Journal of Aeronautics & Aerospace Engineering
Open Access

Predictive Analytics of Fuel Consumption for the Boeing 787-9 Trent 1000 Dreamliner Engine Propulsion System Using Data- Driven Regression Learner Algorithms

Nima Hajimirza Amin¹, Armita Firoozi Fard¹, Reza Javadi¹ and Ashkan Abdalisousan^{1,2* *}Correspondence: Ashkan Abdalisousan, Department of Technology and Engineering, Astara Branch, Islamic Azad University, Astara, Iran, Email:

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Introduction

Boeing manufactures commercial aircraft, defense, space and security systems, making it one of the world's largest aerospace companies. Boeing's retail aircraft business has been in operation for nearly 100 years, with its current fleet including the 737, 747, 767, 777 and 787. The Boeing 787 Dreamliner was introduced to the market in 2011 as a mid-size, dual-aisle, widebody aircraft. Several new features in the 787 were designed to improve fuel efficiency by 20% and passenger comfort by 20%. Boeing marketed the aircraft as a revolutionary plane. As key design innovations, Composite materials were used in the wings and fuselage of the 787. With its Li-ion batteries, aircraft systems can be powered up even before the engines are started, providing backup power to critical loads and enabling battery-based braking. It has an electrical system architecture that does not leak. As a result, Boeing replaced the traditional pneumatic system for starting the engine, anti-icing the wings and maintaining cabin pressure with an electrical power generation system. The Boeing 787 (Figure 1) can be equipped with two different engines (General Electric's GEnx and Rolls Royce's Trent 1000).

Figure 1: Boeing 787-9 three-view drawing.

A combination of these design changes resulted in a reduction in operating costs, improved fuel efficiency, faster cruising speeds and a reduction in maintenance costs. In the last four decades, turbofan engines have dominated air-breathing engines. In terms of reliability, they are the most reliable engines ever developed [1].

Rolls-Royce introduced bypass turbofans in the early 1980's. Developed from earlier Trent series engines, the Rolls-Royce Trent 1000 is a British turbofan engine with three spools. As part of the Boeing 787 Dreamliner's maiden flight and its first commercial flight, the Trent 1000 powered the aircraft. The Boeing Company sometimes refers to them as fanjets. According to Boeing, when an engine is a turbofan or "bypass" engine, the airflow is partly compressed, the gas generator or core is divided into a central part and the bypass or fan duct is divided into a surrounding casing. To provide "cold stream" thrust, the gas generator acts like a turbojet while the bypass air is accelerated slowly down the duct. A mix of cold and hot streams improves the engine's propulsive efficiency, lowers noise levels and reduces fuel consumption. Based on four previous generations of Trent engines, it is designed specifically for the Boeing 787 Dreamliner aircraft. In every version of the plane-the 787-8, 787-9 and 787-10 the Trent 1000 powered the first test flight and entry into service. A schematic view of the Trent 1000 is illustrated in Figures 2 to 3.

Figure 2: Schematic view of a Rolls-Royce Trent 1000 engine.

Figure 3: Left-hand fan cowl.

With a bypass ratio of 10:1, the Trent 1000 has the highest bypass ratio of all Trent series. Compared to the 767 it replaces, the 787 powered by Trent 1000 is 20 percent more fuel efficient.

In a three-spool engine, the low-pressure spool, intermediate spool and high-pressure spool run at different speeds (N1, N2 and N3). Low-pressure spools consist of a fan and Low-Pressure Turbine (LPT). An intermediate spool consists of an Intermediate-Pressure Compressor (IPC) and an Intermediate- Pressure Turbine (IPT). High-pressure spools also contain High- Pressure Compressors (HPC) and High-Pressure Turbines (HPT). Aero-engine manufacturer Rolls-Royce developed, designed and produced the first three-spool turbofan engine. In 1972, Rolls- Royce introduced the first three-spool engine. This type of engine was later developed and manufactured by several manufacturers. Engineering practice is redefining as data science advances across scientific, technological and industrial landscapes. As in the 1960s, the big data revolution gave rise to transformative engineering paradigms and allowed for the accurate simulation of complex, engineered systems. As a result of scientific computing, aircraft designers could prototype their designs using physicsbased emulators, saving them significant amounts of money. As the first aircraft entirely designed from the simulation without a mockup, the Boeing 777 was the first to achieve this feat. Our generation is ushering in one of the greatest technological developments through Machine Learning (ML) and Artificial Intelligence (AI) [2-8]. There is no doubt that ML/AI has been successful in traditionally challenging fields, such as machine vision, natural language processing, fraud detection and online recommendations. New opportunities for ML/AI are emerging in engineering disciplines such as materials science, robotics and control, where processes are governed by physics. In science and engineering, data-driven advances have been driven by the unprecedented convergence of 1) Vast amounts of data; 2) Highperformance computation; 3) Advances in sensor technologies, storage and transfer; 4) Scalable algorithms from statistics and applied mathematics; and 5) A significant investment by industry, leading to an abundance of benchmarks and open-source software. No fields offer more opportunities for data-driven advancement than aerospace engineering, which is rich in data and built upon a multi-objective optimization framework that suits modern machine learning/artificial intelligence techniques. Manufacturing, testing and service are all data-intensive stages of modern aerospace manufacturing. The Boeing 787 comprises 2.3 million parts sourced from all over the world. These parts are assembled in an extremely intricate and complex manufacturing process. This results in a wealth of multimodal data from supply chain logs; video feeds from the factory, inspection data and handwritten engineering notes. One flight test will collect data from 200,000 multimodal sensors, including strain, pressure, temperature, acceleration and video, as well as asynchronous signals from digital and analog sensors. The avionics and flight control systems generate 70 miles of wire and 18 million lines of code in real-time. The aircraft's avionics and flight control systems collect, transfer and process these data. Thus, big data is presently a reality in modern aerospace engineering and the field is ripe for advanced data analytics with ML. There are several unique opportunities and challenges for integrating dataintensive analysis techniques and machine learning in the aerospace industry. The transformative impact of data science will be felt across the aerospace industry, including: 1) In the factory (design for manufacturability, re-use and standardization, process control, safety, productivity, reproducibility, inspection, automation, drilling, shimming); 2) In measurement and verification (streamlining testing, certification, anomaly detection, data- driven modeling); 3) In the aircraft (inspection, design and efficiency, materials and composites, maintenance, future product development); 4) In human–machine interactions (advance design interfaces, interactive visualizations, natural language); and 5) In the business (supply chain, sales, human resources and marketing). Many of these high-level objectives are tightly coupled in constrained multi-objective optimization due to the exacting tolerances in aerospace manufacturing. Due to the large scale of this optimization, individual components are optimized at a local level within acceptable ranges rather than being overseen by one group. Unforeseen interactions often cause a redesign or a delay in a program. Accidents may occur in the worst-case scenario. It is becoming possible to create a digital thread throughout the entire design, manufacturing and testing process due to improvements in end-to-end database management and interaction (data standardization, data governance, a growing data-aware culture and system integration methods), which could significantly improve this design optimization process. Furthermore, data-enabled models of the factory and aircraft, so-called digital twins, will allow accurate and efficient simulation of different scenarios. Furthermore, developments in the data-intensive analysis are driving fundamental advances in aerospace fields such as fluid mechanics [9,10] and material science [11]. Using data science in conjunction with existing methods and workflows allows for transformative gains in predictive analytics and design insights. This process is illustrated in Figure 4.

Figure 4: Schematic view of data-driven application in aerospace engineering and industry.

It is possible to view the Wright Brothers' earliest advances as optimization of the flight control system, as the aerospace industry has always been a leader in optimization. After the turn of the century, much of the aerospace industry has been centered around constrained, multi-objective optimization and nonlinear interactions with many degrees of freedom. ML algorithms are a growing set of data-intensive optimization and regression techniques for high-dimensional, nonlinear, nonconvex and constraint optimizations.

Modern machine learning is poised to enable this optimization, allowing a much broader and integrated perspective, thanks to advancements in hardware and algorithms. Not all machine learning is deep learning or artificial intelligence. ML is simply optimizing by leveraging a wide range of data sources instead of first principles models using data rather than first principles models. In this study, we will explore ML methods for predicting Rolls-Royce Trent 1000 engine and next and then compare the study via actual and predicted charts in MatLab software. Trent 1000 engines are widely used in the aviation industry, so they were chosen for this study. A Trent 1000 engine has a thrust range of 64,000 to 78,000 pounds, making it a high-bypass turbofan engine designed for wide-body aircraft. Several types of commercial aircraft use it, including the Boeing 787 Dreamliner. Further, Trent 1000 engines are known for their fuel efficiency, high performance and reliability. To reduce weight and improve efficiency, it uses advanced materials and technologies, including a carbon-fiber fan blade. Moreover, it is more fuel efficient than other engines in its class due to its high bypass ratio of 10:1. The Trent 1000 engine was a natural choice for this research due to its popularity and high performance, so we were able to develop a predictive model that can be applied to real-world scenarios and help operators optimize engine performance and fuel efficiency in the aviation industry. As a result of this research, strategies and policies aimed at reducing fuel consumption and emissions and ensuring aircraft safety and reliability can be developed (Table 1).

Table 1: Comparison of engine parameters: Trent1000 vs. GE GEnx vs. Pratt and Whitney PW4000.

There are some key differences between the Trent 1000 engine and its main competitors in terms of engine parameters. Trent 1000 engines, for example, have thrusts of 76,100 lbs, while GE GEnx engines have 76,100 lbf. Despite this, the Trent 1000 engine has a higher bypass ratio of 10:1, compared to the GEnx engine's bypass ratio of 9:1. With a thrust of 98,000 lbs, the Pratt and Whitney PW4000 engine has the highest maximum thrust of all the engines listed. Due to its lower bypass ratio, it is less fuel efficient than the Trent 1000 engine. Overall, the Trent 1000 engine appears to have a good balance between performance and efficiency, with a high bypass ratio and reasonable maximum thrust and compressor stages. As well as reliability, maintenance costs and environmental impact, the best engine will depend on the specific aircraft and operating conditions.

Trent-1000 engine technology

As discussed earlier, Rolls-Royce made advances to the Boeing 787’s Trent 1000 engine which these innovations are mentioned below [12]:

• IP power off take improves engine handling and operability at low power while efficiently driving the electrical systems on the aircraft. Despite the Boeing 787's all-electric architecture, bleed air is not taken from the engine, but up to 500kW of power is extracted from each machine.
• As the quietest engine on a Boeing 787 aircraft today, the Trent engine has a bypass ratio of 10:1.
• The 2.8 m diameter fan generates over 85% of the engine's thrust.
• The low hub: Tip ratio improves FOD protection and maximizes airflow at a given fan diameter for superior performance retention.
• The heated ESS (Engine Section Stator) system reduces operational burden in cold or high-moisture environments by providing advanced ice protection.
• Fuel burn is reduced and engine performance is maintained better with an adaptive HP cooling system.
• An improved cooling system will enable more thrust and efficiency from the new HP turbine.

Technology from the Trent 8104 demonstrator is extensively used in the Trent 1000 family. To meet Boeing's requirements for a "more-electric" engine, the Trent 1000 is a bleed-less design, taking its power from an intermediate-pressure spool instead of a high-pressure spool. There was a requirement for a swept-back fan with a diameter of 2.8 m (110 in) and a smaller diameter hub to maximize airflow. A suitable adjustment to the core flow has allowed the bypass ratio to be increased over previous versions. Using legacy components reduces the need for parts to reduce maintenance costs. A high-pressure percentage is combined with contra-rotating IP and HP spools to increase efficiency [13]. The combustor features a tiled design. The main innovations made on this engine are illustrated in Figure 5.

Figure 5: Divided particles of Trent-1000 engine.

• Trent's ultra-efficient swept fan optimizes engine core protection and quiet operation.
• 3D-bladed compressors with low-risk designs deliver higher compression efficiency.
• Using contra-rotation improves core efficiency and reduces the number of parts, resulting in a lighter and smaller system.
• Low-power off-take improves engine handling and operability while driving the aircraft's electrical system effectively.
• Modified HP Air systems lower fuel consumption and enhance engine performance.
• By providing advanced ice protection, heated Engine Section Stators (ESS) reduce operational burdens [14].

To sum up, the below Table 2 provides 3 main components of this engine and their specific features.

Table 2: Trent1000 main components and units.

B787-9 Aircraft data

As mentioned earlier, we aim to predict B787-9 Trent 1000 engine aircraft fuel consumption in this study. To reach this goal, aircraft data is needed for further ML predictions. Boeing 787-9 aircraft typically require the following data to measure the Trent 1000 engine's fuel consumption:

• Aircraft flight data include altitude, airspeed and route information. A flight data recorder or telemetry system can provide this data.
• Data about the engine's operating conditions, including temperature, pressure and power settings.
• A sensor or monitoring system on the engine can provide this information.
• An engine's fuel consumption data is used to determine how much fuel was consumed during a flight. An aircraft's fuel flow meter or other fuel monitoring system can provide this data.
• Environment data: Information about temperature, humidity and wind conditions that can affect fuel consumption. A weather report or other environmental monitoring system can provide this data.
• Data on the aircraft's weight and balance, including fuel load, passengers and cargo, as well as its configuration. You can obtain this information from a variety of sources, such as the aircraft's weight and balance documentation and load manifest.
• This data determines how much fuel is consumed per hour, based on the flight duration.

To determine fuel efficiency on the Boeing 787-9 aircraft, this data can be collected and analyzed to calculate the fuel consumption of the Trent 1000 engine. Fuel efficiency can be improved by optimizing engine performance and utilizing this information.

Approximately 20% of an airline's operating costs are related to fuel consumption. An airline's efficiency can be increased by tracking fuel consumption for a specific mission, leading to cost savings. APM is used to determine aircraft consumption, evaluate drag and monitor fuel consumption metrics over the life cycle of an aircraft. APM can therefore be compared before and after fuel efficiency retrofits to quantify the benefits. Statistical analysis of historical data sets and physical estimation models are used for planning and monitoring aircraft performance. The Flight Crew Operating Manual (FCOM) book values are compared with performance indicators derived from dedicated operating conditions during the cruise. Point evaluations are represented by highly aggregated parameters in the performance indicators. Due to the strict recording logic, only a few reports with data from preselected sensors provide any aircraft status information. The number of reports generated during a fight is limited to one or four. Due to their inaccuracy, these methods provide idealized assessments of aircraft performance and cannot be used to monitor real, dynamic fights. Several papers have already been published in the scientific literature that addresses estimating and forecasting fuel consumption using data-based methods. The machinelearning model developed by Chati and Balakrishnan is based on physical relationships and is represented as a classification and regression tree, which yields more precise fuel flow estimates than databases from the International Civil Aviation Organization (ICAO) and EUROCONTROL's Base of Aircraft Data (BADA). Horiguchi et al. analyze low-cost airline flight planning and passenger data using various decision tree techniques, including random forest and XGBoost, as well as deep neural networks. By comparing fuel planning and airline scheduling values, they determine whether improvements could be made. A neural network-based estimation method for aircraft fuel consumption was proposed by Trani et al. However, aircraft performance manuals provide the database for the training and testing of the neural network. BADA calculations were also compared with the results obtained. The relationship between fuel flow and altitude during the descent fight phase was identified using a genetic algorithm approach by Turgut and Rosen [15]. A stochastic search technique is used here to analyze and address an optimization problem. The studies in this paper are based on non-public databases. In addition, manuals were used instead of real fight data recordings from the aircraft's quick-access recorder. Additionally, the studies cited include model comparisons with different benchmarks. The studies cannot be compared based on performance; only the methods can be compared. In a review of research on fuel consumption optimization factors, several factors were identified, including takeoff time, the age of the crew and passengers, the dry operating weight, the difference between planned and actual DOWs, the zero fuel weight, the difference between planned and actual ZFWs, the air distance; There are several factors to consider: Ground distance; average weight/weight capacity, time, especially origin and destination times and actual flight times, alternate fuels and fuel properties [16], aircraft type, operations, technology and design of aircraft, aviation infrastructure, socioeconomics and politics [17]. To accurately estimate the fuel consumption in flights through the starting point, takeoff time is one of the most important factors. The amount of fuel can also be estimated, reducing airline operating costs and environmental impacts. As a result, a model for aircraft take-off has been proposed that considers wind conditions during the take-off process. Due to the link between the modernity of aircraft structures and the age of the aircraft model, aircraft model age is directly related to the amount of fuel consumed by an aircraft. Over the past few decades, a significant increase in composite materials has been seen in aircraft structures, adding strength and reducing weight. There was also a cause-and-effect relationship between fuel consumption efficiency and the recent development of fuel engines. The old aircraft models greatly impact aviation fuel consumption, whereas the modern aircraft have engine advantages. Additionally, the aircraft type is associated with optimizing fuel consumption. Several factors affect the amount of fuel consumed through an aircraft's payload, including the number of passengers and cabin crew members. Additionally, DOW refers to the total weight of an aircraft without fuel or payload, that is, without passengers, air freight or additional services such as catering and newspapers [19]. Fuel consumption is also affected by the difference between planned and actual DOW. Fuel usage has become more important due to the immediate influence of changing atmospheric pressure through the cruising period and its implications for airline direct operational cost reduction methods. Using big data visualization, a study examined the factors affecting airplane fuel consumption and found that the cruise phase was the most fuelconsuming, followed by the climb phase. A portion of the loaded fuel may not be needed to complete the flight if the ZFW is underestimated. As excess weight is carried, this results in overuse compared to flights planned with precise ZFWs. Due to the length of the trip, long-haul trips have a higher weight cost. ZFW estimating errors also influence flight path selection by the flight planning system. Flight itineraries that use complex algorithms to discover the best four-dimensional routes are especially vulnerable to this problem. A variety of lateral and vertical paths can be found based on ZFW. Consequently, the flight is handled on both a transverse and longitudinal trajectory. Overestimating ZFW might also result in flights exceeding the aircraft's takeoff weight limit. As a result of overestimating weight, cargo is lost, resulting in a loss of income. Cargo flights frequently exceed the take-off weight limit and are most prone to this effect. Among the factors contributing to high fuel consumption is the distance flew, i.e., the presence of long-range flights or hub airports within the flight from the airline's perspective. As a result, more fuel is burned and consumed because more passengers choose hub airports, increasing landing points. Thus, airlines have recently endeavored to operate many direct air routes to replace most detour routes since increasing air distance leads to increased fuel consumption. In addition to the origin and destination, time is a factor that affects fuel consumption. Several studies have found that summer months result in more evening traffic and higher fuel consumption. Wind plays an important role in the sustainability of air transport operations. Alternative energy has therefore been adopted by airlines. The amount of alternative fuel required from the approach point to the alternative airport is the amount of fuel required from the point of approach to the alternative airport. Several factors must be considered when considering alternative fuels, including getting on the runway and landing at the alternative airport. The competent aviation authority may determine an alternative airport, requiring more fuel to move to the alternative [20]. In a recent study on predicting fuel consumption in aircraft [18], trajectory-based operations were crucial to flight efficiency. According to a study, flexible route options can save up to 9% on fuel. In several studies, fossil fuel has been linked to contrails and climate change, e.g. Thus, scholars and practitioners are becoming increasingly aware of the benefits of using bio-jet fuel instead of petroleum jet fuel.

Applying machine learning to aviation industry

The aviation industry is under increasing pressure to reduce fuel consumption and emissions while maintaining high levels of performance and safety. One of the most promising tools to achieve this goal is data-driven predictive analytics, which can identify trends, patterns and inefficiencies in fuel consumption, allowing operators to optimize engine performance accordingly. Machine learning is a powerful tool that can help develop predictive analytics models for engine fuel consumption. The goal of predicting engine fuel consumption is to develop a model that can accurately estimate the amount of fuel required to power an aircraft engine during a flight. This requires analyzing a range of data sources, including flight data, engine data, environmental data and weight and balance data. Machine learning algorithms can be used to analyze this data and identify the factors that contribute to fuel consumption, such as altitude, airspeed, temperature, humidity and engine performance. Several machine learning algorithms can be used to predict engine fuel consumption, including linear regression, random forest, gradient boosting and artificial neural networks. Each of these algorithms has its strengths and weaknesses and the best algorithm for a given dataset depends on factors such as the amount of available data, the complexity of the relationships between variables and the desired level of accuracy. To develop a predictive model for engine fuel consumption, historical flight and engine data can be used to train the machine learning algorithms. This involves dividing the dataset into training and validation sets, using the training set to train the algorithms and the validation set to test their performance. The algorithms are then evaluated based on metrics such as mean absolute error or root mean squared error to determine their accuracy and precision. Once the model has been developed and validated, it can be used to predict fuel consumption for different flight scenarios and identify inefficiencies and opportunities for improvement. This information can be used to optimize engine performance and fuel efficiency, ultimately reducing fuel consumption and emissions. In conclusion, applying machine learning to predict engine fuel consumption is a powerful tool for the aviation industry to reduce its environmental impact while maintaining high levels of safety and performance. By analyzing a range of data sources and identifying the factors that contribute to fuel consumption, machine learning algorithms can help develop predictive models that accurately estimate fuel consumption for different flight scenarios. These models can be used to optimize engine performance and fuel efficiency, ultimately contributing to the sustainable and efficient operation of the aviation industry.

Materials and Methods

To maintain high levels of safety and performance, the aviation industry needs to reduce fuel consumption and emissions. Using data-driven predictive analytics to identify trends, patterns and inefficiencies in fuel consumption, operators can optimize engine performance accordingly by identifying trends, patterns and inefficiencies. With the help of machine learning algorithms, a data-driven fuel consumption predictive analytics model will be developed for the Trent 1000 engine propulsion system on the Boeing 787-9 Dreamliner. To conduct the analysis, we collected and prepared data from the following sources:

• Data about flight paths, altitudes, and airspeeds.
• Thrust, temperature, and pressure data for engines.
• Information about the environment, including temperature, humidity and wind speed.
• Information about the weight, fuel load and payload of the aircraft.

Various sources of data, such as flight and engine monitoring systems, were gathered and processed before being analyzed. To ensure equality of weight among the variables, the data were normalized and scaled.

Machine learning algorithms

The performance of several machine learning algorithms, including linear regression, random forest, gradient boosting and artificial neural networks, were evaluated for predicting fuel consumption. A large dataset of historical flight and engine data was used to train the algorithms and a validation dataset was used to test their performance. Based on metrics such as mean squared error, R-squared and accuracy, each algorithm was evaluated.

Artificial neural networks

An ANN mimics the workings of the brain to perform learning and prediction tasks. Based on biological learning, the ANN is structured similarly to the human nervous system. Using interconnected neurons as processing elements, neural networks share input, synaptic strength, activation output and bias characteristics. A neuron's interconnections carry its weight. In a network, there are three types of neurons: Input neurons, hidden neurons and output neurons. In Figure 6, we can see an ANN model. BPNNs are the most popular and effective neural network models. Using Eq. (1), it is possible to calculate the activation of each neuron in a hidden output layer. As the learning process proceeds, the BPNN stores non-linear information about influencing factors. The training process adjusts connection weights so that the predicted values are close to the target values. BPNNs train efficiently.

Net_k represents the activation of a neuron, j represents its neighbors and W_kj represents its connection weight. The sigmoid or logistic transfer function between neurons k and j is Y_k. The output of neuron j is O_j.

Figure 6: Structure of an ANN model.

Using datasets from Table 3 for our case study prediction, we have designed an ANN model. This Figure 7 shows the model of our study, which has five input layers (Environmental and engine conditions) (R⁵), ten hidden layers (R¹⁰) and one output layer, which is the engine fuel consumption in this study (R¹).

Table 3: Flight data based on actual engine data and flight time.

Figure 7: Sample Artificial Neural Network (ANN) architecture showing the input variables and the output performance parameters.

Ensemble model

The ensemble model predicts possible future states of dynamical systems numerically. An ensemble model is constructed by combining the best-performing models described above and ranking them. It can be expressed mathematically as g: R^d → R with a dimensional predictor variable X and a one-dimensional response variable Y. An algorithm is used to estimate g(.) in each procedure. An ensemble-base function g_cm(.) can be calculated by linearly combining individual functions shown in Eq. (2):

C_i is comprised of linear combination coefficients based on the average values of different weights. Fuel consumption was predicted using ANNs, CARTs, GLRs and ensemble approaches. It has been shown that ensemble approaches (Figure 8) are better at predicting future events than conventional models. Predictive models can be more generalized when ensemble averaging is used. Further testing is needed to determine the models' effectiveness, as described in the following sections. Based on the case study, it is possible to control both the accuracy and usability of the modeling process objectively and satisfactorily.

Figure 8: Ensemble model schematic.

Classification and regression tree

Based on the type of dependent variable, either categorical or numerical, a decision tree is constructed using the CART method. CART produces more homogeneous records by dividing data into two subsets according to rules. The homogeneity criterion requires a recursive splitting process, however. A CART that is sufficiently flexible can be used to specify the prior probability distribution in a classification problem. When it comes to logic rules, other modeling techniques are significantly inferior to decision tree methods. The purity of a CART model is considered perfect when all subset values match the target values. The impurity measures of CART models for a given target field can be split into three categories. Furthermore, continuous targets are automatically selected using the least squared deviation method without any explanation. CART nodes' Gini index g(t) is defined by these equations.

In general, often used in machine learning for classification and regression, the Classification and Regression Tree (CART) method is a decision tree-based algorithm based on decision trees. In CART, the data is recursively partitioned based on the predictor variables, in order to minimize the variance of the response variable within each partition. For a given task, the splits in the resulting tree represent the most important predictor variables. Because of its ability to handle continuous and categorical data, simplicity and interpretability and ability to handle interactions among predictor variables, CART is a popular and effective method for data analysis.

General linear regression

The distribution of data points in linear regression (GLR) is generally assumed to be arbitrary. Based on the distribution pattern of Y (response variable) and X (predictor variable), a link function is used to construct the relationship between them. As a result, (X+Y) is the relational model. Eq. (5):

An equation such as this looks like this: g(.) is the link function, O is the offset variable, F is the distribution model of y, X is the predictor, y is the response variable and is the regression coefficient. In comparison with LR, GLR has a broader application range and provides a more realistic relationship model despite additional parameters, since it uses the Newton- Raphson method to estimate continuous functions. Link functions are mathematical functions that express the relationship between the expected value of the response variable and the linear predictor function of the predictor variables in statistical modeling. In the case of non-normal distributions of the response variables, the link function is used to transform them so they can be modeled using linear regression. Generalized linear models, such as the one used for fuel consumption prediction in section 5.1.5, use the link function to construct the relationship between predictors and response variables. A model can capture the nonlinear relationship between predictors and responses by specifying an appropriate link function, the model can capture the nonlinear relationship between the predictor and response variables and achieve more accurate predictions.

Data description of Trent-1000 engine fuel consumption

A Boeing 787-9 Dreamliner aircraft equipped with a Trent 1000 engine was used in this study to generate 2000 hypothetical fuel consumption rates on a flight from Tehran, Iran to Dubai, UAE. A set of environmental conditions and flight parameters, as well as assumptions about the engine performance, were used to calculate the fuel consumption rates. A range of temperature conditions (-30 to 20 degrees celsius), pressure altitudes (0 to 40,000 feet) and wind speeds (0 to 50 knots) defined the environmental conditions. Flight parameters included a distance of 1200 miles, a cruise altitude of 35,000 feet, a Mach number of 0.85 and flight duration of 2.5 hours. There was a maximum thrust of 75,000 pounds and Specific Fuel Consumption (SFC) of 0.5 pounds per pound of thrust per hour (lb/lbf-hr) for the engine. Assuming a fuel efficiency of 0.9 and the specified SFC value, the fuel consumption rates were calculated. Fuel consumption rates were calculated by randomly selecting environmental conditions from the specified ranges and using these conditions to calculate thrust, speed of sound and cruise speed. Based on the distance, cruise speed and SFC value, the fuel consumption rate was calculated. For training and validation of machine learning algorithms, we generated at least 2000 fuel consumption rates. Matlab generates fuel consumption rates in pounds of fuel per hour (lb/hr). Based on the assumption that Jet A-1 fuel has a density of 0.804 kg/L, a conversion factor of 0.565034 was used to convert fuel consumption rates to liters per hour. The dataset contains 2000 hypothetical fuel consumption rates for a Boeing 787-9 Dreamliner equipped with a Trent 1000 engine. Based on a set of environmental conditions, flight parameters and assumptions about engine performance, fuel consumption rates were calculated. A conversion factor of 0.565034 can be used to convert the fuel consumption rates from pounds per hour (lb/hr) to liters per hour (l/hr). Furthermore, we have assumed that the fuel efficiency is 0.9.

In Table 3, actual engine data and flight time are compared with hypothetical fuel consumption rates generated in this study based on flight data. A variety of flight parameters and engine performance parameters are included in the data, including fuel flow rate, engine pressure ratio and interstage turbine temperature. The results of this comparison showed that the hypothetical fuel consumption rates generated were in line with the actual engine data and flight time, indicating that the data generated in this study was a good representation of real-world engine performance parameters. A fuel flow rate is measured in pounds per hour (lb/hr), while an engine pressure ratio has no dimension. Interstage turbine temperatures are measured in degrees celsius. It is worth noting that the data presented in Table 3 is based on actual engine data and flight time. As such, it represents a more accurate representation of fuel consumption rates for given flight conditions. This ensures that the fuel consumption rates are not being overestimated or underestimated and that they are reflective of the actual conditions experienced during the flight. Overall, the data collected from Table 3 is reliable and reflective of the actual conditions of the flight. This provides a valuable tool for pilots, engineers and other aviation professionals to use to accurately assess fuel consumption and adjust their plans accordingly. However, it is imperative to note that the actual fuel consumption rates may deviate from the hypothetical fuel consumption rates generated in this study, due to variations in the environmental and flight conditions. Therefore, it is recommended that the actual flight data presented in Table 3 be used as a benchmark for evaluating the accuracy of the hypothetical fuel consumption rates generated in this study.

Prediction results and performance evaluation

The Trent-1000 fuel consumption has been evaluated through machine learning algorithms and the performance of this system is being modeled through regression analysis. A regression analysis measures the performance of the model using the Mean Square Error (MSE), Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and R-Squared.

MAE: Mean Absolute Error is calculated by averaging differences between actual and predicted values. It is calculated the average of the residuals in the dataset.

MSE: Based on a data set with original and predicted values, the mean squared error represents the average of these differences. It is necessary to measure the variance of residuals. The Root Mean Square Error (RMSE) is the square root of the mean square error. A measure of rigidity is its standard deviation. The coefficient of determination of a linear regression model or Rsquared, indicates what proportion of the variance in the dependent variable is explained by the model. R squared is a scale-free score, so no matter how small or large a value is, it will be less than one. Using Mean Squared Errors (MSEs) and Root Mean Square Errors (RMSEs), we penalize large prediction errors compared to Mean Absolute Errors (MAEs). In contrast, RMSE is widely used to evaluate the performance of regression models along with other random models since it has the same units as the dependent variable (Y-axis). MSE makes mathematical operations easier when compared to nondifferentiable functions like MAE. RMSE is often used in many models to calculate the loss function because of its difficulty in interpretation. An accurate regression model has a lower MAE, MSE and RMSE. There should, however, be a higher R square value. A linear regression model's R Squared and adjusted R Squared are used to explain how well its independent variables explain the dependent variable's variability. When the number of independent variables increases, the R-squared value increases, resulting in redundant variables. This problem can be solved by adjusting R-squared. In our model, adjusted R squared is used to determine the number of separated variables based on the number of predictor variables. The adjusted R squared decreases if the additional variable does not significantly increase it. Due to the camp square, this is the case. The reason is that when comparing linear regression models, RMSE is a better choice than R-Squared. Machine learning evaluated datasets and Prediction model parameters are clearly represented in Table 4.

Table 4: Machine learning evaluated datasets and Prediction model parameters.

In all the algorithms, stepwise linear has the lowest RMSE, indicating that it estimates fuel consumption most closely to the real data. Hence, stepwise linear is the best algorithm for predicting fuel consumption based on the given data for predicting fuel consumption. In addition, it is important to consider other metrics, such as R-squared, MSE and MAE. Despite having the lowest RMSE value among all algorithms, stepwise Linear's R-squared value and MAE value are not the highest. Accordingly, linear SVMs may perform better overall in terms of fitting data and accurately predicting fuel consumption, as they have a higher R-squared value and a lower MAE value than stepwise linear models. As a result, while stepwise linear may be the best algorithm in terms of RMSE, it is important to consider multiple metrics when comparing the performance of different algorithms. Different algorithms may be more suitable based on the specific application and the trade-off between accuracy and computational complexity. Additionally, In Figures 9 to 12, the RMSE, R-Squared, MSE and MAE of the algorithms used in this study are compared. A regression model's accuracy and precision are commonly assessed using these metrics. The values of RMSE for each of the algorithms are presented in Figure 9. Fuel consumption is predicted most accurately by the algorithm with the lowest RMSE value.

Figure 9: Comparison of RMSE results for different applications.

For each algorithm, Figure 10 shows the R-squared values. Based on the R-squared value, we can determine how much of the variance in fuel consumption can be explained by the predictor variables. Data fit is better with an algorithm whose R-squared value is higher.

Figure 10: Comparison of R-Squared results for different applications.

Figure 11 shows the MSE values for each algorithm. In terms of fuel consumption, the MSE is the average squared difference between the predicted and actual values. Predictions with a lower MSE value are more accurate.

Figure 11: Comparison of MSE results for different applications.

The MAE values for each algorithm are presented in Figure 12. The MAE measures the average absolute difference between the predicted and actual fuel consumption values. Lower MAE values indicate better prediction accuracy.

Figure 12: Comparison of MSE results for different applications.

To evaluate the performance of the regression models in predicting fuel consumption, we plotted actual versus predicted fuel consumption for each algorithm. As can be seen in Figures 13 to 23, the actual fuel consumption values are plotted on the x-axis, while predicted fuel consumption values are plotted on the y-axis. For some algorithms, we can observe that the predicted fuel consumption values closely match the actual fuel consumption values, indicating good accuracy and precision. For other algorithms, the predicted fuel consumption values are more widely spread and they are not as closely aligned with the actual fuel consumption values, indicating a lower accuracy and precision. Furthermore, the algorithms performed differently depending on the range of fuel consumption values. For low to medium fuel consumption values, some algorithms performed well, but for high fuel consumption values, they performed poorly. Conversely, some algorithms performed well for high fuel consumption values, but poorly for low to medium fuel consumption values. Overall, the plots of actual fuel consumption versus predicted fuel consumption demonstrate how accurate and precise the regression models are at predicting fuel consumption. Model performance can be compared using these plots and areas for improvement can be identified.

A plot of actual versus predicted fuel consumption was used to evaluate the performance of each regression model. A x-axis plots actual fuel consumption values, while y-axis plots predicted fuel consumption values. We can observe that the predicted fuel consumption values closely match the actual fuel consumption values for some algorithms, indicating good accuracy and precision. Using other algorithms, the predicted fuel consumption values are more widely spread and they are not as closely aligned with the actual fuel consumption values, indicating a lower degree of accuracy and precision. A wide range of fuel consumption values impacted the performance of the algorithms. In low to medium fuel consumption values, some algorithms performed well, but in high fuel consumption values, they did poorly. In contrast, some algorithms performed well for high fuel consumption values, but poorly for low to medium fuel consumption values. A plot of actual fuel consumption versus predicted fuel consumption illustrates how accurate and precise the regression models are at predicting fuel consumption. With these plots, model performance can be compared and improvement areas can be identified. According to the plots in the following that compare the actual fuel consumption value compared to the prediction generated by the machine learning algorithm, the blue dots represent the predicted fuel consumption value derived by the algorithm. Furthermore, the blue dots must fit the line illustrated in all plots in order to achieve the best result and the least RMSE.

Figure 13: Fine Tree with RMSE of 16.725.

Figure 14: Linear SVM with RMSE of 4.9645.

Figure 15: Stepwise linear with RMSE of 1.0532.

Figure 16: Rational quadratic GPR with RMSE of 1.3261.

Figure 17: Narrow neural network with RMSE of 1.2514.

Figure 18: Medium neural network with RMSE of 1.2344.

Figure 19: Wide neural network with RMSE of 1.1495.

Figure 20: Bilayered neural network with RMSE of 1.0559.

Figure 21: Trilayered neural network with RMSE of 15.584.

Figure 22: Quadratic SVM with RMSE of 50.051.

Figure 23: SVM kernel with the RMSE of 50.051.

It is important to consider the limitations and potential areas for improvement in the prediction models when evaluating the performance of the machine learning algorithms for predicting fuel consumption in Table 4 and Figures 13 to 23. One potential limitation is the quality and quantity of training and validation data. If the data used for training is biased or incomplete, it can negatively impact the accuracy of prediction models. For example, if the data gathered for training only contains a certain type of customer demographic, the prediction models may not be able to accurately predict the behavior of customers from other demographics. Additionally, if the data collected for validation is not representative of real-world data, the prediction models could be over or under-fitted and not have high predictive accuracy. Therefore, adding more data and improving the quality of the data can potentially improve the accuracy of prediction models. Additionally, using more advanced data preprocessing techniques such as data normalization, feature scaling and outlier removal can also improve the accuracy of prediction models. Another potential area for improvement is the choice of machine learning algorithms and its hyperparameters. The performance of prediction models depends on the algorithm and its hyperparameters Therefore, fine-tuning the algorithm and its hyperparameters can potentially improve the accuracy of the prediction models. It is also pertinent to note that the prediction models are based on the assumption that flight conditions and engine performance parameters remain constant. However, in real-world scenarios, these factors can vary significantly. Any changes in these factors can affect the accuracy of prediction models. Therefore, it is recommended to periodically update and validate prediction models to ensure accuracy and reliability. In summary, while the machine learning algorithms presented in this study provide a valuable tool for predicting fuel consumption, it is critical to consider the limitations and potential areas for improvement in the prediction models. By continuously improving the quality of the data, fine-tuning the algorithms and their hyperparameters and validating the models periodically, the accuracy and reliability of the prediction models can be improved.

Comparing the predicted data vs. actual data

The predicted fuel consumption dataset we obtained after implementing stepwise linear regression had an RMSE of 1.0532. In comparing predicted fuel consumption values with actual fuel consumption data, we found that the two datasets were very close. To illustrate this point, we have created a table that compares actual fuel consumption with predicted fuel consumption. In the table, the actual fuel consumption values are presented in the first column, while the predicted fuel consumption values are presented in the second column. In the third column, you can see the absolute difference between the actual and predicted fuel consumption (Table 5).

Table 5: Actual fuel data comparison with predicted fuel data.

By far the overall error percentage is 0.45176%. For the first pair of values (125 and 121.9), the absolute difference is 3.1. Accordingly, the actual and predicted data are within 3.1 standard deviations. Based on the table, we can observe that the predicted fuel consumption values are very close to the actual fuel consumption values, with an average absolute difference of only 0.7 units (Figure 24). Accordingly, the stepwise linear regression algorithm was able to accurately predict fuel consumption with a high degree of precision. Ultimately, these results demonstrate the effectiveness of the stepwise linear regression algorithm in predicting fuel consumption. According to the close agreement between actual and predicted fuel consumption values, this approach can be applied with confidence in predicting fuel consumption in other scenarios and can assist operators in optimizing engine performance and fuel efficiency.

Figure 24: Will illustrate the actual vs. predicted fuel consumption data.

Significance of RMSE metric

For evaluating the accuracy of predictive models, Root Mean Squared Error (RMSE) is commonly used. Calculated by taking the square root of the average of the squared differences between the predicted and actual values, it measures the difference between the predicted and actual values. As a metric, RMSE provides a single number that represents the model's overall accuracy. The RMSE can be used to assess the accuracy of the stepwise linear regression model developed in this study to predict fuel consumption. A low RMSE value indicates that the model is capable of accurately predicting fuel consumption, whereas a high RMSE value indicates that the model is less accurate.

Using the RMSE value for the predicted fuel consumption data, the study determined that the stepwise linear regression model was successful in predicting fuel consumption accurately.

Discussion

In order to develop an analytical model that could predict fuel consumption on a Boeing 787-9 Dreamliner powered by Trent 1000 engines, we used a variety of data sources, including flight data, engine data, environmental data, weight and balance data and flight data from the aircraft. Our evaluation of several machine learning algorithms, such as linear regression, random forest, gradient boosting and artificial neural networks, revealed that stepwise linear regression provided the best accuracy in predicting fuel consumption with a 1.0532 RMSE. As a result, the stepwise linear regression algorithm effectively identifies the most significant predictors of the outcome variable in this case, fuel consumption. In this way, the algorithm can identify a subset of predictors which provide the most accurate fuel consumption prediction. Based on the results of our study, predictive analytics has the potential to optimize engine performance and fuel efficiency in the aviation industry. This knowledge can be applied to optimize engine performance and fuel efficiency, reduce fuel consumption and ensure high safety and performance standards. There are, however, some limitations to this approach. Based on the study, the predictive model may not be as accurate for other types of aircraft and engines. Additionally, the study did not take into account the impact of various weather conditions or airspace congestion on fuel consumption. In fact, it assumed clear weather conditions. Considering the impact of various weather conditions may be a significant factor in future research. Based on the close agreement between actual fuel consumption values and predicted fuel consumption values, it can be concluded that stepwise linear regression is capable of accurately predicting fuel consumption. This research also developed a predictive model that can be applied to other scenarios in the aviation industry. This enables it to become an integral part of industry operations. Study findings may be able to inform decisions related to aircraft routing, maintenance schedules, and fuel purchases, as well as lead to cost savings and environmental benefits from more accurate predictions of fuel consumption. Research in the future may investigate the impact of different factors on fuel consumption, such as weather conditions and airspace congestion or compare the performance of different predictive models. In order to determine whether the predictive model is generalizable, it may also be beneficial to test it on other types of aircraft and engines.

Conclusion

This study provides valuable insight into the factors that influence fuel consumption in Trent 1000 engines and that predictive analytics can be used to optimize engine performance and fuel efficiency by optimizing engine parameters in the aerospace industry. This research can be used to develop strategies and policies that will reduce fuel consumption and emissions, as well as ensure aircraft safety and reliability.

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