming model under endogenous uncertainty for the CCS-EOR planning problem

Carbon-capture-and-storage (CCS) is one of the leading technologies to reduce CO2 emissions. A commercial way to deploy CCS on a large scale is to sequestrate CO2 in depleted oil reservoirs and to combine it with enhanced oil recovery (EOR) operations. In this manner, not only the CO2 emission is reduced, but also the oil production increases. The collaborative CCS-EOR planning problem determines the proper allocation of available CO2 to depleted reservoirs and the scheduling of the EOR operations. This problem is of great importance, especially when there are multiple oil reservoirs. This paper presents a deterministic mixed-integer linear programming model as an improvement of an existing model in the literature. Then, it is extended to a multistage stochastic model with endogenous uncertainty in which the parameters expressing the initial oil yields and the periodic depletion factor of oil yields associated with reservoirs are uncertain, and the time of uncertainty realization is decision-dependent. Our deterministic model is computationally more efficient than the existing model in the literature, due to the reduction of binary variables to about one-third. Also, providing the possibility of selecting pipeline types among different options as well as incorporating uncertainty may lead to a significant cost-saving. The proposed models are examined over two case-studies taken from the literature. The results indicate that in comparison to the deterministic model, the cost-saving achieved by incorporating uncertainty is about 8.8%, on average.