4.1. Comparison of BP-Based and BP-MRPSO Neural Networks
A backpropagation (BP) neural network was employed to predict and evaluate the ignition delay properties of hydrocarbon fuels with different carbon levels. The BP network learns the influence of temperature, pressure, and equivalence ratio on the ignition delay during training. Consequently, it effectively incorporates these intricate nonlinear connections inside the model.
To determine the optimal structure of the neural network, this study adopted a strategy combining grid search with 10-fold cross-validation. Initially, a multidimensional parameter space was defined, encompassing a variety of neuron number configurations from simple to complex, ranging from a single layer with 4 neurons to dual layers with up to 15 neurons each. A systematic grid search was employed within this parameter space to enumerate every conceivable neuron combination, from straightforward structures to more complex ones, ensuring comprehensive coverage of experimental data. Subsequently, rigorous evaluation of each neuron configuration was performed via 10-fold cross-validation. During each iteration, data was evenly divided into 10 subsets, with one subset serving as the validation set and the remaining nine used for training. This procedure was repeated 10 times, with a different subset selected as the validation data each time, to guarantee the fairness and accuracy of assessments. Furthermore, upon the completion of each cross-validation cycle, the average performance metrics of the model were computed, and the performance data for each configuration were documented.
Figure 6 provides a comparative analysis of the predictions made by the BP and BP-MRPSO neural networks.
Figure 6 displays a comparative analysis of the performance of two distinct neural network models in predicting the IDT of fuel. The horizontal axis represents the index of the dataset samples, and the vertical axis indicates the ignition delay time. The left side displays the prediction results of the conventional BP neural network, while the right side showcases the prediction results of the BP neural network model that integrates the MapReduce and PSO algorithms. Refs. [
6,
7] refers to a neural network configuration with 7 neurons in the first hidden layer and 6 neurons in the second hidden layer. Similarly, refs. [
15,
24] indicates a configuration of 9 neurons in the first hidden layer and 8 neurons in the second hidden layer, and refs. [
17,
25] represents 12 neurons in the first hidden layer and 11 neurons in the second hidden layer. The model configurations, in descending order, are Chaos et al.; Wu et al. [
25,
26], Pawan et al.; Zhukov et al., [
8,
27], and Wang et al.; Wu et al., [
11,
12], representing the number of neurons in each configuration. Within each picture, the model predicts the IDT with a blue line, whereas a green asterisk shows the experimentally measured IDT. The prediction accuracy increased by 25.34% when the neuron configuration was changed from [
25,
26] to [
8,
27]. This change also increased the average correlation coefficient of the BP-MRPSO model from 0.9745 to 0.9896. Furthermore, the accuracy of the model improved to 38.89%. Similarly, when the neuron configuration was changed to [
11,
12], the accuracy of model increased by 25.02%. The experiments indicate that among various configurations, the neuron configuration of [
8,
9] exhibits the best performance on the validation set, with its average error rate reduced to 2.75%. Simultaneously, its performance on the test set also demonstrates its superior generalization capability. The BP-MRPSO model has superior capability in capturing and learning the intricate features of the IDT compared to the conventional BP model. By examining the traditional BP model depicted in the figure, it becomes apparent that there is a noticeable discrepancy between the actual values (represented by green dots) and the predicted values (represented by the blue line). However, in the BP-MRPSO model on the right, there is a substantial improvement in the agreement between the two, indicating the optimized model has extraordinary accuracy and resilience. Through ongoing optimization of the hidden layer structure and neuron count, our model demonstrates enhanced predictive capability and resilience in handling intricate data, which is a key factor in correctly predicting fuel ignition delay.
The optimized BP-MRPSO neural network model can conduct synchronous studies on activation energy. Regarded as a core output variable, activation energy represents the energy barrier that must be overcome for a reaction to occur and is a key parameter for assessing fuel ignition characteristics. This model utilizes a variety of input features, including but not limited to temperature (T), pressure (p), and equivalence ratio (φ). By learning the relationships between temperature, pressure, equivalence ratio, and activation energy, the BP-MRPSO model reveals how activation energy varies under different conditions, thereby optimizing combustion conditions for efficient burning. For instance, the equivalence ratio, the proportion of fuel to oxidizer (such as air), directly impacts the completeness and efficiency of the combustion reaction. Under ideal equivalence ratio conditions, fuel can burn completely, releasing maximum energy. The BP-MRPSO model allows for the exploration of changes in activation energy under different equivalence ratios, analyzing how conditions of excess or insufficient fuel affect activation energy and combustion efficiency, providing a scientific basis for optimizing the fuel mixture ratio.
Compared to traditional experimental and theoretical computation methods, the optimized BP neural network demonstrates significant advantages. Traditional methods are often constrained by experimental conditions and simplified computational models, making it difficult to capture the complex nonlinear relationships in the combustion process. In contrast, the optimized BP neural network, with its multilayer architecture and strong nonlinear fitting capability, can accurately predict ignition delay times across a broader range of parameters and exhibit equally precise and in-depth predictions for activation energy. This capability enables the model not only to handle large volumes of data but also to accurately capture the complex dynamics of how activation energy changes with combustion conditions, providing deeper insights into the combustion mechanisms of fuels. Especially in analyzing the dependencies of ignition delay times and activation energy on factors such as temperature, pressure, and equivalence ratio, the optimized BP neural network, with its high flexibility and adaptability, can reveal subtle differences in the changes in activation energy during the combustion process, which are often challenging to achieve with traditional methods. The application of this method not only improves the accuracy of predictions but also significantly enhances the efficiency and depth of research, offering a powerful analytical tool for optimizing aviation fuels and enhancing combustion efficiency.
In practical aeronautical engineering applications, the optimization model of hydrocarbon fuel ignition characteristics based on BP neural network can provide accurate combustion dynamics prediction for engine design, optimize combustion efficiency, and improve energy utilization. The model can accurately predict the fuel ignition characteristics in various flight conditions by examining the intricate reaction process. Additionally, it may offer valuable guidance for designing engine combustion chambers and help to develop more effective fuel management systems. The model can forecast combustion behavior in extreme situations, offering extra confidence in ensuring flight safety. Hence, this model improves the field of aeroengine design and offers vital data to support the future development of aviation fuels.
4.2. Analysis of Experimental and Prediction Results of BP-MRPOS
For data on the ignition characteristics of various hydrocarbon fuels,
Figure 7 compares the experimental results with the predicted results.
The following presentation displays the prediction results of the BP neural network model, which integrates MapReduce and PSO algorithms. Jet A fuel and aviation kerosene are utilized as illustrative instances. By comparing the experimental values with the predicted values, it is evident that the BP-MRPSO neural network accurately predicts the IDT of hydrocarbon fuels across various conditions.
Figure 7a,e display the experimental and projected values of the IDT of the mixture at various pressures, assuming an equivalence ratio φ of 1. The data points collected at various pressure levels clearly demonstrate the substantial impact of pressure on the ignition process. The data points collected at various pressure levels clearly demonstrate the substantial impact of pressure on the ignition process.
Figure 7b,f display the measured and estimated IDTs for various oxygen concentrations for an equivalence ratio φ of 1. The correlation between the rise in IDT and the decrease in ignition temperature can be seen by the relationship with a 1/T increase. The IDT of Jet A fuel and aviation kerosene decreases as the oxygen concentration increases. This means the fuel oxidation reaction rate is enhanced when more oxygen is available, resulting in faster ignition. The IDTs of experimental and predicted values for various equivalence ratios are displayed in
Figure 7c,g. The IDT of the combination with a mixture equivalence ratio φ of 1.5 is greater than that of the correct ratio mixture, indicating that the fuel concentration also plays a role in the igniting process.
Figure 7d,h demonstrate the relationship between fuel concentration and IDT at an air-fuel ratio φ of 1. The results indicate that the IDT decreases when the fuel concentration increases regardless of the equivalence ratio remaining the same.
Table 5 shows some of the data comparing the experimental values with the predicted values based on the BP-MRPSO model, where the absolute error indicates that the difference between the predicted values and the actual values does not exceed 6 μm at most, and the error is controlled in a relatively small range. The relative error is less than 5%, which indicates that the prediction model can predict the experimental values with a relatively high degree of accuracy. Based on the absolute and relative errors, this data set shows that the prediction model has good accuracy and reliability.
Based on the information in
Table 5, the computed accuracy R
2 of the projected ignition characteristics is 90% or above in all cases. The prediction accuracy of the IDT is influenced by multiple parameters, as indicated by the trend of the curves in
Figure 7. Combustion is an intricate chemical reaction process that includes numerous reaction stages and intermediate species. The speeds of these reaction steps frequently fluctuate with slight variations in temperature, pressure, and mixing ratio. Furthermore, slight deviations in experimental parameters, such as the precision of temperature regulation, the precision of pressure assessments, and the uniformity of fuel–air blending, can significantly influence the ignition delay. Furthermore, slight disparities in the chemical makeup of the fuel between different batches might also result in changes in igniting characteristics. Collectively, these elements contribute to the ignition process, rendering it challenging for even the most refined model to comprehensively encompass all variances, thereby restricting further enhancements in forecast precision.