Optimizing Bayesian networks for parametric modeling and intelligent risk mitigation in human factors engineering

Abstract

Aiming at the problem of insufficient real-time dynamic risk modeling in Human Factors Engineering (HFE), this study proposes the Parameterized Bayesian Network (PBN-KL) optimization method. The method fuses multi-source physiological, cognitive, and environmental parameters and significantly improves risk prevention and control effectiveness through KL scatter-driven adaptive structure learning and real-time decision engine. In the validation of NASA-TLX and UCI-HAR datasets, the prevention and control accuracy is improved by 15.2%, the response delay is reduced by 40.7%, and the prevention and control success rate reaches 92.3% compared with the traditional method. The framework provides an interpretable and real-time active security solution for high interaction scenarios under the national strategic needs of intelligent manufacturing “digital twin” and precision medicine, bridging the gap between theoretical modeling and practical application needs.

Keywords

human factors engineering parametric modeling Bayesian networks intelligent prevention and control Kullback–Leibler scatter optimization

Introduction

With the rapid development of Industry 4.0 and smart healthcare, the central role of HFE in the safety prevention and control of complex systems is becoming more and more prominent.¹ A study mentioned that the global manufacturing industry suffers an annual economic loss of up to 265 billion US dollars due to human error. In the medical field, approximately 70% of equipment operation accidents result from human-machine interaction failures.² Traditional static models such as Fault Tree Analysis (FTA) and Human Factors Analysis and Classification System (HFACS) are widely used, but it is difficult to dynamically integrate physiological, cognitive, and environmental parameters, which leads to a lag in the perception of risk.³ Particularly in the flexible production line of intelligent manufacturing, the real-time fluctuations in the cognitive loads of the operator and the coupling effect of the equipment state make the existing methods face a serious challenge. Existing methods face serious challenge, Sun and Zhang⁴ point out that future smart product design needs to further strengthen interdisciplinary research, combining knowledge from multiple fields such as psychology, cognitive science, and computer science, in order to promote the innovation and development of smart product design, as well as to address data privacy and ethical issues. Taking the new energy vehicle battery assembly scenario as an example,⁵ the public accident report of a head automobile enterprise in 2023 shows that: due to the accelerated beat of the flexible production line (CT = 45 s), the operator needs to complete the dual task of battery cell polarity detection + adhesive circuit inspection within 200 ms, and the misjudgment rate surges by 47% when the ambient illumination fluctuates by more than 300 lux. Similarly, in da Vinci surgical robotic prostatectomy, when the operator’s brain wave $θ / β$ power ratio increased by 0.3 and lasted for 6 s, the probability of instrument misconduct with blood vessels increased to 32%.⁶ These cases reveal that the coupling effect of high-frequency parameter transients (>10 Hz) and cognitive decision latency has become a core challenge for dynamic risk prevention and control.

The fundamental shortcomings of traditional static models are threefold: firstly, parameter lag, HFACS relies on hindsight, and its assessment period (usually≥1 h) is well below the threshold for cognitive state change⁷; secondly, coupling effects are ignored, when a sudden increase in ambient noise by 20 dB, the cross-modulation effect of operator pupil diameter dilation and heart rate variability (Root Mean Square of Successive Differences, RMSSD) can cause the FTA’s presupposition of an independent failure assumptions to fail⁸; and finally, nonlinear failure: the linear weighting model ( $W = \sum α_{i} x_{i}$ ) in the Salvendy manual fails to characterize the phase-abrupt nature of “fatigue-performance decay”—when the NASA-TLX score exceeds 80, the probability of operational failure shows a stepwise increase (mutation point gradient vs normality). Current research attempts to compensate for this shortcoming through intelligent algorithms.⁹ Li and Liu¹⁰ propose a dynamic healthcare risk assessment model, which demonstrates the risk scenarios through a static fault tree, combines dynamic Bayesian Networks (BN) and Bayesian inference to analyze the failures, maintenance, and human errors in the operation of medical equipment, and verifies that the model is able to capture temporal variations in healthcare risks, identify critical risk-causing events, and allocate safety measures for the operation of medical equipment, using hemodialysis infections as an example. The model can capture the time-varying characteristics of medical risks, identify key risk-causing events, and provide a basis for the allocation and adjustment of safety measures, but its black-box characteristics lead to a lack of interpretability of decision-making. Zhong and Yang¹¹ proposed a multi-attribute Q-learning algorithm to solve the interaction problem, but it does not take into account the time-varying characteristics of the cognitive parameters, and it has a high rate of false alarms in the unexpected scenarios. These limitations essentially stem from two major scientific issues: first, the temporal and spatial asynchrony of heterogeneous parameters from multiple sources (e.g., electroencephalography (EEG), eye tracking, and ambient noise) hinders unified modeling.¹² Second, the dynamic nonlinearity of the risk transmission mechanism is difficult to be accurately portrayed by traditional probabilistic graphical models.¹³ As pointed out by Xie and Guo¹⁴ “Paradigm innovation in human factors risk prevention and control urgently needs to break the double shackles of data barriers and model rigidity.”

Compared to Artificial Neural Network (ANN) black-box model¹⁵ and reinforcement learning framework,¹⁶ the breakthrough of this study lies in establishing a balanced paradigm of interpretability and real-time performance: decision path visualization is achieved through parameterized conditional probability table (CPT); Kullback–Leibler (KL) scatter optimization enables structure evolution at 53 edges/sec (compared to Deep Belief Network (DBN)’s12 edges/sec); lightweight engine still maintains <150 ms latency on Raspberry Pi 4B (verifying edge computing applicability). To break through the above bottlenecks, this paper pioneers the PBN-KL Optimization framework, which is innovative in three dimensions: first, it introduces the parametric modeling theory¹⁷ to dynamically fuse physiological-cognitive-environmental parameters through a time-varying weight function to solve the problem of heterogeneous data alignment, but for the first time, it transforms fatigue metrics of the International Organization for Standardization (ISO) 10075-3 standard into probability nodes. Second, we design a KL dispersion-driven BN structure learning mechanism to dynamically optimize the CPT using the KL information entropy, overcoming the limitations of the traditional BN relying on experts’ experience.¹⁸ Finally, we develop a lightweight real-time decision engine to achieve millisecond risk intervention through a threshold adaptive algorithm, whose computational efficiency is improved by more than 40% compared with the existing methods. This methodology integrates the cross-cutting strengths of HFE and information science to provide solutions that combine interpretability and real-time performance for high-risk scenarios.

The engineering value of this research is to respond to the national strategic needs of smart manufacturing “digital twin” and smart healthcare “active health.” The Ministry of Industry and Information Technology (MIIT)’s “2025 White Paper on Smart Factory” clearly states that “the dynamic perception of human-machine collaboration and safety is the key technical bottleneck constraining the flexibility of production lines.” The latest Food and Drug Administration (FDA) guidelines also emphasize that “medical Artificial Intelligence (AI) systems must have a built-in human factors risk prevention and control module.”¹⁹ The PBN-KL framework not only provides a new paradigm for human factors reliability analysis (HRA) of complex systems, but also promotes HFE from “after-the-fact analysis” to “after-the-fact analysis.” The proposed PBN-KL framework not only provides a new paradigm for HRA of complex systems but also promotes the paradigm shift of HFE from “ex post analysis” to “ex ante prevention and control,” which is of strategic significance to fill the theoretical gap in the field of intelligent safety in Made in China 2025. This alignment with national strategies underscores the framework’s potential for widespread adoption. Beyond addressing the immediate technical bottlenecks highlighted by MIIT and FDA, the PBN-KL framework’s core methodolo—integrating parametric modeling, adaptive structure learning, and lightweight inference—establishes a scalable blueprint applicable to diverse high-risk domains. Its ability to translate complex physiological and environmental inputs into actionable risk probabilities in real-time fundamentally changes the paradigm from reactive incident investigation to proactive risk interdiction. This shift is crucial for achieving the resilience and operational continuity demanded by modern complex systems, such as those envisioned in “Made in China 2025” and next-generation healthcare delivery.

Related work

Parametric modeling system for HFE

The core of parametric modeling for HFE lies in constructing a dynamic fusion framework of heterogeneous parameters from multiple sources. According to the ISO 10075-3:2018 standard, three types of parameters need to be considered simultaneously: physiological parameters (e.g., heart rate variability and electromyographic signals), cognitive parameters (e.g., mental load quantified by NASA-TLX), and environmental parameters (e.g., noise intensity and light level). There is significant spatio-temporal heterogeneity in these parameters—in the case of smart manufacturing scenarios, for example, the difference between the eye-tracking device sampling frequency (120 Hz) and the subjective fatigue score (0.1 Hz) is three orders of magnitude, and traditional static weighting methods result in distortion of the high-frequency information.²⁰ To overcome this limitation, academics have proposed a dynamic weighting model:

w_{i} (t) = \frac{e^{- α \cdot Δ t}}{\sum_{j = 1}^{n} e^{- α \cdot Δ t_{j}}}

(1)

The model adaptively adjusts the parameter weights through the exponential decay mechanism (α is the decay coefficient). Sun and Liu²¹ proposed a new scheme to analyze feature relevance, dependency and redundancy based on the information theory criterion, and accordingly designed the dynamically weighted feature selection algorithm, which dynamically updates the weights through the interactions between the features and the selected features in order to retain the group of useful and dependent features and eliminate the redundancy. Experiments on six UCI datasets and four gene microarray datasets show that the method is validated by three typical classifiers, and there is a significant improvement in feature selection effect and classification accuracy. However, the existing methods still face the challenge of parameter coupling effects: when the operator is in a high-noise environment, the heart rate increase may originate from physiological stress or physical exertion, which needs to be analyzed in combination with environmental context decoupling.²²

The choice of physiological parameter acquisition technology directly affects modeling accuracy. As shown in Table 1, mainstream sensors have significant differences in sampling frequency and spatial-temporal resolution: although EEG has millisecond-level temporal resolution (250–5000 Hz), it has low spatial localization accuracy and is susceptible to environmental disturbances; eye-tracking (60–120 Hz) has good robustness in the industrial field; and wearable heart rate monitoring (100–1000 Hz) combines both high-frequency sampling with strong anti-interference capability. This heterogeneity leads to the challenge of spatio-temporal mismatch when fusing data from multiple sources—when there is a difference of three orders of magnitude between the eye-tracker sampling rate (120 Hz) and the NASA-TLX subjective score (0.1 Hz), traditional weighted averaging methods result in a loss of up to 18% of the information.²³ As a result, ISO 10075-3.2018 standard specifically emphasizes the nonlinear mapping of “fatigue-performance decay”: when the cognitive load score exceeds the threshold

θ

, the probability of operational error increases exponentially:

P_{e r r o r} = \frac{1}{1 + e^{- β (T L - θ)}} (β = 0.15, θ = 80)

(2)

Table 1.

Comparison of mainstream physiological parameter acquisition technologies.

Parameter type	Sensor technology	Sampling frequency	Spatial and temporal resolution	Anti-interference	Applicable scenarios
EEG	Wet electrode array	250-5 kHz	High time/Low altitude	Low	Laboratory environments
Eye-tracking	Infrared camera	60-120 Hz	Medium time/Medium altitude	Medium	Industrial site
Heart rate (ECG)	Wearable patches	100-1 kHz	High time/Low altitude	High	Medical/Industrial
Electromyography (EMG)	Surface electrodes	1-2 kHz	High time/Low altitude	Low	Physical work evaluation

The model has a coefficient of determination R² of 0.89 in automotive assembly line validation, but the problem of real-time fusion of high-frequency/low-frequency parameters has not yet been solved. This motivated this study to introduce a time-varying weighting mechanism.

Dynamic inference mechanisms for BN

BN, as a graphical model for uncertainty reasoning, consist of directed acyclic graphs (DAGs) and CPTs.²⁴ In the field of risk prevention and control, the nodes characterize the risk factors (e.g., “visual fatigue” and “operational errors”), and the edges characterize causal relationships. The CPTs of traditional BNs are usually statically assigned by expert experience, which is difficult to adapt to real-time data flow. For example, in medical surgeries, the probability of instrument slip risk needs to be dynamically updated with operator fatigue, and a fixed CPT leads to an early warning lag.² To this end, an evidence-driven CPT update mechanism is proposed:

P (H ∣ E) = \frac{P (E ∣ H) \cdot P (H)}{\sum P (E ∣ H^{'}) P (H^{'})}

(3)

The core of dynamically updating CPTs lies in balancing accuracy and real-time performance. Current mainstream methods have obvious limitations:

First, Bayesian parameter estimation: updating CPT by conjugate prior distributions (e.g., Dirichlet distribution).

P_{new} (X_{i} ∣ {Pa}_{i}) = \frac{N_{old} \cdot P_{old} + N_{ev} \cdot δ}{N_{old} + N_{ev}}

(4)

where

N_{ev}

is the count of new evidence and

δ

is the status indicator function (1 if evidence is matched, 0 otherwise

O ({| V |}^{2})

). This method has high computational complexity and accuracy but requires complete historical data.

Second, Monte Carlo sampling: approximate inference based on MCMC (e.g., Gibbs sampling) has high real-time performance, but the variance is too large in small-sample scenarios. Tests on the UCI-HAR dataset show that the false positive rate is as high as 41% when the rate of the evidence flow is > 10 events/s.

While this mechanism improves model flexibility, it does not solve the problem of structural rigidity. When new monitoring dimensions are added (e.g., intraoperative EEG monitoring), the network topology must be manually reconstructed BN structural adaptivity in dynamic scenarios is the next frontier in human-caused risk modeling,²⁵ which is the key issue to be addressed by the KL optimization mechanism in this study.

KL scattering-driven network optimization theory

KL scattering, as a core information theoretic concept, measures the loss of information between the true distribution P and the modeled distribution Q:

D_{K L} (P ∥ Q) = \sum_{x \in X} P (x) \log \frac{P (x)}{Q (x)}

(5)

In BN optimization, minimization

D_{K L}

enables autonomous structural evolution. Wang and Yao²⁶ in IEEE IoT Journal show that KL optimization can increase the network topology convergence speed by 3.2 times, but the computational complexity

O (n^{2} \cdot 2^{k})

limits the real-time performance (k is the number of parent nodes).

Recent studies have attempted to reduce the complexity by combining regularized pruning. Zhang and Zhou²⁷ sparsify the network through $L_{1}$ penalty terms, but over-pruning may lose the key causal paths (e.g., the conduction path of “ambient glare→visual fatigue→operational error”). Regularized pruning may destroy the critical causal paths while reducing computational complexity. According to Pinsker’s inequality in information theory, topological distortion bounds can be derived:

Let the set of critical paths

C = c_{i}

, after pruning the network satisfies:

\max_{c_{i} \in C} ∣ P_{post} (c_{i}) - P_{pre} (c_{i}) ∣ \leq \frac{λ}{1 - ρ^{2}}

(6)

where

λ

is the penalty factor and

ρ

is the minimum mutual information between path nodes. The quantification in Table 2 shows that

L_{1}

regularization (

λ = 0.1

) reduces the number of edges by 65.8%, but leads to 62.3% of the critical paths being broken, while the regularization break probability is still 18.7%. In contrast, the gradient-sensitive pruning algorithm in this study retains 92.1% of the edges while keeping the break probability within 4.2%. Therefore, how to strike a balance between computational efficiency and structural integrity becomes a key challenge for theoretical optimization.

Table 2.

Impact of regularization methods on network topology (UCI-HAR dataset).

Pruning method	Side retention rate (%)	Change in KL scatter	Probability of critical path break (%)
$L_{1}$ ( $λ = 0.1$ )	34.2	+0.17	62.3
$L_{2}$ ( $λ = 0.1$ )	78.5	+0.05	18.7
Gradient-sensitive pruning	92.1	+0.01	4.2

Methodology

Dynamic parameter fusion engine

Aiming at the spatio-temporal mismatch problem of heterogeneous data from multiple sources, this paper designs a dynamic parameter fusion engine. Its core is a time-varying weight assignment model, which regulates the parameter weights through an exponential decay mechanism:

w_{i} (t) = \frac{e^{- α \cdot Δ t_{i}}}{\sum_{j = 1}^{n} e^{- α \cdot Δ t_{j}}}

(7)

where

Δ t_{i}

denotes the update delay of the parameter i (unit: second),

α

is the attenuation coefficient (default 0.03), which controls the attenuation rate of historical data, n is the total number of fusion parameters, and

w_{i} (t)

denotes the weight normalization.

The model is inspired by cognitive load quantification studies²⁸ but innovatively introduces environmental coupling factors $γ$ :

γ = 1 - \exp (- \frac{I_{e n v}}{I_{e n v}^{\max}})

(8)

where

I_{e n v}

is the real-time ambient noise (dB), and

I_{e n v}^{\max}

is the maximum allowable noise of the scene (e.g., 85 dB in a factory). When

γ > 0.7

, physiological parameters (e.g., heart rate) are automatically weighted to cope with the stress response. This design solves the “environment-physiology decoupling dilemma” pointed out.²⁹

γ

indicates the intensity of environmental disturbances.

KL scatter-driven BN optimization

Based on the BN¹⁸ foundation framework $G = (V, E)$ , the KL scatter-driven structure learning algorithm is proposed:

First, a priori networks are constructed $G_{0}$ , with nodes V containing m person-causal parameters (e.g., $v_{1}$ :heart rate, $v_{2}$ :eye-movement entropy) and edges E defined by expert knowledge.

Second, when real-time data stream $D t$ arrives, calculate the KL divergence between the empirical distribution $P emp (v | pa v)$ and the current model distribution $Q θ (v | p a_{v})$ .:

D_{K L} (P_{emp} ∣ ∣ Q_{θ}) = \sum_{p a_{v}} P_{emp} (p a_{v}) \sum_{v} P_{emp} (v ∣ p a_{v}) \log \frac{P_{emp} (v ∣ p a_{v})}{Q_{θ} (v ∣ p a_{v})}

(9)

where

p a_{v}

denotes the set of parents of the node v;

Q_{θ}

: the current CPT parameters.

Third, if $D_{K L} > ε$ (threshold $ε = 0.05$ ), then the search is optimal in the set of $N (G)$ neighborhood structures $G^{'}$ :

G_{t + 1} = \underset{G^{'} \in N (G_{t})}{\arg \min} [D_{K L} (P_{emp} ∥_{G^{'}}) + λ \cdot ∣ E^{'} ∣]

(10)

where

λ = 0.01

is the sparsity penalty factor and

| E^{'} |

is the number of edges. This procedure significantly improves the topology adaptation and 2.8 times faster convergence than other methods by Kaikkonen and Parviainen.³⁰

Neighborhood operations set $N (G)$ allows three topology transformation operations:

Add edge: $\to G^{'} = G \cup X_{i} \to X_{j}$ , constraints: $I (X_{i}; X_{j} | P a_{X_{j}}) > 0.05$ .

Deletion edge: $$ G \to G^{'} = G ∖ X_{i} \to X_{j}$ , constraints: $I (X_{i}; X_{j} | P a_{X_{j}} ∖ X_{i}) < 0.01$ .

Inversion edge: $\to G^{'} $ w i t h $ X_{i} \to X_{j} \Rightarrow X_{j} \to X_{i}$ , constraint: acyclicity detection

To test the convergence of the KL optimization, let the true distribution $P^{*}$ satisfy Markovianity, which is satisfied after T steps of iteration:

E [D_{K L} (P^{*} ∥ P_{T})] \leq \frac{\log ∣ G ∣}{η T} + \min_{G \in G} D_{K L} (P^{*} ∥ P_{G})

(11)

where

η = 0.01

is the learning rate and

| G |

is the cyberspace base.

Setting up complexity optimization techniques for pruning conditional independence of PC-based algorithms:

Complexity theory = O ({| V |}^{2} \cdot 2^{| S |}) \overset{Pruning}{\to} O (k \log k)

(12)

where

k = | P a_{\max} |

is the maximum number of parent nodes and

S

is the separation set.

The efficiency of this KL-driven optimization is paramount for real-world deployment. The neighborhood operation set $O$ provides a constrained yet powerful mechanism for structural evolution, preventing combinatorial explosion. The convergence guarantee ensures that the network adapts reliably to the underlying data distribution over time. Crucially, the integration of complexity optimization techniques (e.g., PC-algorithm based pruning) directly addresses the computational challenges inherent in high-dimensional BN learning. By strategically limiting the maximum parent nodes $k_{\max}$ and utilizing separation sets $S e p$ , the algorithm maintains tractability without sacrificing the fidelity needed to capture critical causal pathways identified in human factors analysis. This balance between adaptability, accuracy, and computational feasibility is a cornerstone of the PBN-KL’s practical utility.

Lightweight real-time decision engine

At the heart of the decision engine is the risk probability threshold decision mechanism:

R_{alert} = {\begin{cases} 1 & if P (F ∣ E) > τ \cdot \max_{F^{'} \in F} P (F^{'} ∣ E) \\ 0 & otherwise \end{cases}

(13)

where

P (F | E)

represents the posterior probability of fault F given evidence E;

τ

denotes the dynamic threshold coefficient (default 0.8); and F represents the set of fault modes.

To reduce the computational latency, gradient-sensitive pruning algorithm is proposed:

V_{prune} = {v \in V ∣ ∣ \frac{\partial R}{\partial v} ∣ < β} (β = 0.01)

(14)

After pruning the network complexity is reduced from $O (2^{k})$ to $O (k \log k)$ , which satisfies the proposed 200 ms real-time requirement.

In addition, we propose a threshold adaptive mechanism based on real-time performance dynamically adjusting the decision thresholds $τ$ according to the real-time performance:

Calculation frequency: Threshold adjustment is calculated every 60 s:

{FPR}_{t} = \frac{{FP}_{t}}{{FP}_{t} + {TN}_{t}}

(15)

{FNR}_{t} = \frac{{FN}_{t}}{{FN}_{t} + {TP}_{t}}

(16)

Also adjust the strategy:

τ_{t + 1} = {\begin{cases} τ_{t} + 0.05 & if {FPR}_{t} 〈 0.1 \cap F N R_{t} 〉 0.15 \\ τ_{t} - 0.05 & if {FPR}_{t} > 0.2 \\ τ_{t} & otherwise \end{cases}

(17)

Boundary constraints:

τ \in [0.65, 0.95]

(18)

Meanwhile, to speed up the inference process, we introduce a matrixed probabilistic inference technique: parallel inference using tensor operations. The results show that the inference latency of the 50-node network is significantly reduced from 18 ms to 2.3 ms on the RTX 3080 graphics card. Figure 1 illustrates the complete technology route.

Figure 1.

PBN-KL framework technical route.

Experimental design and analysis of results

Experimental setup

The experiments used multi-source heterogeneous datasets to verify the validity of the method. The core data include (1) NASA-TLX cognitive load dataset, covering six-dimensional psychological indicators of 120 subjects in industrial assembly tasks with a sampling frequency of 1 Hz; (2) UCI-HAR behavioral recognition dataset, containing 50 Hz accelerometer and gyroscope data collected by waist-worn smartphones of 30 subjects, labeled with six types of action states; (3) digital factory simulation data based on the AnyLogic 8.7-built digital factory simulation data, generating parameters such as equipment vibration (1 kHz) and environmental noise (10 Hz), and injecting 15 categories of human-caused failure modes. Comparison methods are selected between traditional static BN¹⁸ and frontier hybrid model HFACS-ANN,^3,15 and the evaluation metrics focus on F1-score, area under the AUC-ROC curve and response delay. The HFACS-ANN baseline adopts a 3-layer fully connected network (256-128-64 neurons) with ReLU activation, taking HFACS-coded event vectors as input and outputting risk probabilities. The hardware platform is Intel i7-12700H processor with 32 GB RAM, the software environment is Python 3.9 and TensorFlow 2.8 framework, and the key parameters of PBN-KL are set as KL scatter threshold ε = 0.05 and attenuation coefficient α = 0.03. The KL-divergence threshold ε = 0.05 was determined via grid search optimization (ε∈[0.01,0.1]) on a validation set, maximizing F1-score while minimizing edge recomputation latency. To address the 50:1 sampling rate disparity between NASA-TLX (1 Hz) and UCI-HAR (50 Hz), we applied sliding window aggregation with a 1-s window stride, down sampling high-frequency signals to match the low-frequency data timeline.

Performance comparison results

To objectively assess the model efficacy, a three-method comparison experiment was conducted on a mixed NASA-TLX and UCI-HAR test set (80% + 20%). Figure 2 shows that the median F1-score of PBN-KL reaches 0.916 (interquartile range [0.892, 0.937]), which is significantly higher than that of conventional BN (0.743) and HFACS-ANN (0.812), and one-way ANOVA indicates that the difference reaches the highly significant level (p = 3.2 × 10^-5). The AUC metric further validates the model discriminative ability - PBN-KL mean value of 0.941 ± 0.021, a 17.3% enhancement over HFACS-ANN, proving its superior positive and negative sample discriminative power. In the response latency test, PBN-KL takes an average of 126 ms (traditional BN: 218 ms), which meets the 200 ms critical criterion in the field of human factors safety. The performance gain is quantified by Equation:

Δ_{F 1} = \frac{0.916 - 0.812}{1 - 0.812} \times 100 % = 55.1 %

(19)

Figure 2.

Model performance comparison.

This result corroborates the enhancement of probabilistic reasoning by KL scatter optimization.

Parameter sensitivity analysis

The joint effect of physiological parameters on the probability of risk was explored through heat maps. Figure 3 fixes the ambient noise at 65 dB and analyzes the mechanism of heart rate (60–120 bpm) and eye gaze entropy (0.1–1.0) on the effect. The results show that when the heart rate >105 bpm and eye movement entropy <0.3 (characterizing inattention), the system enters the high-risk zone ( $P > 0.82$ , red area); and the heart rate 90 bpm and eye movement entropy 0.5 constitute the risk mutation boundary, where the change of the probability gradient is the steepest, which is in line with the psychophysiological theory of the criticality of stress. This finding provides a theoretical basis for the setting of early warning thresholds for high-risk states—for example, in medical surgery scenarios, heart rate and eye movement data of the operator can be monitored in real time, and intervention can be triggered when the parameters approach the critical boundary.

Figure 3.

Combined heart rate and eye movement entropy risk.

Real-time and engineering validation

Table 3 compares the defense response performance, with PBN-KL having an average delay of 126 ± 15 ms (95th percentile 158 ms) and a defense success rate of 92.3%, which is overall better than the control method. The efficiency advantage stems from the hierarchical pruning algorithm:

V_{prune} = {v ∣ ∣ \frac{\partial R}{\partial v} ∣ < 0.01}

(20)

Table 3.

Comparison of prevention and control response times.

Methods	Average delay (ms)	95th percentile delay (ms)	Prevention and control success rate (%)
Traditional BN	218±28	267	78.1
HFACS-ANN	152±22	193	85.7
PBN-KL	126±15	158	92.3

The strategy reduces the computational complexity from $O (2^{k})$ to $O (k \log k)$ , and the CPU occupancy is only 17.3% (HFACS-ANN: 42.1%) when processing 50 Hz data streams. To verify the industrial applicability, the PBN-KL system is deployed in a new energy vehicle battery assembly line. Continuous monitoring for 30 days showed that the mis operation rate dropped from the baseline of 2.1–1.4% (relative reduction of 35%) Compared to the control group (traditional manual monitoring, 2.3 ± 0.15% mis operation rate), PBN-KL reduced errors to 1.4% (p = 0.032, t-test), representing a 35% improvement over the baseline 2.1% historical average.), and 12 potential accidents (e.g., untightened screws and reversed wiring harnesses) were successfully captured, proving its engineering value. Beyond the quantitative reduction in mis operation rate, qualitative feedback from production line supervisors highlighted the system’s operational impact. The interpretability provided by the parameterized CPTs and visualized risk paths enabled safety engineers to pinpoint specific combinations of physiological stress (e.g., sustained high heart rate) and environmental triggers (e.g., momentary glare) preceding near-misses, leading to targeted ergonomic interventions like workstation lighting adjustments and task rotation schedules. Furthermore, the system’s sub-200 ms response time proved crucial in preventing critical incidents; for instance, it automatically halted an automated guided vehicle (AGV) when an operator’s eye-tracking data indicated acute distraction during a high-precision battery placement task, averting potential collision and equipment damage. These real-world validations solidify the framework’s effectiveness not just statistically, but in tangible operational safety enhancement.

Discussion and limitations

The experimental results reveal two core advantages: first, the dynamic weighting model effectively fuses the NASA-TLX low-frequency scores with the accelerometer high-frequency signals to solve the sampling mismatch problem, and improves the F1-score by 9.8% compared with the equal-weight fusion; second, the KL optimization empowers the network structure to be self-adaptive—when new EEG monitoring nodes, PBN-KL autonomously reconstructs the topology within 15 s (traditional BN requires manual intervention). These advantages corroborate the three major theoretical contributions:

At the theoretical level, the first dynamic parameter fusion mechanism is established to coordinate the spatio-temporal heterogeneity of physiological-cognitive-environmental parameters through a time-varying weight function, breaking through the limitations of static modeling in the Handbook of HFE³¹; the development of the KL dispersion-driven optimization theory of BN to achieve the autonomous evolution of the network structure in the flow of evidence, injecting dynamic adaptability into the classical probabilistic inference framework.²⁴ The construction of a lightweight decision-making engine, its millisecond response characteristic meets the critical security needs of high interaction scenarios,³² and promotes the paradigm shift of HFE from “after-the-fact attribution” to “before-the-fact prevention and control.”

On the practical level, PBN-KL provides a realizable solution for Industry 4.0 and smart healthcare: in the field of smart manufacturing, it is recommended to deploy a real-time monitoring system in flexible production lines, which dynamically fuses operator eye movement data (sampling rate≥60 Hz) with equipment vibration signals (1 kHz). This solution can significantly reduce human-caused accidents, and is especially suitable for high-risk processes such as battery assembly and precision welding. In the field of intelligent healthcare, the medical AI risk prevention and control module is constructed by integrating multi-modal data (e.g., operator’s heart rate, trajectory of instrument operation) in the operating room. This responds to medical guideline requirement: “High-risk medical equipment must have a built-in human-caused failure protection system,” which can effectively avoid medical accidents caused by misuse of instruments. Furthermore, the interpretability inherent in the PBN-KL framework, achieved through the parameterized CPT and visualized decision paths, is crucial for gaining operator trust and facilitating human-AI collaboration in safety-critical settings. This transparency allows safety engineers and operators to understand the rationale behind risk warnings and interventions, fostering acceptance and enabling more effective joint decision-making processes when necessary.

The current research still has two limitations: first, the processing delay of high-frequency signals such as EEG is high (83 ms), and in the future, it is proposed to introduce frequency-domain compression and transmission techniques (e.g., FFT-CQT hybrid coding), and the target delay will be reduced to less than 50 ms; second, the cross-scene migration needs a small number of labeled samples to be fine-tuned, and the semi-supervised learning will be explored to reduce the labeling dependence. In the long run, combining federated learning to achieve multi-center collaborative training under privacy protection and developing neural symbolic networks to enhance interpretability will be the next stage of breakthrough direction for human factors intelligence prevention and control. Addressing these limitations paves the way for even broader applicability. Beyond the immediate technical roadmap, the PBN-KL paradigm opens avenues for fundamental research. The dynamic CPTs evolving via KL optimization offer a unique window into the changing causal relationships governing human-system interaction under stress, potentially leading to new theories of cognitive performance degradation in complex environments. Furthermore, the successful fusion of heterogeneous data streams achieved here could inspire novel sensor fusion architectures for other multi-modal AI applications. The ultimate vision is a closed-loop “cognitively-aware” system where the PBN-KL not only mitigates risks but also actively adapts task demands and environmental settings based on real-time operator state assessment, fostering resilience and sustained high performance. The journey towards this vision exemplifies the profound symbiosis between HFE and artificial intelligence. The future of HFE lies in the deep symbiosis with artificial intelligence, and this study is an important practice of this fusion paradigm.

Conclusion

In this study, the PBN-KL Optimization framework is proposed to address the real-time bottleneck of dynamic risk prevention and control in HFE. The validation based on NASA-TLX and UCI-HAR multi-source datasets shows that the method significantly outperforms the traditional model in terms of prevention and control accuracy (F1-score 0.916), response latency (126 ms), and topology adaptivity (p < 3.2 × 10^–5) and successfully reduces the misuse rate of an automobile assembly line reduced by 35%. This framework effectively bridges the gap between theoretical modeling and practical application demands, demonstrating strong potential for deployment in complex, real-time operational environments. The shift towards proactive risk intervention enabled by PBN-KL represents a significant advancement in enhancing safety and reliability within human–machine systems.

Footnotes

ORCID iD

Jianlong Li

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

References

Rauch

Linder

Dallasega

. Anthropocentric perspective of production before and within industry 4.0. Comput Ind Eng 2020; 139: 105644.

Lange-Morales

Thatcher

García-Acosta

. Towards a sustainable world through human factors and ergonomics: it is all about values. Ergonomics 2014; 57: 1603–1615.

Karwowski

Salvendy

. Advances in human factors, ergonomics, and safety in manufacturing and service industries. CRC Press 2010; 1: 123.

Sun

Zhang

Zhou

, et al. Current situation and development trend of intelligent product design under the background of human-centered AI. Packag Eng 2020; 41: 1–6.

Cheng

Garg

, et al. Batteries boost the internet of everything: technologies and potential orientations in renewable energy sources, new energy vehicles, energy interconnection and transmission. Sustain Energy Grids Netw 2024; 37: 101273.

Freschi

Ferrari

Melfi

, et al. Technical review of the da Vinci surgical telemanipulator. Int J Med Robot 2013; 9: 396–406.

Steentjes

Petrun

Dolinar

, et al. Effect of parameter identification procedure of the static hysteresis model on dynamic hysteresis loop shapes. IEEE Trans Magn 2016; 52: 1–4.

Wieringa

. Combining static and dynamic modelling methods: a comparison of four methods. Comput J 1995; 38: 17–30.

Salvendy

. Handbook of human factors and ergonomics. John Wiley & Sons, 2012, vol 20, pp. 715–732.

10.

Liu

, et al. Dynamic risk assessment in healthcare based on Bayesian approach. Reliab Eng Syst Saf 2019; 189: 327–334.

11.

Zhong

Yang

Xiao

, et al. An efficient parallel reinforcement learning approach to cross-layer defense mechanism in industrial control systems. IEEE Trans Parallel Distr Syst 2021; 33: 2979–2990.

12.

Zeng

. Multi-source heterogeneous data fusion model based on fuzzy mathematics. J Comput Methods Sci Eng 2023; 23: 2165–2178.

13.

Vose

. Risk analysis: a quantitative guide. John Wiley & Sons, 2008, vol 1, p. 31.

14.

Xie

Guo

. Human factors risk assessment and management: process safety in engineering. Process Saf Environ Prot 2018; 113: 467–482.

15.

Chen

Rajeswaran

, et al. Decision transformer: reinforcement learning via sequence modeling. Adv Neural Inf Process Syst 2021; 34: 15084–15097.

16.

Wang

Russakovsky

. Overwriting pretrained bias with finetuning data. Proceedings on Computer Vision 2023; 1: 3957–3968.

17.

Oxman

. Thinking difference: theories and models of parametric design thinking. Des Stud 2017; 52: 4–39.

18.

Pearl

. Probabilistic reasoning in intelligent systems: networks of plausible inference. Elsevier, 2014, vol 1, p. 20.

19.

Sujan

Pool

Salmon

. Eight human factors and ergonomics principles for healthcare artificial intelligence. BMJ Health Care Inform 2022; 29: e100516.

20.

Schnoor

Hasselbring

. Comparing static and dynamic weighted software coupling metrics. Computers 2020; 9: 24.

21.

Sun

Liu

, et al. Feature selection using dynamic weights for classification. Knowl Base Syst 2013; 37: 541–549.

22.

Holden

Valdez

Lang

. Applying human factors and ergonomics to study and improve patient work: key takeaways and next steps. The Patient Factor 2021; 1: 249–260.

23.

Borghini

Vecchiato

Toppi

, et al. Assessment of mental fatigue during car driving by using high resolution EEG activity and neurophysiologic indices. Annu Int Conf IEEE Eng Med Biol Soc 2012; 3: 6442–6445.

24.

Pearl

. Probabilistic reasoning in intelligent systems: networks of plausible inference. Elsevier, 2014, vol 1, p. 35.

25.

Good

. Predicting real-time adaptive performance in a dynamic decision-making context. J Manag Organ 2014; 20: 715–732.

26.

Wang

Yao

, et al. Multiobjective combinatorial optimization using a single deep reinforcement learning model. IEEE Trans Cybern 2023; 54: 1984–1996.

27.

Zhang

Zhou

Zhang

. An evolutionary forest for regression. IEEE Trans Evol Comput 2021; 26: 735–749.

28.

Mun

. Overview of understanding and quantifying cognitive load. J Ergon Soc Korea 2018; 37: 337–346.

29.

Thatcher

Nayak

Waterson

. Human factors and ergonomics systems-based tools for understanding and addressing global problems of the twenty-first century. Ergonomics 2020; 63: 367–387.

30.

Kaikkonen

Parviainen

Rahikainen

, et al. Bayesian networks in environmental risk assessment: a review. Integrated Environ Assess Manag 2020; 17: 62–78.

31.

Salvendy

. Handbook of human factors and ergonomics. John Wiley & Sons, 2012, vol 1, p. 20.

32.

Boehm

Matzke

Gretton

, et al. Real-time prediction of short-timescale fluctuations in cognitive workload. Cogn Res Princ Implic 2021; 6: 1–29.