Environmental changes and human activities have caused serious degradation of murals around the world. Scratches are one of the most common issues in these damaged murals. We propose a new method for virtually enhancing and removing scratches from murals; which can provide an auxiliary reference and support for actual restoration. First, principal component analysis (PCA) was performed on the hyperspectral data of a mural after reflectance correction, and high-pass filtering was performed on the selected first principal component image. Principal component fusion was used to replace the original first principal component with a high-pass filtered first principal component image, which was then inverse PCA transformed with the other original principal component images to obtain an enhanced hyperspectral image. The linear information in the mural was therefore enhanced, and the differences between the scratches and background improved. Second, the enhanced hyperspectral image of the mural was synthesized as a true colour image and converted to the HSV colour space. The light brightness component of the image was estimated using the multi-scale Gaussian function and corrected with a 2D gamma function, thus solving the problem of localised darkness in the murals. Finally, the enhanced mural images were applied as input to the triplet domain translation network pretrained model. The local branches in the translation network perform overall noise smoothing and colour recovery of the mural, while the partial nonlocal block is used to extract the information from the scratches. The mapping process was learned in the hidden space for virtual removal of the scratches. In addition, we added a Butterworth high-pass filter at the end of the network to generate the final restoration result of the mural with a clearer visual effect and richer high-frequency information. We verified and validated these methods for murals in the Baoguang Hall of Qutan Temple. The results show that the proposed method outperforms the restoration results of the total variation (TV) model, curvature-driven diffusion (CDD) model, and Criminisi algorithm. Moreover, the proposed combined method produces better recovery results and improves the visual richness, readability, and artistic expression of the murals compared with direct recovery using a triple domain translation network. Murals are a precious part of the world’s cultural heritage and have enormous historical and research value. They are the spiritual home of modern man and a symbol of world civilisation, reflecting the social, political, economic, religious, cultural, and artistic development of countries around the world . HoweverVirtual restoration has attracted research attention in the field of cultural heritage conservation in recent years because of advancements in computer vision technology. New technologies such as computer image processing, graphics, virtual reality, and hyperspectroscopy are gradually being applied to the field of cultural relic protection and restoration . For exaWith the development of artificial intelligence, deep learning is gradually being applied in the field of digital preservation of cultural heritage. Deepak Pathak et al.  first prScratches are different from small defects such as cracks, as they punctate losses, are often seen in large areas of structural damage, and are irregular in shape. This poses difficulties for the restoration of wall paintings. The majority of existing literature has focused on the restoration of punctate loss, fading, cracks, and other defects in the mural images. However, to date, there are few methods for recovering large areas of scratch damage in mural images. We observed that the scratches in the mural were similar to the creases in the old photograph. The scratches in the mural and the folds in the old photograph are both large, elongated, and white in appearance. In our study, we used pretrained models  of old pTherefore, we opted to use spectral information for line enhancement, a 2D gamma function to enhance local dark information, and a triplet domain translation network pretrained model and a Butterworth filter to virtually restore scratches. After radiation correction, the mural’s hyperspectral data were subjected to principal component analysis (PCA) and high-pass filtering, producing improved hyperspectral images, and thereby improving the linear information and contrast between scratches and the backdrop of the mural. Second, the mural’s improved hyperspectral picture was synthesised to a true colour image that was converted to the HSV colour space. A multi-scale Gaussian function was used to estimate the image’s lighting component. Thereafter, a 2D gamma function was used to correct the brightness and overcome the problem of poor light in murals. Finally, the triplet domain translation network pretrained model received the augmented mural images. The local branch of the network performs overall image quality restoration to address fading and noise in the image. A partial nonlocal block was used to recover structured defects in the image to resolve scratches, and a Butterworth filter was applied to make the final result clearer. This methodological approach will help us gain a sharper and more comprehensive understanding of murals.In this study, we have used the murals of the Baoguang Hall at Qutan Temple as an example of virtual restoration of large scratch lesions on their surfaces. The main contributions of this study are summarized as follows.(1)A method combining linear information enhancement and triplet domain translation network pretrained model is proposed to recover the scratch lesions in the mural images, which includes using hyperspectral data for principal component analysis and enhancing the first principal component with high-pass filtering, replacing the original first principal component with the enhanced first principal component by principal component fusion, and recovering the data dimension with principal component inversion to produce an improved hyperspectral mural image. Then, a triplet domain translation network pretrained model was used to complete the repair of the scratch lesions. In addition, we added a Butterworth high-pass filter after the pretrained model restoration to produce sharper and higher visual quality mural restoration results. As such, this study fills a gap in the existing literature on the virtual restoration of mural scratches.(2)The 2D gamma function light uneven image correction algorithm is applied to the mural to solve the problem of local low luminance, enhance the information in the dark areas, and provide more accurate restoration results.(3)The proposed method can provide auxiliary reference and support for the actual restoration of murals. It is helpful to provide conservators with a scratch-free appearance of the murals before the restoration process begins. In addition, the work in this study is an attempt to provide novel ideas for the digital conservation of wall paintings for World Heritage sites.The rest of the paper is organized as follows. A scratch is a mark produced by an external force that damages mural patterns . Mural pData from the experimental area were collected with the hyperspectral image analysis system THEMIS-VNIR/400H from Themis Vision System, USA, with a spatial resolution of 1392 × 1000 pixels and a sampling interval of 0.6 nm. The spectral resolution was 2.8 nm, and the images were collected in 1040 bands ranging from 377.45 (visible light) to 1033.10 nm (near-infrared). During the data collection process, the distance between the hyperspectral camera and the mural was about 1 m. Two halogen lamps were used as light sources.(1)Data denoising using radiometric correction;(2)Mural line information enhancement based on principal component transformation, high-pass filtering, and principal component fusion;(3)Enhancement of local dark information in the mural using multiscale Gaussian and 2D gamma functions;(4)Extraction and repair of scratched murals using a triplet domain translation pretrained network model and Butterworth high-pass filter.Hyperspectral techniques allow extraction of the maximum amount of information from murals without damaging them owing to their non-contact, non-destructive detection characteristics . HyperspDuring data acquisition with hyperspectral imaging systems, data can be affected by ambient light and the instrument’s dark current noise. Reflectance correction can be used to reduce this type of noise with the following correction formula:We synthesized true colour images in the red, green, and blue bands at wavelengths of 640.31, 549.79, and 460.20 nm, respectively, to meet the memory requirements of the network restoration model and maintain the integrity of the scratched murals, as a direct restoration would be inaccurate and cause the lines in the murals to fade. Before restoring the network, we used the hyperspectral data from the murals to improve the line information and produce better restoration outcomes. A PCA of the hyperspectral images of the murals to be restored was carried out to compress or combine image information from multiple bands into one image . The higPrincipal component fusion is a PCA transformation of the obtained . The firA 2D gamma function, light inhomogeneity image correction algorithm was applied to the murals to solve the problem of localised low brightness in their images . AccordiAs the multiscale Gaussian function could effectively compress the dynamic range and accurately estimate the brightness component of the scene ,26, it wThe convolution of the Gaussian function with the original image yielded an estimate of the light component with the following mathematical expression:The 2D gamma function can effectively correct the brightness of an image without changing its overall magnitude . It convImages in HSV space are converted to RGB  colour space to correct for the brightness of localised darkness in the murals. The mathematical expression is as follows:As described above, the scratches in the mural were more similar to the creases in the old photograph. We therefore applied the pretrained model of the triplet state domain translation network  used to The triplet domain translation network model consists of two variational autoencoders , The first item is the latent space loss,  network .One of the triplet domain translation network datasets is from the Pascal VOC dataset  and the To produce clearer results of the mural restoration, we apply the Butterworth high-pass filter to the restored results of the network to produce visually clearer and sharper restoration results of the mural images. The transfer function of the Butterworth high-pass filter is shown in Equation (10):As shown in As shown in We use Python to provide the experimental environment needed to build the pretrained model. In this case, the images of the mural to be restored were fed into the pretrained model as a test set. The details of the experimental environment are shown in The enhanced mural images obtained in the previous step were fed into the network model as test sets to repair the scratches. The first step was the full recovery of the unstructured degradation of the murals using local branches. Thereafter, for scratches, the image was segmented using the U-net network  in the pTo illustrate that the direct use of pretrained models to recover scratch lesions is not ideal, we chose to omit the enhancement of mural line information, local dark enhancement, and Butterworth high-pass filtering steps, while keeping the other processes unchanged to verify the feasibility of the combined enhancement and restoration method proposed in this work. Considering Area 1 as an illustrative example, the results are shown in The total variation (TV) model, curvature-driven diffusion (CDD) model, and Criminisi algorithm are all commonly used approaches for image restoration and can be used for the virtual restoration of scratched murals. A comparative analysis of the methods in this study was carried out. The TV model  and CDD As shown in To demonstrate the generality of the method in this paper, we selected other wall images with scratches from the Baoguang Hall of Qutan Temple . In addition, we also restored two scratched murals on the west wall of Guanyin Hall in Heilongmiao Village, using data collected during July 2017 (g1 and h1). The results of their recovery are shown in In historical conservation applications, repairing scratched murals is a challenging task. We applied the pretrained model of old photographs to the restoration of fresco scratches. However, there are some differences between mural images and old photographs, and the direct use of this model for mural restoration could cause some of the restoration results to be overly smoothed, resulting in slight blurring or even incorrect restoration of some areas. In response, we proposed a combination of enhancement and restoration that goes some way to improving the outcome of the mural restoration. Linear information enhancement was used to improve the discrimination between scratches and the background in murals. Furthermore, a combination of optical component extraction and 2D gamma function correction was used to enhance local dark information in the mural. The triplet domain translation network pretrained model and Butterworth high-pass filter were used to restore the scratches on the murals. The results produced good aesthetic outcomes, and the repair of scratched murals using different methods was evaluated objectively. In addition, because of the non-reproducible nature of murals as cultural artefacts, scratched murals do not have their intact counterparts as real values to use as a reference. This will be considered in our further work to create some mockups of the murals as true values and artificially carve some scratches on them as synthetic murals. In this way, enough mural images can be collected to create a mural dataset, and a network model can be trained specifically for mural recovery, which helps develop more appropriate restoration techniques to produce better virtual restorations of scratched murals.


Coherence between tunnel-split states of a methyl quantum rotor can be generated and observed in stimulated and spin-locked echo experiments, if hyperfine coupling of a nearby electron spin to the methyl protons breaks C Methyl groups are ubiquitous in materials and biopolymers as well as in many organic solvents. At ambient temperature and above, they rotate fast on the timescale of hyperfine anisotropy of their protons. At temperatures around 80 K and slightly below, their rotation is still sufficiently fast to induce changes in the hyperfine field at a nearby electron spin that are observable in electron spin echo (ESE) experiments . RotatioThis paper is structured as follows. First, we derive the sequence of basis transformations and level orderings that allow us to formulate the spin Hamiltonian on a basis of localized states for the two methyl groups. This step involves transformation of the rotor-rotor coupling Hamiltonian to the localized basis. We discuss the effects of state mixing induced by this coupling Hamiltonian. Second, we demonstrate that, in situations of practical interest, EPR experiments are confined to a single ro-vibrational state. We discuss computational limitations to the accuracy of deriving the Hamiltonian as well as the excitation and detection operators for such ro-vibrational states. Third, we show that with approximate solutions for these operators in hands, it is feasible to predict the outcome of any pulse EPR experiment on such a system by density operator formalism. We illustrate this approach by computations for rotation barriers and coupling potentials that lead to tunnel frequencies in the ESEEM range. We conclude with a general assessment of the information that can and cannot be obtained by such experiments on the quantum-rotor system.I is its moment of inertia, We start with a reformulation of our previous treatment for a single rotor  that proK so that K can be found by checking convergence of the tunnel frequency and of the energies of the ro-librational states with increasing K. The finite-dimensional Hamiltonian can be expressed asr, the states Er. For even r, the A state has lower energy than the two E states, whereas for odd r it has higher energy \documentsion Eq. . This prIt is instructive to look at the off-diagonal matrix elements of m {rrc}^{}$$\end{dm {rrc}^{}$$\end{dmentclass2pt{minimTo set up quantum dynamics computations, we perform sub-space diagonalization of the Hamiltonian given by Eq.  for the T the temperature. Spin operators By density operator formalism, we can compute the signal for any pulse sequence applied to the coupled two-rotor-spin system. The thermal equilibrium density operator is given byWe now test whether tunnel ESEEM can separate the rotation barrier  by Eqs. . We restIn a first step, we considered the problem of two coupled rotors in the absence of electron and nuclear spin and assume That way we simulated ESEEM data at a magnetic field of 1.175 T corresponding to Q-band measurements and a temperature of 10 K for all three parameter pairs (Fig. We have then tested whether the same inseparability of Our findings indicate that the multiple tunnel ESEEM peaks observed in Mn-doped [(CHcoupling  do not ad by Eq.  only appIf our conclusion holds, the appearance of multiple tunnel frequencies under hyperfine decoupling may indicate heterogeneity of the metal-organic framework that is sensed by the methyl quantum rotors. A trivial source of such heterogeneity is manganese doping in itself. In the crystal structure of [(CHentclass1pt{minimamentclasspt{minimaAlternatively, the additional peaks might be a result of the group spin  systems . PrelimiFurther, if our conclusion holds that weak rotational coupling is unseparable by ESEEM experiments from a change in the rotation barrier, potential effects of methyl tunneling on electron spin decoherence  can be selements , the \doperiment , 17 and For rotor-rotor couplings much smaller than the rotation barrier, the 1192-quantum state problem of two tunnel-split methyl groups in the vicinity of an electron spin can be solved with moderate computational effort. The numerical solution indicates that, in this regime, the coupling changes only the tunnel splitting compared to the case with the same rotation barrier in the absence of coupling. It does not lead to a qualitative difference in the hyperfine-mediated tunnel ESEEM effect. As a consequence, in this regime ESEEM data depend only on the tunnel splitting and not on the particular combination of single-rotor potential and rotor-rotor coupling that causes this splitting. This applies also to hyperfine-decoupled ESEEM, where the pure tunnel splitting is recovered. If these conclusions hold also for a more sophisticated treatment of the coupled-methyl rotor tunneling problem, electron spin decoherence induced by methyl groups bound to sp


This paper explores extensions and restrictions of shallow convolutional neural networks with fixed kernels trained with a limited number of training samples. We extend the work recently done in research on Receptive Field Neural Networks (RFNN) and show their behaviour using different bases and step-by-step changes within the network architecture. To ensure the reproducibility of the results, we simplified the baseline RFNN architecture to a single-layer CNN network and introduced a deterministic methodology for RFNN training and evaluation. This methodology enabled us to evaluate the significance of changes using the  Bayesian comparison. The results indicate that a change in the base may have less of an effect on the results than re-training using another seed. We show that the simplified network with tested bases has similar performance to the chosen baseline RFNN architecture. The data also show the positive impact of energy normalization of used filters, which improves the classification accuracy, even when using randomly initialized filters. Convolutional neural networks bring, along with considerable advantages, a number of challenging problems. One of them is the choice of hyperparameters for the individual layers. From previous research, we know the effects of the activation function, depth of the network, different types of normalization, preprocessing, and optimization methods on the overall accuracy achieved . The opeAnother not less-important problem of classic deep networks is their representative complexity, where it is not entirely clear what transformation the network performs and what the individual features mean. Therefore, some authors also believe the direction that research should take is to create simpler rather than deeper models ,8. This Last but not least, the need for a large amount of data for the training process itself significantly limits the wider deployment of deep learning. Although there are ways to achieve good results on smaller datasets, such as using transfer learning and expanding the training set by image augmentation , these tWith regard to the success of deep neural networks, the main motivations for their simplification are deployment on devices with limited computing resources, as well as a deeper understanding and easier interpretation of the created models. One of the major simplifications was tested by Iandola et al. , who proOne of the other approaches is the replacement of some convolutional kernels by approximated Gabor filters. In convolutional computational layers, these filters are used as fixed kernels for the extraction of intrinsic features. Some authors used Gabor filters only in the first convolutional layer ,18, whilIn addition to these methods, there are many approaches based on compression, regularization, and pruning ,25.One of the possible solutions that could at least partially solve these problems is to replace standard convolutional kernels with a linear combination of predefined and fixed filters in convolutional neural network architectures. This influential concept, proposed by Jacobsen et al. , definesAlthough the architecture of RFNNs are specific to their Gaussian derivative basis, other bases have also been tested. Verkes  proposedAlthough several bases have been proposed , a validt-test.In this work, we analyse and extend RFNN to study the consequences of changes in the individual compact bases. We restrict RFNN into shallow architectures to look more closely at the impact of different parameters and introduce a deterministic methodology for obtaining reproducible results and evaluation in the form of a Correlated Bayesian The paper is structured as follows. In j-th feature map In neural network architectures, a convolution layer is commonly used for feature extraction. It may differ in implementation, but usually this layer performs a discrete convolution denoted by the ∗ operator between the input tensor We can decompose the regular convolution into two simpler operations: extraction of features in the spatial plane using dephtwise convolution and subsequent channel recombination using pointwise convolution, effectively creating a depthwise separable convolutional layer ,45. Deptj-th feature map Subsequent pointwise convolution can be seen as regular convolution with a Equation ).(3)hjyThe original set of parameters The main idea of the RFNN computational layer is to replace the parameters of 2D spatial filters Equation ).(4)hy=By introducing fixed filters from a certain domain, the convolutional kernels can be treated as functions, while the network parameters are also reduced, as only A set of fixed two-dimensional kernels ;The number of output feature maps .The baseline architecture is a convolutional neural network with three layers of receptive fields and is used to classify the known problem of handwritten digits into ten classes. A detailed description of the individual layers together with the output dimensions and number of parameters is given in Fixed convolution kernels from the Gaussian basis were formed in the same way for all layers with a difference in size. In the first layer, the convolutional kernels have a size of All used frameworks were set to deterministic mode;All parameters were initialised based on one chosen experimental seed;To ensure variability, the selected experimental seed was used to generate a seed vector for all runs of the experiment.Although we managed to verify the performance of the baseline architecture see  and event-test [t-test was performed on the validation part of the training set within the cross validation. However, a numerical evaluation was performed on the excluded test set containing the same 10,000 samples to obtain an objective view of the real accuracy of the model. A possible alternative is to combine the training and test sets into one dataset. We chose not to use this procedure in order to be able to compare the results obtained on a dedicated test set with previous research in this area. The final training and evaluation methodology for ensuring repeatability is shown in Based on the recommendations in ,49 we cht-test . We usedt-test . The resIn this section, we describe our experiments with RFNN architecture using the MNIST database. In Receptive field neural networks excel when not enough data are available to use common deep learning models. We used a limited number of training samples in the range from 300 to 60,000 samples, i.e., the whole training set. For each experiment, the entire MNIST test set, consisting of 10,000 samples, was used to evaluate the classification accuracy. Apart from normalizing data to the range <0,1>, no other form of sample pre-processing was used. The network was trained by a standard backpropagation algorithm using an average cross-entropy loss with a mini-batch size of 25 images. An Adadelta optimizer with decay rate The resulting classification accuracy of the reference architecture Since we were unable to achieve the original published values for three repetitions, we decided to repeat each experiment 300 times and evaluate the results by displaying the full range <lin plot . In addiWe can confirm that we have managed to achieve comparable results to those presented by Jacobsen et al. . The RFNIn this section, we focus on the most important contribution of the RFNN architecture, which is the ability to achieve high accuracy with a limited number of training samples. Analysing the results, we observed a high variability of classification accuracy for the smallest number of training samples, which is evident from the violin graph . From thFirst, we replaced random with stratified sampling as a way to eliminate sampling bias and thus a possible source of variance. The resulting violin graph in In the following experiment, in addition to the original methodology, we used early stopping as follows: 10% of the 300 random samples were selected via stratified sampling in the validation set. The remaining 90% of samples were used for training. During training, the cross-entropy loss on the validation set was evaluated after each epoch. If this loss was reduced, we saved the current parameters of the model and continued training. If the validation loss did not improve during Prechelt . Figure Choi et al.  showed tFor a valid comparison of the impact of changes in the RFNN architecture, we simplified the reference network as much as possible. Due to the possible mutual influence of parameters in deep architectures, we omitted the normalization and regularization layers and simplified the neural network to a shallow architecture with one computational RFConv layer. The architecture is described in detail in t-test for the random selection of 300 samples.Another simplification was the removal of computational layers  for which we could not ensure repeatability when training on a GPU. We kept the base and number of filters according to the original architecture. For training, we used the same settings as in the previous experiments except for changing the optimizer to AdamW using a fixed learning rate with a value of t-test evaluated on a validation set in each cross-validation split. Compared to the original architecture, the results deteriorated significantly, which was expected. For a ROPE of 1%, the probability that In this experiment, we analysed the impact of sample selection and Energy Normalization on the achieved accuracy of the created model. The settings and methodology of the training were the same as in the previous section. We chose We conditioned the selection of samples by changing the deterministic seed that affected the result. We trained again on a random selection of 300 samples and re-evaluated classification accuracies using the same methodology. A comparison of the results obtained with the seed change is shown in The results differ due to a different selection of samples for the training set despite the same k-th filter elements t-test evaluated on a validation set in each cross-validation split are shown in Normalization in neural network architectures can help to improve both convergence and generalization . DiffereEquation ).(5)θknThe results of both experiments show that base energy normalization helped to improve classification accuracy. When using the original Gaussian derivative base, we found that In the original article , the Gauy et al. . We compt-test with respect to the simplified reference architecture We evaluated neural models using a Correlated Bayesian parately . The resIn the previous experiment in t-test using 10 times repeated 10-fold cross-validation. By switching to this evaluation methodology, we ensured a reproducible environment for reliable comparison of results where not only the selection but also the order of the samples during training remained the same. To ensure repeatability within the neural network, we simplified the original t-test, we found that the probability that the same model with different initial seedings and training sets are practically equivalent was only t-test  as a promising simplified model that uses a Gaussian derivative basis inspired by the scale-space theory. When validating the original results, we identified a problem with a large variation in the achieved test classification accuracy, especially with a small amount of training data. To enable the reproducibility of the results by introducing deterministic methodology, we simplified the baseline RFNN architecture to a single-layer CNN network whose input of computational layers was a set of fixed filters of any size and number. Subsequently, we experimentally verified that bases other than Gaussian can be used as fixed filters within the RFNN architecture. We found that a change in base may have less of an effect on the results obtained than re-training the network using another seed in failing to ensure repeatability of results. We also verified the positive impact of energy normalization of used filters, which improves the achieved classification accuracy even when using randomly initialized kernels. Further research is needed to establish specific differences between individual bases and the influence of various hyperparameters within the RFNN architecture.


L0 = 5000 μm to a weighted average fiber length of Lp = 571 μm in the molded part. This is an improvement over Lp = 285 μm for a short fiber-reinforced resin under comparable processing conditions. The mechanical characterization shows that for the long fiber-reinforced materials, the benefit of the increased homogeneity outweighs the disadvantages of the reduced fiber length. This is evident from the increase in tensile strength from σm = 21 MPa to σm = 57 MPa between the lowest and the highest mixing energy input parameter settings.Glass fiber-reinforced phenolic resins are well suited to substitute aluminum die-cast materials. They meet the high thermomechanical and chemical demands that are typically found in combustion engine and electric drive train applications. An injection molding process development for further improving their mechanical properties by increasing the glass fiber length in the molded part was conducted. A novel screw mixing element was developed to improve the homogenization of the long fibers in the phenolic resin. The process operation with the mixing element is a balance between the desired mixing action, an undesired preliminary curing of the phenolic resin, and the reduction of the fiber length. The highest mixing energy input leads to a reduction of the initial fiber length  Phenolic resins are versatile polymers that are used in a variety of industrial and consumer applications. For example, they are used as binding systems for wood composites, paper, abrasives, and friction materials . They alTypical applications for phenolic molding compounds that are established in the state of the art are oil pump housings, intake manifolds, valve blocks ,5, and oThe most significant mechanical disadvantage of parts made from phenolic molding compounds are their low elongation at break and their high brittleness compared to thermoplastic polymers . Long fiTypically, there are two possibilities for increasing the fiber length in molded parts: First, using a semi-finished material, such as a long fiber granulate; or second, using a direct process in which longer fibers are incorporated into the final part. This decision-making process is a trade-off between the higher material costs of a semi-finished long fiber material and the more complex manufacturing processes of a direct process, most of which also involve a higher capital investment ,19. For Thermoplastic long fiber granulates are available in a variety of different lengths, typically ranging between ranulate . The grand 24 mm . For comnd 24 mm  and Rascnd 24 mm .injection molding compounder”}), a co-rotating twin screw extruder is combined with an injection unit. The process was patented by Putsch [Composite Products, Inc.”}). It combines a continuous compounding process with a discontinuous injection process using a melt buffer [Several process variants with direct fiber feeding were developed for thermoplastic materials ,31,32,33y Putsch  and firsy Putsch . Anothert buffer . The meldirect compounding injection molding”}) process, invented by Exipnos and KraussMaffei Technologies, couples a single screw compounding extruder with a traditional injection molding machine [direct incorporation of continuous fibers”} process (direct incorporation of continuous fibers), invented by Truckenmüller at the University of Stuttgart, continuous fibers are directly pulled into the screw of the injection molding machine [fiber direct compounding”}), the unreinforced thermoplastic granulate is passively pulled into the screw and melted, such as in a conventional injection molding machine [By conducting the melting and compounding discontinuously, matching the injection molding cycle, no melt buffer is required. This reduces the capital investment costs and makes the direct compounding feasible for lower-volume applications. The direct compounding injection molding  .(1)Lc=D Lc=2 mm  and Lc=8[Lc=8 mm . During the injection molding process, the fibers are subjected to high mechanical loads, causing fiber damage and breaking. Three distinct mechanisms for fiber shortening are identified ,38,39,40fiber length distribution”}) defined by Meyer et al. according to Equation (2) [Agglomerations and fiber bundles reduce the overall extent of the fiber shortening, resulting in a higher average fiber length compared to well-homogenized parts. Opening the fiber bundles works in the same way as breaking the fibers. Truckenmüller  investigtion (2) .(2)FLD=The average fiber length g fibers .(3)Ln=∑Meyer et al. calculated a theoretical value of With modern data acquisition technologies, the quantification of energy input into the polymer during plasticization and injection is possible. This is particularly important for reactive thermoset materials, such as phenolic resins. The screw torque during the plasticizing process uwendaal , it is aUsing the hydraulic efficiency t values . The funt values . In genet values  concludet values ,50 used In Equation (6), , Kruppa  observed, Kruppa . With inLucyshyn et al. , as wellAs outlined above, no process for the direct feeding of long glass fibers into the injection molding process for thermoset resins in general and for phenolic resins in particular exists in the state of the art. In this paper, the development of such a process is described. An essential part of the process development and a significant addition to the state of the art is the application of a novel screw mixing element for the injection molding of fiber-reinforced phenolic resins. The machine process data are analyzed and used for the process development by calculating the injection and plasticizing work. By means of the structural and mechanical properties of the molded parts, the long fiber injection molding process is evaluated and compared to the state-of-the-art processing of short glass fiber-reinforced phenolic molding compounds.The methods and the results that are presented within this paper were partially published in earlier publications by the authors. In publication , the met® X6952 short glass fiber-reinforced compound by Sumitomo Bakelite . The material has a tailored composition of short glass fibers (SGF) and long glass fibers (LGF). The SGFs of the type DS5163-13P with a diameter of x-LGFx. The variable x indicates the fiber weight content The phenolic molding compound used within this work is based on the Vyncolitlication . In publlication , the detFor this paper, the focus will be on material formulations with a total fiber content of The long fiber thermoset injection molding process enables a flexible combination of SGF and LGF by separating the two mass flows see .The SGF are gravimetrically fed as a part of the phenolic molding compound, whereas the LGF are chopped from the continuous rovings. Both mass flows are fed into the plasticizing unit with a twin screw sidefeed. The injection molding screw is a conveying screw with an interchangeable screw tip, which allows for the adaption of either a conventional conveying geometry or a newly designed, thermoset specific Maddock mixing element, which is shown in The mixing element is set apart from a conventional Maddock mixing element by three distinct geometrical features. First, the inlet channels have a gradual slope at their ends to facilitate the flow of material and to avoid material accumulations. Second, the thermoset Maddock mixing element has an edge fillet on the mixing flight, which results in additional elongational stresses on the material when passing through the shear gap. The third main feature is the reversed positioning of the mixing flight and wiping flight compared to the state of the art; traditionally, the pushing flank is also the wiping flank of the mixing element. Since thermoset molding compounds only start to melt in the foremost screw flights under the influence of screw flank pressure, the material close to the pushing screw flanks is molten, whereas the material distant from the screw flanks might still be granular . If the During all injection molding trials with the long fiber process variants, rectangular plates with a size of The test specimens were cut out of the molded and post-cured plates by waterjet cutting according to the cutting patterns shown in The quasistatic mechanical testing was carried out according to the technical standards of DIN EN ISO 527-2 (tensile testing)  and DIN The fiber length measurement procedure, as well as the validation investigations regarding fiber damaging and selectivity towards longer or shorter fibers, are described in detail by the authors in the publication . In the fiber length measurement system (no abbreviation)”} system by IDM systems . The cropping of the image and thresholding were done manually, but the fiber detection was done automatically using the algorithms provided by the FASEP system. Per Petri dish, approximately The dilution and sample taking process steps are accomplished by opening the outlet tap and refilling the beaker with distilled water. Once the desired degree of dilution was reached, measurement samples were taken through the outlet tap and transferred to a Petri dish, which was then analyzed using the FASEP { XE “FASEP” \t “In contrast, the mixing element has a significantly lower initial pressure peak and a lower pressure requirement during the filling phase. Towards the end of the injection stroke, the pressure rises sharply until the switchover point to the holding pressure is reached. When comparing the two different plasticizing screw speeds  element a, the hiQ, which is adjusted by the peripheral devices (gravimetric loss-in-weight feeder and fiber chopper), approaches as close to the maximum possible feeding rate as possible, so that the plasticizing time is minimized.For the same material formulations as above, For the long fiber formulation PF-SGF0-LGF30 in The characteristic values plasticizing work and injection work are used for the evaluation of the process stability and to determine the process limits of the long fiber direct injection molding process. In contrast to a conventional injection molding process, in which the screw is flood fed by pulling the granulate out of the material hopper, the long fiber direct injection molding process offers the possibility to starve feed the screw due to the adjustability of the material feeding rate. The material throughput, and therefore the plasticizing time, is defined by the mass flow provided by the gravimetric dosing of the granulate and the cutting speed of the fiber chopper. It is independent of the screw speed, which means that the screw speed can be used as a parameter for influencing the mixing quality and the energy input into the material. , the injection work rises despite a constant plasticizing work. The cycle 12 was the last moldable part of this parameter study. Despite reducing the screw speed to For each injection molding cycle, . For both parameter combinations, respectively, 10  and 9  injection molding cycles were performed after a stable process was established.For both screw speeds, the plasticizing work is stable. The effect of the increased screw speed on the plasticizing work and the injection work is in accordance with the values measured during the parameter study shown in The plasticizing work was analyzed for both the mixing element and the conveying screw for several material formulations see . For the conveying screw geometry, a clear increase in plasticizing work with increasing fiber content is visible. This is valid for short glass fiber (SGF), long glass fiber (LGF) and combined (PF-SGFx-LGFx) material formulations. In contrast to the conveying screw geometry, no clear correlation between the fiber content and the plasticizing work can be drawn for the mixing element. The mixing element causes an overall significantly higher plasticizing work. Formulations containing long glass fibers require a significantly higher plasticizing work compared to formulations with only short glass fibers. As noted above, the allowable material throughput had to be adjusted based on the material formulation. Lowering the throughput was required for higher fiber contents and longer fiber lengths. With both factors, the apparent density of the granulate–fiber dry blend decreases and the shear energy input during plasticizing increases. This means that less material is pulled into the screw per screw rotation (apparent density), and at the same time, the screw rotational speed must be decreased (to keep the shear energy input of the mixing element in a controllable range and to avoid overheating). Both aspects result in an increase in plasticizing time. For long glass fiber materials with For evaluating the effect screw mixing element on the mechanical proper, the focus of this section will be on the formulations with a fiber content of Switching from the conveying screw geometry to the Maddock mixing element significantly increases the tensile strength for all formulations and for both specimen orientations. Increasing the plasticizing screw speed when using the mixing element leads to a further increase in tensile strength for the PF-SGF0-LGF30 formulation in The direct comparison of samples with a total fiber content of ment see .Both for the PF-SGF0-LGF30 and the PF-SGF16-LGF14 material, the puncture impact energy increases significantly when using the mixing element. An increase in screw speed with the mixing element has no significant effect; the average value of puncture impact energy decreases, but within the scattering of the measurement. Compared to the SGF material, both formulations that contain LGF have significantly higher puncture impact energy when using the mixing element. The SGF material in Comparing the LGF specimens manufactured with the conveying screw in Analyzing the detail SEM images on the right side of The fiber length measurement results are shown in For PF-SGF0-LGF30, the weighted average fiber length in the molded part is reduced from When using a pure SGF compound, the fiber shortening is less pronounced. For both screw geometries, a fiber shortening of It was possible to run a stable injection molding process with the developed thermoset-specific mixing element. In comparison to the conventional conveying screw geometry, the process value scatter, both during the injection and the plasticizing phase of the process, is reduced. The reduced process value scatter is especially visible for material formulations containing long fibers. It is assumed that the shear gaps of the mixing element reduce the backflow during the injection phase due to the flow resistance being higher, as compared to the standard conveying screw geometry. This assumption is in accordance with the findings of Kruppa et al. ,63, who The increased plasticizing work input by the mixing element is visible from the reduced pressure peak at the beginning of the injection stroke, which is typically attributed to the cold plug in the nozzle. The lack of this pressure peak indicates that the material in front of the screw is hotter and consequently has a lower viscosity and a less pronounced cold plug. The increase in injection pressure requirement towards the end of the stroke can be attributed to the advanced chemical reaction progress, which in turn results in an increased viscosity. It is deducted that the effect of backflow prevention accomplished by the mixing element outweighs the backflow-increasing effect of the lower material viscosity. To investigate the lower process scattering with the mixing element during the plasticizing phase of the injection molding process, the back pressure and the screw position during plasticizing is analyzed see .With the conveying screw geometry, the pressure that is required for melting and homogenizing the compound is applied by the injection molding machine’s hydraulic system. Especially for long fiber materials with a low apparent density, the injection molding machine’s hydraulic system had difficulties maintaining a constant back pressure. It is assumed that this scatter in back pressure resulted in the unsteady backward screw movement. When using the mixing element, the pressure for melting is applied geometrically by the reduction of the flow channel cross section in the shear gap of the element . The bacBased on the parameter study findings, an upper plasticizing work limit of From the plasticizing times that were recorded with the mixing element and the conveying screw, it is concluded that the short glass fiber formulations PF-SGFx-LGF0 can be molded up to a fiber content of polyamide 6.6 with glass fibers”}. As an exception to the general consensus, Rohde et al. [Switching from the conveying screw to the mixing element increases the plasticizing work input, which leads to a stronger shortening of the fibers. In this regard, no difference to thermoplastics was found. Most studies of thermoplastics state that the fiber length in the molded part decreases with increasing screw speed, which is represented by the increased plasticizing work. Moritzer and Bürenhaus  confirmee et al.  only fouIn the SEM fracture surface images, a reduction of fiber bundle size and count is observed when using the mixing element. The very small amount of resin residue on the fibers indicates a very weak fiber–matrix adhesion for the specimens manufactured in the long fiber direct process. For manufacturing those samples, the LGF of the type 111AX11 , with a It is remarkable that using the screw mixing element leads to a higher fraction of the skin layer, which consequently leads to a higher fraction of fibers oriented parallel to the direction of the material flow. The process development results show that the mixing element and the screw speed both increase the plasticizing work, i.e., the energy input into the resin during plasticization. This likely results in a further advance in the resin’s curing process. The formation of the skin layer happens by the incremental curing of the resin on the surface . EnglichdThe results of the puncture impact testing clearly show that the absorbed impact energy increases with increasing LGF content and is further improved by using the mixing element. The puncture impact specimens have a diameter of With the developed long fiber direct thermoset injection molding process, a significant increase in the fiber length in the molded parts was achieved. The average weighted fiber length was up to four times higher than the state-of-the-art short fiber-reinforced phenolic resins, resulting in values in the range of In terms of the specific processing challenges presented for the long fiber thermoset injection molding process, the plasticizing work input by the screw mixing element must be carefully controlled to avoid overheating and curing. The characterization results show that in the conflicting field between fiber dispersion and fiber length, the focus must be on the good fiber dispersion in the phenolic matrix. Every mechanical property characteristic that was investigated was increased by an improved material homogeneity, despite the accompanying fiber shortening. Besides the glass fiber length, other structural characteristics, such as the distinctiveness of the skin and core layer structure, are influenced by the mixing element. The additional mixing energy input leads to a clearer development of this structure, as well as to a tendentially higher skin layer fraction, which in turn leads to a higher fraction of fibers oriented parallel to the direction of the flow. The poor fiber–matrix adhesion reduces the expressiveness of some results. Despite those restrictions, it is concluded that the central key to good mechanical properties is a homogeneous distribution of the fibers in the phenolic resin matrix. This homogenization is more important than the fiber length. With the successful process development and the invention of the screw mixing element for thermoset molding compounds, future research studies will now focus on more detailed material and process parameter variations.


Hypertrophic cardiomyopathy is a hereditary disease characterized by asymmetric ventricular hypertrophy as the key anatomical feature. Currently, there exists no effective method for the early diagnosis of hypertrophic cardiomyopathy. In this analysis, we incorporated multiple GEO datasets containing RNA profiles of hypertrophic cardiomyopathic patient tissues, identified 642 differentially expressed genes, and performed GO and KEGG analyses. Furthermore, we narrowed down 46 characteristic genes from these differentially expressed genes using random decision forests and conducted transcription factor regulation analysis on them. Using 40 genes that showed overlap between the training set and the verification set, the artificial neural network was trained, and the final MPS scoring model was constructed, and a receiver-operating characteristic (ROC) curve was drawn. We used the MPS model to predict the verification dataset and drew the ROC curve, which demonstrated the good prediction performance of the model. In conclusion, this study combines a random decision forest and artificial neural network to build a diagnostic model for hypertrophic cardiomyopathy to predict the disease, aiming at early detection and treatment, prolonging the survival time, and improving the quality of life of patients. Hypertrophic cardiomyopathy (HCM) is a common inherited heart disease characterized by unexplained left ventricular hypertrophy. HCM occurs in about 1/500–1/200 of the general population . For patHCM can lead to adverse outcomes such as sudden arrhythmic death , heart fDeep learning methods are emerging as an important tool in clinical diagnosis. We hypothesized that a deep learning method based on the characteristic gene signatures of HCM could be used to develop a diagnostic model for HCM. Towards this goal, we used random decision forests and artificial neural networks. A random decision forest is a classifier that contains multiple decision trees and is a supervised learning method. It evaluates the importance of variables when deciding on categories, making it well suited for feature filtering. On the other hand, an artificial neural network is an algorithmic mathematical model that simulates the behavioral characteristics of animal neural networks and parallel distributed processes. It is similar to a biological neuron structure and, like any neural network processing framework, has an input layer, an implicit layer, and an output layer. In this study, we aimed to develop a diagnostic model for hypertrophic cardiomyopathy using random decision forest and artificial neural networks to understand disease pathology and aim at early detection and treatment. The diagnostic model could thereby help prolong the survival time of patients and improve their quality of life.https://www.ncbi.nlm.nih.gov/geo/) for the construction of the diagnostic model and for verifying the performance of the model, respectively. The training dataset GSE36961 consisted of transcriptomic profiling of 145 surgical myectomy tissue samples, as shown in GSE36961 and GSE141910 were downloaded from GEO . Using these cut-offs, a total of 642 differentially expressed genes were identified, which included 250 upregulated and 392 downregulated genes.The gene expression data were analyzed by using the R software package limma to obtain the differentially expressed genes between HCM and normal myocardial tissues in the training dataset GSE36961. The differentially expressed genes between HCM (case) group and the normal myocardial tissue (control) group in the training dataset were screened based on the multiple of difference (fold change [FC] > |1.5|) and significance  and KEGG pathway databases. Through GO analysis, we obtained the biological process (BP), cellular components (CC), and molecular function (MF) of differentially expressed genes. Through KEGG analysis, we obtained the abundant signaling pathways involved with the differentially expressed genes. A random decision forest is a classifier that contains multiple decision trees and is a supervised learning method. It evaluates the importance of variables when deciding on categories, making it well suited for feature filtering. We used the randomForest package in R to construct a random decision forest model and screen the characteristic genes.The differentially expressed genes were used to train the random decision forest model, and the genes with the negative characteristic importance index (mean decrease accuracy) are deleted to obtain a new expression matrixThe random decision forest model is retrained with the new expression matrix, genes with negative feature importance are deleted, and the step is cycled until the feature importance no longer has a negative value. This results in a primary characteristic gene setThe above two steps are repeated 10 times resulting in 10 primary characteristic gene sets. The genes that appeared more than three times were screened out as the final set of characteristic genesThe filtering steps used are as follows:https://www.grnpedia.org/trrust/), and the TF regulatory network data of characteristic genes were obtained. The regulatory network diagram was drawn using Cytoscape software.The human TF regulatory network data were downloaded from the TR TRRUST database  in each layer is solved layer by layer. According to the following chain rule:The partial derivative of the cost function for a neuron in the whole network from the following derivation:The partial derivatives products of the cost function flowing through all fingers of this parameter are superimposed so that the partial derivatives of all parameters can be obtained by one operation, that is, the gradient of the cost function. The gradient is transferred layer by layer from back to front.Although the prediction of the neural network model is very good, the hidden layer and the nonlinear activation functions make the interpretability of the model low. We deleted the deviation in the model and the weights of some hidden layers and obtained a linear model on the characteristic genes, which enhances the interpretability of the model.We used GSE36961, a transcriptomic profiling database from HCM patients downloaded from GEO as a training dataset. Another dataset GSE141910, which included transcriptome profiling from nonfailing donors was used as the verification set and preprocessed to obtain gene expression data. We performed data pretreatment as follows: the downloaded dataset is used as log2-transformed quantity-normalized signal intensity. First, the probe is mapped to the gene, and the empty probe is removed. In case multiple probes correspond to the same gene, we selected the probe with the highest median and used it to calculate the expression value of that gene.A total of 642 differentially expressed genes were identified by comparing the HCM tissue samples and the control tissues from the training dataset using limma in R as shown in α attenuated HIMF-induced cardiomyocyte hypertrophy.Next, we performed enrichment analysis on 642 differential genes as described in the “Materials and Methods” section, using the clusterProfiler package in R. We performed GO and KEGG analysis on the differential genes and screened out the top 10 pathways to draw a bubble diagram, as shown in We then proceeded to narrow down the characteristic genes from the differentially expressed genes. We selected a total of 46 characteristic genes according to step 4 of the “Materials and Methods” . According to the constructed neural network model, Gene_Weight of each gene was obtained, as shown in We then sought to construct an artificial neural network model to develop the diagnostic model. We found that six of the 46 genes screened out according to the random decision forest algorithm did not exist in the verification set GSE141910. Therefore, we excluded these six genes from the input variable of the neural network model resulting in 40 genes. It is a prerequisite to standardize the data before constructing the neural network model. Hence, we used the standard deviation method to convert the expression amount to The diagnostic model formula was calculated based on the characteristic gene and gene_weight, and the receiver-operating characteristic (ROC) curve was used to evaluate the diagnostic efficiency.The product of Gene_Score and Gene_Weight of each gene was added up to obtain the MPS value of each sample, as shown in the following formula. The ROC curve was constructed based on the MPS value of the samples and whether they were ill. AUC = 1 may be due to the small sample size . (4)MPS=Using the GSE141910 dataset as the verification set, the disease samples in the GSE141910 dataset included tissues from dilated cardiomyopathy (DCM) and peripartum cardiomyopathy (PPCM) patients in addition to HCM. We selected only the HCM samples and compared them to the control samples and calculated the MPS value of each sample based on the obtained gene_weight and expression value of each gene. According to the MPS value and the disease status of the samples, we made the ROC curve , and theDCM and PPCM, like HCM, belong to the category of cardiomyopathy; hence, they might also have similarities in gene networks associated with them. We also used our model to assess whether we can predict DCM and PPCM. Towards this goal, we selected DCM, PPCM, and control samples from the GSE141910 dataset. As described above, the MSP value of each sample was calculated based on the obtained gene_weight and expression value of each gene. According to the MPS value and sample illness, the ROC curve was made , and theHCM is the most common inherited heart disease characterized by asymmetric hypertrophy of ventricular walls, and its incidence rate is about 1/500 . AlthougCurrently, deep learning is the most widely used machine learning method in medical research , 25. DueConventional clinical diagnosis of HCM is based on other unexplained left ventricular hypertrophy determined by ECG or CMRI –32. DespIn this study, for the first time, we put forward a new model for the diagnosis of hypertrophic cardiomyopathy utilizing transcriptomic profiling and gene strategies in combination with a random decision forest and artificial neural networks. Previous studies have mainly focused on the role of a single gene in the pathogenesis of hypertrophic cardiomyopathy. Our diagnostic model included the differentially expressed genes thereby delineating the genetic features of hypertrophic cardiomyopathy more comprehensively. Our model could update our understanding of the diagnosis and treatment of hypertrophic cardiomyopathy significantly.The limitation of this study is that the number of samples is small, which could compromise the validity of the study results. Therefore, in future experiments, expansion of sample size is required to verify the predictive value of the model. Also, the age group and ethnicity/race of the study population could mean that the generalization of the results needs to be tested in other population groups. Further, in the future, the scope of the data collection could be expanded to test the hypothetic diagnostic model put forward in this paper.In this analysis, we screened out a total of 642 differentially expressed genes from an RNA seq database of HCM and normal patient tissues and conducted GO and KEGG analysis on the differentially expressed genes. Furthermore, we narrowed it down to 46 characteristic genes from the list of differentially expressed genes using random decision forests and conducted transcription factor regulation analysis on the characteristic genes. There were 40 genes with an intersection between the training set and the verification set among the 46 characteristic genes. We used these 40 genes and trained the artificial neural network and constructed the final MPS scoring model and drew the ROC curve. Then, we used the MPS model to predict the verification set and drew the ROC curve, which validated that the model had good prediction performance.In the era of the constant evolution of healthcare and information technology, several data science and other information technologies are used to personalize healthcare and enhance patient interactions. With the rapid development of computer science and technology, artificial intelligence (AI) and deep learning technology will continue to develop and be applied in the field of cardiovascular disease research. In the future, diagnostic research should involve a large sample size, multiple centers, and diverse population demographics of patients with hypertrophic cardiomyopathy. This would allow AI, machine learning, and deep learning to play a greater role in the diagnosis and treatment of hypertrophic cardiomyopathy.


The integrated process of design and fabrication is invariably of particular interest and important to improve the quality and reduce the production cycle for structural joints, which are key components for connecting members and transferring loads in structural systems. In this work, using the generative design method, a pioneering idea was successfully realized to attain a reasonable configuration of the cross joints, which was then consecutively manufactured using 3D printing technology. Firstly, the initial model and generation conditions of a cross joint were constructed by the machine learning-based generative design algorithm, and hundreds of models were automatically generated. Then, based on the design objective and cost index of the cross joint, three representative joints were selected for further numerical analysis to verify the advantages of generative design. Finally, 3D printing was utilized to produce generative joints; the influences of printing parameters on the quality of 3D printing are further discussed in this paper. The results show that the cross joints from the generative design method have varied and innovative configurations and the best static behaviors. 3D printing technology can enhance the accuracy of cross joint fabrication. It is viable to utilize the integrated process of generative design and 3D printing to design and manufacture cross joints. Joints are significant components for connecting members and transferring loads in various types of rod structural systems ,2. The cOn the one hand, the design of cross joints still mainly depends on the engineers’ experience. Engineers first propose a preliminary joint model based on the conceptual design, and then the mechanical performances of the initial joints are calculated and analyzed in detail by finite element (FE) technology. Finally, the model’s adjustment is conducted according to the computation results. The above process is generally cyclic and repeated several times, and model testing must sometimes be carried out. Therefore, the traditional design method based on the engineers’ experience has a long cycle time and high energy consumption . In partIn recent years, the appearance of modern buildings is progressively complex, and it is difficult to design rational joint configurations by relying purely on the engineers’ experience. For structural safety, engineers normally assign more material to cross joints, which easily results in the design problems of excessive mass and insufficient geometric optimization. In response to the above problems, many scholars have conducted optimization design research on joints with the help of topology optimization methods ,8,9, sucWith the rapid development of artificial intelligence technology, the design of joints can be achieved by introducing more automatic and efficient methods. Generative design is a modern approach to comprehensive design schemes that explores the entire design space to achieve purposes such as minimal structural compliance, given a set of functional requirements and constraints based on geometry, material specifications, and fabrication considerations ,11,12. AOn the other hand, using the casting process of pouring liquid steel into a mold in one piece, various joints with complex configurations can be produced, and overlapping welds at the intersecting parts can be avoided during welding . TherefoThis work is presented as follows: In Generative design is a hybridization of the design and optimization method, usually integrated into a computation-intensive machine learning algorithm executed on powerful cloud computing technology ,32,33,34In the whole design process, the generative program can automatically complete the various contents, effectively prevent the large number of repeated calculations and adjustments required by traditional methods, and markedly upgrade the efficiency and intelligence of the structural design ,43,44. TGenerative design starts from a series of problem solutions and evaluates multiple solutions in the design space to maximize the quality of the generated model. To attain more diversified structural design alternatives, this study combines space-filling criterion and non-cohesion criterion based on the generative design method. The space-filling design is normally applied in computer experiments, and the non-cohesion criterion is a potent rule to ensure that there will be no interference between design schemes ,45. The Design space The generative design objectives are to explore p and q. According to the maximum distance criterion, the minimum value of In high-dimensional design space, Audze space-filling criteria will place different alternatives on the boundary of design space, which is not desirable . Hence, p and q; In Equation (5), In a generative design, each iteration is accomplished by performing capacity , the maxThe generative design does not depend on the initial structural model and only requires specifying the reserved geometry and obstacle geometry of the structure. Reserved geometry refers to the geometric features that need to be included in the final structural shape. Obstacle geometry refers to the geometric features that need to be excluded. In this study, four-branch pipes are selected as the reserved geometry; the middle part is the generative design area, which is used to obtain the initial cross joint model for generative design, as shown in Subsequently, the constraint and load are applied to the initial joint, as shown in After checking the input parameters, the cloud platform is set for iterative calculations to generate multiple design schemes based on the structural performance requirements. The generative design leverages the powerful operational capacity of cloud computing to simultaneously design thousands of cross joint models in a short period. This study lists only some particular design schemes generated automatically by the generative design and codes them, as shown in There is no material in the middle of generative joints 4 and 9, and each branch is connected by a hollowed-out cube;The transition between each branch and the generative design area of generative joint 5 is smooth;The generated part of generative joint 7 looks like a shape that has been cut by a tool and has an excellent visual effect;Generative joints 26 and 29 seemingly come from the same iterative design, and their branches are united in a crescent shape, which is symmetrical as a whole. It can also be seen that generative joint 26 has a higher degree of evolution than 29, and the model is lighter and simpler.It is easy to see from The above joints embody the powerful model generation ability of the generative design method. Furthermore, the generative joint configurations are different from the cross joint shapes in engineering applications, which is beyond the scope of imagination based on the engineers’ experience. In summary, the generative design method can automatically generate multiple neoteric structural configurations under the given conditions. The physical index values of each generated result also are obtained by the generative algorithm, such as volume, mass, maximum equivalent stress, and maximum displacement, which provides convenience for designers to choose the most appropriate scheme.To further verify the mechanical performance of the generative cross joints, the general software (HyperWorks 2021) was used to carry out linear FE analysis. Due to the large number of generative joints, the workload of one-by-one numerical verification is substantial. Therefore, this work comprehensively considers the practical application requirements and cost indexes of the cross joint and selects the representative joints with lighter mass for further numerical analysis. To choose representative joints more intuitively, this paper integrates the data values obtained by the generative algorithm into a scatter plot, as shown in The detailed characteristics of the generative design area for the representative joints are depicted in The joint models are imported into the software HyperWorks 2021 in step format. The material PSOLID entity attributes are created and provided in HyperMesh. In this study, to ensure the quality of mesh generation, 2D mesh generation is first performed on the joint model, and the 2D mesh is checked in detail. The 2D mesh is then converted to a 3D mesh through Tetra mesh, the quality of the 3D mesh is checked, and any failed mesh is modified. Finally, the FE model of the cross joint is attained. The load and constraint are consistent with the original model of generative design. All nodes on the bottom-edge surface of the lower pipe are selected on the joint FE model to constrain the translational and rotational degrees of freedom in the X, Y, and Z axes. An axial tension of 645 kN is arranged on the top-edge surface of the remaining three branch pipes. Because the cast steel material has obvious plasticity, the ideal elastoplastic model is adopted, obeying the von Mises yield criterion. The static analysis results of displacement and the equivalent stress of the generative joints are shown in The static analysis results show that the stress distribution of generative joints is uniform, and the displacement and stress distribution of each joint are identical, which indicates the rationality of the generative results. To further analyze the practical optimized design effect of the generative cross joints, the static behaviors are compared with those of traditional flat polygon joints and topology-optimized joints.The flat polygon is a commonly used connection for cross joints, so it has been selected to compare its mechanical performance with the generative joints . The flaThe mass of the flat polygon cross joint is 15.062 t. Under the same working conditions as the generative joints, the static analysis results are shown in According to the research status of joint design, the topology optimization method can minimize the weight while ensuring the excellent mechanical performance of joints ,9. HenceBased on our recent research for the optimization design of cross joints, topology optimization using traditional substructure and bionic substructure partitioning methods has better overall performance than the joint model obtained by conventional topology optimization, and the related achievements have been published previously in journals . To fullThe static analysis results of the cross joint obtained by the traditional substructure topology optimization are shown in The static analysis results of the joint obtained by the bionic-based substructure topology optimization method are shown in To facilitate the comparative analysis for the mechanical performances of the above joints, the mass, maximum displacement, and equivalent stress are summarized in It can be seen from In recent years, 3D printing has become an emerging industrial intelligent manufacturing technology. Different from the traditional manufacturing method, the technology converts the concept of subtracting materials into adding materials . Based oLimited to experimental equipment and by cost, this paper utilizes FDM technology to manufacture scale models of the generative joints with polylactic acid (PLA) plastic as materials to verify the feasibility of 3D printing technology in restoring joint features and enhance the intuitive understanding of generative joints. FDM technology works by squeezing materials heated at high temperatures through a nozzle to build a physical model layer by layer ,54,55. TAfter many experiments, it was confirmed that the reasonable setting of some parameters is the key to attaining high precision joint models, such as printing temperature and speed, support, and nozzle diameter. The printing temperature is the most important parameter affecting the accuracy and mechanical performance of the finished model during the FDM printing process. The temperature of the printer nozzle should be kept 4~6% higher than the melting temperature of the printing material. The printing speed must be controlled within an appropriate range. If the printing speed is too quick, the underlying material will not have enough time to solidify. If the printing speed is too slow, the cooling time of the material will be longer, which may cause the adhesion between adjacent layers to be weakened, along with the layers’ uneven shrinkage. In addition, this study also lists the support type influence on the printed product. Support is mainly divided into no support, local support, and global support. 3D printing can highly reproduce the details of the joint model, which is very difficult to manufacture by traditional fabrication processes. It can be seen from In this work, a pioneering idea using the generative design method is successfully realized to attain a reasonable configuration for cross joints, which are consecutively manufactured using 3D printing technology. The main conclusions are as follows:(1) The generative design method has powerful model generation ability and innovation ability. Generative design can automatically generate multiple new cross joint configurations. Most of the generative joints have novel shapes that are beyond the imagination of designers based purely on experiences. Furthermore, it is not always possible to manufacture joints generated by generative design because of the production limitations, molds, etc.(2) Generative design can enhance the design optimization level of cross joints. The numerical simulation results indicate that the generative joints have a lighter mass and better mechanical performance. Moreover, the boundary and constraint conditions of the generative design method are straightforward, and the whole design process is more automatic and intelligent.(3) Generative cross joints have excellent manufacturability and aesthetics. In this paper, 3D printing technology is applied to produce a reduced-scale model of the generative joints. The solid model shows that the joint formation effect is excellent, and the surface is smooth.(4) The development of 3D printing technology ameliorates the manufacturing technology of cross joints. High precision joints can be produced using 3D printing.(5) The combination of generative design and 3D printing is an efficient way to realize the integrated process of the design and manufacture of cross joints.