1 Introduction

Physical education (PE) classes are dwindling as a result of the rising percentage of cultural classes in everyday teaching accomplishments, which is contributing to the continuous reduction of primary, secondary school pupils [1]. It is considered as important to focus on the pupils’ physical qualities [2]. Arm strength of elementary and secondary school pupils are deprived due to lack of physical activity, and numerous students’ arm strength tests fall short of required indices. Hence, it is necessary to increase arm length [3]. Students’ arm strength and flexibility is improved by throwing substantial balls [4]. Because of advances in science and technology, students’ requirements cannot be satisfied by the traditional PE education approach [5]. The conventional PE teaching approach is enhanced, and a brand-new approach based on solid ball teaching suggested. Project-based learning (PBL) revolutionizes traditional education by immersing students in authentic, inquiry-based projects where they tackle real-world problems collaboratively. Rooted in constructivist principles, PBL empowers students to actively engage in interdisciplinary exploration, critical thinking, and problem-solving [6]. Guided by teachers as facilitators, students take ownership of their learning, developing essential skills such as communication and collaboration while gaining a holistic understanding of complex concepts [7]. By fostering learner-centered, hands-on experiences, PBL organizes students for success in the dynamic and interrelated twenty-first-century world, embodying a transformative approach to education that cultivates lifelong learners and critical thinkers. The project-based learning approach has made some progress in exploring a variety of areas. It is implemented to the solid ball instruction for enhancing physical fitness of elementary as well as middle school pupils [8]. Many research specialists analyze PBL as a teaching strategy in the modern day for teaching a variety of disciplines [9]. Researchers put Hybrid-PBL model into practice and used it with physics instructor’s electronic modeling [10]. It effectively increases pupils’ motivation to learn [11]. The evaluated mathematic communication abilities of junior high school pupils using the PBL paradigm are discovered [12, 13]. In this instance, they used the PB teaching approach to instruct students in cooperative scripting [14]. It is discovered that the PBL teaching approach is used to teach literature and has a substantial influence on students’ critical thinking [15]. Studies discovered that the PBL teaching approach enhances students’ explanatory skills as well as their analytical, open-minded, and fair character traits [16]. These findings demonstrate how the PBL teaching approach is up to date with contemporary demands and effectively raise the caliber of instruction in a variety of topic areas [17]. However, due to laziness, many students are unwilling to engage in physical activity [18]. Therefore, there are important issues that need to be resolved regarding encouragement of students’ interest in participating sports and increase effectiveness of classroom instruction [19]. Deep Learning (DL) in this situation, and novel teaching strategy based on PBL is suggested. Here the PBL affected basketball play. The descriptive statistical findings show that extra accomplishments completed. PBL is beneficial while using audio–visual media to play basketball [20]. The PBL affects students’ motivation in phonetics science courses. They identifies element that affect emotive traits, including emotion, person’s own physical link [21]. They discovered that the PBL design frequently undervalued. Students who actively participate in physical education courses after approach has been employed might see the connection among knowledge and action in teaching process [22]. Interested students actively participate in physical education courses after the approach has been employed might see connection between knowledge, action in teaching procedure. PBL was created using DL [23]. The technique involved two middle school classes of students in one location in an attempt to address the issue of students’ declining physical health and the decline in physical education of primary and secondary schools [24]. DL is integrated with PBL to investigate wellness of pupils’ interest in learning solid ball tossing [25]. Then physical fitness of students’ indices measured to see whether this innovative teaching method employed in PE [26]. Idea of PBL outlined and relevant in DL theory elaborated. The fundamentals of PBL are discussed and the pertinent in DL theory is elaborated [27]. In addition, a fresh lesson strategy based on PBL and DL is recommended [28]. The students’ physical fitness scores are then examined by a questionnaire survey to determine the viability of this instructional strategy [29, 30]. In this paper, introduce a pioneering approach to project-based learning (PBL) design for Chinese teaching, merging the ITFCZNN technique with PBL methodologies. The rationale for adopting ITFCZNN stems from its proficiency in classifying and optimizing parameters within intricate datasets, rendering it ideally suited for the nuanced analysis required in educational contexts. By harnessing ITFCZNN, we seek to elevate the precision and efficacy of our PBL design, thereby enriching the delivery of Chinese education. Moreover, the integration of project-based learning (PBL) has garnered considerable attention due to its capacity to cultivate active learning, critical thinking, and practical application of knowledge. The chief novelty of this research lies in its pioneering integration of the ITFCZNN technique with Battle Royal Optimization (BRO) for Project-Based Learning Design in Chinese Teaching (PBLD). Leveraging the specialized LATIC Dataset, the study employs innovative preprocessing techniques, including the Unscented trainable Kalman filter (UTKF), to enhance data quality. By transmitting preprocessed data to ITFCZNN for classification and optimizing weight parameters using BRO, the research introduces a novel framework for effectively tailoring project-based learning approaches to Chinese teaching contexts. This unique fusion of advanced computational methods and specialized dataset utilization sets a new standard for educational data analysis, facilitating the customization of learning experiences while providing comprehensive performance evaluation metrics.

The primary contributions of this research paper are abridged below:

  • The research proposes a novel methodology by integrating the ITFCZNN technique with Battle Royal Optimization (BRO) specifically tailored for Project-Based Learning Design in Chinese Teaching (PBLD).

  • By utilizing the LATIC Dataset, which encapsulates comprehensive information about students’ interests, learning abilities, and physical qualities, the research ensures a robust foundation for data-driven decision-making in PBL design.

  • The application of the UTKF in pre-processing marks a significant contribution by enhancing data quality through noise reduction.

  • Through the transmission of preprocessed data to ITFCZNN for classification and subsequent optimization of weight parameters using BRO, the research introduces a systematic framework for identifying and optimizing PBL approaches tailored to Chinese teaching contexts.

  • The comprehensive evaluation of performance metrics represents a substantial contribution to the field. This thorough analysis offers valuable perceptions to the efficacy and limitations of the proposed methodology, guiding informed decision-making and continuous improvement in educational practices.

Continual paper is structured as follows: division 2 portrays the literature survey, division 3 designates the proposed approach, and division 4 exemplifies the outcomes, division 5 offers conclusion.

2 Literature Survey

Many researches were suggested in the literature on deep learning under Project-Based Learning in Chinese Teaching; a few recent works are divulged here,

Liu and Mu [31] have presented computer network technology analysis on novel media problem-basis Learning Technique. Computer network technology upholds the three variables of learning objectives, projecting components, and teaching methodologies. The presented study disregards reality that students with different degrees have various logical thought processes. The presented study disregards the reality that students with different degrees have various logical thought processes, which only utilizes students from one degree as its experimental subjects. As an outcome, the author expands sample size and research type materials in presented study. With its unique perspective on information, learning, and students, structuralism is a scientifically informed educational paradigm that has provided the theoretical underpinning for teaching and provided theoretical guidance for many instructors’ instruction. The presented method attains higher sensitivity. It attains lower accuracy.

Li et al. [32] have presented the integration of production and education using PBL technique in a physical education classroom. The study presents problem-based learning and novel PE education method based on deep learning’s convolutional neural network. The experimental volunteers are instructed in solid ball tossing using this technique. Through questionnaire survey, solid ball’s physical characteristics, learning capacity, student interest were examined. Academic success of students in solid ball throwing, problem-solving capability, group cooperation, theory learning were increased. They run 1000-m race faster and have flexibility in bodies. Therefore, it was thought the presented new instructional method based on Deep learning contributes to physical development of kids. It provides greater F1 Score and lower Precision.

Fan et al. [33] have presented Interdisciplinary project-based learning: experiences with reflections from teaching electronic engineering at China. A unique course was created as part of UESTC’s undergraduate electrical engineering curriculum using the project-based learning approach. A variety of more conventional electrical engineering courses to construct this novel course’s professional and technical abilities considering teams collaborating on vaguely specified issues are necessary for engineering projects in the real world. The two projects were developed using PBL methodology and assess them as real world. Based on interdisciplinary PBL activities revealed considerable improvement in student fulfilment, according to presented evaluation, which was finished by all 40 of our registered students, 65% students preferred interdisciplinary PBL course contrast with standard lecture. It attains higher Precision. It attains lower Sensitivity.

Jiang and Pang [34] presented Enhancing design thinking in engineering pupils using project-based learning. Here the mixed-method pretest–posttest used in the presented study examines DT-PBL effects on engineering students’ desire for education and imagination. Data from quantitative testing and in-depth interviews indicate the experimental group has higher overall learning desire than comparison group. Students DT, engineering application, and innovation skills are enhanced through complete training assignment that combines software and hardware. The overall creativity was higher in the experimental group than comparison group. The experimental group pupil was more creative and thinks rapidly when it comes to user requests. The presented method attains greater ROC. It attained higher Error Rate.

Kim et al. [35] suggested Analysing Teacher Competency using TPACK for K-12 AI Education. To identify teacher competences required for enhancing K–12 teaching and learning of AI using Technological Pedagogical Content Knowledge paradigm in the presented work. First, the materials now available for AI education and the fundamental AI concepts taught to K–12 students. The research presents TPACK-based analysis of AI curricula and resources to determine teacher competency for K–12 AI education. We conclude that to build, prepare, and manage project-based classrooms where students use AI technology to solve issues, trainers who train AI to K–12 pupils need TPACK. It attains higher Sensitivity. It attains lower F1 Score.

Chen and Du [36] have presented Chinese as Foreign Language Teaching and Learning Intercultural Online Collaborative Projects. Here, sequential empirical mixed-method approach combines quantitative data from the project product evaluation and knowledge exam with qualitative data from conversation logs, semi-structured interviews. The experimental class students beaten control class in project results, despite findings reveals no difference in knowledge exam scores between two courses and good project work from both classes. The findings present that PBL approach benefits CFL novices. The pupils’ deep considerate of target culture theory, micro-setting life experience sustenance CFL learning at an entrance level, even if online intercultural collaboration features not matter for knowledge learning part. The presented method attains lower Computation Time and greater ROC.

Barak and Yuan [37] have presented a cultural viewpoint on project-basis learning and the expansion of creative thinking. Here the Chinese international students and local students valued PBL’s contribution to creative thought development. Data were gathered through focus groups, pre- and post-questionnaires, and a mixed-methods case study approach. Both groups’ perceived innovative thinking was fostered by the PBL method, albeit there were disparities in the behaviors. The local students who developed new ideas cited advantages of idea networking, whereas the Chinese students identified advantages of observing behaviors. It attains greater Precision and lower Accuracy.

Li and Zhu [38] have presented the development of students’ transferrable abilities in a mixed, project-based learning environment was presented through a new three P model. Academic desire and course design are prerequisite variables that favorable effect learner engagement and process components of a blended learning experience. The transferrable abilities development as product variable was positively impacted by learning engagement as a process variable and academic motivation as cause variable. Both have positive effect on transferrable abilities develop product variable. By raising students’ academic motivation and optimizing course design, it is vital to boost their sense of experience and engagement in blended learning with projects, so fostering growth of students’ transferrable abilities. It provides lesser computation time and lesser accuracy.

In Sect. 2, a comprehensive literature survey is provided, encapsulating recent research contributions in project-based learning (PBL) within Chinese teaching contexts. The review includes analyses of various innovative approaches, such as the application of deep learning methods in physical education by Li et al. [32], the interdisciplinary project-based learning approach in engineering education by Fan et al. [33], and the exploration of teacher competencies for K-12 AI education by Kim et al. [35]. Additionally, insights into the cultural perspective of PBL and its impact on innovative thinking among students are examined by Barak and Yuan [37], while the development of transferrable abilities in a mixed, project-based learning environment is discussed by Li and Zhu [38]. By synthesizing these diverse findings, the presented section aims to offer a complete understanding of existing research laying the groundwork for subsequent expansion of the proposed method.

3 Proposed Methodology

In this step, PBLD-ITFCZNN-BRO is discussed. The block diagram of proposed PBLD-ITFCZNN-BRO presented in Fig. 1. Dataset, pre-processing, categorization and optimization are the four main processes that simplify the procedure. The detailed explanation part is described beneath,

Fig. 1
figure 1

Proposed methodology diagram of project-based learning design for Chinese teaching based on ITFCZNN

Full size image

3.1 Data Collection

The data are gathered from LATIC dataset [39]. The learners of non-native Mandarin Chinese are the main emphasis of LATIC. An annotated database of non-native Chinese speech is accessed in online for any available purpose. Automatic speech grading, assessment, derivation-L2 instruction, education of Chinese as foreign language are examples of related usage areas. A very small scale and extremely effective training deviation dataset is approached to deliver.

3.2 Data Pre-processing by Unscented Trainable Kalman Filter

In this section, UTKF is used for pre-processing method [40], the unscented transition (UTKF), which transfers variables and cannot modify raw distribution of LATIC Dataset employed to elucidate nonlinear function, reduce estimate fault. Forecast must locate and fill gaps in the measurement’s incomplete information. The prediction accuracy and error accumulation would fall if networks trained solely on disconnected data. Then formula is formulated as Eq. (1)

$$\in \left( {g + 1} \right) = l\left( {a\left( {g + 1} \right),\hat{a}\left( {g + 1} \right)} \right),$$
(1)

where \(\in \left( {g + 1} \right)\) denotes residual at time \(g + 1\), \(\hat{a}\left( {g + 1} \right)\) denotes prediction state vector at time \(g\), \(l(a(g + 1))\) denotes residual function. Additionally, the transition function is linearized using the Jacobian matrix. Then the formula is formulated as Eq. (2)

$$\hat{a}\left( {g + 1} \right) = u\left( {F_{1:g} \left( g \right)} \right),$$
(2)

where \(F_{1:g} (g)\) denotes state time-series matrices from initial time to time \(g\), \(\hat{a}\left( {g + 1} \right)\) denotes prediction state vector at time \(g\).Unscented transition (UT), transfer variables without altering underlying data distribution, used to get rid of nonlinear function and reduce estimate error. Then the prediction procedure gives sigma points. Then the formula is formulated as Eq. (3)

$$A^{\left( j \right)} \left( {g + 1} \right)\, = \,\hat{A}\left( {g + 1} \right) - \left[ {\sqrt {\left( {j + \lambda } \right)\sum\limits_{{}}^{ \wedge } {_{a} \left( {g + 1} \right)} } } \right]j,$$
(3)

where \(A^{\left( j \right)} \left( {g + 1} \right)\) signifies \(g{\text{th}}\) sigma point of prediction \(A(g + 1)\); \(\sum\limits_{{}}^{ \wedge } {_{a} \left( {g + 1} \right)}\) signifies predicting state covariance matrix; \(j\) as 2 to \(n + 1\),\(n + 2\) to \(2n + 1,\) respectively;\(\left( . \right)j\) signifies \(j\) column of matrix,\(\sqrt .\) signifies Cholesky factorization operation. The measuring procedure characterized as follows after formation of sigma points. Then the formula is formulated as Eq. (4)

$$\sum\limits_{{}}^{ \wedge } {_{C} \left( {g + 1} \right) = \sum\limits_{J = 1}^{2n + 1} \theta }^{(j)} \left( {\gamma {}^{(j)}(g + 1) - \hat{C}(g + 1).(\gamma^{(j)} (g + 1) - \hat{C}(g + 1)} \right)^{G} + L(g + 1),$$
(4)

here \(\theta (j) = {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {2N}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${2N}$}},\quad j = 1,2, \ldots ,2N + 1\) denotes weights; \(\gamma {}^{(j)}(g + 1)\) signifies sigma point of measurement; \(\hat{C}(g + 1)\) signifies measurement matrix-based prediction; \(L(g + 1)\) denotes measurement process noise matrix; \(\sum\limits_{{}}^{ \wedge } {_{C} \left( {g + 1} \right)}\) signifies measurement variance matrix. Using this method, it removes noise from data which is collected from LATIC Dataset. Then the pre-processed data are transmitted to classification Phase.

3.3 Classification by Interference-Tolerant Fast Convergence Zeroing Neural Network

In this section, ITFCZNN is discussed [41, 42]. The popular Chinese teaching based on ITFCZNN method enhanced to become multiple classification recognition method. The label information from the authentic and fake samples is integrated into noise reduction and convergence to ITFCZNN in fixed time. Furthermore, compared with exponential or finite and fixed-time convergence generate with conditional information. Then it is adjusted to the output type of ITFCZNN. Then the formula is formulated as Eq. (5)

$$\phi \left( a \right) = \left( {\left| a \right|^{{{\raise0.7ex\hbox{$l$} \!\mathord{\left/ {\vphantom {l s}}\right.\kern-0pt} \!\lower0.7ex\hbox{$s$}}}} + \left| a \right|^{{{\raise0.7ex\hbox{$l$} \!\mathord{\left/ {\vphantom {l s}}\right.\kern-0pt} \!\lower0.7ex\hbox{$s$}}}} } \right)\,{\text{sgn}} \left( a \right) + G_{1} a + G_{2} {\text{sgn}} \left( a \right),$$
(5)

where \(\phi \left( a \right)\) denotes element of \(\Phi\); \(\Phi\) denotes activation function; \({\text{sgn}}\) denotes signum function; \(G_{1} a\) denotes noise suppression in convergence;\(\left( {\left| a \right|^{{{\raise0.7ex\hbox{$l$} \!\mathord{\left/ {\vphantom {l s}}\right.\kern-0pt} \!\lower0.7ex\hbox{$s$}}}} + \left| a \right|^{{{\raise0.7ex\hbox{$l$} \!\mathord{\left/ {\vphantom {l s}}\right.\kern-0pt} \!\lower0.7ex\hbox{$s$}}}} } \right)\) denotes fixed-time convergence than advanced exponential or convergence of limited time, and then value of \(l > 0\,,\quad G_{1} > 0\quad {\text{and}}\quad G_{2} > 0\) is considered. Then the ITFCZNN model with additive noises is and the next part will discuss the ITFCZNN’s interference-tolerant and quick convergence capabilities, then the formula is formulated as Eq. (6)

$$X\left( {T_{m} } \right)A\left( {T_{m} } \right) = - X(T_{m} )A\left( {T_{m} } \right) - \lambda \Phi \left( {X\left( {T_{m} } \right)A\left( {T_{m} } \right) - P} \right) + Q\left( {T_{m} } \right),$$
(6)

where \(\Phi\) signifies activation function;\(X\left( {T_{m} } \right)A\left( {T_{m} } \right)\) realize fixed-time, convergence noise suppression simultaneously and \(Q\left( {T_{m} } \right)\) denotes additive noise and constant or time-changing noise. Under proper estimated conditions of Chinese learning, \(l\,\,and\,\,s\) satisfy \(l\,\, > > \,\,s\) and the convergence time \({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 \gamma }}\right.\kern-0pt} \!\lower0.7ex\hbox{$\gamma $}}\) which consumed while project-based learning (PBL). Then the formula is formulated as Eq. (7)

$$T_{t\max } \le \frac{1}{G}\,\left| {\frac{1}{{1 - {\raise0.7ex\hbox{$l$} \!\mathord{\left/ {\vphantom {l h}}\right.\kern-0pt} \!\lower0.7ex\hbox{$h$}}}} + \frac{1}{{{\raise0.7ex\hbox{$h$} \!\mathord{\left/ {\vphantom {h l}}\right.\kern-0pt} \!\lower0.7ex\hbox{$l$}} - 1}}} \right|\, = \,\frac{1}{G}\left| {\frac{{1 + {\raise0.7ex\hbox{$h$} \!\mathord{\left/ {\vphantom {h l}}\right.\kern-0pt} \!\lower0.7ex\hbox{$l$}}}}{{1 - {\raise0.7ex\hbox{$h$} \!\mathord{\left/ {\vphantom {h l}}\right.\kern-0pt} \!\lower0.7ex\hbox{$l$}}}}} \right|,$$
(7)

where \(T_{t\max }\) irrelevant to initial state \(a(0)\), and relates to design parameters \(l\), \(h\) of system; \(\frac{1}{G}\) used as counterparts compared with this work. This method states that ITFCZNN model’s dynamic error matrix \(f(T_{m} )\) may be written as \(\frac{{em\left( {T_{m} } \right)}}{en} = \lambda \Phi \left( {f\left( {T_{m} } \right)} \right)\,\) and its \(m^{2}\) subsystem can be obtained. Then the formula is formulated as Eqs. (8) and (9).

$$\frac{{em\left( {T_{m} } \right)}}{en}\, = \,f_{ij} \left( {T_{m} } \right)\,{\text{sgn}} \left( {f_{ij} \left( {T_{m} } \right)} \right),$$
(8)
$$\frac{{em\left( {T_{m} } \right)}}{en}\, = \, - \lambda \phi \left( {f_{ij} \left( {T_{m} } \right)} \right)\,{\text{sgn}} \,\left( {f_{ij} \left( {T_{m} } \right)} \right),$$
(9)

where \(\frac{{em\left( {T_{m} } \right)}}{en}\) bounded time \(f_{ij}\) of \(ij{\text{th}}\) subsystem;\(f_{ij} \left( {T_{m} } \right)\) selected to demonstrate ITFCZNN model fixed-time convergence; \({\text{sgn}}\) signifies signum function. To implement neural networks practically, interference and noises are unavoidable; in this section, ITFCZNN model with different interference and noises addressed. Then the formula is formulated as Eqs. (10) and (11)

$$\frac{{em\left( {T_{m} } \right)}}{en}\,\, = \,\,2f_{ij} \left( {T_{m} } \right)\,f_{ij} \,\left( {T_{m} } \right),$$
(10)
$$\frac{{em\left( {T_{m} } \right)}}{en}\,\, = \,\,2f_{ij} \,\left( {T_{m} } \right)\,\left( { - \lambda \phi \left( {f_{ij} \,\left( {T_{m} } \right)} \right) + m_{ij} \left( {T_{m} } \right)} \right),$$
(11)

where \(\frac{{em\left( {T_{m} } \right)}}{en}\) bounded time \(f_{ij}\) of \(ij{\text{th}}\) subsystem;\(f_{ij} \left( {T_{m} } \right)\) selected to demonstrate prove ITFCZNN model fixed-time convergence; \(\phi \left( a \right)\) signifies element of \(\Phi\);\(\Phi\) signifies activation function;\(\lambda\) prove fixed time convergence of ITFCZNN technique. Finally, ITFCZNN describes the project based learning among students. The artificial intelligence-basis optimization technique is used in ITFCZNN classifier because of its pertinence and ease. The Battle Royal Optimization (BRO) employed to optimize ITFCZNN. Here, BRO is used for tuning weight and bias \(\phi\) parameter of ITFCZNN. Step-by-step description of the Battle Royal optimization algorithm process is given below,

3.4 Optimization Using Battle Royal Optimization

The weight parameter \(\phi\) of propose ITFCZNN is optimized using the proposed BRO [43]. Optimization using battle royal optimization (BRO) provides a versatile and efficient approach to solving a wide range of optimization problems. BRO stands out for its ability to search for global optima, avoiding the pitfalls of local optima common in many optimization algorithms. By incorporating both exploration and exploitation strategies, BRO effectively balances the need to explore new regions of the solution space while exploiting promising areas. Its population-based approach allows for parallel exploration of multiple solution candidates, facilitating thorough exploration of complex search spaces. BRO is highly adaptable, making it suitable for various optimization tasks, and its efficiency in converging to high-quality solutions makes it particularly valuable for time-sensitive applications. Additionally, BRO’s robustness to problem complexities and ease of implementation further enhance its appeal for researchers and practitioners across different domains. It is a novel nature-inspired algorithm. It was inspired from Battle Royal social behavior and moving strategies. Each person is represented as a soldier or player in the population-base algorithm, whom seeks to migrate toward the safest (optimal) location and eventually live.

3.4.1 Stepwise Process of BRO

BRO distributes the random population uniformly throughout the problem space. Every soldier/player attempts to hurt the nearby soldier by firing a weapon. Therefore, soldiers in best positioning cause harm to their nearby soldiers. The damage level of soldiers rises by one when it is injured by another. The step-by-step process is delineated to obtain unique value of ITFCZNN depending upon BRO. Initially, BRO provides the similar dispersing populace to enhance optimal \(\phi\) of ITFCZNN. The best solution is upgraded using BRO method and the associated flowchart is represented in Fig. 2.

Fig. 2
figure 2

Flow Chart of BRO for Optimizing ITFCZNN

Full size image

Step 1: Initialization.

The initial populace of BRO is generated by randomness. Then the formula is formulated as Eq. (12)

$$R\, = \,\left\{ \begin{gathered} R_{1a} \,\,\,\,\,\,\,\,R_{1b} \,\,\,\,\,\,\,\,R_{1c} \hfill \\ R_{2a} \,\,\,\,\,\,\,\,R_{2b} \,\,\,\,\,\,\,\,R_{2c} \hfill \\ .\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,.\,\,\,\,\,\,\,\,\,\,\,\,\,\,. \hfill \\ .\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,.\,\,\,\,\,\,\,\,\,\,\,\,\,\,. \hfill \\ R_{na} \,\,\,\,\,\,\,\,R_{nb} \,\,\,\,\,\,\,\,\,\,R_{nc} \hfill \\ \end{gathered} \right\},$$
(12)

where \(R\) denotes initially generated random population of solider in battle field and distributed in range \(\left[ {0,1} \right]\). The soldiers like to change their position instantly after taking damage, so attack enemies from other side. So, to focus on exploitation, the injured soldier moving towards the point anywhere amongst the prior state and best state identified up to now (elite player) using Eq. (13),

$$R_{Dam,\,D} = R_{Dam,\,D} + Rg\left( {R_{GlobalBest,D} - R_{Dam,D} } \right),$$
(13)

where \(Rg\) signifies randomly created number uniformly dispersed in \(\left[ {0,1} \right]\) range,\(R_{Dam,\,D}\) denotes damaged soldier location in element \(D\), \(R_{GlobalBest,D}\) signifies collected best solution of the solider in the battle field, respectively.

Step 2: Random generation.

After initialization, input parameters are created at random. The explicit hyperparameter condition determines the optimal fitness value selection.

Step 3: Fitness Function.

A random solution is created by the fitness function using initialized values. Fitness function is calculated using optimizing parameter. Then the formula is formulated as Eq. (14)

$$Fitness\,Function = optimizing\,\,\,[\,\phi ],$$
(14)

where \(\phi\) is for increase accuracy.

Step 4: Exploration Phase.

Here, the soldiers will randomly respawn from viable problem space with their injury may reset to zero if their degree of damage exceeds a predetermined threshold. By doing this, early convergence is avoided and better exploration is provided. Equation (15) shows the soldier returning to problem space after being killed.

$$R_{Dam,\,D} = e\left( {ij_{D} - kj_{D} } \right) + kj_{D} ,$$
(15)

where \(ij_{D}\) and \(kj_{D}\) specifies lower, upper bounds of \(D\) dimension at problem space. The problem’s viable search space starts to condense towards optimum solution. It involves moving the problem to manageable place as ideal global solution starts to become less possible. In this phase, BRO will approach in searching of global best location it. Additionally, because the new location is determined at random, BROs exploration power is increased. Then the formula is formulated as Eq. (16)

$$qy_{D} = R_{GlobalBest,\,D} - TD\left( {\overline{R}_{D} } \right),$$
(16)

where \(TD\left( {\overline{R}_{D} } \right)\) denotes standard deviation of whole populace at dimension \([D]\); \(R_{GlobalBest,\,D}\) denotes global ideal solution position found in battle field and \(R_{GlobalBest,\,D} - TD\left( {\overline{R}_{D} } \right)\) which does not exceeds actual lower and upper bound, then set as original; \(Wy_{D} \,and\,qy_{D}\) denotes lower, upper bounds of \(D\) dimension at problem space.

Step 5: Exploitation phase for optimizing \(\phi\).

In every \(\Delta\) iteration, the problem’s viable search space starts to constrict in the direction of the optimal solution. The initial value is expressed in Eq. (17),

$$\Delta = \log_{10} \left( {Maxcicle} \right),$$
(17)

where \(Maxcicle\) refers maximum generations. BRO in this area will search best area towards their global best new location along with the leaders. BRO would move to their new position according the leaders. Then the algorithm provides a better solution for the best location, then the potential increases during the exploitation phase. So, the BROs moving position is derived mathematically. Then the formula is formulated as Eq. (18)

$$Wy_{D} = R_{GlobalBest} + TD\left( \phi \right),$$
(18)

where \(R_{GlobalBest,\,D}\) denotes global best solution position found in battle field,\(R_{GlobalBest,\,D} + TD\left( \phi \right)\) exceeds actual lower or upper bound, then leads as original; \(Wy_{D} \,and\,qy_{D}\) denotes lower, dimension \(D\) upper bounds in problem space. Because BRO strikes a better balance between exploration and exploitation, it is able to find the global optimum fast and resist being readily caught by local optima. An ideal balance between exploitation and exploration is achieved by having people migrate after taking damage, respawns, and finally having a small viable search space.

Step 6: Termination.

From ITFCZNN, the weight parameter \(\phi\) generator is enhanced through BRO, otherwise repeat step 3 until fulfil the halting criteria \(R = R + 1\). Finally, the PBLD-ITFCZNN-BRO effectively assesses quality of Project Based Learning Design for Chinese Teaching with better accuracy by decreasing computational period without error.

4 Results and Discussion

The stimulation output of PBLD-ITFCZNN-BRO is discussed in this segment. The PBLD-ITFCZNN-BRO method is done in PYTHON using PC through Intel Core i5, 2.50 GHz CPU, 8 GB RAM, Windows 7 through LATIC Dataset. The acquired outcomes of PBLD-ITFCZNN-BRO approach are analyzed with existing CNT-PBLTM [31], PBL-DL-PEC [32], and Interdisciplinary PBL-EEC [33] systems.

4.1 Performance Measures

The performance of PBLD-ITFCZNN-BRO approach is examined utilizing mentioned performance metrics.

4.1.1 Accuracy

This is a fundamental performance metric to measure the effectiveness of categorization models, including those used in project-based learning design for Chinese teaching. It calculates the ratio of accurately categorized samples among the total samples evaluated. Then the formula is formulated as Eq. (19)

$$Accuracy = \frac{{\left( {TP + TN} \right)}}{{\left( {TP + FP + TN + FN} \right)}}.$$
(19)

Let TP symbolizes true positive, TN symbolizes true negative, FP epitomizes false positive, FN epitomizes false negative.

4.1.2 Precision

It measures the percentage of accurate positive predictions among every model’s positive predictions. It is calculated using Eq. (20)

$$\Pr ecision = \frac{{TP_{{}} }}{{\left( {TP + FP} \right)}}$$
(20)

4.1.3 F Score

This is also termed as the F1 score and is measured as the harmonic mean of precision with recall which offers a balanced measure of model’s accuracy. This is expressed in Eq. (21)

$$F{\text{ - Score}} = 2 \times \frac{{{\text{recall}} \times {\text{precision}}}}{{{\text{recall}} + {\text{precision}}}}.$$
(21)

4.1.4 Sensitivity

This is a metric used to evaluate the capability of a method to appropriately identify positive instances from every actual positive instance. The rate of true positives to the sum of true positives and false negatives using Eq. (22),

$${\text{Sensitivity}} = \frac{{{\text{TN}}}}{{\left( {{\text{FP}} + {\text{TN}}} \right)}}.$$
(22)

4.1.5 ROC

A binary classifier system’s diagnostic potential is indicated graphically by the ROC curve, which shows the system’s variable discrimination threshold. This is computed by Eq. (23),

$${\text{ROC}} = 0.5 \times \left( {\frac{{{\text{TP}}}}{{{\text{TP}} + {\text{FN}}}} + \frac{{{\text{TN}}}}{{{\text{TN}} + {\text{TP}}}}} \right).$$
(23)

4.1.6 Error Rate

It is a fundamental performance metric to measure the accuracy of predictive models or categorization algorithms. It measures the ratio of incorrect predictions produced by the technique with the total predictions. This is expressed in Eq. (24)

$${\text{Error}}\;{\text{rate}} = \left( {1 - {\text{Accuracy}}} \right).$$
(24)

4.2 Performance Analysis

The simulation result of PBLD-ITFCZNN-BRO is shown in Figs. 3, 4, 5, 6, 7, 8, 9. In these figures, the performance is compared to the existing CNT-PBLTM, PBL-DL-PEC and PBL-EEC methods.

Fig. 3
figure 3

Accuracy analysis

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Fig. 4
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Computation time analysis

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Fig. 5
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Error rate estimation

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Fig. 6
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F1 score estimation

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Fig. 7
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Precision analysis

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Fig. 8
figure 8

Performance sensitivity analysis

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Fig. 9
figure 9

ROC estimation

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Figure 3 portrays accuracy analysis. In the context of the proposed optimization methodology, accuracy reflects the techniques’ capacity to appropriately classify and predict results related to project-based learning in Chinese teaching. A greater accuracy value indicates a more reliable and precise model, whereas a lower accuracy value suggests a need for refinement or optimization of the methodology. The proposed PBLD-ITFCZNN-BRO method attains 15.26%, 20.42% and 21.27%greater accuracy compared with existing CNT-PBLTM, PBL-DL-PEC and PBL-EEC methods.

Figure 4 depicts computation time analysis. A shorter computation time indicates higher efficiency, enabling faster iteration cycles and quicker decision-making processes. However, it is essential to balance computation time with other performance metrics, such as accuracy and precision, to ensure that efficiency does not compromise the quality of results. The proposed PBLD-ITFCZNN-BRO method attains 28.58%, 21.12% and 19.01% lower computation Time compared with existing CNT-PBLTM, PBL-DL-PEC and PBL-EEC models.

Figure 5 determines error rate estimation. A lower error rate indicates higher accuracy and better performance of the model in making correct predictions. Conversely, a higher error rate suggests lower accuracy and potential shortcomings in the model’s predictive capabilities. The proposed PBLD-ITFCZNN-BRO method attains 7.12%, 14.89%, and 20% lesser Error Rate compared with existing CNT-PBLTM, PBL-DL-PEC and PBL-EEC models.

Figure 6 depicts F1 score estimation. The model makes accurate positive predictions while limiting false positives and false negatives when it has a high F1-score, which is indicative of high precision as well as high recall. It is especially helpful when interacting with datasets that are unbalanced or where recall and precision are essential components. The proposed PBLD-ITFCZNN-BRO method attains 16.71%, 19.50% and 22.24% greater F1-score compared with existing CNT-PBLTM, PBL-DL-PEC and PBL-EEC methods.

Figure 7 depicts precision analysis. A high accuracy number is a model with low false positive rate, which means that is accurate when it forecasts a positive result. In the project-based learning design of Chinese teaching, precision reflects the model’s capacity to precisely recognize successful learning outcomes or effectively categorize students into relevant groups based on their traits. The proposed PBLD-ITFCZNN-BRO method attains 15.61%, 17.50% and 20.24% greater precision compared with existing CNT-PBLTM, PBL-DL-PEC and PBL-EEC methods.

Figure 8 depicts sensitivity analysis. A greater sensitivity value represents a better ability of the technique to detect positive instances, while a lower sensitivity value suggests a higher rate of false negatives, indicating missed positive instances. In the context of evaluating the optimization method for project-based learning design in Chinese teaching, sensitivity provides insight into the model’s effectiveness in correctly identifying successful learning outcomes or meeting predefined learning objectives. The proposed PBLD-ITFCZNN-BRO method attains 19.16%, 20.42% and 22.27% greater sensitivity compared with existing method CNT-PBLTM, PBL-DL-PEC and PBL-EEC methods.

Figure 9 depicts ROC estimation. In the context of evaluating the optimization method for project-based learning design in Chinese teaching, the ROC curve serves as a valuable performance metric for measuring the classifier’s capacity to distinguish among positive and negative outcomes. The proposed PBLD-ITFCZNN-BRO method attains 19.02%, 21.89% and 14.76% greater ROC compared with existing methods like CNT-PBLTM, PBL-DL-PEC and PBL-EEC methods.

4.3 Discussion

The integration of ITFCZNN enhanced with Battle Royal Optimization (BRO) for Chinese teaching for students depends on Project based Learning. The proposed technique goal is to improve the educational process with offering a dynamic, engaging setting in which students can investigate and become proficient in different subject areas. The model can efficiently assess and understand students’ categories at many scales to ITFCZNN, which captures complicated patterns and dependencies in the LATIC Dataset. The network’s bidirectionality makes it possible to process Chinese learning data in both forward and backward contexts, improving its capacity for character recognition and improving learning interpretation and performance evaluation. By identifying the ideal collection of hyper-parameters, BRO optimization of the ITFCZNN enhances the model’s performance even more. Battle Royale’s foraging behavior is imitated by BRO’s nature-inspired search process, which helps it move across the parameter space and converge on superior solutions. The ITFCZNN is well adapted to the unique requirements of the Chinese learning training courses, it is a fine-tuning procedure that increases the classification of Chinese learning under the mentioned metrics. Through this immersive experience, students can practice their newly acquired abilities in groups inside authentic environments, which aids in the development of their stage presence, confidence, and flexibility in a variety of performing contexts. Chinese language proficiency in PBL improves students’ comprehension of difficult concepts and develops a greater respect for the art form. Several performance metrics are used to examine performance of proposed method. These metrics show how well the system is at predicting students learning system. The model’s error rate measures its overall prediction inaccuracy, demonstrating its dependability in real-world teaching situations. In addition, computing time is an essential parameter to assess the effectiveness of the model and its practicability for use in practical settings. The real-time interactive aspect of the project-based Chinese learning system is not slowed down by a computational time that is kept under control by an ITFCZNN that has been optimized using BRO. Students gain a deeper understanding and appreciation of studying Chinese as a result of the interactive and engaging learning environment that is created by combining cutting-edge deep learning methods, nature-inspired optimization, immersive project-based learning. The thorough assessment employing many performance indicators assure that the proposed technique is successful, effective, and appropriate for project-based learning of Chinese language instruction. Implementing the PBLD-ITFCZNN-BRO methodology in real educational settings necessitates careful consideration of practical implementation and scalability. Educators require access to adequate computational resources for executing the ITFCZNN and BRO algorithms, along with seamless integration into existing educational frameworks. Teacher training and support are paramount to assure the efficiency in methodology utilization, while adherence to data privacy regulations is essential for safeguarding student information. Scalability hinges on optimizing algorithms to accommodate diverse student cohorts and instructional contexts, supported by continuous evaluation and feedback mechanisms to assess effectiveness and refine implementation strategies.

5 Conclusion

Due to the growing number of cultural courses in current primary and secondary Chinese education curriculum, lessons are increasingly being cut back and traditional teaching techniques are ineffective in piquing students’ interest in studying. So, a PBL and DL-based teaching strategy is suggested. PBL teaching method suggested depend on ITFCZNN in DL. The performance of proposed PBLD-ITFCZNN-BRO approach contains 19.16%, 20.42% and 22.27% greater sensitivity, and 16.71%, 19.50% and 22.24% greater F-score, compared with existing methods like CNT-PBLTM, PBL-DL-PEC, and Interdisciplinary PBL-EEC, respectively. The methodologies utilized in this article may exhibit several potential shortcomings. The dependency on specialized techniques such as ITFCZNN and BRO could restrict the applicability of the findings, potentially requiring substantial computational resources or not being universally adaptable to diverse educational contexts. The effectiveness of the proposed methodology, PBLD-ITFCZNN-BRO, hinges heavily on the quality and quantity of the input data that introduce biases or inaccuracies if not rigorously curated and validated. In future, several promising avenues emerge from the findings and limitations of this study. Further exploration into hybrid optimization approaches to bolster efficiency and robustness. Additionally, efforts to address the limitations of data quality and quantity could involve the integration of diverse sources or the development of novel data collection methodologies, ensuring greater representativeness and reliability in student profiling.