Startseite Analysis of digital intelligent financial audit system based on improved BiLSTM neural network
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Analysis of digital intelligent financial audit system based on improved BiLSTM neural network

  • Xincai Zhu EMAIL logo
Veröffentlicht/Copyright: 3. Juli 2025
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Nonlinear Engineering
Aus der Zeitschrift Nonlinear Engineering Band 14 Heft 1

Abstract

Traditional auditing methods have difficulties in detecting various financial issues hidden in massive amounts of data. With the continuous advancement of deep learning and digital technology, new audit methods have been provided for computer auditing. Therefore, in order to achieve intelligent analysis and processing of audit reports, this study innovatively applies the convolution operation of convolutional neural networks to the forward and backward layers of bidirectional long short-term memory networks, obtaining more accurate feature recognition and prediction results. Meanwhile, by introducing radial basis functions for nonlinear mapping of the data space, the model’s ability to fit complex data is enhanced, thereby improving the analytical capability of the digital intelligent financial audit system. The experimental results show that the comprehensive average accuracy of the improved algorithm reaches 92.31%, and the F1-score of the reconciliation function reaches 80.55, which are significantly higher than the other four algorithms. This indicates that the digital intelligent financial audit model proposed in this study can accurately analyze financial audit data, proving that it can comprehensively process various types of financial data and effectively improve the efficiency of modern enterprise audit data analysis.

Keywords: financial analysis; BiLSTM; CNN; RBF; data prediction

1 Introduction

The function of audit is to supervise the authenticity, legitimacy, and efficiency of the finance, financial revenue, and expenditure of the audited entity through the inspection of the financial data [1,2,3]. In the environment of information technology and big data, financial fraud means are more hidden, and various financial problems are hidden in large amount of data [4,5]. The traditional audit method based on sampling has difficulty in finding these problems, and can no longer meet the actual needs of current audit work. In order to adapt to the changes in the auditing business under the information environment, it is necessary to adjust the auditing methods. Against the backdrop of rapid development of computerized accounting, digital intelligent financial auditing (DIFA) has gradually been widely applied in various enterprises [6,7,8]. Financial auditing plays an indispensable role in both enterprises and government departments, and is a necessary condition for maintaining the normal operation of organizational structures. In the current fiercely competitive market environment, more and more enterprises are adopting intelligent accounting and financial analysis and forecasting to propose corresponding strategies for their development. At the same time, DIFA can achieve unified planning and processing of financial accounting and expense reimbursement for different fields and branches, and can also improve work efficiency to a greater extent, saving time and costs [9,10,11]. Thus, it can promote enterprises to better comply with current accounting standards and achieve integrated development. However, in the field of financial audit, how to improve the interpretability of the improved bidirectional long short-term memory (BiLSTM) neural network, especially for specific decisions in financial audit (such as anomaly detection, risk assessment, etc.), is an important research gap. At the same time, although the improved BiLSTM network has a strong ability of sequence modeling, how to effectively deal with these data quality problems and improve the accuracy and robustness of the model is still a difficult problem that has not been completely solved [12,13,14]. Therefore, it is of great significance to develop a DIFA system with simple operation, multiple data analysis methods, comprehensive processing of various types of financial data and lasting management of audit results. However, the current DIFA system is not perfect on the whole, and some models have problems such as too local feature extraction, low prediction accuracy, low recall rate, and low adjustment function value.

In response to the above situation and problems, this study innovatively adopts a convolutional neural network (CNN) based on BiLSTM network, and combines it with radial basis functions (RBFs) to construct an improved algorithm for feature extraction and data prediction. The contribution of this study lies in proposing a method that combines BiLSTM-based CNN with RBFs help to capture key features in financial data more comprehensively, improving the accuracy and efficiency of data prediction. This study can make practical contributions to promoting the further development of DIFA systems, and provide more reliable and efficient financial audit solutions for enterprises and organizations.

2 Review of the literature

In the field of digital finance, many domestic and foreign scholars have conducted research on the prediction and analysis methods of financial difficulties and crises, and have achieved some inspiring results. Among them, the study of financial risk forecasting method provides ideas and technical reference for the analysis of DIFA system in this study. Sun et al. used time-weighted machine learning method for dynamic financial distress prediction, combined with expert voting methods based on error analysis and time series for further processing. The experimental results of sample testing showed that the method is more accurate for time-varying dynamic financial distress prediction [15]. Kalaiselvi et al. added additional weighted numerical updates to the traditional BP neural network to be able to accurately predict stock prices and indices, which was used to adjust the balance point between the backward learning-based algorithm and back propagation (BP) neural network. The experimental results found that the improved method has more accurate prediction performance [16]. Munoz-Izquierdo’s team combined accounting and auditing data and developed a logit prediction model to accurately predict the company’s financial distress and crisis [17]. Shetty and Vincent collected samples of bankrupt companies and an equal number of well performing companies, developed two binary logistic regression models M1 and M2 with financial and non-financial variables, and tested the predictive diagnostic ability of the models through sensitivity, specificity, and annual accuracy. The results indicated that the newly developed model has better predictive and diagnostic capabilities [18]. Gunawardana developed a new neural network to analyze panel regressions considering 5 years cross-sectional data of the selected sample of companies and was able to determine the relationship between leverage, price/earnings ratio, and the significant relationship between the prediction of the company’s financial distress, and the results showed that the model has a high predictive accuracy [19]. Henrique et al. used multiple learning models to predict financial market prices using a bibliographic survey technique to analyze the consistency of sample data for different indicators, and finally concluded that support vector machine has better results conclusion [20]. Nguyen et al. used autoregressive-based approach to predict the future financial position of stock exchange traded companies using factor analysis and F-score analysis as a benchmark for prediction and finally concluded that the accuracy of the prediction results is high [21]. To improve the accuracy of financial risk prediction, Wei et al. used a transformer model to integrate multimodal data and identified potential high-risk events in the financial market by combining different data sources. The results verified the advantages of this model in processing complex multimodal information, providing an effective method for improving financial risk management [22].

BiLSTM model is mainly used in the task of time series prediction. The improvement method and application of this model provide further technical reference for this study. Gong’s team extracted disease-related entities from autism-related biomedical literature by using BiLSTM as well as conditional random field models to perform deep learning. Experimental results showed that the method was evaluated through the GENIA corpus and obtained an F-score of 76.81%, providing a significant improvement in the overall performance of prediction [23]. Gan et al. proposed a multi-channel extended joint structure of CNN-BiLSTM model for analyzing the sentiment tendency of Chinese texts. The structure could extract both raw contextual features and multi-scale high-level contextual features, and an attention mechanism including local attention and global attention was employed to further distinguish the differences of features. The results of the study showed that the method improved the accuracy and F1-score by more than 3.416% and 4.324% points, respectively, compared to the traditional method on the NLPCC2017-ECGC corpus [24]. Bou-Rabee et al. used a deep learning approach combined with BiLSTM to combine solar irradiance data for extracting and understanding symmetric hidden data patterns and correlations, which are then used to predict future solar irradiance. Simulation results showed that the attention-based BiLSTM model outperformed other deep learning networks in solar irradiance prediction analysis [25]. Liu et al. proposed a BiLSTM deep complex network combined with automatic modulation identification to extract modulated signal features containing phase and amplitude information. The BiLSTM layers were connected to the disease to build a memory model based on the extracted features. Experimental results showed that the model can achieve 90% recognition rate for 11 modulated signals when the signal-to-noise ratio exceeds 4 dB [26]. Zhang et al. proposed a hybrid CNN-BiLSTM model to predict PM2.5 concentrations in the near future. The study used a sliding window approach for preprocessing and divided the corresponding data into training, validation, and test sets. The parameters of this network structure were determined by the minimum error in the training process, including the size of convolution kernel, activation function, batch size, exit rate, and learning rate. The results of the study showed that the prediction accuracy of this network is significantly higher than several other conventional algorithms [27]. From the improvement and application results of the BiLSTM model by the above scholars, it can be seen that the prediction and recognition performance of the model can be further improved by combining deep learning. This provides ideas for optimizing the BiLSTM model based on the characteristics of financial auditing in this study.

To sum up, researchers at home and abroad have conducted a lot of exploration work in the perspective of prediction and identification, and have also carried out in-depth discussion on the improvement methods of BiLSTM model, which can improve the accuracy and efficiency of audit and provide the basis for digital audit. However, in practical applications, there are still insufficient performance caused by computational complexity and storage requirements for large-scale financial data processing, and the accuracy needs to be improved. Therefore, this study combines CNN with BiLSTM, and adds RBF on this basis for feature identification and extraction as well as analysis and prediction in digital financial audit. The innovation of this research lies in that through the feature extraction capability of RBF-CNN, the model can more accurately identify and capture key patterns in financial data, improve the accuracy and robustness of the model, and thus overcome the shortcomings of current research, and further help enterprises to improve financial performance and reduce risks more effectively.

3 Application of RBF-CNN-BiLSTM in intelligent financial auditing

3.1 Model construction of CNN-BiLSTM

When analyzing the DIFA system, it is necessary to conduct a reasonable analysis of the large amount of complex data, that is, to identify and extract data features, and make predictive analysis based on the features. For this purpose, a CNN BiLSTM model was constructed. First, conduct structural analysis on LSTM. The processing mode of LSTM can solve the long sequence dependence problem in recurrent neural networks and can solve part of the gradient disappearance problem. The cell structure of LSTM is shown in Figure 1.

Figure 1 Structure diagram of LSTM cell.
Figure 1

Structure diagram of LSTM cell.

The LSTM performs learning, and the activation function uses the Tanh function. The expression of the memory cell of the LSTM is shown in Eq. (1).

(1) C t = C t − 1 f t + i t C ˜ t ,

where C t is the memory cell. C t − 1 denotes the last moment memory cell. f t is the forgetting gate. i t is the input gate. C ˜ t is the candidate vector, and t represents a moment in the operation. The output of the LSTM at t can be expressed as shown in Eq. (2) by combining the memory cells to learn the hidden state value at the moment before forgetting and updating the hidden state information.

(2) LSTM ( H t − 1 , H t ) = h t ,

where h t is the hidden layer vector and H is the output of the LSTM layer. For time series related prediction, to be able to improve the accuracy of the analysis and prediction, the positive directional information pattern of the time series data is integrated, i.e., the BiLSTM is constructed. The BiLSTM consists of two LSTM layers, each of which consists of several neurons and the number of neurons in both layers is equal [28,29].

The gate control units in BiLSTM include forget gates, input gates, and output gates, which play a crucial role in BiLSTM. The function of the forget gate is to determine which information should be forgotten from memory units. It uses the sigmoid activation function to selectively forget unimportant information. The function of the input gate is to determine which new information should be stored in the memory unit. It combines the sigmoid activation function and tanh activation function. The sigmoid part determines which values need to be updated, while the tanh part generates new candidate value vectors. The output gate determines the value of the next hidden state, which generates the output of the current time step and passes it on to the next time step. It uses the sigmoid activation function to determine which information should be output. As a result, the BiLSTM model can better capture and maintain long-term dependencies, avoiding the gradient vanishing problem in traditional RNNs. BiLSTM combines forward and backward output information, commonly achieved through concatenation and weighted averaging, allowing the model to obtain richer representations from contextual information in two different directions. In the forward LSTM layer, the forward data are first obtained for forward input, and then the corresponding output data are obtained according to the oblivious layer and other processing. In the reverse LSTM layer, the previously obtained data are input in reverse, and the corresponding reverse output data are obtained and reversed again, and then the final output of the reverse LSTM layer is obtained. After obtaining the respective outputs of the forward and the reverse LSTM layers, these outputs are linearly superimposed with certain weights to obtain the final BiLSTM output [30]. The structure of the BiLSTM is shown in Figure 2.

Figure 2 Structure diagram of BiLSTM.
Figure 2

Structure diagram of BiLSTM.

Based on BiLSTM, a CNN-BiLSTM network is formed to enable better feature extraction and recognition. The input layer is a pixel matrix, which is used to obtain a feature map with geometric characteristics after simple operations such as scale unification, data normalization or dimensionality reduction of the sample data. The convolutional layer contains multiple feature data, and the global information is obtained by learning the feature representation, using local perception to process each corresponding feature and then using synthesis operations to process the local area. Local perception makes full use of the relationship between the size of feature relevance and its distance in the data, which makes the number of weights in the convolution layer reduced, so that the training of CNN is simpler, and the convolution process is more stable because the convolution kernel weights do not change in size due to the sharing of parameters during the convolution process. After the output of the convolutional layer is input to the activation layer, the activation function performs a nonlinear mapping, which allows the convolutional layer to extract more abstract features and thus improve the functionality of the CNN. The activation function generally uses the ReLU function and the Sigmoid function [31]. The pooling layer is between the two convolutional layers and makes the size of the parameter matrix effectively reduced. The number of parameters in the fully connected layer is also reduced. The pooling operation usually consists of maximum pooling and average pooling. The overall structure of CNN is shown in Figure 3.

Figure 3 Schematic diagram of CNN structure.
Figure 3

Schematic diagram of CNN structure.

The essence of the convolution operation is the process of extracting valid features from the initial feature map by convolutional layers. Assuming that the initial feature map of each convolutional layer with input is x j , the convolution operation is shown in Eq. (3). In Eq. (3), f ( x ) is the activation function, M j represents the set of initial feature maps, i is the matching result, k i j is the input of the i th initial feature map and the output of the j th initial feature map of the convolutional layer.

(3) x j l = f ∑ i ∈ M j x i l − 1 ⋅ k i j l + c j .

When the weights and updated values of all neurons on the l layer need to be solved, the sensitivity magnitude at all nodes needs to be solved first, and the value is noted as θ . The sum of the sensitivity values defined by the interest from the connection layer l to l + 1 is θ j l + 1 , multiplied with the corresponding weights W , and then the activation function is obtained by taking the inverse of f ( u l ) to obtain Eq. (4). In Eq. (4), u is the input value of the neurons in the l layer.

(4) θ j l = θ j l + 1 W j l + 1 ⋅ f ( u l ) .

A modified linear activation is applied to the CNN structure, and the linear activation equation is shown in Eq. (5). The kernel function of Eq. (5) places restrictions on the input. Using this 1 × 1 convolution allows the feature map to be downscaled to expand the application scale of the network, increases the width and depth of the CNN, and improves the application performance of the network.

(5) ψ ( x ) = x , x > 0 0.1 x , x ≤ 0 .

The convolutional operation of CNN runs in the forward and reverse layers of BiLSTM to obtain more accurate feature recognition and prediction results through bi-directional convolutional operation and forgetting. The CNN-BiLSTM model combines 1D CNN structures with attention mechanisms to complete the BiLSTM classification task. The specific structure is shown in Figure 4. The CNN structure consists of multiple 1D convolutional layers, activation layers, and pooling layers stacked together. Researching a fixed stacking layer of 3, changing the size of the convolutional kernel can enhance the CNN’s ability to extract features. In order to improve the convergence of the model, a BN layer is added after the 1D convolutional layer. During model training, the Adam optimizer is used for parameter updates.

Figure 4 Structure diagram of CNN-BiLSTM model.
Figure 4

Structure diagram of CNN-BiLSTM model.

3.2 CNN-BiLSTM algorithm improvement with fused RBF

CNN-BiLSTM algorithm has many advantages, such as accurate feature recognition and high efficiency of feature extraction. However, CNN-BiLSTM still has some defects, such as the possibility of falling into local convergence and the lack of global characterization in feature extraction and recognition. To improve the defects of CNN-BiLSTM algorithm, the RBF network is fused into the algorithm to form RBF-CNN-BiLSTM algorithm. RBF is mainly used in the intermediate layer of neural networks as the activation function of the hidden layer neurons, which is characterized by the fact that any one of the training inputs produces the corresponding output only in a local region of the input space. The RBF network can be used to solve the problems of nonlinear classification, function approximation, and the core of which lies in the ability to perform the nonlinear mapping of the data space to enhance the model’s ability to fit complex data. In the CNN-BiLSTM algorithm incorporating RBF, the introduction of RBF aims to further enhance the model’s ability to deal with nonlinear data, especially in feature extraction and long-term dependency capture. RBF can be used as a powerful nonlinear mapping tool, combining the spatial features extracted by the CNN and the time series information captured by the BiLSTM, to enhance the model’s ability to fit the complex data structure and function approximation in the field of financial auditing through nonlinear transformation. This approach can enhance the performance of the financial auditing system in handling high-dimensional data analysis, discovering potential risk patterns, and improving auditing efficiency and accuracy.

RBF network is a forward-looking network, which contains three layers. Usually, the first layer is the input layer, the second layer is the single-hidden layer, and the third layer is the output layer. The input layer consists of signal neurons formed by connecting the network to the external environment, and the dimensionality of the input signal determines the number of neurons. The number of layers in the single-hidden layer is determined by the number of layers required to describe the object, and the neurons are a non-negative nonlinear function with radially symmetric decay at the center point. The output layer, i.e., the corresponding response to the input model, is used to obtain the output information [32]. The overall structure of RBF is shown in Figure 5.

Figure 5 Basic structure diagram of RBF.
Figure 5

Basic structure diagram of RBF.

The excitation function of RBF is usually a Gaussian function, which defines a monotonic function of the Euclidean distance r between any point in the space x to a center c , whose Gaussian function is shown in Eq. (6).

(6) h ( x ) = exp − ( x − c ) 2 r 2 .

The Gaussian function can calculate the distance between the input and the center of the function, and this distance is used to calculate the weight, which is shown in Eq. (7), where a , b , and c are customizable real constants and a > 0.

(7) f ( x ) = a e − ( x − b ) 2 2 c 2 .

RBF uses a gradient descent method for learning and defines the objective as shown in Eq. (8), where c is the number of neurons in the output layer, t k denotes the desired output value of the k th output neuron, and z k denotes the actual output value of the k th output neuron.

(8) E = 1 2 ∑ b = 1 c ( t k − z k ) 2 .

The actual output value of the k th output neuron is calculated as shown in Eq. (9), where m is the number of neurons in the single hidden layer, W k j denotes the weights from the hidden layer to the output layer, x is the input sample value, and C j denotes the data center of the j th hidden layer neuron.

(9) z k = ∑ j = 1 m W k j ⋅ ϕ ( ∣ x − C j ∣ ) .

The RBF network learning in the hidden layer mainly considers the data centers of each basis function and the normalization constants, and in the output layer mainly considers the weights of the output nodes [33]. The RBF consists of two main parts, in order, the connection from the input layer to the hidden layer, and the connection from the hidden layer to the output layer. The first layer performs a nonlinear mapping of the input vector to the input data in the n dimensional space to the m dimensional space, as shown in Eq. (10).

(10) h j = f j ( x 1 , x 2 , … , x n ) ,

The value of j in Eq. (10) is a positive integer between 1 and m . The second layer is then calculated by linear weighted summation using the output of the neurons in the hidden layer to obtain the output of the output layer, as shown in Eq. (11).

(11) y m = ∑ j m w j h j ,

where w j denotes the weight of the connection from the hidden layer to the output layer. After determining the body of the whole neural network, the parameters need to be adjusted using RBF, and the neuron centroids of the hidden layer of the network need to be continuously learned in order to be adjusted, while the parameters need to be adjusted with reference to the connection weights of the hidden layer to the output layer, etc. [34]. Parameter selection should be based on the performance metrics of the whole network, and the performance metrics function of the neural network is shown in Eq. (12).

(12) E k = 1 2 ( y k − y m , k ) 2 ,

where y k is the actual output of the target object at the time of k and y m , k is the output of the RBF in space. After that, gradient descent is performed again to make the model parameter estimates corrected based on the negative gradient direction of the performance indicator function, so that the indicator function is gradually minimized. The calculation is shown in Eq. (13).

(13) ∂ y m , k ∂ u k = ∑ j w j h j c 1 j − x 1 b j 2 ,

where u k is the first output of the RBF at the time of k , ∂ denotes the partial derivative, c 1 j denotes the centroid value of the j th hidden layer neuron, b j denotes the normalization constant, and x 1 is the width of the RBF function. After that, the centroid of the whole RBF-CNN-BiLSTM is selected according to the RBF, and the distance of the data to the centroid is plotted against the activation state as shown in Figure 6.

Figure 6 Relationship between distance from centroid and activation state.
Figure 6

Relationship between distance from centroid and activation state.

Usually, data center selection is done randomly in the sample or using multiple clustering centers in the training sample set [35]. To be able to run the whole network algorithm smoothly and to be able to analyze the complex data in the DIFA system, the study uses a center selection method based on association rule data centers. In the first stage, the various factors that have a strong correlation with feature identification as well as analytical prediction are obtained, mainly support and confidence. The larger values of support and confidence represent the prediction results that are closer to the sample values. Therefore, the data center location of neurons should be selected as close as possible to the sample input values with strong correlation to enhance the learning efficiency of the algorithm and the accuracy of feature extraction and prediction [36].

After selecting the data center, the nonlinear single-input single-output system is modeled with the RBF-CNN-BiLSTM model of NARMAX [37]. The excitation function of the hidden layer is a Gaussian function, at which point the expression is shown in Eq. (14), where R j ( x ) is the RBF, x is the input of the whole neural network, and n is the number of nodes in the input layer.

(14) R j ( x ) = exp − ∥ x − c j ∥ 2 2 b j 2 , j = 1 , 2 , … , n .

Prior to sample training, all sample data need to be pre-processed. First, the data are downscaled, and a normalization algorithm is added to the data downscaling operation to adjust the data feature values to a uniform range [38,39]. The expression of the standardization algorithm is shown in Eq. (15), where a ⌢ p is the normalized data feature value, a p is the original feature, a ¯ p is its mean value, and S p is its variance.

(15) a ⌢ p = ( a p − a ¯ p ) / S p .

For larger datasets, iterative training is used for processing. In each training iteration, the study first selects a portion of data from the dataset for training, and then updates the model parameters. For smaller datasets, research expands the dataset by adding existing data. This method mainly makes minor changes to the data, without significantly altering the model output. In addition, to address data privacy and security issues during the financial audit process of the model, research has been conducted on encrypting financial data before data processing, using secure encryption algorithms and key management systems to prevent unauthorized access or tampering during data transmission and storage. At the same time, it needs to regularly backup financial data and securely store the backup data offline and away from office areas. It should be noted that the entire financial audit and model application process follows applicable laws, regulations, and industry standards, which can effectively protect user privacy and data security.

4 Prediction results and analysis of sample data under multiple algorithm testing

4.1 Parameter sensitivity test results

By adjusting hyperparameters such as learning rate, iteration times, layer size, and batch size, the performance of the proposed RBF-CNN-BiLSTM model in the dataset is observed to help optimize model performance. The study first preprocessed the financial audit data. After the data entry was completed, data verification work was carried out, with a focus on account balance, financial account classification, and data consistency. Then, data correction was performed and any errors or anomalies that occur were corrected promptly. Error correction methods include modifying data or re inputting data. During the error correction process, detailed records of the reasons for the errors should be kept, and corresponding approval processes and authorization mechanisms should be established to ensure the accuracy of the data. At the same time, the study integrated financial data from multiple sources to ensure data consistency and integrity, avoiding data redundancy or inconsistency. For the handling of missing values in financial datasets, when the number of missing values is small and there is no clear pattern, the study directly removes these missing values. But for situations where there are many missing values or clear patterns, interpolation is used to fill in the missing values, mainly through mean, median, or pattern. The reason is that the interpolation method is very simple and efficient, the calculation cost is low, and does not require complex models or hyperparameter tuning, and the use of this method can minimize the consumption of computing resources. After data preprocessing is completed, we select 60% of the data in the dataset as the training set, 15% of the sample data as the validation set, and 25% of the data as the test set. Through such data partitioning, the stability and consistency of the model can be better validated, and the generalization ability of the model can be truly evaluated. Evaluating the model in two different test subsets can further validate its adaptability to different data distributions. The parameter sensitivity test results of the RBF-CNN-BiLSTM model are shown in Table 1. From Table 1, it can be seen that the proposed model can achieve good convergence speed and performance at moderate learning rates (such as 0.001 or 0.01). The number of iterations is usually around 103, which can balance underfitting and overfitting. When the number of BiLSTM units is around 128, higher accuracy is achieved. Therefore, the RBF-CNN-BiLSTM model parameters are set according to this situation to achieve optimal performance.

Table 1

Results of parameter sensitivity test

Parameter Value Train loss Validation loss Train accuracy (%) Validation accuracy (%) Changing situation
Learning rate 0.0001 0.35 0.38 88.26 85.15 Slow convergence
0.01 0.18 0.23 94.79 92.31 Best
0.1 0.25 0.57 92.82 75.9 Overfitting
Iterations 56 0.32 0.36 88.37 86.05 Under-fitting
103 0.18 0.21 94.75 92.30 Best
154 0.15 0.24 96.2 90.80 Overfitting
Number of BiLSTM layer units 64 0.24 0.30 92.43 88.57 Weak
128 0.18 0.22 94.71 92.36 Best
256 0.22 0.28 95.69 90.74 Increased computational burden
512 0.28 0.35 96.86 87.52 Overfitting

4.2 Performance testing

This study proposes a CNN-BiLSTM model for DIFA and further improves it through RBF. To verify the effectiveness of the model, common metric tests were conducted. In addition to the RBF-CNN-BiLSTM algorithm proposed in this study, the same experimental comparisons were conducted using CNN-LSTM, CNN-BiLSTM, BiLSTM, and faster CNN to analyze whether the improved algorithm proposed in this study has performance advantages. The testing indicators mainly include accuracy, recall, and F1 score. Accuracy is the ratio of the number of samples correctly classified by a model to the total number of samples in a given test dataset. Recall rate refers to the proportion of correctly predicted samples among all actual positive samples predicted by the classifier. The F1 score considers both accuracy and recall, aiming to achieve both the highest score and balance.

The accuracy results of the two datasets obtained from the testing of each algorithm are shown in Figure 7. In Figure 7, the accuracy of the RBF-CNN-BiLSTM algorithm was significantly higher than the other four algorithms in dataset 2, while the size relationship could not be clearly seen in dataset 1. Combining the average results of the two datasets, the average accuracy of the RBF-CNN-BiLSTM algorithm was 92.31%, while the accuracy of the four algorithms, CNN-LSTM, CNN-BiLSTM, BiLSTM, and faster-CNN, was 81.36, 88.53, 80.81, and 86.32%, respectively, with the accuracy of the CNN-BiLSTM close to that of the improved algorithm, and the other three algorithms had a large gap. According to the significance analysis, the overall average results were significantly different from those of the other four algorithms, so the RBF-CNN-BiLSTM algorithm has a significant performance advantage in terms of overall accuracy of prediction.

Figure 7 Accuracy rate results of two datasets. (a) Dataset 1 and (b) Dataset 2.
Figure 7

Accuracy rate results of two datasets. (a) Dataset 1 and (b) Dataset 2.

The precision results of the two datasets obtained from the testing of each algorithm are shown in Figure 8. From Figure 8, the precision of the RBF-CNN-BiLSTM algorithm was significantly higher than the other four algorithms in the two datasets. The average precision of RBF-CNN-BiLSTM reached 79.54% for both datasets, which was significantly different from the other four algorithms, indicating that the RBF-CNN-BiLSTM algorithm has a significantly superior performance in precisely distinguishing the positive example data from the negative example data.

Figure 8 Precision results of two sets of data sets. (a) Dataset 1 and (b) Dataset 2.
Figure 8

Precision results of two sets of data sets. (a) Dataset 1 and (b) Dataset 2.

The recall results for the two datasets obtained from the testing of each algorithm are shown in Figure 9. From Figure 9, the overall recall rate of the RBF-CNN-BiLSTM algorithm was higher than that of the other four algorithms, and the overall average recall rate reached 65.93% in a comprehensive view. According to the significance result analysis, the overall average recall rate of the RBF-CNN-BiLSTM algorithm was significantly different from the other four algorithms, indicating that the improved algorithm has a significant performance advantage in the accuracy of positive example data recognition.

Figure 9 Recall rate results of two datasets. (a) Dataset 1 and (b) Dataset 2.
Figure 9

Recall rate results of two datasets. (a) Dataset 1 and (b) Dataset 2.

The results of the F1-score of the reconciliation function for the two datasets obtained from the testing of each algorithm are shown in Figure 10. As seen in Figure 10, the F1-score of the RBF-CNN-BiLSTM algorithm was significantly higher than that of the other four algorithms. In the overall results of both datasets, the average F1-score of the RBF-CNN-BiLSTM algorithm reached 80.55, while the F1-score of the four algorithms of CNN-LSTM, CNN-BiLSTM, BiLSTM, and faster-CNN was 72.56, 61.12, 71.46, and 69.89, respectively. According to the results of the significance analysis, the F1-scores of the reconciliation function of the improved algorithm were significantly different from the other four algorithms, indicating that RBF-CNN-BiLSTM has a significant performance advantage over the other four algorithms in terms of comprehensive performance, and is not prone to the imbalance between recall and accuracy.

Figure 10 F1-score results of two datasets. (a) Dataset 1 and (b) Dataset 2.
Figure 10

F1-score results of two datasets. (a) Dataset 1 and (b) Dataset 2.

Error analysis is an important means of evaluating and improving model performance. For this purpose, a detailed error analysis was conducted in the study. First, the prediction accuracy is evaluated using Mean Absolute Percentage Error (MAPE), which reflects the difference between the predicted value and the actual value. Figure 11 shows the MAPE results obtained by each algorithm in two datasets. From Figure 11, it can be seen that the average MAPE value of the RBF-CNN-BiLSTM algorithm in both sets of data is 0.3243%, and the trend of change between different groups is relatively stable, which is better than the MAPE values of the other four algorithms. This indicates that the RBF-CNN-BiLSTM algorithm has better error control performance in testing.

Figure 11 MAPE value test results in two datasets. (a) Dataset 1 and (b) Dataset 2.
Figure 11

MAPE value test results in two datasets. (a) Dataset 1 and (b) Dataset 2.

Further error analysis was conducted through root mean square error (RMSE), mean absolute error (MAE), and determination coefficient (R 2). RMSE is the square root of mean square error, used to measure the difference between predicted and true values. MAE is the average of the absolute sum of the difference between the predicted value and the true value, which provides a visual understanding of the prediction error. R 2 is an indicator that measures the degree of variability of explanatory variables in a model, with values ranging from 0 to 1. The larger the value, the better the fit of the model. Meanwhile, the study utilized over 1.4 million economic texts as training data for the model. Use 2000 audit question texts extracted from the audit report as experimental data, and divide them into training and testing sets in an 8:2 ratio. Table 2 shows the test results of five methods in this dataset. From Table 2, it can be seen that the RMSE and MAE values of RBF-CNN-BiLSTM are 2.121 and 1.453, respectively, with the lowest RMSE and MAE, and the highest R 2 value, indicating that this method has the smallest prediction error and better performance.

Table 2

Error analysis results of five prediction methods

Methods RMSE MAE R 2
Faster-CNN 2.563 1.879 0.828
BiLSTM 3.026 2.154 0.759
CNN-LSTM 2.847 1.965 0.792
CNN-BiLSTM 2.684 1.926 0.801
RBF-CNN-BiLSTM 2.121 1.453 0.911

4.3 Ablation experiment

In the RBF-CNN-BiLSTM model, ablation experiments are used to evaluate the contribution of different components in the model to the final performance. By gradually removing certain components, research can gain a clearer understanding of the roles of each module in the entire model. When the experiment shows that removing a certain part leads to a significant decrease in performance, it can be considered that the part is crucial to the model’s performance, and vice versa. Specifically, RBF, CNN, and BiLSTM are the three key components of this model. The comparative models for ablation experiments include BiLSTM, CNN-BiLSTM, RBF-BiLSTM, and the RBF-CNN-BiLSTM models proposed in this study. Figure 12 shows the accuracy changes of four models at different iterations. From Figure 12, it can be seen that both CNN-BiLSTM and RBF-BiLSTM improve the accuracy of the BiLSTM model. Removing the RBF and CNN modules will result in a decrease in the performance of the model. After adding CNN and RBF modules, the accuracy of the RBF-CNN-BiLSTM model exceeded 90%. This indicates that the combination of the advantages of CNN in extracting local features and RBF in improving the model’s nonlinear expression ability further improves the overall performance of the model.

Figure 12 Results of ablation experiment testing.
Figure 12

Results of ablation experiment testing.

4.4 Robustness testing

In DIFA systems, robustness testing is crucial for evaluating the performance of models under different conditions. Therefore, the RBF CNN BiLSTM model was tested under different noise levels and data volumes, and compared with the transformer model and the attention enhanced CNN (Attention CNN). Based on the prediction accuracy and computation time results, the computational efficiency and robustness of the model were demonstrated to verify the superiority of the proposed model. The obtained test results are shown in Figure 13. From Figure 13(a), it can be seen that as the amount of data increases, the accuracy of the RBF-CNN-BiLSTM model gradually increases, reaching around 97%, and the training time is lower than that of the transformer model and the Attention CNN model, with the longest being only 25 min. These results indicate that the proposed model exhibits good scalability and accuracy as the data volume increases, but the training time also increases accordingly, while the proposed RBF-CNN-BiLSTM model still has significant advantages. From Figure 13(b), it can be observed that in the absence of noise, the accuracy of the RBF-CNN-BiLSTM model can reach 96.9%. Although the addition of noise and the absence of some data reduce the accuracy, it still approaches 90%, which is still superior to the transformer model and Attention CNN model. Overall, the RBF-CNN-BiLSTM model exhibits good robustness under different conditions.

Figure 13 The robustness test results of the model. (a) Test results under different data volumes and (b) test results under different conditions.
Figure 13

The robustness test results of the model. (a) Test results under different data volumes and (b) test results under different conditions.

4.5 Actual financial audit testing

Finally, the improved RBF-CNN BiLSTM algorithm will be tested in practical financial auditing environments. Research cooperation with a listed company in China, focuses on 1,850 financial audit reports for the company’s audit projects. The results show that audit reports can be roughly divided into two categories, namely, unqualified opinions and qualified opinions. The unqualified opinion report considers that the audited financial statements comply with relevant accounting standards in all material respects, while the qualified opinion report indicates that there are qualified opinions or uncertainties in certain aspects of the statements. This classification helps to clearly express the auditor’s audit conclusion on the financial condition of the audited entity. Meanwhile, in the testing, some of the latest models were selected for comparison, namely, the GA-BP model [40], the predictive models from previous literature [41,42], and the results are shown in Table 3.

Table 3

Comparison results of four prediction methods

Methods RMSE MAE R 2
GA-BP 0.4538 0.3511 0.8545
Reference [41] 0.3369 0.3784 0.8612
Reference [42] 0.2052 0.2279 0.8753
RBF-CNN-BiLSTM 0.1106 0.1268 0.9724

From Table 3, all four methods could to some extent predict the trend of changes in financial audit opinions. By analyzing the data in Table 3, the proposed RBF-CNN-BiLSTM model had the lowest error and an R 2 value of 0.9724. This proved that this method could more efficiently predict audit opinions. At the same time, the study demonstrated the efficiency and accuracy of this method by using real-life financial audit data, providing a solid foundation for further practical application in the future.

5 Conclusion

With the rapid development of the economy, many companies are facing various challenges based on the analysis of DIFA system, and more investment is needed to ensure the normal analysis and accurate prediction of financial situation. In response to the current situation that the analysis requirements of the financial auditing system become more and more demanding, an improved RBF-CNN-BiLSTM algorithm based on BiLSTM was proposed, and the improved algorithm was used to conduct training and simulation experiments on sample data. The experimental results showed that the overall average MAPE value, the average accuracy, the average precision, the average recall rate, and the average F1-score of the reconciliation function of the improved algorithm were 0.3243, 92.31, 79.54, 65.93, and 80.55%, respectively, except that the MAPE value was significantly lower than the other four algorithms, and the rest of the data were significantly higher than the other four algorithms. The experimental results showed that the improved RBF-CNN-BiLSTM algorithm has significant advantages in all aspects of performance and can be applied to the analysis of the DIFA system. This study effectively solved the difficulty of low efficiency in current financial auditing, improved the efficiency and accuracy of financial auditing, and achieved better DIFA, providing an efficient and intelligent solution for financial auditing work. Although this study has achieved certain results, it did not consider the regional, industry, and scale biases in the distribution of financial datasets, and did not analyze the false positives and false negatives caused by imbalanced data in the model. Therefore, in the future, domain adaptation techniques need to be adopted to enable the model to adapt to different data distributions across industries and regions, and generate more minority class samples through generative adversarial networks to help the model better learn minority class features. Meanwhile, in the future, research will focus on using financial embedding techniques to transform financial data into low dimensional dense vector representations, combined with reasonable feature design, including financial ratio feature extraction, to enable the model to better learn potential patterns and further improve its performance. In addition, given the black box nature of the model proposed in this article, in the future, interpretability tools such as SHapley Additive exPlans or Local Interpretable Model agnostic Explanations will be integrated to improve the transparency and comprehensibility of the model, in order to help non experts understand the reasons why the model makes a certain prediction and enhance the transparency and credibility of the model in the field of financial auditing.

  1. Funding information: Author states no funding involved.

  2. Author contribution: Author has accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: Author states no conflict of interest.

  4. Data availability statement: All data generated or analyzed during this study are included in this published article.

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Received: 2024-08-13
Revised: 2025-01-16
Accepted: 2025-03-30
Published Online: 2025-07-03

© 2025 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/nleng-2025-0130
Schlagwörter für diesen Artikel
financial analysis; BiLSTM; CNN; RBF; data prediction
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Artikel in diesem Heft

  1. Research Articles
  2. Generalized (ψ,φ)-contraction to investigate Volterra integral inclusions and fractal fractional PDEs in super-metric space with numerical experiments
  3. Solitons in ultrasound imaging: Exploring applications and enhancements via the Westervelt equation
  4. Stochastic improved Simpson for solving nonlinear fractional-order systems using product integration rules
  5. Exploring dynamical features like bifurcation assessment, sensitivity visualization, and solitary wave solutions of the integrable Akbota equation
  6. Research on surface defect detection method and optimization of paper-plastic composite bag based on improved combined segmentation algorithm
  7. Impact the sulphur content in Iraqi crude oil on the mechanical properties and corrosion behaviour of carbon steel in various types of API 5L pipelines and ASTM 106 grade B
  8. Unravelling quiescent optical solitons: An exploration of the complex Ginzburg–Landau equation with nonlinear chromatic dispersion and self-phase modulation
  9. Perturbation-iteration approach for fractional-order logistic differential equations
  10. Variational formulations for the Euler and Navier–Stokes systems in fluid mechanics and related models
  11. Rotor response to unbalanced load and system performance considering variable bearing profile
  12. DeepFowl: Disease prediction from chicken excreta images using deep learning
  13. Channel flow of Ellis fluid due to cilia motion
  14. A case study of fractional-order varicella virus model to nonlinear dynamics strategy for control and prevalence
  15. Multi-point estimation weldment recognition and estimation of pose with data-driven robotics design
  16. Analysis of Hall current and nonuniform heating effects on magneto-convection between vertically aligned plates under the influence of electric and magnetic fields
  17. A comparative study on residual power series method and differential transform method through the time-fractional telegraph equation
  18. Insights from the nonlinear Schrödinger–Hirota equation with chromatic dispersion: Dynamics in fiber–optic communication
  19. Mathematical analysis of Jeffrey ferrofluid on stretching surface with the Darcy–Forchheimer model
  20. Exploring the interaction between lump, stripe and double-stripe, and periodic wave solutions of the Konopelchenko–Dubrovsky–Kaup–Kupershmidt system
  21. Computational investigation of tuberculosis and HIV/AIDS co-infection in fuzzy environment
  22. Signature verification by geometry and image processing
  23. Theoretical and numerical approach for quantifying sensitivity to system parameters of nonlinear systems
  24. Chaotic behaviors, stability, and solitary wave propagations of M-fractional LWE equation in magneto-electro-elastic circular rod
  25. Dynamic analysis and optimization of syphilis spread: Simulations, integrating treatment and public health interventions
  26. Visco-thermoelastic rectangular plate under uniform loading: A study of deflection
  27. Threshold dynamics and optimal control of an epidemiological smoking model
  28. Numerical computational model for an unsteady hybrid nanofluid flow in a porous medium past an MHD rotating sheet
  29. Regression prediction model of fabric brightness based on light and shadow reconstruction of layered images
  30. Dynamics and prevention of gemini virus infection in red chili crops studied with generalized fractional operator: Analysis and modeling
  31. Qualitative analysis on existence and stability of nonlinear fractional dynamic equations on time scales
  32. Fractional-order super-twisting sliding mode active disturbance rejection control for electro-hydraulic position servo systems
  33. Analytical exploration and parametric insights into optical solitons in magneto-optic waveguides: Advances in nonlinear dynamics for applied sciences
  34. Bifurcation dynamics and optical soliton structures in the nonlinear Schrödinger–Bopp–Podolsky system
  35. Review Article
  36. Haar wavelet collocation method for existence and numerical solutions of fourth-order integro-differential equations with bounded coefficients
  37. Special Issue: Nonlinear Analysis and Design of Communication Networks for IoT Applications - Part II
  38. Silicon-based all-optical wavelength converter for on-chip optical interconnection
  39. Research on a path-tracking control system of unmanned rollers based on an optimization algorithm and real-time feedback
  40. Analysis of the sports action recognition model based on the LSTM recurrent neural network
  41. Industrial robot trajectory error compensation based on enhanced transfer convolutional neural networks
  42. Research on IoT network performance prediction model of power grid warehouse based on nonlinear GA-BP neural network
  43. Interactive recommendation of social network communication between cities based on GNN and user preferences
  44. Application of improved P-BEM in time varying channel prediction in 5G high-speed mobile communication system
  45. Construction of a BIM smart building collaborative design model combining the Internet of Things
  46. Optimizing malicious website prediction: An advanced XGBoost-based machine learning model
  47. Economic operation analysis of the power grid combining communication network and distributed optimization algorithm
  48. Sports video temporal action detection technology based on an improved MSST algorithm
  49. Internet of things data security and privacy protection based on improved federated learning
  50. Enterprise power emission reduction technology based on the LSTM–SVM model
  51. Construction of multi-style face models based on artistic image generation algorithms
  52. Research and application of interactive digital twin monitoring system for photovoltaic power station based on global perception
  53. Special Issue: Decision and Control in Nonlinear Systems - Part II
  54. Animation video frame prediction based on ConvGRU fine-grained synthesis flow
  55. Application of GGNN inference propagation model for martial art intensity evaluation
  56. Benefit evaluation of building energy-saving renovation projects based on BWM weighting method
  57. Deep neural network application in real-time economic dispatch and frequency control of microgrids
  58. Real-time force/position control of soft growing robots: A data-driven model predictive approach
  59. Mechanical product design and manufacturing system based on CNN and server optimization algorithm
  60. Application of finite element analysis in the formal analysis of ancient architectural plaque section
  61. Research on territorial spatial planning based on data mining and geographic information visualization
  62. Fault diagnosis of agricultural sprinkler irrigation machinery equipment based on machine vision
  63. Closure technology of large span steel truss arch bridge with temporarily fixed edge supports
  64. Intelligent accounting question-answering robot based on a large language model and knowledge graph
  65. Analysis of manufacturing and retailer blockchain decision based on resource recyclability
  66. Flexible manufacturing workshop mechanical processing and product scheduling algorithm based on MES
  67. Exploration of indoor environment perception and design model based on virtual reality technology
  68. Tennis automatic ball-picking robot based on image object detection and positioning technology
  69. A new CNN deep learning model for computer-intelligent color matching
  70. Design of AR-based general computer technology experiment demonstration platform
  71. Indoor environment monitoring method based on the fusion of audio recognition and video patrol features
  72. Health condition prediction method of the computer numerical control machine tool parts by ensembling digital twins and improved LSTM networks
  73. Establishment of a green degree evaluation model for wall materials based on lifecycle
  74. Quantitative evaluation of college music teaching pronunciation based on nonlinear feature extraction
  75. Multi-index nonlinear robust virtual synchronous generator control method for microgrid inverters
  76. Manufacturing engineering production line scheduling management technology integrating availability constraints and heuristic rules
  77. Analysis of digital intelligent financial audit system based on improved BiLSTM neural network
  78. Attention community discovery model applied to complex network information analysis
  79. A neural collaborative filtering recommendation algorithm based on attention mechanism and contrastive learning
  80. Rehabilitation training method for motor dysfunction based on video stream matching
  81. Research on façade design for cold-region buildings based on artificial neural networks and parametric modeling techniques
  82. Intelligent implementation of muscle strain identification algorithm in Mi health exercise induced waist muscle strain
  83. Optimization design of urban rainwater and flood drainage system based on SWMM
  84. Improved GA for construction progress and cost management in construction projects
  85. Evaluation and prediction of SVM parameters in engineering cost based on random forest hybrid optimization
  86. Museum intelligent warning system based on wireless data module
  87. Optimization design and research of mechatronics based on torque motor control algorithm
  88. Special Issue: Nonlinear Engineering’s significance in Materials Science
  89. Experimental research on the degradation of chemical industrial wastewater by combined hydrodynamic cavitation based on nonlinear dynamic model
  90. Study on low-cycle fatigue life of nickel-based superalloy GH4586 at various temperatures
  91. Some results of solutions to neutral stochastic functional operator-differential equations
  92. Ultrasonic cavitation did not occur in high-pressure CO2 liquid
  93. Research on the performance of a novel type of cemented filler material for coal mine opening and filling
  94. Testing of recycled fine aggregate concrete’s mechanical properties using recycled fine aggregate concrete and research on technology for highway construction
  95. A modified fuzzy TOPSIS approach for the condition assessment of existing bridges
  96. Nonlinear structural and vibration analysis of straddle monorail pantograph under random excitations
  97. Achieving high efficiency and stability in blue OLEDs: Role of wide-gap hosts and emitter interactions
  98. Construction of teaching quality evaluation model of online dance teaching course based on improved PSO-BPNN
  99. Enhanced electrical conductivity and electromagnetic shielding properties of multi-component polymer/graphite nanocomposites prepared by solid-state shear milling
  100. Optimization of thermal characteristics of buried composite phase-change energy storage walls based on nonlinear engineering methods
  101. A higher-performance big data-based movie recommendation system
  102. Nonlinear impact of minimum wage on labor employment in China
  103. Nonlinear comprehensive evaluation method based on information entropy and discrimination optimization
  104. Application of numerical calculation methods in stability analysis of pile foundation under complex foundation conditions
  105. Research on the contribution of shale gas development and utilization in Sichuan Province to carbon peak based on the PSA process
  106. Characteristics of tight oil reservoirs and their impact on seepage flow from a nonlinear engineering perspective
  107. Nonlinear deformation decomposition and mode identification of plane structures via orthogonal theory
  108. Numerical simulation of damage mechanism in rock with cracks impacted by self-excited pulsed jet based on SPH-FEM coupling method: The perspective of nonlinear engineering and materials science
  109. Cross-scale modeling and collaborative optimization of ethanol-catalyzed coupling to produce C4 olefins: Nonlinear modeling and collaborative optimization strategies
  110. Unequal width T-node stress concentration factor analysis of stiffened rectangular steel pipe concrete
  111. Special Issue: Advances in Nonlinear Dynamics and Control
  112. Development of a cognitive blood glucose–insulin control strategy design for a nonlinear diabetic patient model
  113. Big data-based optimized model of building design in the context of rural revitalization
  114. Multi-UAV assisted air-to-ground data collection for ground sensors with unknown positions
  115. Design of urban and rural elderly care public areas integrating person-environment fit theory
  116. Application of lossless signal transmission technology in piano timbre recognition
  117. Application of improved GA in optimizing rural tourism routes
  118. Architectural animation generation system based on AL-GAN algorithm
  119. Advanced sentiment analysis in online shopping: Implementing LSTM models analyzing E-commerce user sentiments
  120. Intelligent recommendation algorithm for piano tracks based on the CNN model
  121. Visualization of large-scale user association feature data based on a nonlinear dimensionality reduction method
  122. Low-carbon economic optimization of microgrid clusters based on an energy interaction operation strategy
  123. Optimization effect of video data extraction and search based on Faster-RCNN hybrid model on intelligent information systems
  124. Construction of image segmentation system combining TC and swarm intelligence algorithm
  125. Particle swarm optimization and fuzzy C-means clustering algorithm for the adhesive layer defect detection
  126. Optimization of student learning status by instructional intervention decision-making techniques incorporating reinforcement learning
  127. Fuzzy model-based stabilization control and state estimation of nonlinear systems
  128. Optimization of distribution network scheduling based on BA and photovoltaic uncertainty
  129. Tai Chi movement segmentation and recognition on the grounds of multi-sensor data fusion and the DBSCAN algorithm
  130. Special Issue: Dynamic Engineering and Control Methods for the Nonlinear Systems - Part III
  131. Generalized numerical RKM method for solving sixth-order fractional partial differential equations
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© 2025 De Gruyter Brill
Heruntergeladen am 20.11.2025 von https://www.degruyterbrill.com/document/doi/10.1515/nleng-2025-0130/html?lang=de
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