Fractional time derivatives of a heat equation with a rotational field are used to probe the model during photo-excitation processes. Micropolar-thermoelasticity theory, which the model implements, introduces the microelongation scalar function to characterize the processes occurring inside the microelements. When the microelongation parameters are considered following the photo-thermoelasticity theory, the model investigates the interaction scenario between optical-thermo-mechanical waves under the impact of rotation parameters. During electronic and thermoelastic deformation, the key governing equations have been reduced to dimensionless form. Laplace and Fourier's transformations are used to solve this mathematical problem. Isotropic, homogeneous, and linear microelongated semiconductor medium's general solutions to their respective fundamental fields are derived in two dimensions (2D). To get complete solutions, several measurements must be taken at the free surface of the medium. As an example of numerical modeling of the important fields, we will use the silicon (Si) material’s physicomechanical characteristics. Several comparisons were made using different values of relaxation time and rotation parameters, and the results were graphically shown The significance of semiconductors has lately developed as a result of advancements in materials research. Semiconductors play a crucial role in the growth of contemporary industries, particularly those that rely on the existence of low-voltage electric currents, such as sensors and transistors. Unlike copper or glass, semiconductors are poor electrical conductors and poor insulators under normal conditions. Yet, their internal resistance starts to diminish when they are subjected to a steady rise in temperature as a consequence of being impacted by light falling on them or laser beams. As a result, the physical characteristics of semiconductors became more of a focus in the second part of the twentieth century. It has been discovered that when the temperature of these materials changes, so do their interior characteristics, most noticeably their internal composition (microelements). Light-excited electrons are transferred to the surface, giving rise to the photothermal (PT) hypothesis and the so-called electronic deformation (ED). Yet, the thermoelasticity hypothesis emerges when the interior particles begin to vibrate, leading to thermoelastic deformation (TD). The preceding elastic deformations and thermodynamic deformations cause a crossover between the photo-elastic theory (PT) and the thermoelastic theory (TE), giving rise to the photo-thermoelasticity theory. As the microelements of the semiconductor are responsible for the variation in internal resistance, their influence during the microinertia process must be considered during the interference operations .1. In this case, the degrees of freedom (director) of semiconductor characteristics rely on the micropolar theory1. The board of directors is unbending when it comes to studying the microstretch and micropolar theories of semiconductors. When the directors are orthogonal and contract, the microelongational theory of material arises as a specific instance. In introducing the micropolar theory, Eringen2 considered the microstructure of the elastic body. Instead, Eringen3 presented a new microstretch–thermoelasticity model that captures the interplay between the microstretch parameters and thermoelasticity theory. Elastic bodies subjected to external fields are the focus of several studies that use the generalized microstretch thermoelasticity hypothesis9. Casson fluid flow over porous media of varying thickness was the subject of research by Ramesh et al.10. Hydromechanics of one-relaxation-time viscoelastic porous media were investigated by Ezzat and Abd-Elaal11 using a viscoelastic boundary layer flow. To study the effects of an internal heat source on wave propagation inside a microelongated elastic media, researchers have turned to Refs.13. The thermo-elastic microelongated governing equations were established by Ailawalia et al.16 to analyze the plane strain deformation of an elastic material with an embedded heat source. According to thermoelasticity theory, the double porosity structure is developed using the micropolar theory of the elastic body17. Sheoran et al.20 studied the wave propagation according to thermo-mechanical disturbances in a 2D initially stressed with temperature dependent in a rotating thermo-diffusive medium with two-temperature. On the other hand, some applications for a thermodynamical nonlocal micropolar semiconductor media are investigated according to functionally graded properties22.At the macro-scale, where matter is assumed to be continuous, classical continuum mechanics is sufficient to describe the mechanical behavior of solids; but, at the micro-scale, where the mechanical behavior is size-dependent, this theory fails. To explain both the microstructure and the macro-scale size issues, consistent size-dependent continuum mechanics was necessary. Microelongation parameters and the influence of heat effect on the internal structure of semiconductors are investigated. Therefore there are four possible orientations for a microelongated semiconductor. One is caused by the rotating movement (microelongation) of electrons during ED deformation, while three others are dependent on the change happening during TD deformation25. When a semiconductor is exposed to a strong laser beam, heat is often generated as an unwanted consequence26. To fully comprehend how successfully a semiconductor absorbs the laser energy, one must first grasp how freely moving electrons and holes interact with one another inside the material29. Heat transfer properties are crucial in semiconductor laser interactions because of their impact on device quality and performance33. For the laser to function, pulsed excitations must be applied, which is why semiconductors are so prevalent in optical communication systems and energy pumping38. The active zone of lasers that are activated by periodic pulses may overheat if their temperature does not fall to that of the heat sink before the next cycle starts. It is important to understand the thermodynamic responses, notably the thermal time constant, to get the most out of a laser diode's power output41. Recently, the use of fractional differential equations as a foundation for theoretical models has received a lot of attention. Mathematical frameworks with a fractional order differential equation may provide a greater understanding of the phenomena due to the memory effect and the fact that it is rotating.The study of semiconductor properties dates back to the late nineteenth century. As a consequence of scientific and economic developments during the twentieth century, semiconductors saw amazing application in a wide variety of fields, from the incorporation of medical equipment to electrical circuits and even solar cells that create renewable energy. The internal systems of semiconductor implants were discovered to possibly vary with temperature, especially when exposed to light or a laser beam )By studying semiconductors, it was found that excited electrons move about and scatter toward the semiconductor's surface, creating an electron cloud called carrier density (plasma). The finding of this electron cloud is significant since it is the source of the diffusion processes that ultimately result in the passage of electric current. In addition, as part of the recombination process, electrons leave holes behind when they go through a material, even if they are in the shape of a cloud. These situations often arise during hole diffusion processes, and in recent years thermo-optical theory has shown to be a valuable tool for describing the corresponding system of equations. Thermoelastic deformation processes for these semiconducting materials may also be described by introducing and implementing the notion of thermoelasticity into this area. The primary motivation for introducing this subject is to investigate, within the framework of photo-thermoelasticity theory, the impact of microelongation parameters during the investigation of semiconductor materials. In this study, the photo-thermoelasticity theory is used in the investigation of a microelongated semiconductor material in a rotating field. The model is formulated using the fractional-order heat conduction equation. Here, we account for the microinertia and microelements of the semiconductor medium. Using dimensionless variables, the governing equations in 2D deformation are translated into their non-dimensional versions. By using the Laplace and Fourier transforms approach, we can derive the physical domain expressions for a variety of physical variables with specific boundary conditions. The rotation field's influence on the simulated wave propagations is shown visually, along with some comparisons, concerning the micro-elongation parameters and fractional parameters.45:Plasma wave propagation is described by the optical function, which is the carrier density mentclass2pt{minim16:According to the photo-thermoelasticity theory, the microelongated constitutive equations of semiconductors in the tensor form are46:It is possible to express the plasma transport (diffusion) equation in such a way that it describes the interaction between thermal waves and plasma waves as47:When the medium is in a state of microelongation in accordance with the processes of microelements, the motion and microinertia equations, which are valid under the influence of the rotating field, may be presented as follows20:Following is a definition that may be presented in accordance with the Riemann–Liouville fractional integral operator28:The Riemann–Liouville fractional integral of order On the other hand, the definition of the fractional derivative proposed by Caputo is:16:Elastic-electronic body theory yields the following form for the time-fractional heat conductive equation in a microelongated semiconductor medium:  terms may be transformed into the non-dimensional ones.By deleting the superscripts, Eq.  may be uHelmholtz's theorem allows us to express translations as functions in both scalar The above set of Eqs. –17), ma, ma17), Recasting the 2D constitutive relations yields:Initial conditions satisfying the following homogeneous requirements may be considered in finding a solution to the problem:Using their specified Laplace and Fourier transformations for every function Applying the transformation of Eq.  for the Equations –30) are are30) a of Eqs. –(30) as:The following is a possible factorization of Eq. :33\documGeneral form linear solutions to Eq.  may be eThe components of displacement and stress components described in Eqs.  and 31)31), in t44. The requirements might be stated as.At the boundary , we, we\docuThe complete solutions of the main physical quantities are obtained when the above system of according to Eq. , which aThe inversion of the above main equations in the time physical domain is required to get the full solutions of the 2D distributions of dimensionless physical field variables. For problems in two dimensions in Cartesian coordinates, this is the generic solution in the domain of the Laplace–Fourier transform.It is possible to express the inverse Fourier transform as:36.Nonetheless, a Riemann-sum approximation approach is employed for the numerical inversion of Laplace transformsThe inverse of a function 36.The Fourier series expansion can be used for the function 15:Microelongation theory When the plasma wave effect is disregarded, thermoelasticity under the influence of a rotating field is achieved  are used to run numerical simulations. The numerical findings may be visually shown in MATLAB (2022a). The Si parameters needed to create a graphical simulation using the SI unit of the physically relevant constants areIn this work, we calculate the wave distributions of the principal fields in 2D using non-dimensional variables. Small-time numerical simulations are performed in the 52. For three distinct photo-thermoelasticity models, the distribution of microelongation vibration against distance is shown in the second inset figure. Three different instances of the thermal relaxation time  are shown in Fig. The influence of relaxation time on the variation of basic fractional physical variables as a function of horizontal distance . Microelongated silicon semiconducting media are simulated numerically under controlled circumstances. All physical distributions of waves in propagation have been shown to eventually settle into a stable equilibrium. All physical quantities tend to vary more consistently. It was also discovered that the wave propagation of the physical variables under examination is significantly affected by the relaxation times. Compared to the LS, and CD theories of photo-thermoelasticity, DPL has been shown to have superior vibrational behavior. The results of the thermoelastic heat equation are significantly impacted by the existence of the fractional time derivative. Moreover, the propagating waves show an obvious influence on the rotation parameter. Microelongated semiconductor silicon is very important to research and has several potential applications in today's state-of-the-art electronic gadgets, including but not limited to sensors, computer processors, diodes, accelerometers, inertial sensors, and electric circuits.


Click-through rate (CTR) prediction is a research point for measuring recommendation systems and calculating AD traffic. Existing studies have proved that deep learning performs very well in prediction tasks, but most of the existing studies are based on deterministic models, and there is a big gap in capturing uncertainty. Modeling uncertainty is a major challenge when using machine learning solutions to solve real-world problems in various domains. In order to quantify the uncertainty of the model and achieve accurate and reliable prediction results. This paper designs a CTR prediction framework combining feature selection and feature interaction. In this framework, a CTR prediction model based on Bayesian deep learning is proposed to quantify the uncertainty in the prediction model. On the squeeze network and DNN parallel prediction model framework, the approximate posterior parameter distribution of the model is obtained using the Monte Carlo dropout, and obtains the integrated prediction results. Epistemic and aleatoric uncertainty are defined and adopt information entropy to calculate the sum of the two kinds of uncertainties. Epistemic uncertainty could be measured by mutual information. Experimental results show that the model proposed is superior to other models in terms of prediction performance and has the ability to quantify uncertainty.  With the rise of multimedia applications, CTR prediction tasks have appeared in many scenarios, such as precise advertising placement and product recommendations on e-commerce platforms. Since every user’s click behavior can be regarded as a display of their preferences, CTR prediction is the process of learning user preferences from stored historical user data and then using them to predict future behavior.The development of CTR prediction models can be divided into two aspects: automatic feature engineering and improving model capabilities. Since the features in CTR prediction are usually in specific fields, how to effectively learn rich information from feature interaction becomes a key challenge of CTR prediction. For the early CTR prediction model, due to the limitation of computing capacity, artificial feature engineering and a simple machine learning model were adopted. The method used in the CTR prediction task was linear models, such as the logistic regression (LR)  model, wSubsequently, significant progress has been made in CTR prediction due to advances in deep neural networks (DNNs) in learning representations. Models, such as the product-based neural network (PNN) , deep crBecause of the limitation of available training samples and the existence of incoherent noise, quantification uncertainty should be an integral part of any prediction system. While the development of machine learning tools means large progress, the uncertainty in the models maintains a huge gap worth exploring. In essence, most existing research is based on deterministic models and is short of the capability to acquire uncertainty. As we all know, Bayesian theory is commonly used to describe modeling errors and also provides mathematical tools for the uncertainty of inference models. Deep learning and Bayesian statistical theory are combined as Bayesian deep learning to offer uncertainty estimates for deep structures. In contrast to traditional deep learning models that produce deterministic predictions, Bayesian machine learning provides not only predictions but also uncertainty, which is estimated by the probability density of the outcome.Gal et al.  proposedThe Innovations of this work can be summarized as:(1) We propose a CTR prediction model based on Bayesian deep learning, which learns high-order feature interaction information and models of two kinds of uncertainties. The model achieves efficient and reliable prediction.(2) A framework combining feature selection and feature interaction is proposed. In the feature selection module, CNN and MLP are used to generate meaningful feature interactions. The feature interaction part is modeled by squeeze network and DNN parallel for feature interactions, respectively.(3) In the above framework, the Monte Carlo dropout is used to perform a posteriori approximate inference on the parameters of the model and obtain the integrated prediction results. The uncertainty of the model is quantified by information entropy.(4) Experiments on three datasets evidence that the prediction performance of our proposed model performs better than the most advanced models. A reliable uncertainty quantification is carried out for the model.The remainder of our work is made up of the following: (1) CTR PredictionIn recent years, CTR prediction tasks have developed rapidly and have made very big breakthroughs. Its research mainly uses machine learning methods to predict the user’s clicks on advertisements in subsequent times based on the historical behavior data of users and attribute information.Initially, some shallow models were used. The combination of the LR model and artificial feature engineering, such as mixture of logistics regression (MLR) , gradienFactorization machines deep neural network (FNN)  was the The DIN model is the first method to introduce attention to user behavior modeling, which assigns different weights to users according to their historical behavior and the relevance of current goods through the attention module. On this basis, the DIEN and deep session interest network (DSIN)  models a(2) Uncertainty in the ModelsDeep learning models with uncertainty measurements have been widely used in many applications. For example, Wang et al.  proposed(1) CTR prediction. Given training data (2) The epistemic uncertainty is a measure of the uncertainty of the model parameters. It derives from the limited representation ability of the observed value, which denotes the difference between the predicted value (3) The aleatoric uncertainty measures the noise intrinsic in the data. This uncertainty cannot be eliminated. It is expressed as the output of a function, which is represented by the difference between the predicted entropy and mutual information;(4) Objective function. Logloss is regarded as the loss function for a binary classification problem. We train our model by minimizing the following objective function:The design idea of the Bayesian deep learning model is shown in In this paper, we first exploit the strengths of the CNN to extract the neighbor feature interactions, while complementing it with a recombination layer to extract the global feature interactions. Then the squeezing network and DNN are applied to learn the high-order feature interactions in parallel. The diagram of the FiBDL is displayed in (1) Feature selection. The feature selection module aims to identify useful local and global patterns to generate meaningful feature interactions. In the original feature space, meaningful feature interactions are always sparse. CNN has a parameter sharing and pooling mechanism, which can extremely decrease the number of parameters applied to discover important local patterns, which provides an idea for feature selection. Since it only produces neighbor feature interactions, many meaningful global feature interactions have been lost. So we use MLP to reorganize them to learn the global feature interaction.Let A max-pooling layer is applied after the convolutional layer to obtain the most important feature interactions. The output can be denoted as:Performing the above process multiple times can generate new features.(2) Squeeze network. We have designed a squeeze network that is inspired by the CIN module in the xDeepFM model. The structure is shown in The features of the input and the hidden layer in the squeeze network are, respectively, organized into a matrix, denoted as The calculation of the hidden layer can divide it into two steps:(1) The specific approach is the outer product of the vectors of each row of (2) The second step is to perform a convolution calculation on the result of the first step to obtain a new feature map result. Each convolution calculation will perform a convolution calculation on the entire feature map, as shown in The characteristics of the squeeze network are that the order of the feature interaction that is finally learned is decided by the number of layers of the network, and each hidden layer is connected to the output through a pooling operation, thus ensuring that the output unit can see feature interaction modes of a different order.(3) Deep neural network. This module is composed of fully connected layers, which is a network with a multi-layer perceptron. There is a non-linear activation function between layers, a layer that is hidden from both input and output, and also needs to maintain a high degree of connectivity, which is determined by the weight of the network. The formula is as follows:The difference from the traditional Bayesian theory is that the Bayesian neural network introduces parameters into the prior distribution. To obtain the uncertainty estimation of the FiBDL model, the prior distribution is placed on the parameters of the deep neural network to determine the posterior distribution of parameters to achieve the best prediction.The epistemic uncertainty is a measure of the uncertainty of model parameters. It derives from the limited representation ability of the observed value, which denotes the difference between the predicted value Given BDL with Upon determining an appropriate prior distribution based on prior knowledge, the model likelihood is Under this posterior, if we have a new input instance The target of Bayesian inference is to obtain the posterior o (MCMC)  and variSpecifically, this method defined an easy-to-evaluate distribution log-likelihood expectation. It can be approximated by MC integration with a single sample It has been proved in that the minimization of the KL divergence is equivalent to the maximization of the evidence lower bound. Maximizing it will result in the variational distribution According to the approximate posterior log-likelihood is approximated by MC integration of Equation (13). It is equivalent to performing Next, our predictive For CTR prediction, the general practice is to compress the model output by the In classification settings, uncertainty can be measured by predictive entropy For a new input In a Bayesian neural network, Our main work is to construct a prediction model and measure the uncertainty. In this section, we validate the FiBDL model from two aspects. The first one is to illustrate the superiority of the model in CTR prediction by comparing it with several benchmark models. The second is to quantify the uncertainty of the proposed model in its predictions.(1)Datasets(1) Taobao dataset is a dataset of CTR prediction about display ads, which is displayed on the website of Taobao. The dataset consists of two parts: user_profile and ad_features.(2) Avazu dataset is published in the CTR prediction contest on Kaggle in 2014. It contains four types of attributes: user, website, advertisement, and time. Each click sample has 24 data fields, including 22 category features.(3) ICME dataset is utilized to predict whether users will finish watching and like videos. Each click sample has two dense features and nine sparse fields.Following shuffling, all of the datasets are further randomly divided into train and test sets. We randomly placed 80% of the sample data in the training set and 20% in the test set.(2)Evaluation metricsIn this paper, we use Logloss and RMSE, two metrics to measure the prediction performance of all models.Logloss is a criterion widely applied for classification problems. It balances the difference between the predicted value and the true value. Its definition is as in Equation (1).RMSE is a criterion of the deviation between the predicted value and the true value. As a metric for uncertainty in this article, the RMSE is denoted as:(3)BaselinesLR. The LR model can only learn linear combinations of features and lacks the ability to obtain feature interactions;FM. The FM model only can learn second-order feature interaction information but cannot model high-order feature interactions;AFM. The AFM added an attention mechanism to the FM model to obtain feature weights of effective features;FNN. The FNN model placed FM pre-trained low-dimensional features on DNN, enabling it to generate high-order features automatically;WDL. The WDL adopted a dual-path structure, which joins the generalization of the deep model with the memory of the wide linear model;xDeepFM. The xDeepFM proposed CIN for vector-wise feature interaction that can obtain explicit and implicit high-order feature interactions simultaneously;AutoInt. The AutoInt model employed a multi-head self-attention network to attain explicit higher-order feature interactions;FiBiNET. The FiBiNET adopted SENET to learn the importance of features, and learn feature interactions by a bilinear function;DIFM. The DIFM model utilized fully-connected layers and multi-head self-attention networks, respectively, to obtain feature interactions from bit-wise and vector-wise levels;DeepFEFM . The DeeDCN V2 . The DCNMoFM. The MoFM model combined LR, FM, and self-attention networks to obtain both low- and high-order feature interactions;XCrossNet . The extThe FiBDL model is compared with the following models, each model is briefly described as follows:Compare the prediction performance of the FiBDL model with the existing classical efficient model described in the previous section. The performance of all models is shown in The performance of LR is worse than other models, which illustrates the ability of the performance of both factorization models and deep neural network-based models. FM and AFM models can model second-order feature interactions to improve prediction accuracy. AFM significantly outperforms FM on all datasets, which is probably attributed to the performance of the attention mechanism in feature learning. Models, such as FNN, xDeepFM, etc., have achieved further performance improvements by combining FM and neural networks into a framework. The reason is that neural networks help FM-based models draw out helpful information for the prediction task. Furthermore, both FiBiNET and DIFM can measure feature importance in the feature learning stage. Models that combine core architectural components that learn explicit or implicit feature interactions with deep neural network components are beneficial for improving prediction performance.Experimental results show that compared with the classical shallow prediction methods , the FiBDL has an advantageous position in prediction performance. The improvement stems from the fact that the FiBDL model learns high-order feature interaction information. The performance of the FiBDL model significantly outperforms the best and most advanced models. The performance metric Logloss is decreased by about 3.25%, 11.99%, and 1.81% compared to the best baseline method on all datasets, respectively. The reason may be that we completed the feature selection in the initial stage, which pruned redundant feature information. This is useful and positive for feature learning. Learning both implicit and explicit higher-order feature interactions simultaneously plays an important role in prediction tasks and is useful for improving performance.Of the three datasets, FiBDL is about 1.95%, 9.77%, and 0.55% lower than the best performing model on the RMSE criterion, respectively. According to the results of Logloss and RMSE on the three datasets, the superiority of the proposed FiBDL model in the CTR prediction task is verified.To verify the effectiveness of using Monte Carlo with dropout to model uncertainty, we compare the FiBDL model with the basic model without dropout. According to No feature selection (FS): removing the feature selection module means that meaningful features cannot be selected for feature interaction;No squeeze network (SN): removing the squeeze network indicates that the model cannot learn higher-order feature interactions explicitly;No DNN: removing the deep neural network, then the model cannot model higher-order feature interactions implicitly.To verify the validity of each part in the FiBDL model and to better understand their relative importance, in this set of experiments, one part is removed and the rest are kept constant.(1)Prediction performanceObserve the two metrics that measure the CTR prediction performance, as can be seen in Removing the feature selection module, the performance of the model on the Avazu dataset degrades significantly. It increased by about 3.67% and 3.12% in Logloss and RMSE, respectively. For the other two datasets, there is 0.38% and 0.75% heightened in Logloss (0.23% and 0.67% by RMSE). It demonstrates that the selection of the input data before feature interaction can improve the prediction performance.Once DNN was deleted, the Logloss of the model on all datasets was significantly reduced by about 1.28%, 2.23%, and 3.43%, respectively. The performance degradation was significant on three datasets. It proved that the modeling of high-order feature interaction implicitly by DNN has a considerable influence on the model.Following the removal of the squeeze network, the performance of the model on the Avazu dataset has remarkably fallen. The Logloss on the remaining two datasets is not significant. The RMSE on the three datasets has increased approximately by 0.25%, 2.26%, and 0.64%, respectively. It demonstrates the effectiveness of squeeze networks in learning explicit higher-order feature interactions. It can be seen that FiBDL outperforms all ablation methods. This validates that any component of the FiBDL model proposed is critical for prediction performance.(2)Uncertainty QuantificationAs To examine how the predictive performance and two types of the uncertainty of the FiBDL model vary as the training data increases, we use 20%, 40%, 60%, 80%, and 100% of the training data, respectively, to train the FiBDL model.As shown in (1)Effect of the Dropout RatioDropout is a regularization technique that prevents overfitting. It refers to temporarily dropping neurons from a deep learning network at a given probability during training. In this paper, we conduct experiments with a dropout ratio ranging from {0.05, 0.1, 0.15, 0.2, 0.25, 0.3}.(2)Effect of the Network DepthIn the deep part, adding hidden layers can better separate the features of the data. The number of network layers is changed, and we observe how the model performance and uncertainties change with the increase of the network layers.By increasing the depth of the neural network, the number of MC dropout layers of the FiBDL model will also increase. The results are shown in (3)Effect of the Training EpochThe experiments on the training epoch of the model are tested in this section. Experiments were performed on the same randomly generated train-test splits of the data. Experiments are on the same training-test dataset.The uncertainty results are shown in Aiming at the uncertainty problem in the CTR prediction model, we propose a CTR prediction model based on Bayesian deep learning. To improve the representation of the features used in the model, we build a prediction structure that combines feature selection and feature interaction. Feature selection module is used to select meaningful global feature interactions, squeeze network, and DNN in parallel and is used to model higher-order feature interactions. we train a dropout network and use dropout to obtain prediction Monte Carlo samples at test time, and then use information entropy to quantify the uncertainty. Bayesian deep learning architecture can reliably estimate the uncertainty and improve the robustness of the model by introducing uncertainty into the parameters of the neural network. Experimental results show that this model can provide reliable prediction and effective uncertainty estimation.


Hermetia illucens (L.) (Diptera: Stratiomydiae) has gained popularity across the globe due to its usefulness mainly in animal feed production and waste management. The short cycle time taken to rear the BSF and the high protein content present in its larvae makes it a suitable source of feed for a variety of animals ; the livestock bred as food for humans. However, despite the farming of black soldier fly larvae (BSFL) as a source of feed, its production levels are low and do not meet the existing market demand. This study explored data science and machine learning modeling approaches to discern optimal rearing conditions for improved BSFL farming. The random forest regressor machine learning algorithm gave the best prediction results. The algorithm also ranked the variables that contributed most to the prediction of the expected larvae weight. Given the studied rearing conditions, the prediction algorithm can discern and predict the expected weight of BSFL to be harvested. Tuning the production system parameters according to the order of the ranked parameters can further optimize the production of BSFL. BSFL are a source of feed for the animals that are a source of food for humans; therefore, this research contributes to alleviating food insecurity.In recent years, farming the black soldier fly (BSF) Hermetia illucens (L.) (Diptera: Stratiomydiae), as a source of feed stands out due to its sustainability and reliability. Black soldier fly larvae (BSFL) have the ability to convert organic substrates to high-quality biomass rich in protein for animal feed. They can also produce biodiesel and bioplastic and have high biotechnological and medical potential. However, current BSFL production is low to meet the industry’s needs. This study used machine learning modeling approaches to discern optimal rearing conditions for improved BSF farming. The input variables studied include the cycle time in each rearing phase , feed formulation type, length of the beds  at each phase, amount of young larvae added in the first phase, purity score , feed depth, and the feeding rate. The output/target variable was the mass of wet larvae harvested (kg per meter) at the end of the rearing cycle. This data was trained on supervised machine learning algorithms. From the trained models, the random forest regressor presented the best root mean squared error (RMSE) of 2.91 and an R-squared value of 80.9%, implying that the model can be used to effectively monitor and predict the expected weight of BSFL to be harvested at the end of the rearing process. The results established that the top five ranked important features that inform optimal production are the length of the beds, feed formulation used, the average number of young larvae loaded in each bed, feed depth, and cycle time. Therefore, in that priority, it is expected that tuning the mentioned parameters to fall within the required levels would result in an increased mass of BSFL harvest. These data science and machine learning techniques can be adopted to understand rearing conditions and optimize the production/farming of BSF as a source of feed for animals e.g., fish, pigs, poultry, etc. A high production of these animals guarantees more food for humans, thus reducing food insecurity.As the world population continues to grow, there is a need to come up with alternative sources of feed and food to combat the existing challenge of food insecurity across the globe. The use of insects, particularly the black soldier fly (BSF)  Hermetia illucens (L.) (Diptera: Stratiomydiae) larvae as a source of feed for farmed animals which in turn are used to provide food for humans [It is estimated that the world population will grow to approximately 8.5 billion by 2030 and 9.7 billion by 2050; on the African continent, it is expected that 26 out of the 54 countries in the region will experience a population increase that is at least double their current size by 2050 . TherefoBlack soldier fly larvae (BSFL) stand out from other commonly farmed insects due to several reasons. They have a short maturity period  . This imAs a result, this research employed a machine-learning-driven approach to investigate the rearing parameters with the aim of incorporating data-driven decision making in the farming of BSFL to optimize its production. In this context, the term optimize refers to the best possible combination of rearing parameters that result in maximum weight harvest of the larvae based on the rearing process. The BSFL farming process at the (anonymized) factory is mechanized and encompasses the use of Internet of Things (IoTs) devices to collect data and monitor larval growth. This study utilized the data collected by IoTs and employed data science and machine learning approaches to generate insights for the purpose of facilitating data-driven decision making in addition to coming up with a model to optimize and predict the harvested larvae weight.Data were collected from a mechanized BSF factory (anonymized), from the month of February to September 2022, with the assistance of domain experts. In the factory setup, the rearing process was divided into two phases (1 and 2). Thereafter, the BSFL were harvested. The total mass was measured using a weighing balance, and the mass was recorded separately for each bed. The final dataset had 14 variables; 13 input variables and 1 target variable. In this context, the target variable refers to the mass of larvae harvested, while input variables refer to the features that impact the mass of larvae harvested. The variables are explained in In Phase 1, the hatched eggs were reared for a period of 3–7 days on different substrate  compositions. After that, the larvae were then moved to Phase 2, where they were introduced to a different substrate (Formulation SM and B) composition. The larvae stayed in Phase 2 for 7–10 days. Just before the larvae transitioned into the pre-pupae stage, the BSFL per bed were harvested by sieving them from the substrate, and washed. Their wet weight was measured using a weighing balance and recorded. The weighing balance used in measuring the weight was a highly customized Yaohua A12 electronic weighing scale (model number TCS2-A12E).This process entails cleaning the dataset for purposes of analysis. Different procedures can be used in this process, including handling missing values , outliers , and duplicates (repeated entries). (a)Missing completely at random (MCAR): MCAR happens when missing entries are randomly distributed across variables and are unrelated to other features. Kenyhercz and Passalacqua  came acr(b)Missing at random (MAR): This study also identified missing at random (MAR) data entries. In MAR, the missing data in one variable can be explained by another variable in the same dataset. For this study, the variables imputed using this approach include the feeding rate and the number of young larvae loaded at the first phase. To solve this, this research integrated the weight class adjustment approach. It was implemented using the group-by methodology  based onMissing data values refers to random null values (empty entries) within the dataset. In this context, this could have been due to technical errors during the data collection process. The following items discuss the specific missing data problems that were identified in the dataset and how they were imputed/calculated:Lp) and values above the upper percentile (Up) were considered to be outliers and were floored and capped respectively. The ranges for flooring and capping percentiles, shown in df represents the data frame, x is the variable of interest, and An outlier is an extreme value that is isolated from other values. In this study, outliers were not removed from the dataset; instead, a flooring and capping approach was used to replace the outliers with the respective floor and capping computed values. Flooring entails replacing all the values that fall below the selected minimum in a data column with a calculated value that falls within the set range, while capping entails replacing all the higher-side values that fall above the selected maximum . Table 2Feature transformation involves techniques that convert variables to be useful for further analysis. For instance, one-hot encoding was integrated to convert categorical variables  into numerical data for machine learning. One-hot encoding is a technique that is used to convert categorical data to numerical data to facilitate the learning process since machine learning models are incapable of processing plain texts in their raw form . In thisFeature splitting was used in cases where variables contained information that could be split into two or more columns. In the context of this study, feature splitting refers to the separation of a variable into two distinct columns. For example, the date variable comprising the month and year of the rearing process was split into years and months to create two new distinct columns of months and years, thus facilitating a comparison of production performance within different month periods.y and expressed in kg/mThis research notes that the bed length and width were measured in meters (m). At the end of the rearing process, the weight of the BSFL harvested was measured in kilograms (kg). In this context, feature aggregation, a technique used to combine features with the aim of creating a robust feature, was adopted. For instance, the weight in kilograms (represented as Equation :(3)y=ωφThe data was split into a ratio of 70:20:10. In total, 70% of the data was used to train the models, 20% was used for validation and 10% was used as the test set. Feature scaling is a data pre-processing technique that transforms numeric features of the dataset to be within a specified range with the aim of improving the performance of machine learning models . In thisEquation :(4)z=x−uAfter completing data prepossessing and preparation, the next step entailed training/fitting approximately seven supervised machine learning models that are inbuilt and available in the Scikit-learn Python library .The trained machine learning models were linear regression, ridge regression, decision tree regressor, random forest regressor, bagging regressor, adaboost regressor, and XGBoost regressor. All the models were trained with the understanding that the best model would be selected. Sklearn’s Gridsearchcv was used to select the best combination of hyperparameters for performance tuning. From these, the best-performing machine learning model was selected and compared with those from existing literature. Previous studies that applied machine learning algorithms to investigate various BSFL growth phenomena include generalized linear model  and statN is the number of observations in the dataset, p is the number of predictors (independent variables).To evaluate the developed models, five metrics were selected to measure the performance of machine learning algorithms. The metrics were, namely, the root mean squared error (RMSE), the mean absolute error (MAE), the mean absolute percentage error (MAPE), R-squared, and adjusted R-squared, which are defined in Equations –9), res, res9), RMSE, defined in Equation , is exprMAE, defined in Equation , calculaMAPE, defined in Equation , measureR-squared, defined in Equation , evaluatAlthough each of the above metrics gives insights into the performance of the models, a complete assessment of the model performance requires a combination of more than one metric. As such, the model performance in this study was assessed by generating scores for each of the above metrics and picking the highest-performing model based on the best combination of the scores. Essentially, when comparing models, the lower values of RMSE, MAE, and MAPE are desired, while the higher values of R-squared and adjusted R-squared are better.f, t, and m represent the features, trees in the random forest regressor, and nodes, respectively. The To rank the features in terms of their importance  for the prediction of BSFL expected weight, this study utilized the inbuilt feature importance function in the Scikit-learn  Python lportance :(10)ImpoIn addition, this research compared all the input variables  of input variables that gave optimal production. Therefore, a farmer should tune the input variables within those levels to achieve an optimal harvest. Moreover, this research trained seven machine learning models to predict the expected weight of BSFL to be harvested. The random forest regressor was found to be the best-performing model. Consequently, during the rearing process, the farmer can measure the parameters and obtain the projected/predicted expected BSFL weight to be harvested, i.e., a decision support system. As such, a farmer can tune the production system input variables to the expected levels to obtain an optimal harvest at the end of the rearing process. Moreover, the random forest regressor ranked the input variables studied in order of importance. Among others, the length of the bed was found to be the most important parameter to tune, meaning that it was necessary to tune the input variables as per that order of ranking since it contributed the most to high production. In the future, this study proposes to expand the analysis by combining the current rearing variables with environmental variables. This will facilitate a detailed investigation of how the combined features affect the growth and production of black soldier fly larvae to improve/optimize the farming process. In conclusion, these approaches can be widely adopted in the farming of black soldier fly larvae as a source of feed for animals , which in turn are a source of food for humans, hence contributing to reducing food insecurity.


Distributed structure health monitoring has been a hot research topic in recent years, and optic fiber sensors are largely developed for the advantages of high sensitivity, better spatial resolution, and small sensor size. However, the limitation of fibers in installation and reliability has become one of the major drawbacks of this technology. This paper presents a fiber optic sensing textile and a new installation method inside bridge girders to address those shortcomings in fiber sensing systems. The sensing textile was utilized to monitor strain distribution in the Grist Mill Bridge located in Maine based on Brillouin Optical Time Domain Analysis (BOTDA). A modified slider was developed to increase the efficiency of installation in the confined bridge girders. The bridge girder’s strain response was successfully recorded by the sensing textile during the loading tests that involved four trucks on the bridge. The sensing textile demonstrated the capability to differentiate separated loading locations. These results demonstrate a new way of installing fiber optic sensors and the potential applications of fiber optic sensing textiles in structural health monitoring. Structural health monitoring (SHM) is becoming increasingly important in the management of civil engineering structures such as bridges, tunnels, and buildings. SHM is the process of continuously monitoring the structural integrity of a structure, assessing any potential damage or deterioration, and ensuring that the structure remains safe and operational ,2,3. It To overcome these limitations, advanced sensing technologies, including distributed fiber optic sensors (DFOS), have been developed for SHM ,14,15,16Due to the fragile nature of optical fibers, complicated installation and transportation are two of the main disadvantages of DFOS. A method of embedding optic fiber sensors into the precast piles by slotting the piles’ surface was presented , and thiBrillouin Optical Time-Domain Analysis is a state-of-the-art fiber optic sensing technique used for SHM applications ,26,27. BCapitalizing on these advantages, this research paper employs a distributed fiber optic sensing textile to measure variations in strain resulting from load changes, with the sensor installed inside a girder of the Grist Mill Bridge. In this sensing textile, a U-shape single-mode fiber pattern was designed to cover the sensing section twice. The BOTDA technique was utilized in this experiment for static tests. To demonstrate the sensor’s strain response, the baseline profile of strain distribution along the girder was collected. Furthermore, two loading tests with different locations on the bridge were presented. This approach reduced the labor cost of transportation and installation of fiber sensors, ensured the flexibility of researchers on sensor pattern design, and demonstrated the ability to monitor the strain distribution on bridge girders.The paper is organized as follows. Brillouin Optical Time Domain Analysis is a fiber-optic sensing technique that measures strain or temperature changes along the length of an optical fiber. The principle of BOTDA is based on stimulated Brillouin scattering. When a laser pulse is sent through an optical fiber, it interacts with the acoustic phonons present within the fiber. These acoustic phonons are created by thermal fluctuations and mechanical deformations within the fiber ,30,31,32The frequency shift is caused by the Doppler effect, which is due to the movement of the acoustic phonons. The detected frequency shift can be used to determine the temperature or strain at that location. Since the scattered light experiences a Doppler frequency shift, the Brillouin shift essed as :(1)VB=2Vresearch , the staDue to the temperature variation, the deformation of fiber material can also apply strain and result in Brillouin frequency shifts. The Brillouin shift can be expressed as:The sensing textile was designed to collect strain data, using a U-shaped sensing fiber design to get a reference sensing section. This design was depicted in To embed the fiber, an affordable reinforcing fabric by Saint-Gobain  (XP414 laid scrim) was utilized. This particular textile was created through a chemical bonding process that interlocked a continuous filament yarn within an open mesh structure . The fibThe sensing textile was deployed at Grist Mill Bridge, situated in Hampden, Maine, as illustrated in To address these problems and enhance the efficiency of the installation inside the small bridge girder, we designed and fabricated an installation slider in the lab, as shown in The process began by placing a slider in the girder and securing it in place with epoxy. One member of the research team then entered the girder and unrolled the sensing textile onto the epoxy-coated surface of the girder. The epoxy was carefully distributed using a brush to ensure even coverage, and any bubbles presented were removed using plastic scraper blades. This process was repeated until the entire bottom surface of the girder was covered with the sensing textile. To facilitate the epoxy refilling process, a small cart was utilized to transport supplies to the team member working within the girder. As seen in To collect the strain distribution on the Grist Mill Bridge, a field test was conducted on 31 December 2020. The output Brillouin frequency of the bridge without any loading was collected as the baseline. Five continuous sets of data were recorded to verify the stability of the fiber optic sensing system, as shown in After collecting the baseline Brillouin frequency response of the bridge, we demonstrated two different live-loading tests by locating four overloaded dump trucks in different positions on the bridge. The schematic of the loading tests was shown in From To improve the process of applying epoxy, we could use more tools in the future. For example, wider brushes to spread epoxy and scraper blades to remove bubbles. The sensing surface should also be suitably treated to ensure that it is clean and flat. The textile can choose some thicker material to improve the stiffness. As the limitation of spatial resolution of the BOTDA system, we could use a better technique, such as Optical Frequency Domain Reflectometry (OFDR), to increase the spatial resolution and the sampling rate. However, the sensing range of the OFDR system in our lab was limited to 50 m while the presented U-shape sensing textile system required a length of 91 m in total.During field tests of the installation of fiber sensing textiles, we encountered a challenge with storing the fiber connectors. While the sensor was placed inside the girder, the connectors needed to be kept outside for easy connection to our demodulation system during testing. However, this exposed them to a harsh environment, leading to aging and damage. To address this, we developed a plug-and-play fiber connecting box that integrates different types of connectors for the sensing fiber and DAQ for strain gages. The extra launching fiber can be looped and stored inside the box, which provides more protection for the fibers in different environmental conditions. The connecting box will be installed later after the permission of Maine DOT. This solution greatly improves the durability of the fiber connecting parts and provides better protection for the fibers in the long term. By utilizing the connecting box, we not only enhance the protection of the fibers but also greatly improve the convenience of use.The most challenging problem in scaling this technology for larger structures would be the quality of the installation. The system’s performance largely depends on the quality of the installation, and this would prove time-consuming and increase labor costs in larger structures. Advanced planning and reserving fiber installation locations can greatly reduce potential installation issues and improve installation quality, thereby better enabling the application of fiber sensing textiles in structural health monitoring.This research paper proposes an innovative approach to enhancing the performance of distributed structural health monitoring systems. The study introduces a novel installation process and a newly designed fiber optic sensor embedded in textile materials. This method aims to improve the durability of the sensing system and enhance its transportability. In particular, the multi-purpose slider has been modified to address the challenges associated with installing the sensing textile in narrow bridge girders. By reducing the working hours of the installation process, this approach offers a more efficient and effective way to monitor structural health.To evaluate the effectiveness of the proposed system, the strain responses of a bridge girder under various live loadings were investigated. The U-shaped sensing textile was tested at Grist Mill Bridge in Maine, and the results demonstrated its ability to collect the strain distribution of the bridge girder. Furthermore, the sensing textile differentiated the live loading provided by four trucks in separate locations. The sensing textile system can provide a 1 m spatial resolution and is suitable for large-scale structure monitoring.This research presents a comprehensive approach to the development of fiber optic sensing systems for structural health monitoring. The novel installation process and the specially designed sensing textile provide an effective solution for monitoring the performance of bridge structures under heavy loads. This study’s findings demonstrate the potential of this approach to advance state-of-the-art approaches in distributed structural health monitoring and promote the safety and reliability of our critical infrastructure.


A parallel high-resolution underwater target detection network is proposed to address the problems of complex underwater scenes and limited target feature extraction capability. First, a high-resolution network (HRNet), a lighter high-resolution human posture estimation network, is used to improve the target feature representation and effectively reduce the semantic information lost in the image during sampling. Then, the attention module (A-CBAM) is improved to capture complex feature distributions by modeling the two-dimensional space in the activation function stage through the introduction of the flexible rectified linear units (FReLU) activation function to achieve pixel-level spatial information modeling capability. Feature enhancement in the spatial and channel dimensions is performed to improve understanding of fuzzy targets and small target objects and to better capture irregular and detailed object layouts. Finally, a receptive field augmentation module (RFAM) is constructed to obtain sufficient semantic information and rich detail information to further enhance the robustness and discrimination of features and improve the detection capability of the model for multi-scale underwater targets. Experimental results show that the method achieves 81.17%, 77.02%, and 82.9% mean average precision (mAP) on three publicly available datasets, specifically underwater robot professional contest  and pattern analysis, statistical modeling, and computational learning visual object classes (PASCAL VOC2007), respectively, demonstrating the effectiveness of the proposed network. With the development of computer vision and the exploitation of marine resources, biological detection in underwater environments has become a hot research topic with applications in underwater robotics , underwaCurrently existing target detection models can be classified into two types: anchor-free and anchor-based. Anchor-based detectors include the region-based convolutional network (R-CNN) series ,10,11,12Recent research on underwater objects, for example, Victor et al.  providedIn the field of underwater environments, researchers have made important contributions by proposing various target detection algorithms ,26,27. FThe task of target detection becomes particularly difficult in the underwater environment due to blurred feature information, severe color distortion, and low visibility, requiring simultaneous localization and classification. In order to improve the accuracy and portability of underwater target detection capabilities, we have chosen to improve the classical CenterNet model in the anchor-free family and propose a parallel high-resolution network model to address the challenges faced in this domain. The effectiveness of our proposed model is demonstrated by conducting experiments on underwater images.The innovations in this study are as follows: (1) aiming at the problem of complex underwater scenes and limited target feature extraction capability, a lighter high-resolution human posture estimation network (HRNet)  is used From the literature, it can be seen that by having a multi-resolution network parallel connection structure and fusing feature maps of different resolutions so that each resolution feature map can accept information from other resolution feature maps many times, output feature maps can be obtained that contain both high-resolution positional information and low-resolution semantic information, which can enhance the expression of target features and reduce the semantic information lost in the sampling process. However, the separate use of low- and high-resolution features still cannot meet our needs for high-quality recognition. If the attention mechanism can be properly used to enhance the target information in the feature map from both spatial and channel dimensions, it can guide the model to increase its attention to key information. It also improves its activation function to model the 2D space in the activation function stage to capture the complex feature distribution. In addition, the receptive field module demonstrates the model’s ability to obtain rich semantic information about the target context.In convolutional neural networks, high-resolution images contain richer detail information and play a crucial role in target detection. However, high-resolution feature maps also have a higher computational cost, resulting in more operations. In addition, in the deeper layers of the model, low-resolution feature maps contain rich semantic information that helps improve the model’s ability to detect targets.HRNet fuses low-resolution feature maps with high-resolution feature maps by connecting networks of different resolutions in parallel, so that the feature extraction network outputs high-resolution feature maps that contain rich semantic information. The feature maps of different resolutions are obtained through different branches of the image, and the feature maps of each branch are fused with the feature maps of all scales in the previous stage, so that the feature maps of each branch take into account both high- and low-resolution feature information, thus retaining more target feature information.The key feature of HRNet is that it maintains high resolution throughout the model’s processing of the image and generates multiple low-resolution feature maps simultaneously, which are used to augment the feature information of the high-resolution feature maps. Unlike previous networks, HRNet does not use extended convolution or upsampling to pass low-resolution features to recover the high-resolution representation. Instead, HRNet maintains the high-resolution representation throughout the modeling process and continuously performs cross-scale fusion to learn richer feature representations. HRNet is designed using a stage-by-stage incremental strategy, starting with a high-resolution subnet and then gradually adding new subnets in parallel to form multiple stages, with the resolution of the current subnet being 1/2 the resolution of the previous subnet. This process is repeated multiple times, eventually forming four stages. Based on these considerations, HRNet is a lighter weight network for high-resolution human posture estimation.Attention mechanisms are becoming popular in various fields and are often applied in a weighted manner. In computer vision tasks, where different regions of an image or video frame may have different levels of importance, attention mechanisms have been found to allow more flexible processing of visual information. The basis of this mechanism is similar to the human selective attention mechanism. Humans tend to ignore irrelevant information when observing objects and focus on information that is useful for decision making. Attention mechanisms are based on the idea of acquiring task-critical information. Therefore, an attention mechanism is often used to automatically select features or regions of interest during target detection.Models that process target images contain a large number of “meaningless” regions that do not contain information about the target, which interferes with feature extraction of valid targets. To improve feature extraction, researchers have proposed attention mechanisms to guide models to focus on target regions. The design of attention mechanisms is inspired by the unique brain signal processing mechanism of human vision. When the human eye observes an image, it generates a focus of attention that concentrates on certain key regions to eliminate the interference of irrelevant information, thus improving the accuracy and efficiency of information processing.Attention mechanisms in neural networks are plug-and-play learnable modules that work by assigning weight coefficients to values in the feature map tensor to enhance information in the focus region. They mainly include the channel attention mechanism and the spatial attention mechanism. The channel attention mechanism achieves dynamic enhancement of the features in each channel by assigning weights to the channel dimension of the feature map, while the spatial attention mechanism assigns weights in the spatial dimension and learns the dependencies of different locations on the image to dynamically enhance the features in the spatial dimension. Self-attention mechanisms, on the other hand, are a branch of attention mechanisms developed from the field of natural language processing and are unique in that they do not rely on the guidance of external information but rely on their own input to establish global dependencies to generate weight coefficients. By combining the structure of these two mechanisms, the target information in the feature map can be strengthened in terms of spatial and channel dimensions. In addition, the activation function can be enhanced to capture complex feature distributions by modeling the 2D space using the activation function stage. The FReLU activation function, which is specifically designed for vision tasks, is chosen to replace the ReLU activation function in the CBAM module. The FReLU activation extends ReLU to a two-dimensional activation function by adding a negligible spatial conditioning overhead, which improves target detection accuracy by capturing complex visual layouts in two-dimensional space. In addition, spatial conditioning implements pixel-level modeling capabilities in a simple way to capture complex visual layouts through regular convolution. FReLU, on the other hand, is a spatial context-dependent 2D condition that helps to extract the spatial layout of target features.Small targets occupy fewer pixels in images, resulting in insufficient information about their characteristics. In order to optimize the recognition effect, an optimization idea can be adopted, which is to use the information of the target’s environment to support the recognition, called the target contextual semantic information. Usually, the objects in the image do not exist independently, and there is some relationship between them and the environment. Therefore, by making full use of the target contextual semantic information, the feature representation of the target can be effectively enriched. One of the commonly used optimization methods is to expand the receptive field of the neural network by using null convolution. The receptive field module takes advantage of the population receptive field properties of human vision and constructs a multi-branch structure using hollow convolutional kernels of different sizes and eccentricities. This receptive field module on the input image is usually first processed with three ordinary convolution kernels of different sizes . Then, three feature maps with different receptive fields are separately obtained using hollow convolution with different centrifugal rates. By fusing these feature maps, feature enhancement results can be obtained. To reduce the computational effort, alternative convolution kernels can be used, e.g., the 5 × 5 convolution layer can be replaced by a 3 × 3 convolution layer, and the 3 × 3 convolution layer can be replaced by 1 × 3 and 3 × 1 convolution layers.Compared to the traditional convolutional module, the feature maps produced by the lower centration branches of the module are able to condense feature information that includes parts or the target as a whole. The higher centrifugal branches can condense the feature information including the target itself and the surrounding environment. The advantage of fusing multiple branches is that the higher centrifugal branch can provide contextual semantic information to the lower centrifugal branch, while the lower centrifugal branch can compensate for the loss of detail caused by the convolutional kernel diffusion of the higher centrifugal branch.The structure of the receptive field is borrowed and both scale and centrifugal rate are taken into account. Compared to the use of a computationally intensive and deeply layered backbone network, the module uses a lightweight backbone network. By combining the receptive field module, the receptive field augmentation module proposed in this paper achieves a stronger feature representation capability, which enables the detector to have a faster inference speed while maintaining excellent performance. In addition, the training process does not require too many complex tricks, so the training resources of the model are less.In the existing one-stage and two-stage detectors, they usually face the dilemma of good performance but slow speed or fast speed but unsatisfactory performance. To address this problem, this paper proposes a scheme that uses a lightweight backbone and enhanced receptive field module to achieve faster inference while maintaining performance. The design elegantly combines feature fusion with different centrifugal velocities, bringing significant performance gains to the target detection task.In order to effectively integrate high-resolution shallow feature information and low-resolution deep feature information, this paper proposes a network structure based on the parallel connection of multi-resolution subnetworks designed by CenterNet. The underwater object detection capability is enhanced by using a backbone network (HRNet), improving the attention module (A-CBAM), and constructing a receptive field augmentation module (RFAB). It consists of two parts: the AR-HRNet backbone network and the recognition module. The improved network structure is shown in The input image is first passed through four parallel subnetworks of the HRNet, allowing for the rapid extraction of features at four different resolutions. The four different resolution features are then fed into the attention module (A-CBAM), which improves model performance by increasing the spatial and channel dimensions. In the CBAM structure, complex feature distributions are captured in the activation function stage by modeling the two-dimensional space through the introduction of the FReLU activation function to achieve the ability to model spatial information at the pixel level. It then passes through the receptive field augmentation module (RFAB) to further capture rich semantic and positional information to enhance target detection at multiple scales underwater. Finally, the fused features are passed to three separate branches to generate key point heatmaps, position offsets and target width and height, and the final detection results are obtained through decoding operations.The benchmark network CenterNet adopts Hourglass-104 as the backbone network; although it can achieve high detection accuracy, the network has a complex structure and a larger number of parameters, which greatly increases the computational complexity of the network and reduces the detection speed of the network. Therefore, in order to improve the detection speed of the algorithm while maintaining high detection accuracy, this paper changes the backbone network to a HRNet network from the perspective of lightweight network structure.Originally used for human posture estimation, HRNet is a feature extraction network designed to overcome the information loss and ambiguity problems that occur with traditional deep learning networks when processing high-resolution images. HRNet effectively improves the network’s ability to perceive detailed information by parallelizing multiple branches to process feature maps at different resolutions and by interacting and fusing between them.The core idea of HRNet is to maintain the transfer and use of high-resolution features. It enables the network to maintain high-resolution features at different resolutions by keeping information fluid between branches. Specifically, HRNet allows the network to maintain both global receptive field and detail information by performing resolution-by-resolution upsampling and feature fusion multiple times. This multi-level feature fusion design allows HRNet to better capture targets at different scales in target detection tasks and provide more accurate and detailed detection results. The structure of the HRNet network is shown in HRNet is divided into four stages: each stage is a parallel connection of multi-resolution subnetworks and consists of a series of standard convolutions; the feature map resolution of the same subnetwork does not change with the depth of the network, while the feature map resolution of the parallel subnetworks decreases in turn by 1/2, while the number of channels increases by a factor of 2. Starting from the backbone network, the image is processed by a 3 × 3 convolution with a step size of 2. The feature map size obtained is 1/4 of the original image and the number of channels is increased from 3 to 64. A high-resolution subnetwork is constructed and the first stage consists of a subnetwork using four bottleneck  modules The four subnetworks of HRNet downsample the images by 4, 8, 16, and 32 times to extract feature maps of different resolutions. The original HRNet only uses the output of the high-resolution subnetwork, but to make full use of the multi-scale feature information, this paper uses the feature maps generated by the four parallel subnetworks as the output of the backbone network. This can effectively fuse features at different scales to improve the performance and accuracy of target detection.The CBAM consists of a linear stack of the channel attention module (CAM) and the spatial attention module (SAM). This paper improves the ReLU activation function in the CBAM module by replacing it with the FReLU activation function, which is specifically designed for visual tasks. FReLU activation extends ReLU to a two-dimensional activation function by adding negligible spatial conditioning overhead, which captures complex visual layouts in two-dimensional space, improving target detection accuracy. In addition, spatial conditioning implements pixel-level modeling capability in a simple way to capture complex visual layouts through regular convolution. FReLU, on the other hand, is a spatial context-dependent 2D condition that helps to extract the spatial layout of target features. Based on this, we have designed a new attention mechanism called the A-CBAM attention mechanism. By applying the A-CBAM attention mechanism, we expect to further improve the target detection performance. Its structure is shown in The function of the aforementioned channel attention module is to compress the spatial dimensionality of the feature map by applying average pooling and max pooling operations based on width and height, transforming it into a one-dimensional vector and then processing it. Average pooling and max pooling can be used to aggregate the spatial information of the feature map. The feature vectors are then passed to the fully connected layer, where the spatial dimensions of the input feature map are compressed and then summed and merged element by element. Finally, the channel attention map is generated by applying a sigmoid activation function. The structure is shown in F is the input, AvgPool is the average pooling, and MaxPool is the maximum pooling. Its formula is:To obtain the attentional features of the feature map in the spatial dimension, we performed global maximum pooling and global average pooling on the feature map output using the channel attention module to rescale the dimension of the feature map from H × W to 1 × 1. Next, we performed convolution using a 7 × 7 convolution kernel and applied the sigmoid activation function to reduce the dimensionality of the feature map. We then merged the feature map normalized by the sigmoid activation function with the feature map output by the channel attention module to complete the rescaling of the feature map in both spatial and channel dimensions. The structure is shown in Its formula is:A key component of CBAM is the Multilayer Perceptron (MLP), a module that uses ReLU as the activation function for implementing non-linear activation. The introduction of the ReLU function solves the gradient disappearance problem in the backpropagation algorithm. However, in order to achieve pixel-level spatial information modeling capability and improve accuracy in the activation function stage, this paper replaces the original ReLU activation function with a FReLU activation function specifically designed for vision tasks. The ReLU function is represented as In the above formulation, c denotes the c-th channel, and c-th channel at the two-dimensional spatial position In the above equation, The CBAM structure with the addition of the FReLU activation function is called A-CBAM. FReLU has a stronger context capture capability, resulting in a better understanding of fuzzy targets and small target objects. In complex cases, the A-CBAM structure is able to capture irregular and detailed object layouts better than the CBAM structure.The receptive field is the size of the region in which the pixel points on the feature map output by each layer of the convolutional neural network are mapped onto the input image. Neurological studies have shown that in the human visual cortex, the size of the population receptive field correlates with retinal eccentricity and that the size of the population receptive field varies in different retinal regions. To simulate this finding and to improve the deep features learned by lightweight convolutional neural network models, Liu et al.  proposedThe receptive field module combines the parallel convolution of dilated convolution  and InceBr1, Br2, and Br3 denote the outputs of the three branches. The + denotes the feature fusion operation. We use the symbol The original RFB has three branches, each with a different sized convolution kernel; the sizes of the convolution kernels are 1 × 1, 3 × 3, and 5 × 5, and the end of the branch has a dilated convolution layer; the dilated rates are 1, 3, and 5, respectively, which determines the spacing of the convolution kernel processing data. The larger the dilated rate, the larger the spacing of the convolution kernel processing data. To adapt to different situations, we propose the RFAM structure, which has more branches than RFM and contains four branches, with different branches corresponding to the respective convolutional and dilated layers. RFAM uses 1 × 1 convolutional kernels in each branch to adjust the number of channels and uses a series of 3 × 3 convolutions instead of 5 × 5 convolutions to reduce the number of parameters in the model to increase the detection speed while increasing the model’s nonlinearity. In addition, we replaced the original 3 × 3 convolution with a 1 × 3 convolution and a 3 × 1 convolution. The results of the 4 branches are concatenated and passed through a 1 × 1 convolution and then fed into the activation function with a residual edge as input. The effect of the residual edge is to allow the input image signal to propagate directly from bottom to top, mitigating the gradient divergence caused by an overly deep network. Its calculation is shown below:The total loss function in this paper’s algorithm can be divided into three components: heat map loss, center bias loss, and width–height loss, and the three loss functions are weighted and summed.Heat map loss a and β of the focal losses were considered as well as the number of key points in the image N and the predicted value α = 2 and β = 4 and normalized all the focal losses. In addition, when dealing with easily classifiable samples, we reduced their training weight appropriately.In CenterNet, the hyperparameters R is the sampling factor, typically R = 4, p is the target frame centroid, and During the downsampling process of the model, the resolution of the feature maps extracted by the backbone network decreases due to the output span, which leads to the loss of details in the images and, thus, causes a bias in the prediction results. Therefore, we introduced the centroid bias value Let the target bounding box coordinates be Combining the above types of losses gives the total loss In this section, we validate the effectiveness of the proposed method through several sets of experiments. First, we conducted experiments on four types of underwater image datasets, including comparison experiments with popular target detection algorithms, ablation studies, and comparison experiments with existing underwater target detection algorithms. Then, we conducted experiments on the PASCAL VOC2007 dataset to verify that our method not only performs well on underwater datasets but is also applicable to standard datasets.® Core™ i9-10900X CPU and an NVIDIA RTX308Ti graphics card. The Intel® Core™ i9-10900X CPU is manufactured by Intel, while the RTX3080Ti graphics card is manufactured by NVIDIA. Intel is headquartered in Santa Clara, CA, USA, and NVIDIA also has its headquarters there. For training, the input image size was 416 × 416. A total of 200 epochs were used to train the network. The learning rate is 0.001 for the first 25 epochs, 0.0001 for epochs 25 to 100, and 0.00001 for epochs 100 to 200. A total of 1000 iterations are performed for each of the first 25 epochs. After 25 epochs, 2000 iterations are performed for each epoch. To achieve higher accuracy and generalization performance, data enhancement is performed on underwater data. By introducing color dithering, horizontal flipping, random rotation, and random cropping, it adapts to the color state changes of underwater targets under different shooting conditions.The experimental environment is Python 3.8, Pytorch 1.7.0, Torchvision 0.7.0, and the rest of the Python modules can be downloaded and installed from third parties. The hardware consists of an Intel(1)The speed of network detection is evaluated using the FPS metric, with higher values indicating faster network detection;(2)AP metric is used to evaluate the detection accuracy of each category, which can be calculated as follows:The P is precision, the probability that all detected targets are correctly detected, and R is recall, the probability that all true positives are correctly detected, which can be calculated as follows:TP is the number of positive samples correctly recognized, FP is the number of samples recognized as positive but actually negative, and FN is the number of samples recognized as negative but actually positive;The performance of the network is objectively evaluated using three metrics: frames per second (FPS), average precision (AP), and mean average precision (mAP) as follows:(3)mAP, and the calculation can be expressed as follows:The combined detection accuracy of the model is evaluated using N is the number of categories and iAP is the average precision of category i;(4)The model complexity uses parameters, and the specific calculation formula is as follows:oC represents the number of output channels, iC represents the number of input channels, and wk and hk represent the width and height of the convolution kernel, respectively.The underwater image datasets URPC2020 and URPC2018 contain 5543 and 4000 images, respectively, covering four classes of marine life, namely holothurian, starfish, echinus, and scallop. Due to the realism of the marine environment, these images typically suffer from low resolution, low signal-to-noise ratio, low contrast, color aberration, and blurred feature information, resulting in the loss of clear contour and texture information, limiting the accuracy of target identification and greatly reducing the effectiveness of our method. In addition, targets are dense and often obscured, presenting significant challenges to target detection. In underwater imagery, the scale of marine life is often small. Of particular note is the fact that some marine organisms, such as sea cucumbers and scallops, have protective colors that blend in with their environment and can hide. Also, due to the aggregation behavior of marine life, there is often a high density of targets in the captured images. All these characteristics make the task of underwater target detection difficult. In order to validate our proposed algorithm, we conducted a series of experiments on an underwater image dataset.In underwater environments, light propagation is affected by water absorption and scattering, resulting in distorted and blurred images. With low resolution, target details may not be clearly visible in the image, affecting the accuracy of target detection. Higher-resolution images can provide more detailed information that can help identify and locate underwater targets. In addition, the scattering and absorption of light introduces noise that can degrade image quality and obscure the target. If the signal-to-noise ratio is low, the target is drowned out by the noise, making it difficult for the detection algorithm to identify it correctly.Looking at the experimental results in Observing the experimental results in As can be seen in In summary, underwater target detection is affected by resolution and the signal-to-noise ratio, making detection difficult. Reducing the input resolution can lead to distortion or loss of some small targets, reducing the detection accuracy of small targets. Increasing the input resolution provides more target detail and helps to detect small targets. Higher-resolution images provide more accurate target localization, allowing the position of the target to be determined more accurately. Higher-resolution images reduce noise and interference in the image, reducing the likelihood of false detections and improving the reliability of the algorithm. In addition, a lower signal-to-noise ratio makes the noise in the image more prominent, blurring the features of the target in the image and, thus, reducing the visibility of the target. A low signal-to-noise ratio can lead to an increase in false alarms. Noise can be mistaken for a target, which can lead to false alarms in the algorithm, affecting the accuracy and reliability of detection. This has an impact on the ability to detect and locate targets in the underwater environment, which ultimately affects underwater target acquisition results.We compared several popular target detection methods on the underwater image dataset URPC2020 and recorded the results as shown in In order to evaluate the effectiveness of the algorithm proposed in this paper, experiments were performed on the URPU2020 underwater object detection dataset, and we compared and analyzed its model complexity with that of the CenterNet algorithm. The experimental results are presented in In addition, this paper performs experiments on the underwater image dataset URPC2018 to compare with the baseline network. The results are presented in To validate the algorithms in this paper, we perform ablation experiments to compare and analyze the detection accuracy and speed. The first row represents the baseline network with Hourglass-104 as the backbone network. The second row replaces the backbone network with HRNet, which slightly reduces the average accuracy but improves the detection speed, further demonstrating that HRNet is a lighter network that reduces model complexity and improves detection speed. With the addition of the enhanced attention module A-CBAM in the third row, excellent spatial information modeling capability is achieved by modeling the two-dimensional space in the activation function stage, capturing complex feature distributions and demonstrating feature enhancement in the spatial and channel dimensions, which improves the quality of the feature maps extracted by the network and increases the detection accuracy as well as the speed of inference. The fourth line introduces a receptive field augmentation module, which makes full use of the semantic and positional information of the network to further improve accuracy while maintaining detection speed.In the evaluation of detection accuracy presented in To further validate the performance of the algorithms in this paper, we conducted experiments on the PASCAL VOC dataset. We used the VOC2007 and VOC2012 training sets to train the network model and tested the network model on the VOC2007 test set. In order to show the detection results of the algorithm in a more intuitive way, four images from the more complex dataset were randomly selected and compared with the original model, as shown in As shown in Based on the above results, further analysis and comparison with existing techniques are performed. The overall performance of our method is improved, and we compare the results of experiments on the underwater dataset URPC2020; is the performance of our method is higher than that of other mainstream target detection algorithms in terms of detection accuracy and higher than the latest YOLOv7 model’s detection accuracy. This shows that the improved algorithm in this paper has more advantages in detecting underwater targets and can achieve higher detection accuracy. It is worth noting that in the detection of underwater images, anchor-free frame detector CornerNet’s detection accuracy is significantly lower than that of this paper’s algorithm and other algorithms. To analyze the reasons why, the above algorithm needs to define a number of key corner points and group them according to the distance between the key points; underwater targets with severe occlusion are present; a wide range of small targets are present; and it is easy to misgroup, significantly reducing the detection accuracy from the point of view of detection speed. In terms of detection speed, the algorithm in this paper is faster than SWIPTNet, Faster R-CNN, CornerNet, and CenterNet, but slower than SSD, RetinaNet, YOLOv5, and YOLOv7 algorithms. The reason for this is that the backbone network of this paper is based on HRNet, which has fewer parameters and improves the detection speed, but due to the repeated multi-scale feature fusion, it is easier to misgroup underwater targets, which significantly reduces the detection accuracy. However, due to the repeated multi-scale feature fusion within the network, the network inference speed is reduced to some extent; in terms of model complexity, the model size, number of parameters, and floating-point operation volume in this paper are only 117.6 M, 29.7 M, and 31. 2 G, which are much lower than those of the benchmark network, indicating that the improved network in this paper is a relatively lightweight network, which can significantly reduce the number of parameters in the model, reduce the complexity of the model, and improve the network inference speed.Replacing Hourglass-104 with HRNet as the backbone of the network results in a slight decrease in average accuracy and an increase in inference speed, further suggesting that HRNet is a lighter network that reduces model complexity and improves recognition speed. With the addition of the enhanced attention module A-CBAM, excellent spatial information modeling capability is achieved by modeling the two-dimensional space in the activation function stage, capturing complex feature distributions and demonstrating feature enhancement in the spatial and channel dimensions, which improves the quality of the feature maps extracted by the network and significantly improves both detection accuracy and inference speed. The receptive field augmentation module is introduced to fully exploit the semantic and positional information of the network to further improve the accuracy while maintaining detection speed.For each type of detection accuracy, both echinus and starfishes have a larger number of targets and clearer feature information. Therefore, under different experimental settings, the model can easily extract target features and achieve high detection accuracy, and the algorithm in this paper can achieve 91.32% and 85.32% accuracy for echinus and starfishes, respectively. However, the total number of targets in the two categories of holothurians and scallops is small. As these two target types are usually small and have fuzzy feature information, their detection accuracies are lower. However, the algorithms in this paper achieve detection accuracies of 76.40% and 71.67% for these two types of targets, which is significantly higher than that of other networks. This indicates that the feature extraction capability of the network is significantly improved by the combination of different enhancement strategies proposed in this paper. To a certain extent, this alleviates the limitation of the scarcity of target data samples and improves the detection ability for small and fuzzy targets.Comprehensively analyzed, the algorithm in this paper achieves the highest detection accuracy compared to other mainstream algorithms, while maintaining a faster detection speed and a lower number of model parameters, which has a significant advantage in detecting underwater targets.To solve a number of problems such as complex underwater scenes and difficult target feature extraction, this paper makes targeted improvements to the CenterNet benchmark framework and proposes a parallel high-resolution underwater target detection algorithm. First, HRNet, a lighter high-resolution human posture estimation network, is used to improve the target feature representation and effectively reduce the semantic information lost in the image sampling process. Then, the attention module (A-CBAM) is enhanced to achieve pixel-level spatial information modeling capability by introducing the FReLU activation function, which captures complex feature distributions by modeling the two-dimensional space in the activation function stage. Feature enhancement in the spatial and channel dimensions is performed to improve understanding of fuzzy targets and small target objects and to better capture irregular and detailed object layouts. Finally, a receptive field augmentation module (RFAM) is constructed to obtain sufficient semantic information and rich detail information to further enhance the robustness and discrimination of features and improve the detection capability of the model for multi-scale underwater targets. The method improves the mAP by 4.96%, 2.62%, and 2.2% on the three publicly available datasets URPC2020, URPC2018, and PASCAL VOC2007, respectively. The experiments on the underwater target detection dataset URPU2020 show that the number of model parameters of the model in this paper is reduced by 159.6 M and compressed by 84.3% compared with the benchmark network. These results show that the algorithm proposed in this paper improves the accuracy and reduces the model complexity, which makes it more conducive to practical applications. Meanwhile, the surface algorithm is not only applicable to the underwater environment, but also to the surface environment. The strong generalization ability of the algorithm is verified.There are several threats to the study of underwater object detection that affect the validity of the work in this paper. At the model level, the use of parallel high-resolution networks and feature extraction processes leads to problems of information loss and redundant parameters. The feature extraction capability of the high-resolution network is also somewhat lacking. A receptive field augmentation module was introduced but, at the same time, it increased the complexity of the model and reduced the speed of model inference. From an image point of view, the number of two types of targets, holothurians and scallops, is low. Since these two types of targets are usually small in size and have ambiguous feature information, their detection accuracy is low.Future research will focus on improving model performance, increasing underwater image datasets, further exploring the potential of convolutional neural networks for marine target detection, and improving detection of fuzzy and small targets, as well as performance in turbid and crowded environments. Methodologically, we will investigate techniques such as model pruning and knowledge distillation and continue to explore lightweight processing approaches to improve the detection speed of the model.