Mean Average Percentage Error Research Articles

Deep Learning Method for Improving Rate of Penetration Prediction in Drilling

Summary The urgent global need to reduce CO2 emissions necessitates the development of sustainable power generation sources. Geothermal power emerges as a renewable and dependable energy option, harnessing the Earth’s natural heat sources for electricity generation. Unlike other renewables, geothermal energy offers uninterrupted power, immune to weather conditions. However, its efficiency hinges on technological innovation, particularly in the challenging realm of geothermal drilling. Rate of penetration (ROP) is a crucial drilling performance metric, and this study explores how deep learning models, particularly transformers, can optimize ROP prediction. Leveraging data from Utah Frontier Observatory for Research in Geothermal Energy (FORGE), we analyze the relationship between drilling parameters and ROP. Traditional drilling optimization methods face limitations, as drilling dysfunctions can disrupt the linear relationship between ROP and weight on bit (WOB). We propose a dynamic approach that allows adapting drilling parameters in real time to optimize ROP. Our experiments investigate optimal sampling intervals and forecast horizons for ROP prediction. We find that a 60-second sampling interval maximizes the transformer model’s forecasting accuracy. Additionally, we explore retraining to fine-tune models for specific wells, improving forecasting performance. Our transformer-based ROP forecaster outperforms deep learning models, achieving a low overall 5.22% symmetrical mean average percentage error (SMAPE) over a forecast horizon of 10 minutes. This model offers opportunities for cost-effective drilling optimization, with real-time accuracy, speed, and scalability. Future work will focus on larger data sets and integration with drilling automation systems to further enhance the model’s practicality and effectiveness in the field.

Handling of problematic ion chromatograms with the Automated Target Screening (ATS) workflow for unsupervised analysis of high-resolution mass spectrometry data

Liquid chromatography (LC) or gas chromatography (GC) coupled to high-resolution mass spectrometry (HRMS) is a versatile analytical method for the analysis of thousands of chemical pollutants that can be found in environmental and biological samples. While the tools for handling such complex datasets have improved, there are still no fully automated workflows for targeted screening analysis. Here we present an R-based workflow that is able to cope with challenging data like noisy ion chromatograms, retention time shifts, and multiple peak patterns. The workflow can be applied to batches of HRMS data recorded after GC with electron ionization (GC-EI) and LC coupled to electrospray ionization in both negative and positive mode (LC-ESIneg/LC-ESIpos) to perform peak annotation and quantitation fully unsupervised. We used Orbitrap HRMS data of surface water extracts to compare the Automated Target Screening (ATS) workflow with data evaluations performed with the vendor software TraceFinder and the established semi-automated analysis workflow in the MZmine software. The ATS approach increased the overall evaluation performance of the peak annotation compared to the established MZmine module without the need for any post-hoc corrections. The overall accuracy increased from 0.80 to 0.86 (LC-ESIpos), from 0.77 to 0.83 (LC-ESIneg), and from 0.67 to 0.76 (GC-EI). The mean average percentage errors for quantification of ATS were around 30% compared to the manual quantification with TraceFinder. The ATS workflow enables time-efficient analysis of GC- and LC-HRMS data and accelerates and improves the applicability of target screening in studies with a large number of analytes and sample sizes without the need for manual intervention.Graphical

An empirical confinement model for ANFO explosive

AbstractAmmonium‐nitrate‐fuel‐oil (ANFO) explosive, one of the most used mining explosives, exhibits highly non‐ideal behaviour. The non‐ideality of the detonation is manifested in the strong dependence of the detonation velocity on the charge radius and existence and the characteristics of confinement. This can lead to the detonation velocities as low as one‐third of the ideal velocity. The literature reported experimental detonation velocities of cylindrical ANFO charges confined in different confiners (aluminium, copper, steel, polymethyl methacrylate, and polyvinyl chloride) are analysed in this paper. An empirical confinement model, which relates the detonation velocity to the charge radius and the mass of the confiner to the mass of explosive ratio per unit length, is proposed. The model predicts the detonation velocity of unconfined and confined ANFO charges with a mean average percentage error of 8.8 %.

Construction of mathematical model for integration of engineering cost prediction and multiple algorithms

As a key link in engineering construction, reasonable evaluation of engineering cost can effectively control the budget and save costs. Therefore, the reliability of the engineering cost estimation will directly affect the economic status of the whole project. However, traditional prediction models are based on a single machine learning method, which is not generalized enough and has low accuracy. In view of this, a mathematical model for engineering cost prediction is constructed by combining a random forest algorithm, ridge regression algorithm, and extreme gradient boosting (XG Boost) algorithm to obtain a prediction model with higher generalization and accuracy, and to evaluate the cost of engineering projects reasonably and scientifically. The average relative error between predicted and actual values was only 0.872%. The root mean square error and average percentage error of the fusion model were relatively small. The superiority of the proposed mathematical model of prediction cost is verified, and the model possesses a certain application value in construction engineering, providing practical reference and guidance for engineering cost prediction.

Approaches to simplify industrial energy models for operational optimisation

Minimising energy consumption in today's industrial sector is a crucial objective for achieving established climate goals. One effective strategy to enhance efficiency is optimising energy system operations within industries. The initial step in establishing operational optimisation involves developing a comprehensive model of the energy system. This model necessitates a specific structure to meet optimisation requirements. However, creating a model from scratch incurs substantial effort. While numerous companies possess energy models, they often lack the requisite structure for optimisation. Consequently, simplifying existing models can significantly reduce the effort needed to implement operational optimisation.This paper investigates the simplification of intricate industrial energy system models for optimisation purposes. The subsequent sections analyse two distinct approaches. One approach involves linearisation, while the other utilises neural networks. To facilitate a comparative analysis of these approaches, a reference model is developed. The assessment of these methodologies includes an investigation into optimisation robustness, computation time, accuracy concerning the reference model, and the effort required for developing and maintaining the simplified models. It proved that both approaches are suitable for operational optimisation. Linearisation exhibits superior computational efficiency compared to the neural network approach. The linearisation modelling approach together with the optimisation only required a few milliseconds for the calculation. The neural network approach needed 3 h for the calculation of the optimum with the genetic algorithm. The simulation of the neural network itself only required a few milliseconds. Hence, an improvement of the genetic algorithm is needed. However, the accuracy of linearisation falls short of that achieved by neural networks. The linearisation achieves a mean average percentage error from only 13%. In comparison the neural network's mean average error is 2.3%. Therefore, the linearisation must be improved. The impact using a piecewise linearisation on the results will be analysed in further research.

Disaggregation Model: A Novel Methodology to Estimate Customers’ Profiles in a Low-Voltage Distribution Grid Equipped with Smart Meters

In the context of increasingly necessary energy transition, the precise modeling of profiles for low-voltage (LV) network consumers is crucial to enhance hosting capacity. Typically, load curves for these consumers are estimated through measurement campaigns conducted by Distribution System Operators (DSOs) for a representative subset of customers or through the aggregation of load curves from household appliances within a residence. With the instrumentation of smart meters becoming more common, a new approach to modeling profiles for residential customers is proposed to make the most of the measurements from these meters. The disaggregation model estimates the load profile of customers on a low-voltage network by disaggregating the load curve measured at the secondary substation level. By utilizing only the maximum power measured by Linky smart meters, along with the load curve of the secondary substation, this model can estimate the daily profile of customers. For 48 secondary substations in our dataset, the model obtained an average symmetric mean average percentage error (SMAPE) error of 4.91% in reconstructing the load curve of the secondary substation from the curves disaggregated by the model. This methodology can allow for an estimation of the daily consumption behaviors of the low-voltage customers. In this way, we can safely envision solutions that enhance the grid hosting capacity.

Performance Evaluation of Support Vector Regression Machine Models in Water Level Forecasting

Understanding and predicting water level rise is crucial for effective water resource management, flood control, disaster risk reduction, and adaptation to climate change. This study utilize the use of Support Vector Regression Machine (SVRM) models in predicting the water level of Mandulog River in the Philippines. To evaluate its predictive capability, two data architectures, various kernels, and parameters were examined to find the optimal configuration. Multiple kernels were compared for accurate pattern discovery, and parameter selection was performed to enhance predictive accuracy. The SVRM models achieved the lowest Mean Average Percentage Error (MAPE) of 2.186%, Root-Mean Squared Error (RMSE) of 0.00601 during the dry season, and MAPE of 2.226% and RMSE of 0.00602 during the rainy season. Both models were deemed suitable for watershed level forecasting.

Machine learning-based surrogates for eVTOL performance prediction and design optimization

<p>Predicting the performance of different electric vertical take-off and landing (eVTOL) vehicle designs is paramount to vehicle manufacturers and hobbyists. These vehicles' maximum flight time (endurance) and maximum flight distance (range) depend on design and operational parameters relating to their structure, propulsion system, payload, and mission profile. In recent years, sophisticated physics-based models have been developed to estimate and optimize their aerodynamic, propulsion, and electrical performance. Integrating and simulating those models can closely estimate a vehicle's endurance and range. However, this demands advanced knowledge of different subsystems utilized and extensive computational resources limiting the wide-scale utilization of such models. This paper showcases the development and implementation of a framework to train simpler machine learning-based surrogates. The surrogate models are trained on a limited number of eVTOL performance estimates generated by physics-based models and can mimic them accurately. Forty-seven thousand eVTOL vehicle designs were simulated to generate the training data for various machine-learning models. These include several decision tree models, K-nearest neighbor models, linear regression models, and a multi-perceptron neural network model. Vehicle design and operational parameters such as propeller size, payload mass, drag coefficient, velocity, and motor and battery parameters are used as features, and vehicle endurance and range estimates are used as targets. Compared to the alternative approaches, these surrogate models are computationally very efficient and easy to understand and use. Testing on hold-out datasets shows excellent performance, with multiple models having a mean average percentage error of less than 2% in estimating vehicle endurance and range.</p>

Development of A Tool Condition Monitoring System for Flank Wear in Turning Process Using Machine Learning

Computer-numerical control (CNC) machining has become the norm in most manufacturing businesses. In order to maximize machining efficiency, prevent unintended damage, and maintain product quality all at once, tool wear measurement is essential. Wear on the tools is typically an inevitable side effect of machining. Because it endangers the machining process, flank wear, the most frequent type of tool wear, should be avoided. This study's objective is to fill this growing need by developing a system that can use machine learning to monitor tool condition during the turning process using MATLAB. The regression method with boosted decision trees and SVR with Gaussian kernels are applied to predict the flank wear based on the vibration signal and cutting parameters. This study found that the regression with boosted decision tree method has a lower mean average percentage error, 6.43%, while SVR is 10.11%. Plus, R2 for regression is slightly better than SVR. It shows that the system successfully produced an accurate prediction of flank wear.

An enhanced interval-valued decomposition integration model for stock price prediction based on comprehensive feature extraction and optimized deep learning

For the purpose of managing financial risk and making investment decisions, interval stock price forecasting is essential. Currently, decomposition integration frameworks are widely used in point-valued stock price forecasting studies, mainly focusing on mining internal information. However, point forecasts are difficult to adequately capture price uncertainty and may suffer from loss of volatile information. Therefore, this paper proposes an enhanced interval-valued decomposition integration model for stock price prediction based on comprehensive feature extraction and optimized deep learning. Firstly, the interval variational modal decomposition with feedback mechanism (FIVMD) is proposed to extract internal features and can decompose interval values into interval trend and residual. FIVMD not only solves the interval decomposition challenge, but also helps to improve the internal feature extraction capability. Secondly, while considering the influencing factors more comprehensively, appropriate feature selection and compression techniques can effectively achieve external feature extraction, obtain the best influencing factors, and improve the modeling capability of high-dimensional data. Finally, the final prediction results are obtained by modeling the interval trend and residuals separately through the optimization algorithm and deep learning model to improve the prediction accuracy. The results of the empirical analysis reveal that the proposed interval decomposition integrated model has the smallest of the three evaluation metrics, where the values of interval mean average percentage errors (IMAPE) are 1.8188%, 1.1244%, 1.9001%, and 2.1542% respectively. This shows that the model is significantly more accurate and stable than the other comparative models, and it is a successful model for predicting interval-valued stock prices.

Prediction of continuous amyloid PET values by CSF tau measures

AbstractBackgroundAlzheimer disease (AD) is a slowly progressive neurodegenerative disorder characterized by the presence of amyloid plaques that can be measured in vivo with positron emission tomography (PET). PET quantifies the lifetime accumulation of amyloid plaques, while cerebrospinal fluid (CSF) biomarkers reflect the production and clearance of Aβ and tau peptides at time of CSF collection. Previous work has demonstrated a relative plateau of CSF values at higher levels of amyloid burden. Our objective was to identify the range of amyloid PET values predicted by CSF measures of tau phosphorylation, which have been found to be strongly associated with amyloid PET burden.MethodCSF was collected within two years of an amyloid PET scan from 417 (63 cognitively impaired) participants enrolled in studies of memory and aging at the Knight Alzheimer Disease Research Center (mean age 69.8 years, standard deviation 8.9 years). PET imaging was performed with Pittsburgh Compound B (PiB). CSF Aβ42, p‐tau181 and Aβ40 were measured with Lumipulse automated immunoassays. The CSF tau phosphorylation occupancies (percent of tau phosphorylated) at T111, T153, T175, T181, S199, S202, T205, S208, T217, and T231 were evaluated with an immunoprecipitation‐mass spectrometry (IPMS) assay. We applied a neural network to generate a simulated PET‐PiB scan and cortical summary estimates using the fluid biomarkers as modeled inputs. We used asymptotic regression to evaluate the range of amyloid PET values predicted by each CSF measure (Figure 1).ResultCombining fluid biomarkers generated a cortical amyloid burden estimate within 12.6% mean average percent error (MAPE). Four of the assessed fluid biomarkers individually generated estimates within 20% MAPE (Figure 2). Of these, CSF Lumipulse p‐tau181/Aβ42, pS208/S208 (%), and pT231/T231 (%) predicted amyloid PET burden up until a high level (3.08 SUVR/91.1 Centiloids; 3.01 SUVR/88.0 Centiloids; 2.79 SUVR/78.1 Centiloids, respectively) (Figure 3). CSF pT217/217 (%) also had high accuracy but a slightly lower prediction threshold (2.65 SUVR/71.8 Centiloids).ConclusionCSF measures including phosphorylated tau predict amyloid PET over different ranges. Combining different measures of CSF tau phosphorylation can generate estimates of cortical amyloid burden. Future work will evaluate the prediction of tau PET by CSF measures.

Efficiency of recurrent neural networks for seasonal trended time series modelling

Seasonal time series with trends are the most common data sets used in forecasting. This work focuses on the automatic processing of a non-pre-processed time series by studying the efficiency of recurrent neural networks (RNN), in particular both long short-term memory (LSTM), and bidirectional long short-term memory (Bi-LSTM) extensions, for modelling seasonal time series with trend. For this purpose, we are interested in the learning stability of the established systems using the mean average percentage error (MAPE) as a measure. Both simulated and real data were examined, and we have found a positive correlation between the signal period and the system input vector length for stable and relatively efficient learning. We also examined the white noise impact on the learning performance.

ANN based-model for estimating the boron permeability coefficient as boric acid in SWRO desalination plants using ensemble-based machine learning

This study examines the relationship between input conditions and the prediction of boron rejection in full-scale seawater reverse osmosis (SWRO) desalination plants using ensemble-based machine learning. While reverse osmosis is the dominant desalination technology, limited research has focused on analyzing plant performance under actual operating conditions. To address this gap, we developed and implemented machine learning algorithms to forecast boron permeability coefficient values, which are indicative of boron rejection concentrations in the permeate. Our analysis utilizes data from a SWRO desalination plant in southeast Spain, examining various input variables and their influence on the prediction of these parameters. The results demonstrate that our ensemble-based machine learning approach can predict boron permeability coefficient values with a reasonable margin of error of 1 mgL−1, as evidenced by mean average error (MAE) and mean absolute percentage error (MAPE) values of 7.93·10–8 and 11.8 %, respectively. In conclusion, an innovative application of artificial intelligence algorithms in the field of water purification under real operational conditions has been introduced, thus introducing valuable insights into the use of machine learning algorithms for forecasting boron rejection concentrations in full-scale SWRO desalination plants. The findings lay the foundation for future researches exploring automated and deep-learning methods in water purification.

Measuring thermal comfort using wearable technology in transient conditions during office activities

This paper presents an experiment for assessing thermal comfort of occupants in the built environment, from a subjective perspective, focusing on office environment; a dedicated measurement campaign using sensors for acquisition of physiological and environmental parameters was conducted. Skin temperature was measured with two sensors: a minimally invasive sensor for measuring wrist temperature, and a thermal camera to retrieve forehead temperature; simultaneously, heart rate variability was measured using a wearable device. 15 participants were exposed to dynamic changes of air temperature. Data was collected to measure the participants’ thermal sensation vote, with machine learning algorithms. Decision Tree provided higher performances, using a dataset made of wrist temperature, heart rate variability features and air temperature, with mean average error and mean absolute percentage error of 0.86 and 20.9%. The research contributes to thermal comfort personalization in the built environment, to improve well-being and productivity of occupants using minimally invasive sensor network.

A novel kernel ridge grey system model with generalized Morlet wavelet and its application in forecasting natural gas production and consumption

Natural gas production (NGP) and consumption (NGC) always exhibit high nonlinearity, posing challenges for accurate small-sample forecasting. In this work, a novel kernel ridge grey system model with an extended parametric Morlet wavelet (GMW-KRGM) is proposed by integrating the kernel ridge regularization and grey system modelling within a partially linear regression framework and trained by the conjugate gradient method to mitigate the ill-posed problem. Besides, a weighted multi-objective optimization strategy is designed for model hyperparameter optimization and solved by the grey wolf optimizer (GWO). Six real-world NGP and NGC forecasting cases are carried out and empirical results demonstrate that the proposed GMW-KRGM model with optimal hyperparameters solved by GWO always yields superior forecasting performance than the other 2 machine learning models and 7 conventional grey system benchmarks with out-of-sample mean average percentage error (MAPE) improved in 7.4245%–91.8392% and 14.7303%–42.67% on average, respectively and yields more precise forecasting accuracy with fast and stable convergence than the other 5 optimization algorithms with improved MAPE range from 9.5608% to 48.2584%, indicating that the proposed model holds the capability to effectively deal with the nonlinear complex system and has great potential in nonlinear small sample forecasting.

Analysis of heat transfer enhancement of passive methods in tubes with machine learning

This study investigates the efficacy of machine learning techniques and correlation methods for predicting heat transfer performance in a dimpled tube under varying flow conditions, including the presence of nanoparticles. A comprehensive numerical analysis involving 120 cases was conducted to obtain Nusselt numbers and friction factors, considering different dimple depths and velocities for both pure water and water-Al2O3 nanofluid at 1%, 2%, and 3% volume concentrations. Utilizing the data acquired from the numerical simulations, a correlation equation, SVM ANN architectures were developed. The predictive capabilities of the statistical approach, ANN, and SVM models for Nusselt number distribution and friction factor were meticulously assessed through mean average percentage error (MAPE) and correlation coefficients ( R2). The research findings reveal that machine learning techniques offer a highly effective approach for accurately predicting heat transfer performance in a dimpled tube, with results closely aligned with Computational Fluid Dynamics (CFD) simulations. Particularly noteworthy is the superior performance of the ANN model, demonstrating the most precise predictions with an error rate of 2.54% and an impressive R2 value of 0.9978 for Nusselt number prediction. In comparison, the regression model achieved an average error rate of 6.14% with an R2 value of 0.8623, and the SVM model yielded an RMSE value of 2.984% with an R2 value of 0.9154 for Nusselt number prediction. These outcomes underscore the ANN model’s ability to effectively capture complex patterns within the data, resulting in highly accurate predictions. In conclusion, this research showcases the promising potential of machine learning techniques in accurately forecasting heat transfer performance in dimpled tubes. The developed ANN model exhibits notable superiority in predicting Nusselt numbers, making it a valuable tool for enhancing thermal system analyses and engineering design optimization.

Modelling the Effects of Temperature and Pressure on Equivalent Circulating Density (ECD) During Drilling Operations Using Artificial Neural Networks

Incorrect evaluation of equivalent circulating density (ECD) while drilling oil and gas wells may result in drilling problems such as lost circulation, kicks, differential pipe sticking etc especially in narrow drilling margins. Due to the incompressible nature of liquids, increase in wellbore pressure will only have appreciable effect on the fluid rheology at higher pressures, whereas a small increase in temperature may cause a decrease in the rheology. One thousand and eleven (1,011) field data obtained from high pressure; high temperature (HPHT) wells were used to develop artificial neural networks (ANNs) for this study. Training data were used to train the network while validation data were used to guarantee that the network generalizes at the training stage. Test data were used to evaluate the prediction capability of the developed model. Four error metrics, namely R-square (R2), mean square error (MSE), root mean square error (RMSE) and average absolute percentage error (AAPE) were used to assess the performance of the developed networks. Forecasts from the testing data indicate the optimized ECD model produced a prediction accuracy; R2 of 0.9993, MSE of 0.000265, RMSE of 0.01628 and AAPE of 0.337. The optimized ECD model performed better than existing ECD models in terms of the prediction accuracy and the calculated errors. The developed ECD model will help in improving the ECD prediction during the pre-drill design phase, which is quite critical in narrow drilling margin wells.

Sequential stochastic and bootstrap methods to generate synthetic solar irradiance time series of high temporal resolution based on historical observations

Generating synthetic solar irradiance data through computational methods has become an attractive approach, especially when obtaining accurate measurements from historical observations or satellite-derived estimates is not feasible. Since solar photovoltaic energy production is influenced by variable weather conditions, having reliable solar irradiance data is crucial for evaluating the performance of photovoltaic systems accurately. In this paper, we propose two methods, namely stochastic method, and bootstrap method, to generate one-day synthetic solar irradiance data at a minimum 60-minute time resolution. Both techniques consider dynamic meteorological behavior and maintain the physical significance of the observed data, effectively capturing the intermittent nature of solar irradiance. Validations were performed for five sites with different climate conditions and significant geographical separation, and different time resolutions, through various metrics, including variability, statistical distribution, and energy production, which demonstrated mean average percentage errors as low as 2.1% for intraday irradiance fluctuations, statistical distribution goodness-of-fit up to 80%, and discrepancy for energy production close to 2.4%. results verify the applicability of the proposed methods regardless the time resolution, the location of the measured data and the procedure to record it (i.e., from ground weather stations or satellite-derived estimates). We also evaluated the computational performance of the proposed methods, synthetic, where the elapsed time to generate the synthetic data takes less than a minute to generate a hundred one-day solar irradiance time series. The novelty of the proposed methods is that it is only needed the information of a single month to generate representative synthetic solar irradiance one-day sequences generated for five climate conditions without the need of a training process (i.e., iterative adjustments of the parameters), being useful for pre-feasibility studies of the photovoltaic project and to train machine learning algorithms that deals with time series. To encourage the reproducibility of the research presented in this paper, the proposed methods to generate synthetic solar irradiance data are freely available in a well-documented GitHub repository from https://github.com/salazarna/synthetic-irradiance-sequence.

A mobile mapping solution for VRU Infrastructure monitoring via low-cost LiDAR-sensors

ABSTRACT LiDAR scanning is a widely-used method for accurately assessing roads and vehicular infrastructure. However, it can be costly and often overlooks infrastructure important for Vulnerable Road Users (VRU) like pedestrians and cyclists. Advances in electronics now permit high-performance LiDAR sensors made of standard semiconductor materials to be integrated into personal devices like smartphones and tablets. This study introduces a new classification category of handheld LiDAR systems for the purpose of VRU infrastructure mapping on a smaller scale. Qualitative experiments using a handheld LiDAR system were conducted to achieve low-cost mobile mapping of VRU infrastructure. The 3D Scanner App facilitated detailed and qualitative point cloud generation at low speeds. Moreover, it demonstrated precise detection of perpendicular potholes and bumps on roads. A quantitative analysis based on several infrastructure damages was performed, revealing mean average percentage errors of 3.53%, 4.43%, and 10.57% in the x-, y-, and z-directions, respectively. While the accuracy in the x- and y-directions is acceptable, the higher z-direction error indicates overestimation of infrastructural damage depth. In conclusion, the sensor's capabilities enable cost-effective mobile mapping solutions for VRU infrastructure monitoring, such as crowd-sourcing for urban data mining and urban digital twin interfaces, significantly reducing expenses compared to traditional sensors.

Analysis of Ship Operation Pattern Base on Bira - Pamatata Crossing

The Bira-Pamatata crossing transportation service is carried out by three ships, namely KMP Bontoharu, KMP Kormomolin, and KMP Balibo. These three ships have different technical specifications, so the cost of production for the three ships is also other at the 60% load factor level as the basis for determining the tariff. However, the tariffs set for the three ships remain the same. Therefore, it is necessary to decide on the basis of the ship's operating pattern that meets the operational feasibility criteria based on the value of the applicable tariff. The results of the frequency base based on the load factor between the three ships are for KMP Balibo as many as 770 trips/year, KMP Kormomolin as many as 464 trips/year, and KMP Bontoharu as many as 439 trips/year. The method used to determine the basic operating pattern equation approach is the trendline method based on the relationship between frequency and load factor that meets the feasibility of operations. The validation results show that the basic operating pattern equation for the three ships is feasible based on the correlation test results and the mean average percentage error so that the equation can be used as the basis for setting the operating pattern of the Bira -Pamatata crossing.