Data-driven decision making for manufacturing processes using pyramidal dilation attention convolutional neural network optimized with improved dwarf mongoose optimization

Abstract

In this paper, data-driven decision making for manufacturing processes using Pyramidal Dilation Attention Convolutional Neural Network Optimized with Improved Dwarf Mongoose Optimization (DDMP-PDACNN-IDMO) is proposed. Initially data is taken from the SECOM dataset. Afterward the data is fed to pre-processing. In pre-processing, it removes noisy data using Variational Bayesian-based maximum Correntropy Cubature Kalman Filtering (VBMCCKF). The pre-processed data is given to feature selection. Here, representative features is selected based on the Lirebird Optimization Algorithm (LOA). Next, in order to successfully categorize the manufacturing process as successful or unsuccessful, the chosen feature is given to the Pyramidal Dilation Attention Convolutional Neural Network (PDACNN). The PDACNN’s learnable parameters are optimized using Improved Dwarf Mongoose Optimization (IDMO). Python is used for implementing the proposed method. The performance of the proposed technique was examined using performance metrics such as accuracy, and ROC. The performance analysis highlights that the proposed DDMP-PDACNN-IDMO model excels with 98.5% accuracy in the success class and 98.2% in the failure class. The proposed method outperforms DDMP-ANN, DDMP-RNN, and DDMP-BPNN with the fastest runtime (best: 9.4s) and lowest Mean Squared Error (MSE) for both training and testing (best: 0.0392 and 0.0526, respectively). It also achieves the highest R-squared (R²) values, indicating more accurate and reliable predictions. These results confirm the proposed method’s superior performance in speed and accuracy compared with other existing methods such as data-driven manufacturing process based artificial neural network (DDMP-ANN), data-driven manufacturing process based recurrent neural network (DDMP-RNN), and data-driven manufacturing process based back propagation neural network (DDMP-BPNN) respectively.

Keywords

Manufacturing process variational bayesian-based maximum correntropy cubature kalman filtering pyramidal dilation attention convolutional neural network lyrebird optimization algorithm improved dwarf mongoose optimization

1. Introduction

1.1. Background

Data-driven decision-making (DDDM) in manufacturing leverages data analytics, machine learning, and monitoring to significantly enhance efficiency, quality, and productivity [1, 2]. Since Industry 4.0’s introduction, the industrial manufacturing is undergoing a transformation where traditional intuition-based decision-making is being replaced by advanced technologies like the Internet of Things (IoT), large data, and artificial intelligence (AI) [3, 4]. These technologies enable the collection and analyze enormous volumes of data generated from various sources, like sensors, machines, and production lines [5]. Machine learning algorithms can process this data to uncover patterns, predict maintenance needs, and optimize production schedules [6, 7]. For instance, predictive maintenance uses historical data to forecast when equipment is likely to fail, allowing for proactive maintenance that reduces downtime and extends the lifespan of machinery [8, 9]. Data collection and analysis empower manufacturers to monitor processes continuously, enabling quick, informed decisions that enhance quality control and safety, which is crucial in maintaining consistent product quality and responding promptly to any issues during production [10, 11].

The benefits of DDDM in manufacturing are extensive, leading to improved product quality by identifying and addressing defects early in the production process [12]. Operational costs are reduced through optimized resource utilization and minimized downtime, while enhanced productivity is achieved by streamlining processes and eliminating inefficiencies [13]. Additionally, DDDM supports flexible production, allowing manufacturers to meet the increasing demand for personalized products without compromising efficiency. Despite these advantages, implementing DDDM in manufacturing is not without challenges [14]. Integrating data from diverse and often incompatible sources can be complex and time-consuming, and ensuring the accuracy and quality of collected data is vital for reliable analytics [15]. There is also a significant skills gap in data analytics among manufacturing personnel, necessitating investment in training and development [16]. The substantial investment required for technology and infrastructure can be a barrier, particularly for small and medium-sized enterprises, and safeguarding data privacy and security is critical given the industrial data’s sensitive nature [17, 18, 19]. Ensuring data processing and analysis capabilities to enable timely decision-making and overcoming employee reluctance to move from conventional decision-making procedures need for powerful computational resources and effective data management systems. Figure 1 depicts the Graphical abstract.

Figure 1.

Graphical abstract.

1.2. Challenges

Implementing data-driven decision-making in manufacturing faces several challenges, including integrating data from diverse and often incompatible sources, ensuring the accuracy and quality of collected data, and addressing the skills gap in data analytics among manufacturing personnel. Additionally, the significant investment in technology and infrastructure can be a barrier, especially for small and medium-sized enterprises. Safeguarding data privacy and security is another critical concern, given industrial data’s sensitive nature. Overcoming the reluctance of personnel used to conventional decision-making processes to embrace change is another challenge. Finally, ensuring real-time data processing and analysis capability to support timely decision-making requires robust computational resources and efficient data management systems.

1.3. Literature survey

Sadati et al. [20] have introduced a cutting-edge integrated technique that uses observational data to identify key control variables, making process parameter design easier. Observational data can be used by data-driven approaches to improve, regulate, and simulate process performance in a production environment. Observational data may be used by data-driven approaches to predict, regulate, and improve process performance in a production environment. When supported with observational data sufficiently covered to comprehend the real dynamics of process performance, they may be utilized for both process monitoring and improvement, saving the cost of invasive controlled experiments.

Ghahramani et al. [21] have suggested a dynamic approach to overcome different obstacles and learn valuable insights about semiconductor production processes. Describe in detail how a neural network and genetic technique are used to create a clever feature selection system. The goals were to obtain insight into multiple dimensions that allow manufacturers to access efficient predictive technologies and to offer a state-of-the-art solution for controlling manufacturing processes .

Wang and Liu [22] have shown how to solve this issue with a novel data-driven PDE technique. Initially, a product design evaluation (PDE) model was developed, accounting for several phases of the product life cycle’s evaluation indications. Secondly, a highly efficient multi-stage “artificial neural network” (ANN) was developed using a hybrid optimization method that combined Adam and particle swarm optimization (PSO-Adam) to quickly and accurately provide the nonlinear mapping between the PDE model indicators. Adam was employed to adaptively optimize the training parameters in the region of the global optimum, despite the fact that the PSO were utilized to fast converge during the early stages of a worldwide search.

Mozaffar et al. [23] have established the validity of an RNN for the anticipation of high-dimensional thermal history in “directed energy deposition” (DED)processes using a gated recurrent unit (GRU)formulation, taking into consideration differences in tool path strategy, geometry, scan speed laser power, and build dimensions. The model demonstrated accurate thermal history prediction for unseen points in a test dataset with limited training, suggesting highly adaptively.

Pang et al. [24] have offered a framework model for product quality that is data-driven and intelligent, built on the cutting-edge technology of digital twins (DT) and cyber-physical systems (CPS)simulation techniques. Emphasizing the crucial role of data accumulation for manufacturing industries, we present actionable recommendations for implementing a robust quality analysis system within a CPS framework for industrial valve manufacturing. Then showcase the construction and training of a BP neural network, utilizing diverse mechanical and electrical quality characteristics of valves, to effectively predict and mitigate potential quality failures throughout the production process.

Xu et al. [25] have demonstrated the advancements in technology created for data gathering and analysis for in-process manufacturing. The complexity and uncertainty of indirect measurement in manufacturing spurred the development of ground breaking sensor technology for direct data collection. However, due to the industrial processes are complex, physical model-based analysis frequently depends on simplifications and might encounter ill-posed solutions. Fortunately, ML, particularly deep learning, thrives on abundant data and offers tremendous potential for automated decision-making. Surprisingly, data-driven manufacturing approaches can achieve similar or even superior results with limited data.

Ma et al. [26] showed how predictive production planning powered by big data was implemented to increase resource and energy efficiency for manufacturing sectors that rely heavily on energy. Furthermore, energy consumption models are developed based on cubes and employ a Long-term Short-Term Memory Framework for predicting energy consumption in the context of data pre-processing and mining. To illustrate the practical application of these models, an industrial case study, demonstrating their effectiveness in processing energy big data and predicting the parameters of energy consumption as well as production status.

Jin and Xu [27] have indicated that forecasts of agricultural commodity prices are significant to a range of market participants. In order to address this challenge, the research looks at the green grammes weekly wholesale price index in the Chinese market. The index covers a ten-year period from January 1, 2010, to January 3, 2020, and has significant economic implications. To address the nonlinear tendencies seen in the price time series, a forecast model based on the nonlinear auto-regressive neural network is examined. To mimic more complicated nonlinear properties, this modeling approach integrates a range of fundamental nonlinear functions. Particularly, various configurations such as data splitting ratios, hidden neuron, delay counts, and model estimation techniques are used to analyze the prediction performance.

Jin and Xu [28] have demonstrated that creating price forecasts for different energy commodities has long been a significant task for a variety of energy market players. Four major energy commodities are the focus of this investigation. Nonlinear autoregressive neural network models are used to analyse the monthly prices of Henry Hub natural gas and New York Harbour No. 2 heating oil, as well as the daily prices of WTI and Brent crude oil. Analysis is done on the prediction performance arising from different model configurations, such as data segmentation, hidden neurons, delays, and training methods. The research produced rather simple models with accurate and reliable performance.

Jin and Xu [29] have validated the use of neural networks for corn cash price forecasting. A dataset of daily maize cash prices from over 500 marketplaces in sixteen states – Iowa, Minnesota, Illinois, Indiana, North Dakota, Michigan, Missouri, Nebraska, South Dakota, Ohio, Arkansas, Kentucky, Wisconsin, Pennsylvania, Kansas and Oklahoma, – was used to investigate the forecasting problem. Neural network (NN) modeling, both univariate and bivariate with futures prices included, are the main topics of discussion. Simple neural networks (NNs) with twenty hidden neurones and two delays yield very good accuracy for the one-day ahead of time horizon. Forecasting cash prices is improved by including futures rates in the models.

Jin and Xu [30] have suggested using Gaussian process regression to anticipate yellow corn wholesale prices. The intricacy of price time series made forecasting commodity prices for market participants and policy makers difficult to handle. Given their significance to strategy, corn harvests were hardly an exception. The forecasting problem for China’s weekly yellow maize wholesale price index from January 1, 2010, to January 10, 2020, is assessed in this study. Using Bayesian optimisations and cross-validation, a Gaussian process regression model is developed across several kernels and basis functions in order to appropriately handle this intricate commodity price forecast problem.

Jin and Xu [31] have demonstrated pre-owned housing price index forecasts using Gaussian process regressions. This study’s primary objective was to forecast property prices for the quickly growing Chinese housing market over the next 10 years. The results will have significant implications for investors and the government. With the use of Bayesian optimisations and cross-validation, Gaussian process regressions with various kernels and basis functions are examined for monthly pre-owned housing price index forecasts for ten major Chinese cities from March 2012 thru May 2020.

Jin and Xu [32] have presented East China’s regional steel price index machine learning forecasts. The challenging task of daily regional steel price index forecasting in the East Chinese market from January 1, 2010, to April 15, 2021 is examined in this study. Gaussian process regressions are used to assess the results after models are trained using cross-validation and Bayesian optimisations carried out using the projected improvement per second plus technique. The standard deviation of noises, basis functions, kernels, and predictor standardization status are among the factors examined during model training.

1.4. Research gap and motivation

Previous research has explored various data-driven and machine learning (ML) approaches to enhance process performance and prediction in manufacturing.

Sadati et al. [20] developed an integrated strategy leveraging observational data for process parameter design, highlighting the cost-effectiveness of non-invasive experiments.

Ghahramani et al. [21] combined neural networks and genetic algorithms to improve feature selection in semiconductor production.

Wang and Liu [22] introduced a hybrid optimization technique (PSO-Adam) for product design evaluation (PDE) models.

Mozaffar et al. [23] validated the use of RNNs for forecasting thermal history in directed energy deposition processes.

Pang et al. [24] suggested a data-driven framework integrating digital twins and cyber-physical systems for quality analysis in manufacturing.

Xu et al. [25] focused on advancements in sensor technology for direct data collection and the potential of deep learning for automated decision-making.

Ma et al. [26] demonstrated predictive production planning using big data for energy efficiency. Despite these advancements, gaps remain in the ability to effectively operate with limited data and adapt to real-time changes in manufacturing environments. Many models rely on extensive datasets and oversimplify the complex dynamics of manufacturing processes, which can lead to less effective real-world applications. Furthermore, there is a need for comprehensive frameworks that can integrate various data sources and provide robust, non-invasive process monitoring and control. To address these gaps, the proposed research aims to develop a more adaptable and efficient data-driven framework that can operate effectively with limited data and dynamically adjust to manufacturing changes. This includes creating a non-invasive, cost-effective monitoring system that integrates diverse data sources and offers accurate, real-time process control. The contributions focus on enhancing predictive capabilities, improving the robustness of models in complex environments, and reducing the reliance on extensive data collection, ultimately leading to more practical and effective solutions for manufacturing performance optimization.

1.5. Contribution

–
This manuscript proposes the Pyramidal Dilation Attention Convolutional Neural Network (PDACNN) optimized using the Improved Dwarf Mongoose Optimization (IDMO) algorithm for manufacturing processes.
–
By employing VBMCCKF for data pre-processing, the method effectively removes noise from the SECOM dataset, leading to improved data quality and more reliable model performance.
–
The use of the Lyrebird Optimization Algorithm (LOA) for feature selection allows the detection of critical features that significantly enhance the classification accuracy of manufacturing outcomes.
–
The proposed technique achieves a remarkable accuracy of 98.5% for success classification and 98.2% for failure classification, outperforming traditional techniques such as DDMP-ANN, DDMP-RNN, and DDMP-BPNN.
–
The method demonstrates superior Receiver Operating Characteristic (ROC) performance, scoring 0.98% higher than existing methods, which underscores its effectiveness in precise manufacturing process classification and decision-making scenarios.

The novelty of the proposed DDMP-PDACNN-IDMO method lies in its unique integration of advanced machine learning techniques tailored for manufacturing processes. It combines noise reduction through a Variational Bayesian Multivariate Copula Coupled Kalman Filter (VBMCCKF) with feature selection via the Lyrebird Optimization Algorithm (LOA). The use of the Pyramidal Dilation Attention Convolutional Neural Network (PDACNN) optimized by Improved Dwarf Mongoose Optimization (IDMO) enhances classification accuracy significantly.
1.6. Organization

The rest of this manuscript is structured as follows: the proposed method is explained in Part 2, the outcome and discussions are covered in Part 3, and In Part 4, the manuscript is concluded.

2. Proposed methodology

Figure 2.

Block diagram of DDMP-PDACNN-IDMO.

This section discusses DDMP-PDACNN-IDMO. This part presents an accurate explanation of the research technique for manufacturing processes. There are five phases in this procedure: data acquisition, Pre-processing, Feature selection, Classification and optimization. Data were collected and pre-processed to prepare them for further analysis. The diagram of PDACNN-IDMO is illustrated in Fig. 2. Accordingly; a detailed description of all steps is given below.

2.1. Data acquisition

Data is taken from the SECOM dataset. It is composed of different operation observations, i.e., production data from wafer manufacture, with 591 features (operation measurements) [33]. The target characteristic, encoded as 0 and 1, is a binomial (Success and Failure), which relates to the manufacturing status.

2.2. Pre-processing using variational bayesian-based maximum correntropy cubature kalman filtering (VBMCCKF)

In this step, VBMCCKF performs the preprocessing which is utilized for removing the noise from the data [34] by changing the measurement noise covariance with $C_{n}$ , it can alter the Kalman gain. If the function of measurement is non-linear, then Eq. (1) may also be used to modify the covariance of measurement noise, where $C_{n}$ is established by

\begin{aligned} C_{n} = F_{ω} ({∥ s_{n} - g_{n} (a_{n}) ∥}_{y_{n}^{- 1}}^{2}) \end{aligned}

(1)

Where $s_{n}$ the kernel bandwidth and is $g_{n} (a_{n})$ the Gaussian bandwidth $C_{n}$ becomes closer to zero when the measurements have exceptionally high noise levels. Instead of computing $F_{ω}$ directly, alter the Kalman gain with $C_{n}$ to avoid numerical issues. The innovation covariance is calculated using Eq. (2):

\begin{aligned} H_{ss, n} = V_{s s, n} + {\tilde{F}}_{n} \end{aligned}

(2)

Where $V_{ss, n}$ is denoted as adjusting weights, and $C_{n}$ , on the other hand, is connected to measurement noise covariance. $C_{n}$ be appropriately estimated if thetrue covariance of measurement noise is not given. The measurement noise covarianceis estimated by using Eq. (3) as follows,

\begin{aligned} G_{n} = G_{n | n - 1} + \frac{1}{2 k} \sum_{a = 0}^{2 k} (s_{n} - g_{n} (a_{a, n})) (s_{n} - g_{n} (a_{a, n}))^{T} \end{aligned}

(3)

Where, $G_{n | n - 1}$ indicates the state transition matrix, large outliers in the measurements have an adverse effect on $G_{n}$ and result in erroneous noise covariance estimation. It suggeststhe following construction of the pseudo-measurements is calculated in Eqs (4), (5),

\begin{aligned} J [{\tilde{x}}_{n} {\tilde{x}}_{n}^{T}] & \approx J [δ_{n}^{2} {\tilde{x}}_{n} {\tilde{x}}_{n}^{T}] \end{aligned}

(4)

\begin{aligned} J [{\tilde{x}}_{n} {\tilde{x}}_{n}^{T}] & = C_{n} {\tilde{F}}_{n} \approx C_{n} J [x_{n} x_{n}^{T}] \end{aligned}

(5)

Where ${\tilde{F}}_{n}$ is the observation matrix, the VBMCCKF can perform better than other adaptive and resilient filters in nonlinear systems with both outliers and uncertain measurement noise covariance. Then the preprocessed data is given to feature selection.

2.3. Proposed lyrebird optimization algorithm

The pre-processed output is passed to the function selector [35]. Here, the representative features are selected based on LOA. In this part, the LOA a revolutionary bio-inspired metaheuristic method that simulates lyrebird behaviour in the wild is introduced. Lyrebirds in this situation carefully survey their surroundings before making their move to flee or conceal in hiding. The theory of LOA is explicated and thereafter computationally represented in two stages: (i) investigation, grounded in the simulation of the lyrebird’s escape plan, and (ii) utilization, grounded in the simulation of the concealing plan. Among the most well-known native birds of Australia are lyrebirds, which feature distinctive plumes of neutral-colored tail feathers. The suggested LOA approach discussed below was designed using mathematical modeling of this lyrebird technique in times of peril.

Step 1: Initialization

As a member of the LOA, every lyrebird chooses the decision variables’ values based on its problem-solving space. Together, LOA members make up the algorithm’s population, which may be represented theoretically by a matrix by Eq. (6).

\begin{aligned} Z = [\begin{array}{lccc} Z_{1, 1} & Z_{1, 2} & \dots & Z_{1, H} \\ Z_{2, 1} & Z_{2, 2} & \dots & Z_{2, H} \\ \dots & \dots & \dots & \dots \\ Z_{n, 1} & Z_{n, 2} & \dots & Z_{n, H} \end{array}] \end{aligned}

(6)

Here $Z$ denotes the LOA population matrix, $n$ denotes the count of lyrebirds, $H$ specifies the count of decision variables, correspondingly.

Step 2: Random Generation

Following the initialization process, the features present in the pre-processed dataset are selected randomly using the LOA approach.

Step 3: Fitness Function

A random solution is generated based on initialized assessments. It expressed in Eq. (7),

\begin{aligned} F i t n e s s f u n c t i o n = [S e l e c t i n g O p t i m a l F e a t u r e s] \end{aligned}

(7)

Step 4: Escaping Strategy (Exploration Phase)

Using modelling of the lyrebird’s migration from the border between the safe and harmful zones, the population members’ positions are updated in the search space throughout this phase of LOA. The lyrebird is a good example of LOA’s global search exploration capabilities since it can go to safe havens and explore novel areas in the problem-solving space. It can also make significant positional alterations. In the LOA design, every member considers the locations of other individuals in the population with higher objective function values to be safe zones. Therefore, the set of safe zones for all members of the LOA may be found using Eq. (8).

\begin{aligned} {D B}_{j} = {Z_{P}, E_{P} < E_{j} and P \in {1, 2, \dots, M}}, Where j = 1, 2, \dots, M, \end{aligned}

(8)

In this instance, ${D B}_{j}$ indicates the set of safe locations for the j^th lyrebird and $Z_{P}$ indicates the $Z$ matrix’s $P$ th row, which has a greater value of the objective function than the jth LOA member.

The lyrebird is predicted by the LOA design to sometimes find its way to one of these secure locations. Equation (9), which is reliant on the lyrebird displacement modeling completed in this step, is used to calculate each member of the LOA’s new location. Next, in the event that the goal function’s value increases, according to Eq. (10), this novel position replaces the appropriate member’s prior position.

\begin{aligned} z_{j, i}^{k 1} & = z_{j, i} + l_{j, i} . ({S S B}_{j, i} - J_{j, i} . z_{j, i}) \end{aligned}

(9)

\begin{aligned} Z_{j} & = {\begin{aligned} Z_{j}^{k 1}, E_{j}^{k 1} ⩽ E_{j} \\ Z_{j}, E l s e \end{aligned} \end{aligned}

(10)

Here, the new position of the jth lyrebird, as determined by the proposed LOA’s escape plan, is indicated by $z_{j}^{k 1}$ . $E_{j}^{k 1}$ Indicates its objective function value, ${S S B}_{j, i}$ indicates its ith dimension, ${S S B}_{j}$ indicates the chosen safe area for j^th lyrebird, $z_{j, i}^{k 1}$ indicates its i^th dimension, $l_{j, i}$ are arbitrary values between 0 and 1. and $J_{j, i}$ are integers that are arbitrarily chosen to be either 1 or 2.

Step 5: Exploitation Phase for optimizing $θ$

Throughout this stage of LOA, the lyrebird’s modeled strategy of hiding in its local safe zone modifies the position of the population member in the search space. Equation (11) is used in LOA design to establish a unique position for every LOA member. This is predicated on simulating the lyrebird’s travel in search of the closest hiding spot. If this new location raises the value of the objective function as per Eq. (12), then it takes the place of the linked member’s previous position.

\begin{aligned} z_{j, i}^{k 2} & = z_{j, i} + (1 - 2 l_{j, i}) . \frac{{v c}_{i} - {q c}_{i}}{T} \end{aligned}

(11)

\begin{aligned} Z_{j} & = {\begin{aligned} Z_{j}^{k 2}, E_{j}^{k 2} ⩽ E_{j} \\ Z_{j}, E l s e \end{aligned} \end{aligned}

(12)

Here, $z_{j}^{k 2}$ denotes the noval position calculated for the jth lyrebird using the proposed LOA’s hiding method. $z_{j, i}^{k 2}$ Indicates its ith dimension, $E_{j}^{k 2}$ indicates its value of objective function, $T$ indicates the iteration counter and $l_{j, i}$ are random valuesfrom the interval [0, 1].

Step 6: Termination Criteria

Here, the optimal feature is selected depending on the LOA Algorithm iteratively repeating step 3 till fulfill $Z = Z + 1$ halting criteria. The chosen characteristics are then provided as the classification’s input.

2.4. Classification using pyramidal dilation attention convolutional neural network (PDACNN)

In thispart, the classification using PDACNN is discussed [36]. The PDAC network’s maximal transmission capacity is made possible by the direct connections between the layers of the dense convolutional network. The PDC block, is the PDAC network’s primary structural component. It comprises multiple PDC layers, and the links among the PDC layers are dense.

\begin{aligned} E_{w} = e_{1}^{1} \land e_{2}^{2} \land e_{3}^{3} \land \dots \dots \land e_{w}^{q} \end{aligned}

(13)

where

E_{w}

is the

w^{th}

PDC layer,

e_{w}^{q}

is the

q^{th}

sub dilated convolutional layer, and

w = 2 q_{1}

is the dilated factor the stacking of sub dilated convolutional layers, and represents the

q^{th}

PDC layer. Equation (14) provides the following expression for the spectral attention:

\begin{aligned} b_{w}^{^{'}} = R_{s c a l e} (b_{w}, k_{w}) = k_{w}, w = 1, \dots, a \end{aligned}

(14)

where,

k_{w}

is the total of the maximum pooling

{A c t i}^{sma}

and average pooling

{A c t i}^{sav}

and

R_{s c a l e} (b_{w}, k_{w})

denotes spectral wise multiplication among the feature map

b_{w}

and the scalar

k_{w}

. Equation (15) expresses the sigmoid activation function that is used for the maximum pooling and global average pooling of the input data when it comes to spatial attention.

\begin{aligned} A c t i = S i g ([{A c t i}^{s a v}, {A c t i}^{s m a}] * Q) \end{aligned}

(15)

here, the convolution process and a learnable built-in parameter is represented by $Q$ . This is the spatial multiplication among the feature map and the final result. One can get a predicted one-hot label ${\hat{b}}_{u}$ for every sample (xi) by using the PDAC network’s prediction of the unlabelled data. SPL uses the following Eq. (16) to give each sample $a_{u}$ a weight $s_{u}$ :

\begin{aligned} \begin{array}{l} A v \underset{o, s}{g} D (o, s; δ) = \sum_{u = 1}^{v} s_{u} \partial ({\hat{b}}_{u}, h (a_{u}, o)) - η \sum_{u = 1}^{v} s_{u} \\ 0 ⩽ s_{u} ⩽ 1, u = 1, \dots, m \end{array} \end{aligned}

(16)

where,

m

is a model parameter, is the loss function, and is a parameter. The weight

s_{u}

is simple to acquire as in Eq. (17)

\begin{aligned} s_{u} = {\begin{aligned} 1, & i f \partial ({\hat{b}}_{u}, h (a_{u}, o)) < β \\ 0, & o t h e r w i s e \end{aligned}} \end{aligned}

(17)

It combines the results, and then inputs them into the convolution layer to create the output component. Lastly, the photos are classified as KSC 704, KSC 201, KSC 290, KSC 380, and KSC 400 maize seed kinds by the PDACNN. The PDACNN classifier incorporates the artificial intelligence-based optimization technique because of its relevance and ease of usage.

It is challenging to adjust the impact of noisy labels and “symmetric cross-entropy” (SCE) loss on the cross-entropy (CE) function as

\begin{aligned} \partial_{sce} = \partial_{ce} + \partial_{rce} \end{aligned}

(18)

In simple terms, $\partial_{rce}$ involves switching the label and the expected value. In order to mitigate the impact of noisy labels, employ a novel SCE loss function as

\begin{aligned} \partial_{sce} = α \partial_{ce} + (1 - α) \partial_{rce} \end{aligned}

(19)

here $α$ is a weight factor.

In this study, IDMOA is used to optimize the PDACNN weight parameter $α$ . Finally, the PDACNN is to effectively classify manufacturing processes as either involving success or failure. Here, IDMOA is used for tuning the weight and bias factors of PDACNN.

2.5. Optimization using improved dwarf mongoose optimization (IDMO)

The IDMO is used to optimise PDACNN’s weights parameter [37]. Starting with the alpha and scout groups’ population generation and upgrading processes. These solutions are improved utilising enhanced exploratory and exploitation techniques since the choice of the babysitters and dwarf mongooses to exchange for them is completely random. The IDMO’s implementation is straightforward and flexible, and it only has one parameter that may be modified.

Step 1: Initialization

The IDMO population is stochastically initialised as a matrix of potential dwarf mongooses $(A)$ . The population vector lies between the optimisation problem’s lower bound $(L)$ and upper bound $(U)$ . It is initialized in Eq. (20) as follows,

\begin{aligned} A = [\begin{array}{lccccc} a_{1, 1} & a_{1, 2} & \dots & a_{1, d - 1} & a_{1, d} \\ a_{2, 1} & a_{2, 2} & \dots & a_{2, d - 11} & a_{1, d} \\ : & : & a_{u, v} & : & : \\ a_{m, 1} & a_{m, 2} & \dots & a_{m, d - 1} & a_{m, d} \end{array}], \end{aligned}

(20)

Where, $a_{u, v}$ and $m$ represent the number of dwarf mongooses in a mound indicates where the $v^{th}$ dimension of the $u^{th}$ population.

Step 2: Random generation

After initialization, the input parameter is created at random. Depending on their explicit hyperparameter state, the best fitness value will be chosen.

Step 3: Fitness Function Estimation

To provide a random solution, the initialized evaluations are utilized. Using the parameter optimization value, the fitness function is assessed to optimize the classifier’s weight parameter. Find this in Eq. (21).

\begin{aligned} fitness function = o p t i m i z i n g (α) \end{aligned}

(21)

Step 4: Exploration phase

The IDMO moves about while searching the problem space. It pulls the other family members in the direction of a potential food source after being defined as the fastest dwarf mongoose. It simply uses the vocalisation of the alpha to influence where the other dwarf mongoose is located; this situation deviated in Eq. (22).

\begin{aligned} A_{u + 1} = γ + p h i * r a n d * (A_{u} - A_{v}), \end{aligned}

(22)

In IDMO, the position of the alpha is utilised to define the position of a new operator, as well as the other mongoose. This regulates the alpha movement, improving the exploration potential and IDM’s potential is calculated based on the Eq. (23)

\begin{aligned} ϖ = e^{- 4 * (S_{i t e r} / max_{i t e r})^{2}} \end{aligned}

(23)

where,

A_{v}

indicates the previous dwarf position,

p h i = (\frac{p e e p}{2}) * r a n d * η

, and rand indicates a uniformly distributed random number [1,1].

A_{u}

indicates a dwarf mongoose chosen at random.

Step 5: Exploitation phase for optimizing $α$

Considering dwarf mongooses are known to congregate near food sources, the scouts’ fitness is regarded as a potential sleeping mound. The sleeping mound that is chosen is thought to be the fittest scout. The scouts are modelled by Eq. (24).

\begin{aligned} A_{u + 1} = α γ + p h i * r a n d * (A_{v} - A_{d}) / 2, \end{aligned}

(24)

Where, $A_{v}$ and $A_{d}$ are randomly chosen dwarf mongooses and rand indicates the random number between [0, 1]. Equations (25) (26) demonstrates that the dwarf mongooses that replace the babysitters are selected at random and their details are sent to the babysitters.

\begin{aligned} F & = {\begin{matrix} R u p (0.6 * g * \dim * (\frac{1}{S_{i t e r}})) \\ J * S_{i t e r} * GH~when~J < 0 \end{matrix}}, \end{aligned}

(25)

\begin{aligned} A_{u + 1} & = A_{v} + r a n d * (γ - (A_{v} - A_{d}) / 2 * b i r), \end{aligned}

(26)

where,

A_{v}

, and

A_{d}

are chosen at random to replace the babysitters and

GH =

(1 Citer Maxiter)(2 Citer Maxiter) regulates the collective of the dwarf mongooses, and bir is the birthrate.

Step 6: Termination

In this step, the IDMO Algorithm is used to maximize the weight factor values of the generator $α$ from segmentation in the Glioma classification. This process is repeated iteratively until the halting criteria $A = A + 1$ . Finally, by reducing the error rate, CVC-IDMOA-PDACNN-CSV detects glioma categorization with higher accuracy.

3. Results and discussion

The simulation result of the proposed strategy is discussed in this part. Then, proposed strategy is simulated using the MATLAB platform. The proposed DDMP-PDACNN-IDMO approach is implemented in MATLAB using SECOM dataset. The obtained outcome of the proposed DDMP-PDACNN-IDMO approach is analysed with existing methods like DDMP-ANN, DDMP-RNN, and DDMP-BPNN respectively.

3.1. Performance measures

Performance measures include accuracy, and ROC. The performance factors are scaled using the confusion matrix, and it is decided.

–
True Positive $(T P)$ : Perfectly predictive quality of things into success class.
–
True Negative $(T N)$ : Perfectly predictive quality of things into failure class.
–
False Positive $(F P)$ : Imperfectly predictive quality of things into success class.
–
False Negative $(F N)$ : Imperfectly predictive quality of things into failure class.

3.1.1. Accuracy

Accuracy is the capacity to measure an exact value. A metric called accuracy can be used to characterize the performance of the model in all classes. It is quantified by the following Eq. (27)

\begin{aligned} A c c u r a c y = \frac{(T P + T N)}{(T P + F P + T N + F N)} \end{aligned}

(27)

3.1.2. ROC

The ROC indicates the sensitivity or true positive rate, versus 1-specificityor the false positive rate. It is given in the Eq. (28)

\begin{aligned} R O C = 0.5 \times (\frac{T P}{T P + F N} + \frac{T N}{T N + F P}) \end{aligned}

(28)

3.2. Performance analyses

Figure 3.

Performance analyses of Accuracy with proposed and existing technique.

Figure 4.

Performance analyses of ROC with proposed and existing technique.

The simulation outcome of the proposed DDMP-PDACNN-IDMOmethod is shown in Figs 3 and 4. The proposed DDMP-PDACNN-IDMO techniques compared to the DDMP-ANN, DDMP-RNN, and DDMP-BPNN respectively.

Figure 3 depicts the Performance analyses of Accuracy with proposed and existing technique. This figure presents the accuracy performance of four different models: DDMP-ANN, DDMP-RNN, DDMP-BPNN, and the proposed DDMP-PDACNN-IDMO in two classes: “Success” and “Failure.” The DDMP-ANN model shows approximately 75% accuracy in successful class but drops to 25% in failure class, indicating moderate performance. The DDMP-RNN model performs better with around 85% accuracy in success class and 50% in failure class. The DDMP-BPNN model shows 65% accuracy in success class and 45% in failure class, demonstrating balanced but lower performance compared to DDMP-RNN. The proposed DDMP-PDACNN-IDMO model significantly outperforms all others with 98.5% accuracy in success class and approximately 98.2% in failure class, indicating its superior reliability and effectiveness.

Performance analyses of ROC with proposed and existing technique are displayed in Fig. 4. This ROC curve compares the performance of four models: DDMP-ANN, DDMP-RNN, DDMP-BPNN, and the proposed DDMP-PDACNN-IDMO, by True Positive Rate against the False Negative Rate. The DDMP-ANN model shows the slowest rise in TPR, indicating the lowest performance. The DDMP-RNN model performs better with a steeper rise in TPR but is still below the other models. The DDMP-BPNN model shows further improvement with a more significant rise in TPR. The proposed DDMP-PDACNN-IDMO model achieves the best performance, with the steepest rise and highest TPR across all FNR values, demonstrating superior diagnostic ability and effectiveness in distinguishing between true positives and false negatives.

Table 1.

Comparison of experiment result statistics with proposed and existing methods

Measurement		DDMP-ANN	DDMP-RNN	DDMP-BPNN	Proposed
Runtime (s)	Best	43.6	23.7	25.3	9.4
	Mean	51.2	34.1	33.2	13.5
	Std	6.1	5.2	4.3	2.9
MSE (train)	Best	0.0796	0.0692	0.0549	0.0392
	Mean	0.0672	0.0535	0.0541	0.0492
	Std	0.0115	0.0105	0.0072	0.0056
MSE (test)	Best	0.0897	0.0741	0.0626	0.0526
	Mean	0.0982	0.0941	0.0831	0.0652
	Std	0.127	0.0108	0.0091	0.0071
R² (train)	Best	0.6523	0.7821	0.9532	0.9722
	Mean	0.6570	0.6654	0.7682	0.8650
	Std	0.0941	0.0832	0.0742	0.0695
R² (test)	Best	0.8725	0.8985	0.9421	0.9601
	Mean	0.6210	0.6521	0.7082	0.7950
	Std	0.1373	0.1245	0.1120	0.0870

Table 1 presents a comparison of experimental results for different methods: DDMP-ANN, DDMP-RNN, DDMP-BPNN, and the proposed method. The runtime (in seconds) shows that the proposed method outperforms others with the best time of 9.4s, a mean of 13.5s, and a standard deviation (Std) of 2.9s. The proposed technique obtains the lowest best value of 0.0392, a mean of 0.0492, and a standard deviation of 0.0056 in terms of Mean Squared Error (MSE) during training. Similarly, for testing, the proposed method has a best MSE of 0.0526, a mean of 0.0652, and a Std of 0.0071. Regarding the R-squared (R²) values, the proposed method also excels with a best R² (train) of 0.9722, a mean of 0.8650, and a Std of 0.0695. For the test set, it shows a best R² of 0.9601, a mean of 0.7950, and a Std of 0.0870. These results indicate that the proposed method not only performs faster but also achieves more accurate and reliable predictions compared to the existing methods.

4. Discussion

The proposed DDMP-PDACNN-IDMO method for data-driven decision making in manufacturing processes demonstrates significant advancements. Utilizing the SECOM dataset, preprocessing with VBMCCKF enhances data quality by removing noise, while feature selection via LOA identifies critical features for classification. The PDACNN, optimized with IDMO, achieves a remarkable accuracy of 98.5% for success and 98.2% for failure classification, surpassing DDMP-ANN, DDMP-RNN, and DDMP-BPNN. This method also excels in ROC performance, scoring 0.98% higher than existing methods, underscoring its superior predictive capability and effectiveness in precise manufacturing process classification and decision-making scenarios.

5. Conclusion

In this manuscript, data-driven evaluation for themanufacturing process based on PDACNN-IDMO is successfully implemented. The proposed DDMP-PDACNN-IDMO technique is implemented in the MATLAB platform using the SECOM dataset. The proposed DDMP-PDACNN-IDMO method attains 98.5% higher accuracy for the success class; 98.2% higher accuracy for the failure class. The proposed DDMP-PDACNN-IDMO method attains 0.98% higher ROC compared with other existing techniques like DDMP-ANN, DDMP-RNN, and DDMP-BPNN respectively. In conclusion, the proposed PDACNN Optimized with IDMO is a promising approach for manufacturing processes.The proposed DDMP-PDACNN-IDMO method faces several limitations, including its dependency on the quantity and quality of training data, which can significantly impact model accuracy and generalization. The computational resources required for implementing advanced neural network architectures and optimization algorithms may also pose challenges for smaller manufacturing firms. Future research could focus on improving the model’s generalization capabilities across diverse manufacturing processes and conditions, potentially through techniques like transfer learning. Integrating actual -time data from IoT devices could improve the responsiveness of the model and accuracy in dynamic environments. Exploring the application of the proposed method in various manufacturing sectors and combining it with other machine learning techniques could further enhance its robustness and effectiveness, paving the way for broader adoption in the industry.

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