Source acquisition device identification from recorded audio aims to identify the source recording device by analyzing the intrinsic characteristics of audio, which is a challenging problem in audio forensics. In this paper, we propose a spatiotemporal representation learning framework with multi-attention mechanisms to tackle this problem. In the deep feature extraction stage of recording devices, a two-branch network based on residual dense temporal convolution networks (RD-TCNs) and convolutional neural networks (CNNs) is constructed. The spatial probability distribution features of audio signals are employed as inputs to the branch of the CNN for spatial representation learning, and the temporal spectral features of audio signals are fed into the branch of the RD-TCN network for temporal representation learning. This achieves simultaneous learning of long-term and short-term features to obtain an accurate representation of device-related information. In the spatiotemporal feature fusion stage, three attention mechanisms—temporal, spatial, and branch attention mechanisms—are designed to capture spatiotemporal weights and achieve effective deep feature fusion. The proposed framework achieves state-of-the-art performance on the benchmark CCNU_Mobile dataset, reaching an accuracy of 97.6% for the identification of 45 recording devices, with a significant reduction in training time compared to other models. Source acquisition device identification from recorded audio comprises research on the identification of recording devices by analyzing the intrinsic characteristics of audio  and is aResearch on recording device source identification focuses on the identification of the source recording device of the audio data, i.e., the attribution category of the target audio is derived by matching with the database through identification. This identification process relies on the signature information of the recording device embedded in the audio data, which is a kind of recording-device-related discriminatory information that is generated in the process of recording the target sound using the recording device. The target audio is often regarded as a part of the human voice perception system, but ambient information is also recorded during the recording process. Device-related information that is not easily perceptible to the human ear is also embedded during the audio generation process. This device-related information is derived from differences in the transfer functions of different devices during recording, which are due to differences in the selection of recording-related components and the design of electronic circuits within each device, causing convolutional distortion in the input speech during recording, leaving device-signature information in the recording . ExistinThe development of research on audio recording device identification in the existing literature has gone through several stages, and the existing methods can be divided into three main stages. The first class of methods is based on research on feature engineering of audio signals, such as the Mel frequency cepstrum coefficient (MFCC) ,9 and thhttps://github.com/CCNUZFW/STRLMA (accessed on 20 March 2023).In this paper, we propose a two-branch network to implement spatiotemporal representation learning for recording device identification. The extraction of deep temporal features is performed by a residual dense TCN, and the extraction of deep spatial features is performed by a CNN. The whole representation learning process is optimized by a structured loss function. The implementation codes of this research are available at In order to collaborate with the spatiotemporal representation network to obtain a better representation of recording devices, we design three attention mechanisms: a spatial attention mechanism, temporal attention mechanism, and branch attention mechanism. The spatial and temporal attention mechanisms assign weights to the input features Gaussian super vector (GSV) and MFCC, respectively, to enhance the representativeness of both features. The branch attention mechanism is applied to the fusion of two-way branches to promote the learning of key information in the fusion process.Compared with six baseline methods, the proposed framework achieves state-of-the-art performance on the benchmark CCNU_Mobile dataset, reaching an accuracy of 97.6% for the identification of 45 recording devices, with a significant reduction in training time compared to baseline models.With the widespread streaming of media on the Web, research on streaming data has become a hot topic, among which spatiotemporal representation learning has been rapidly developed due to its sensitivity to the spatiotemporal properties of streaming data ,19. SpatThe rest of this paper is organized as follows. In this section, we review related studies on audio recording device identification and classify them into the following two categories based on the technical characteristics of each method.In the early stage, some researchers drew on the research in fields such as speaker recognition and used features from these areas as features for source device identification, which has achieved good results. Hanilci et al.  proposedIn addition to MFCC using the speaker recognition domain, GSV  has beenAlthough traditional acoustic features have achieved good recognition results in device source identification, most of these traditional features are constructed based on the human ear auditory system and cannot fully characterize the variability among recording devices. Jin et al.  proposedIn recent years, deep learning has been widely used and achieved improved performances in many fields ,25, mainInfluenced by research in image processing and recognition, several researchers have proposed methods to transform audio signals into two-dimensional images to characterize device source features. Qin et al.  trained In this section, we first formally define the task of audio recording device identification. Then, we explain the definitions related to deep temporal features and deep spatial features used in this paper. Next, we describe the proposed multi-attention mechanism. Definition 1 Audio recording device identification aims at detecting the recording device identity of a test audio signal . Definition 2 The deep temporal features are extracted from the MFCC by RD-TCN. For time-series feature data, which are generally frame-processed features, it is necessary to not only analyze the information of feature vectors within frames but also to analyze the information association between frames. Deep temporal features are extracted from the original features using deep learning, which requires the use of networks with sequence modeling capabilities, such as RNN and LSTM; a modified TCN is used in this paper. The extracted deep temporal features reflect the temporal information in the feature data, including the analysis of similarity information and mutation information between adjacent frames, as well as the analysis of long-term fluctuation information.. Definition 3 The deep spatial features are extracted from the GSV by CNN. GSV is a probability distribution feature extracted by GMM that maps the original feature data to the high-dimensional feature space during GSV extraction, and the extracted GSV reflects the statistical information of Gaussian distribution in the sample space. The extracted deep spatial features reflect the spatial information in the feature data, including the analysis of the correlation between different Gaussian components in the GSV feature matrix, as well as the analysis of the local associations of different regions in the two-dimensional space of the feature matrix.. Definition 4 The multi-attention mechanism proposed in this paper consists of three attention mechanisms, namely a spatial attention mechanism, temporal attention mechanism, and branch attention mechanism, which act in different stages for feature reconstruction and feature fusion, respectively. The core idea is learning the importance distribution in the input features according to the corresponding attention blocks, then enhancing the information related to classification in the features by weight assignment. The reconstruction of the original features by the spatial attention mechanism and the temporal attention mechanism highlights the classification-related information and improves the utilization of effective information in the model. The fusion of the two-way network information by the branch attention mechanism achieves complementary utilization of spatiotemporal feature information and improves the information density.(Multi-Attention mechanism). The feature reconstruction phase is divided into temporal feature reconstruction and spatial feature reconstruction. Temporal feature reconstruction assigns adaptive weights to the features at the temporal scale through the attention mechanism and marks the significant sequences to improve the effects of important feature sequences on the model. Similarly, reconstruction for spatial information involves learning the spatial feature information using the attention mechanism to assign different weights to enhance spatial features.In the deep feature extraction stage, the temporal branch based on RD-TCN is used to extract the deep temporal features, and the spatial branch based on CNN is used to extract the deep spatial features.In the feature fusion phase, a branch attention mechanism is designed for the fusion of deep temporal features and deep spatial features.In the classification decision phase, we apply a multiloss joint computation strategy in order to build an end-to-end network system and optimize the learning process of the two-way branch network and the decision end.The spatiotemporal representation learning framework includes feature reconstruction, deep feature extraction, feature fusion, and classification decisions, and the whole task is jointly trained with end-to-end architecture. The overall framework is shown in The process of the proposed spatiotemporal representation learning model is shown in Algorithm 1.First, in order to obtain a stable representation of the audio signal in the frequency domain, the audio signal , fast Fourier transform (FFT), Mel filtering, logarithmic operation, and discrete cosine transform (DCT). The specific extraction process is as follows:Although MFCC is capable of representing time-based changes in audio information, this raw information contains a large amount of redundant information. The temporal attention mechanism is a typical technique used for time-series data classification to attenuate and remove the noisy or irrelevant parts. In the process of device source identification, the temporal attention mechanism possesses strong practical significance. For example, the presence of many human voices in the device source speech interferes with the device source information, and sequence segments with many similar human voices can be attenuated by the temporal attention mechanism, which can be used to overcome the problem of masking and irrelevant signals. Specifically, the attention mechanism can be used to measure the relevance of each time step, and the temporal attention weights provide significance to meaningful values in the sequence, which helps to distinguish similar regions and mark important information. The temporal attention mechanism constructs weights in the same way as the spatial attention mechanism, using convolutional layers to construct learnable parameters, then adjusting the temporal feature maps.The temporal attention mechanism proposed in this paper first extracts the internal correlation between the contextual relationships and feature vectors in the temporal feature spectrum through a convolutional layer, then assigns weights to the time series using a single-scale maximum pooling layer to control the importance coefficients of each feature vector on the time scale. Finally, weights indicating the degree of importance are assigned to each time node in the temporal feature spectrum by multiplying by the input feature sequence.Algorithm 1 The proposed spatiotemporal representation learning model.Input: MFCC feature          Output: The prediction of the attributed recording device for the input sample1 Reconstruct the input temporal feature  2 Reconstruct the input spatial feature  3 Extract deep spatial features  4 Extract deep temporal features  5 Compute spatial feature loss  6 Compute temporal feature loss  7 Concatenate deep temporal features  8 Compute classification loss  9 Compute the overall loss  10 Predict the source recording device   In summary, the temporal attention mechanism with GSV features have been shown to be effective in research on recording device source identification ,13; the K), the dimension of each MFCC vector is M, and the mean value of each target model is a matrix of The discrepancy information in the GMM model of each target device source mainly exists in its mean value, and the mean vector thus extracted is the GSV feature. For the number of Gaussian components .(5).(5)StepStep 3: Finally, the feature vectors of D devices are adapted by MAP to obtain the device-specific source GMM, and the mean vector of GMM is extracted, which is the GSV features.In device source identification, the information density of different parts of the spatial features is not equal, and only the parts relevant to the classification task need to be attended to. The spatial attention mechanism finds the most important parts of the feature map for processing and displays the importance in the form of probability maps or probability feature vectors to emphasize important information and suppress useless information. The spatial attention mechanism designed in this paper aims to reconstruct the features by including weights for the device source features so that the features retain sufficient device-related spatial information. The spatial attention mechanism uses convolution and pooling to construct learnable parameters, which are jointly optimized with the whole model to construct efficient device source features.T ≫The spatial attention mechanism proposed in this paper captures the spatial relationships in the input feature maps through a 2D convolutional layer and controls the weight assignment of the importance of spatial information by maximum pooling. Then, spatial-attention-based weight assignment is achieved by multiplying the corresponding elements in the input features. In summary, the spatial attention mechanism, with In this paper, a CNN is used to extract spatial feature information from the input data, and after completing the spatial feature extraction, a fully connected layer is used to remove the location information and reduce the sensitivity of parameters in the subsequent fusion process. CNN networks have excellent processing ability for 2D data. The spatial information in the input data is extracted by transforming the input 2D data into a feature map through feature extraction with a convolutional kernel. The CNN local perception and parameter-sharing feature greatly reduces the network parameters, ensures the sparsity of the network, and preserves the local correlation of the samples. In summary, the CNN block, with C is the number of channels and i denotes the i-th channel of the convolution layer; C channels of the input layer (or pooling layer)  ; j-th value of the i-th channel.The CNN used for deep spatial feature extraction is composed of a convolutional layer, pooling layer, and fully connected layer. The convolutional layer is obtained by convolving the feature surface with the local region of the layer’s feature surface through a convolutional kernel; this operation is able to extract the deep features from the feature surface. Setting the convolution kernel as j-th feature mapping after pooling for the The resolution of the eigenfaces is then reduced by pooling operations, while also maintaining the spatial invariance of the eigenfaces.j-th value of spatial feature information extracted by the CNN.After convolution, the data from the previous layer are normalized with different weights by discarding the location information through the fully connected layer to obtain an output result with the following formula for the feature information output from the fully connected layer.The spatial feature losses  ,32 and tTCN has the advantage of parallel processing of data. Unlike RNN-type networks, which require sequential processing of data in a sequential manner, TCN can perform parallel processing of given temporal data, thereby greatly reducing the training time. In addition, TCN can set parameters such as the number of network layers, convolutional kernel size, and the dilation rate according to the task, thereby indirectly setting the receptive field size to accommodate feature data of different complexities.TCNs use causal convolution in order to enable the extraction of temporal information. Causal convolution has a unidirectional structure, which means that there is a preceding cause before there is a subsequent effect, and it is a strictly time-constrained model. Pure causal convolution still suffers from the problem that the modeling length of the time scale is limited by the size of the convolutional kernel, and a very large number of hidden layers needs to be stacked in order to extract longer time series of dependencies. Thus, dilation convolution is used to complete the temporal convolution operation. Dilation convolution allows the input to be sampled at intervals during convolution. Therefore, the dilation convolution makes the size of the effective receptive field grow exponentially with the number of layers, allowing the convolution kernel to parse the extracted features. This allows the convolutional network to obtain a sufficiently large receptive field with relatively few layers.Here, we introduce improvements on the basis of a TCN by constructing an RD-TCN using residual dense blocks, which further enhances the information utilization compared with a normal TCN. A structural diagram of RD-TCN block is shown in We propose the use of a residual dense structure  instead l-th layer are represented by C), which enables us to combine activation values from different layers using skip connections later. When the convolution kernel size is set to three, i.e., the number of time steps beyond which the convolution is applied, the temporal convolution is calculated ast of the l-th layer, the input to the first layer is the deep temporal feature s denotes the rate parameter of the dilation convolution. The result obtained after adding the residual dense connections is calculated asW denotes the a set of weights, where the bias term is omitted for simplicity, and As shown in The temporal feature loss  and MFCC-SVM are two classical methods in the field of recording device source identification, and we used them as reference standards. I-vector and BED features are improved in terms of features to solve the feature information representation problem, and we also used them as features for the baseline methods. In addition, GSV-CNN was added to the baseline method as a representative method of deep learning methods, and a multifeature fusion method using multiple features and deep learning models was added to the baseline method as a novelty.GMM-UBM [GMM-UBM : This meMFCC-SVM [MFCC-SVM : This meI-vector-SVM [ctor-SVM : The i-vBED-SVM [BED-SVM : This meX-vector TDNN-based systems [ systems ,36: ThisGSV-CNN [GSV-CNN : This meMultifeature fusion [e fusion : This me(1) Framework settings: To extract the temporal MFCC features, a Hamming window function is chosen; the length of each signal frame is 30 ms, the overlap is 15 ms, and the length of the extracted single MFCC vector is 39. The spatial GSV features are extracted using 64 fitted Gaussian components, and the feature matrix shape is . (2) Training settings: The method was trained in the same environment as all baseline methods during the training process, with a total of 200 training epochs, a batch size of 128, an initial ® Xeon Gold 5218 × 2; GPU: NVIDIA® TITAN RTX (24 GB video memory); and memory: 32 GB.For the accuracy comparison between this method and the baseline methods on the CCNU_Mobile dataset, In order to verify the effectiveness of the three attention mechanisms, four experiments were conducted, in which three attention mechanisms were present and one of them was removed. It can be seen from the experimental results in In order to verify the effectiveness of the RD-TCN network, comparison experiments were conducted.The parameters of the ordinary TCN-based temporal feature extraction and the RD-TCN-based temporal feature extraction are shown in In the RD-TCN temporal feature extraction network, the original residual blocks of the TCN network are replaced with residual dense blocks. From the experimental results in To optimize the model training process, we used the strategy of joint loss function, which was optimized by combining three losses. To explore the effectiveness of the joint loss function, we compared it with a model using a single cross-entropy loss function and tested the optimal parameters by controlling the proportional coefficients.In this paper, we propose a spatiotemporal representation learning method with a multi-attention mechanism for recording device source identification. In this paper, we used multiple features as input, which is a kind of multiple knowledge representation; this strategy effectively improves the recognition accuracy and contributes to the generalization ability and interpretability of the model . The twoIn terms of experimental performance, the present method shows a small improvement in recognition accuracy relative to methods proposed in our previous work; however, the training time of this method is significantly reduced, and its performance is more stable. The recognition performance on this dataset is close to saturation, and even small improvements are meaningful, so we will subsequently explore application-oriented and effective recognition methods. In future work, we will further optimize the model to obtain more significant recognition performance improvement. However, the present method still has some shortcomings in the feature extraction stage, which require the early extraction of two features before model training, increasing the complexity of the application. We will investigate how to extract more expressive features and research feature extraction methods that are better-matched to the task of recording device identification. In terms of identification models, we will explore the application of self-supervised learning in this area and attempt to improve the application of transformer-based representational learning in recording device identification. We will also improve our method to be applicable to more complex recognition scenarios to promote additional applications.


Given the importance of hyperelastic constitutive models in the design of engineering components, researchers have been developing the improved and new constitutive models in search of a more accurate and even universal performance. Here, a modified hyperelastic constitutive model based on the Yeoh model is proposed to improve its prediction performance for multiaxial deformation of hyperelastic polymeric materials while retaining the advantages of the original Yeoh model. The modified constitutive model has one more correction term than the original model. The specific form of the correction term is a composite function based on a power function represented by the principal stretches, which is derived from the corresponding residual strain energy when the Yeoh model predicts the equibiaxial mode of deformation. In addition, a parameter identification method based on the cyclic genetic-pattern search algorithm is introduced to accurately obtain the parameters of the constitutive model. By applying the modified model to the experimental datasets of various rubber or rubber-like materials , it is confirmed that the modified model not only possesses a significantly improved ability to predict multiaxial deformation, but also has a wider range of material applicability. Meanwhile, the advantages of the modified model over most existing models in the literatures are also demonstrated. For example, when characterizing human brain tissue, which is difficult for most existing models in the literature, the modified model has comparable predictive accuracy with the third-order Ogden model, while maintaining convexity in the corresponding deformation domain. Moreover, the effective prediction ability of the modified model for untested equi-biaxial deformation of different materials has also been confirmed using only the data of uniaxial tension and pure shear from various datasets. The effective prediction for the untested equibiaxial deformation makes it more suitable for the practice situation where the equibiaxial deformation of certain polymeric materials is unavailable. Finally, compared with other parameter identification methods, the introduced parameter identification method significantly improves the predicted accuracy of the constitutive models; meanwhile, the uniform convergence of introduced parameter identification method is also better. Hyperelastic polymeric materials, which possess exceptional hyperelastic properties, have been widely utilized in various fields such as medical devices , flexiblCurrently, constitutive models characterizing hyperelastic properties are usually built by the strain energy density function. In light of the different ways of constructing the strain energy density function, the hyperelastic constitutive models can be divided into two overall categories: the first category encompass statistical mechanics models based on the idealized network structure of molecular chains, while the other category comprise phenomenological models based on continuum mechanics.For statistical mechanical models, it is usually constructed based on the assumption of the network structure of molecular chains inside the polymer . AlthougFor phenomenological models, they are usually constructed based on the strain invariants or principal stretches. Although the parameters of these phenomenological models often do not have practical physical context, they have been widely studied and applied because of their relative advantages . The Mooney model is the earliest constitutive model used to represent the mechanical behavior of polymeric rubber. It has a linearized form, and it usually has better performance in the case with small deformation . Taking Although there are already many classical constitutive models to characterize the hyperelastic property, there are still continuously improved and completely new models emerging. The reason for this may be that the deficiencies of existing models still exist  and the Considering the pursuit of a universal and robust hyperelastic constitutive model, this study aims to improve the Yeoh model to compensate for its shortcoming in performance and applicability. The idea of focusing on improving the Yeoh model is not arbitrary, but rather based on its unique advantages in characterizing untested modes of deformation as explained above. The reason why we want to take advantage of this advantage is because we have indeed encountered the situation in practice where the equibiaxial deformation mode of a used polymer material is not measurable. With the widespread application of different soft polymer materials in engineering design, we believe that the probability of this situation occurring will be higher. So, the actual demand also drives us to carry out this work. Furthermore, it is well known that the Yeoh model will underestimate the equibiaxial mode of deformation when characterizing multiaxial state of stress; hence, it should be further improved in order to have more accurate characterization results. Hitherto, there are several sporadic improved Yeoh models. Earlier, Yeoh proposed to improve the fitting accuracy of the Yeoh model to the data from simple shear by adding an additional exponential term related to the first principal invariant . The comIn this study, we use a thoughtful correction term to modify the Yeoh model, so as to improve its ability for characterizing multiaxial deformations. This correction term is derived from the corresponding residual strain energy when the Yeoh model predicts the equibiaxial mode of deformation, and its specific form is a composite function based on a power function represented by the principal stretches. The strain energy density function of the modified model is represented by the first strain invariant and the principal stretches, and it contains only five parameters to be identified. In the case of specific parameters, the model can be degraded to the neo-Hookean model, the Mooney–Rivlin model, the Yeoh model, and the Biderman model. Therefore, the modified model can also be regarded as the parent model of these four classical models. In addition, we also introduce a special parameter identification method based on the cyclic genetic-pattern search algorithm in order to improve the predicted accuracy of constitutive models. For demonstrating the modified model’s robustness and generality, the modified model is applied to six different types of hyperelastic materials. During this process, in addition to comparing the performance of the modified constitutive model with some landmark constitutive models in the literatures, the stability and convexity of the modified constitutive model is also verified. Finally, the validity of the introduced parameter identification method is also confirmed by comparing it with four existing parameter identification methods.Experimental data involving simple modes of deformation like uniaxial tension (UT), equibiaxial tension (ET) and pure shear (PS) form the basis for parameter identification of the constitutive model. And, it is a common practice to contrast the predicted results of model and experimental data for examining the performance of the model in different ranges of deformation and different modes of deformation. Here, considering the widespread use of the experimental dataset about natural unfilled vulcanized rubber obtained by Treloar , we takeFurthermore, in order to fully verify the characterization ability of the modified model for the multiaxial deformation of different materials, we also considered experimental datasets from another five different types of rubber-like materials –(6), the following expression can be obtained by eliminating As stated in the introduction, the third-order polynomial based on the first strain invariant (Yeoh model) not only has a simple form, but can also reproduce the inverse S-shape of the stress–strain curve of the hyperelastic polymeric materials under different modes of deformation  and it aIn order to more effectively improve the characterization ability of the Yeoh model for the equibiaxial mode of deformation, the corresponding residual strain energy is calculated  is satisfied, the constitutive model with calibrated parameters will possess the poly-convexity.A stable constitutive model obeying the laws of thermodynamics is a prerequisite for subsequent finite element analysis. An unstable strain energy function will adversely affect the nonlinear numerical algorithms in the finite element codes . If the According to the Drucker stability criterion used in the commercial finite element software , the relD) of the above matrix equation is positive definite. The components of the coefficient matrix (D) are as shown in If the hyperelastic constitutive model is stable, it is only required that the coefficient matrix , equibiaxial tension (ET) and pure shear (PS). The relationships between nominal stress and principal stretches under these simple modes of deformation can be derived from Equations (7) and (8) as follows:Identifying the parameters of the constitutive model is an important step during the characterization of the hyperelasticity. Although some optimization algorithms have been used to identify the parameters of constitutive models, these used methods still have their own problems. For example, the damped least squares algorithm based on nonlinear least squares  and the p represents the simple mode of deformation such as uniaxial tension (p = 1), equibiaxial tension (p = 2) and pure shear (p = 3), respectively; pth mode of deformation; pth mode of deformation, respectively; and pth mode of deformation.On these grounds, this study introduces a parameter identification method of the constitutive model based on the cyclic genetic-pattern search algorithm, and its framework is shown in The ability of a constitutive model to accurately predict a single mode of deformation is its foundation to effectively predict multiaxial modes of deformation. In view of this, the single set of deformation data  of natural vulcanized rubber from a large deformation range are first used to identify the parameters of the proposed modified model, respectively. For verifying the prediction ability of the modified model for the multiaxial deformation mode, the data of multiple deformation modes  from the same material dataset are simultaneously used to identify the parameters of the modified model. The following will present the predictive effects of the modified constitutive model on the multi axial deformation state of different materials in sequence. And these results are also compared with the results of other existing models . In order to make these results more visible and clear, Further comparing the predicted results of the modified constitutive model with the Yeoh model, modified Yeoh model and generalized Yeoh model, it can be found that the overall predicted accuracy of the proposed model is several times higher than theirs in all ranges of deformation. In particular, the predicted accuracy on the equibiaxial mode of deformation is improved most obviously  , geneticAccording to the minimum total error shown in This paper presents a modified hyperelastic constitutive model based on the first strain invariant and the principal stretches. In order to more accurately identify the parameters of model, a special method of parameter identification based on the cyclic genetic-pattern search algorithm has also been introduced. Combining the experiment data of different rubber materials with the introduced parameter identification method, the performance of the proposed modified constitutive model is fully evaluated. The results show that the proposed modified model not only possesses a significantly improved ability to predict multiaxial deformation, but also has a wider range of material applicability. This advantage is not only reflected in the comparison with the original Yeoh model, but also in the comparison with other improved Yeoh models . Even compared with the excellent third-order Ogden model and Alexander model, our proposed modified model with only five undetermined parameters is not necessarily inferior in characterizing the multiaxial deformation of rubber materials. For example, the overall prediction accuracy of the modified model for isoprene vulcanized rubber and poly-acrylamide hydrogel is slightly better than that of the third-order Ogden model and Alexander model. Anyway, for the five rubber materials used in this study, our modified model has a similar level of total prediction accuracy as the two models of the third-order Ogden model and Alexander model . Furthermore, our modified model is also proven to have a good ability to characterize the deformation of human brain cortex tissue. Its prediction accuracy for multiaxial deformations of human brain cortex tissue is not only similar to that of the third-order Ogden model (the third-order Ogden model is considered to be the best model currently characterizing the deformation of the human brain cortex tissue.), but also has no loss of convexity compared to the third-order Ogden model. In addition, the proposed modified model in this study is also proven to hold the improved ability to predict the untested equibiaxial deformation of most rubber materials used in this study. The modified constitutive model calibrated based on different datasets is also verified to have a posteriori Drucker stability and polyconvexity, which lays a foundation for the modified constitutive model to be applied to finite element analysis.Based on the above conclusions, we believe that the main advantages of the modified constitutive model proposed by us are as follows:Firstly, although the modified model has five undetermined parameters, it still maintains a relatively simple functional form compared to those models containing logarithmic, exponential or integral expressions, making it easier to perform related mathematical calculations. Having five parameters also ensures that it is neither incompatible with fourth-order weak nonlinear elasticity theory due to having too few parameters, nor does it face difficulties in parameter identification due to having too many parameters.Secondly, thanks to our proposed correction term based on the principal stretch, this modified constitutive model has significantly improved ability for predicting multiaxial deformation. Moreover, this improved predictive ability has certain universality, that is, the modified model can be applied to various different types of rubber materials . There are currently few studies that apply their model to so many types of material.Thirdly, this modified constitutive model can, with relative accuracy, predict the multiaxial deformation of human brain cortex tissue  while ensuring convexity. This gives it the potentiality to characterize the biomechanics of soft biological tissues.Finally, the modified constitutive model also has an improved capacity to predict untested equibiaxial deformation. This advantage is very useful in the situation where equibiaxial tension cannot be completed under limited hardware conditions.Compared with other parameter identification methods, the introduced method of parameter identification has been proved not only to take into account different modes of deformation, but also makes models have better performance. The excellent capability of the introduced method of parameter identification benefits from the strong ability of global search of the genetic algorithm and the strong ability of local search of the pattern search algorithm, and the addition of the cyclic structure further weakens its dependence on the initial value, thereby making its uniform convergence better.


Brachiation robots mimic the locomotion of bio-primates, including continuous brachiation and ricochetal brachiation. The hand-eye coordination involved in ricochetal brachiation is complex. Few studies have integrated both continuous and ricochetal brachiation within the same robot. This study seeks to fill this gap. The proposed design mimics the transverse movements of sports climbers holding onto horizontal wall ledges. We analyzed the cause-and-effect relationship among the phases of a single locomotion cycle. This led us to apply a parallel four-link posture constraint in model-based simulation. To facilitate smooth coordination and efficient energy accumulation, we derived the required phase switching conditions as well as joint motion trajectories. Based on a two-hand-release design, we propose a new style of transverse ricochetal brachiation. This design better exploits inertial energy storage for enhanced moving distance. Experiments demonstrate the effectiveness of the proposed design. A simple evaluation method based on the final robot posture from the previous locomotion cycle is applied to predict the success of subsequent locomotion cycles. This evaluation method serves as a valuable reference for future research. Transverse ledge brachiation robots are bio-inspired climbing robots that mimic climbing athletes ,2,3. TheTransverse ledge brachiation robots first swing their lower limb(s) and body to accumulate adequate kinetic energy. They then release one hand to grab the target ledge while simultaneously adjusting their posture so that the other hand can return to the original double handhold position under the guidance of inertia. This facilitates the beginning of swing excitation in the next locomotion cycle. As the processes of energy storage/release repeat and alternate, the robot traverses along the wall . This unHumans and apes are both primates, so brachiation robots modeled on humans and apes are similar . HoweverTransverse brachiation requires good multi-limb coordination . A simplMost existing studies of transverse brachiation robots used multi-limbed robot designs based on human climbing motions ,26,27,28In this study, we refer to the unique movements of athletes climbing transversely along wall ledges to propose a design process that takes the cause-and-effect relationships in each phase of movement into account. This process enabled us to realize multiple locomotion gaits for coordinated bio-inspired robots. We used a parallel four-link posture as the constraint. Using model-based dynamic analysis, we derived the design parameters and joint trajectories for smooth transitions. Experiments demonstrate the efficacy of the proposed gait design method. Based on these results, we propose an evaluation index to analyze whether the grip posture of the grippers meets the boundary conditions of the swing phase to predict the success rate of achieving the next locomotion cycle. This evaluation tool serves as a valuable reference for future research.The remainder of this paper is organized as follows. In this section, we discuss the locomotion gaits associated with continuous transverse brachiation and hybrid transverse brachiation. Specifically, we explore design requirements based on the movement phases. The complete gait design process is presented in subsequent sections.Sport climbers transverse brachiate using a periodic transverse movement behavior . Figure Transverse ricochetal brachiation is a movement strategy applied by climbing athletes when the target ledge is out of reach. In a single locomotion cycle, this gait can cover a longer distance and enables movement when there are no handholds. Two common modes of locomotion can serve as a simple analogy to describe the two brachiation gaits above: walking and running. Walking is slower, but the entire process is steadier and saves energy. In contrast, running obviously has higher movement efficiency, but it consumes more energy during the process, and the posture of the body when both feet leave, and land on the ground influences the effectiveness and stability of this mode of locomotion. From the perspective of bionics, ricochetal brachiation can, to a certain extent, be compared to the trot gait of multiped robots. However, the gaits of brachiation robots must be paired with robust and coordinated ledge grip motions, as dissimilar to multiped robots, which can stand up and continue even after falling down , it is iPast studies ,5 have hAnother focus of this study was to enable the same robot configuration to realize a hybrid locomotion gait, including transverse brachiation and transverse ricochetal brachiation. This mechatronic realization problem has yet to be solved for ape-like brachiation robots. From This study presents locomotion gait designs for transverse brachiation and transverse ricochetal brachiation with a locomotion cycle comprising four phases. The first two phases are the swinging phase and the approaching-target phase. The method of energy release in the third phase differentiates the two locomotion gaits. After both grippers have grasped the ledge, the robot adjusts its posture to help it enter the initial swing phase of the next locomotion cycle. The gait design contains a total of five different movement phases. We next give a brief introduction to the processes of establishing the dynamic model for each phase and the differences in the mathematical models of the phases. This serves as the foundation for gait parameter analysis and design.We consider the example of a robot performing transverse brachiation to the right. Using the Euler–Lagrange method, we first define suitable origins for the coordinate system based on the various movement phases. Next, we select a state vector Based on the definition above, we can derive the dynamic equation of general standard robots as shown:Swinging phaseIO, as shown in L, and the grippers are gripping the ledge firmly with no slippage occurring. Through the geometric relationships in the four-bar linkage mechanism [Rθ, Lθ, Bθ as follows:In this phase, both grippers are gripping the ledge, and the arms form a parallel four-link geometric configuration with the environment. By swinging the tail, adequate energy is accumulated to facilitate the subsequent transverse movement. Based on the assumption of transverse locomotion to the right, we set the coordinate origin of this phase at the joint of the left wrist, echanism , we can Rθ and body joint angle Bθ can be expressed as functions of left arm joint angle Lθ. Thus, we can select the generalized coordinate vector Equation (3) shows that right arm joint angle 2.Approaching-target phaseIO, as exhibited in After the tail has accumulated enough energy by swinging back and forth, the robot can switch to this phase at an appropriate time and reach for the target ledge; that is, the right hand can let go of the ledge and grasp the ledge to the right as shown in 3.Transition phaseAfter the robot has successfully grasped the ledge in the previous approaching-target phase, it returns to having both grippers gripping the ledge at the same time. Here, we designed a posture transition phase to help the robot return smoothly to its original posture at the beginning of a gait cycle. During this stage, the upper limbs similarly form a four-link configuration with the ledge as they perform in the swing phase, and the robot relies on swinging its tail to correct its overall posture and help the other gripper move forward to its original position. As shown in 4.Hands-on phaseIIO, as shown in Once the robot adjusts to a certain posture in the previous phase, the left gripper releases the ledge and moves to the right back to its original position so that the distance between the two grippers returns to the set distance in the initial swing phase, the posture of the body and the tail is coordinated, and the robot can again begin the excitation and energy storage phase needed for the next locomotion cycle. This can be regarded as a successful locomotion gait cycle. In this phase, we assume that the left gripper releases the ledge as the right gripper has a firm grip on the ledge with no slippage. Thus, the coordinate origin is set at the right wrist joint IIO) (IO) (Reminder: The system state variable em (OII) c and is tem (OI) b. The co5.Two-hand-release phaseIO. While the robot is airborne, there are no geometric constraints for its joints, and there is additional two-dimensional translation along the xy plane. Thus, the state variable that we chose for this phase was In this study, the four movement phases above can be used to express the entire dynamics of the transverse brachiation locomotion gait. However, ricochetal brachiation requires a description of the dynamics when both grippers have released the ledge, and the robot is airborne. We use the two-hand-release phase in Based on the coordinate system, state variable, and input vector defined above, we can derive the system dynamic equation of each phase (Equation (2)), where Phases 1-2-3-4 represent a transverse brachiation locomotion cycle and Phases 1-2-5-4 represent a transverse ricochetal brachiation locomotion cycle. In the next section, we analyze the design parameters that meet the dual-arm robot configuration conditions to enable smooth transitions.Based on the derived dynamic model, this section analyzes the design goals needed to complete an entire locomotion cycle. On the premise of the causal relationship, we explain the means of selecting switch parameters to achieve smooth transitions between phases. We then propose corresponding motion control strategies. We referred to the modified version of a transverse brachiation robot prototype already developed by our lab ,2 for th(1)each movement phase must be executed successfully, and two continuous locomotion gait cycles must be completed; in other words, eight movement phases must be completed continuously;(2)the energy connecting the motion processes of each phase must be maintained and not return to zero at the end of which phase, which would cause uncoordinated motions.To achieve the goal of continuous transverse locomotion, we set two design goals for the robot locomotion gait:The proposed process for the design of transverse brachiation locomotion gaits is presented in the flow chart in In the gait analysis in indexF at 20°. As shown in indexF = 20° represent a good compromise. Following the selection of this parameter value, we introduce the switching conditions and motion planning strategies of the approaching-target phase, the swinging phase, the transition phase, and the hands-on phase according to the steps shown in We assumed that the upper limbs for an isosceles trapezoid with the ledge at the beginning of the transition phase; that is The analysis in the previous section shows that at the beginning of the transition phase, the desired distance between the two grippers, In the approaching-target phase, the transmission of motor torque can be stopped by switching the clutch on the left wrist. Thus, Based on the aforementioned assumption and switching condition in Equation (7), we analyzed the parameters of the swinging phase and the conditions needed for motion planning. We sought to determine the appropriate timing to switch from the swinging phase to the approaching-target phase. As shown in Using dynamic simulation analysis, we derived that the phase switching condition (S→A) satisfying Equation (8) is for the right gripper to release the ledge to enter the approaching-target phase when the arms swing to y component of the system centroid speed at the instance of phase switching should also be greater than 0 (As shown in U). From the figure, we can see that the critical value of potential energy at which the robot can maintain an upward overall centroid speed is approximately −2.455 J. At this point, the lower limb swinging to Combining the above conditions, we can establish an optimization problem as follows:Following the analysis of the first three phases, we substitute the known operating parameters into the dynamic model of the hands-on phase for analysis to complete the gait design. The motions of this phase are shown in In this phase, the right wrist joint can rotate freely (by switching the clutch); therefore, To achieve the posture in Equation (11), performing simulation analysis using the dynamic model of this phase produces the relationship between the final value of the left arm joint angle Swinging phase→Approaching-target phase: arm swing angle becomes Approaching-target phase→Transition phase: vertical position of grasping gripper coincides with ledge position Transition phase→Hands-on phase: tail link swings back until joint angle Hands-on phase→Swing phase: vertical position of returning gripper coincides with the ledge position Following a comparison with The design proposed in The first step in the two-hand-release phase of TLRB is realizing the leap. However, as the left gripper releases the ledge in the instant before the right gripper reaches the ledge, we can assume that the arms begin to resume their original position once the right gripper has grasped the ledge. Based on the joint trajectory planning represented by Equation (11) for the TLB gait, the upper limbs almost form a parallelogram once the left arm resumes its original position. This can be referred to as the locomotion cycle of a TLRB gait.As the execution of the flight stage is short, the various joint angle commands of the robot remain the same as they were at the end of the previous phase .We adopted the same parameter settings as those of the TLB gait for the initial robot posture, excitation frequency, and amplitude in tail joint trajectory planning.Unlike the TLB gait, where the need for a posture adjustment phase causes the grasping distance to be restricted by mechanical flexibility, this gait mainly uses the energy accumulated in the swinging phase to lengthen the grasping distance as much as possible. The analysis results in y coordinates of the left and right gripper joints in the two-hand-release phase.As shown in As shown in Swinging phase→Approaching-target phase: arm swing angle becomes Approaching-target phase→Two-hand-release phase: robot releases the ledge-holding (left) hand when the joint angle of the approaching (right) arm reaches Two-hand-release phase→Hands-on phase: vertical position of approaching hand coincides with ledge position Hands-on phase→End: vertical position of returning hand coincides with the ledge position The phase-switching conditions of the transverse brachiation locomotion gait proposed in this study can be organized as follows:In this section, we apply joint trajectory planning and phase-switching conditions derived from the previous analysis to a self-made transverse brachiation robot. We performed experiments with the two types of locomotion gaits to verify the feasibility of the proposed design and evaluate its locomotion performance.This study adopted a four-link robot consisting of two arms, a body, and a tail to realize anthropomorphic TLB. The shoulder and lower limb joints of the robot are equipped with DC motors with encoders, and we employed the STM32F407 Discovery board to realize the algorithms needed for joint motion control and the overall locomotion gait. Inertial measurement units are installed on the arm and body links, and the motor encoders transmit the various joint angle measurement results wirelessly to a personal computer via a Bluetooth module for further analysis. For a detailed description of the system architecture, please refer to [We first present experimental gait results for a single locomotion cycle and then add experimental results for two locomotion cycles to explain the possible problems and research challenges in the realization of continuous transverse brachiation gaits.SP, AP, TP, and HP. First, trends in experimental and simulation results were relatively similar. The body joint angle (green curve) remains at 90°  during most of the process, and the tail joint (blue curve) swings back and forth until the arm joint angles are large enough for the robot to reach out and grasp the ledge. Before the hands-on phase, the left and right joint angles (red and black curves) are coordinated in sync with almost no phase difference, which demonstrates the feasibility and reliability of the proposed model. Next, we calculated the total energy of the entire gait using the following equation and presented the results in the bottom plot of Based on the switching conditions obtained in RobotT denotes the kinetic energy of the robot, which can be derived from the total translational and rotational kinetic energy of each link; RobotU represents the gravity potential energy of the robot, which can be derived using Equation (9). From SP) are achieved via the swinging of the lower limb. Thus, the energy in SP increases gradually with the number of swings. After entering the approaching-target phase (AP), the system continues the inertia accumulated in the previous phase to perform the transverse motion, so the energy increases at first, but then the overall potential energy swiftly declines due to gravity; thus, the total energy decreases as well. Next, in the posture transition phase (TP), the swinging of the lower limb first increases the overall kinetic energy and potential energy of the system slightly. However, the range in which the upper limbs can adjust is limited; when the posture of the upper limbs is closer to their mechanical limit, the reduction in the kinetic energy of the robot is even more apparent. Although the potential energy of the system continues to increase, the kinetic energy drops at a greater rate. Thus, the plot shows that initially, the total energy of the system increases and then declines rapidly midway. Nevertheless, it does not return to the initial value when the robot is still. The approaching-target phase (HP) mainly relies on the left arm returning to its original position to slightly increase the system energy, so the energy does not change significantly in this phase. The trends in the changes in energy during the locomotion process of the robot show that the designed gait can indeed maintain the energy in the various stages, meaning that after the robot begins to swing, its energy does not suddenly drop to the initial value. Thus, there are no sudden stops that cause incoordination in the gait or affect energy utilization efficiency.In the equation above, dM) under the premise that it is moving to the right, as the final moving distance of the end of the left arm, as shown in Equation (16), where To assess the mobility of the robot, we defined the total moving distance of the robot , after which the left gripper would release the ledge for the leap motion . However, in the experiment, it actually took 2.38 s − 2.2 s = 0.18 s to complete the approaching-target phase, thereby creating a delay of 0.18 s − 0.08 s = 0.1 s. In As can be seen in the figure, simulation and experimental results for the joint trajectories are similar in the swinging phase but differ after the approaching-target phase begins. First, based on the original motion plans and phase-switching condition HP) at 2.4 s, and finally, the top view in HP is only about half or less of the reduction in the HP of the TLB gait. This demonstrates that during the flight phase, the transverse brachiation robot can more efficiently utilize the energy accumulated in the swing phase to achieve a longer moving distance.It is not easy to see the leap of the robot in the images in m is the total weight of the robot; and d denotes the moving distance of a locomotion cycle. Here, we make a simple comparison of the TLRB and TLB experimental results in https://youtu.be/j11oPRQxvqA (accessed on 14 May 2023).The results above show that due to factors such as hardware limitations and environment dynamics, there are many difficulties in realizing the ideal TLRB gait. Even so, our TLRB experiment still achieved a grasping (moving) distance of 102 mm, which is at least 1.5 times that of the distance achieved by the TLB gait (63 mm). Next, we consider factors affecting the energy consumption of the actuators and analyze gait movement performance using the cost of transport (COT)  index, wThis study presents the locomotion design and implementation of an arm-body-tail ledge brachiation robot mimicking the transverse movements of climbing athletes. Under the constraint of two pairs of parallel links, we consider the cause-and-effect relationship between the designed phases to identify phase-switching conditions and desired joint motion. Experiments demonstrate that locomotion without leaping action can be successfully conducted for two consecutive cycles, and the locomotion of ricochetal brachiation represents a significant improvement in terms of grabbing distance and energy efficiency. However, the experiments all terminated during the locomotion process due to deviation in the hand-holding postures; this impeded energy accumulation in the next cycle and greatly increased the risk of falling. Future research could investigate landing posture dynamics using improved mechatronic design and three-dimensional modeling. Active posture compensation methods and advanced robot locomotion control could further improve the safety and robustness of transverse ledge brachiation.


The fundamentals contribution of multi-hazard assessment lies in its ability to guide and identify directions for territorial development, aiming to reduce vulnerability through the implementation of appropriate measures. In the present study, Multi-Criteria Decision Making supported by Geographic Information System was utilized to solve spatial problems related to territorial sprawl. Considering this perspective, an analysis was conducted on the susceptibility of land to the occurrence of geo hazards in the Moldova catchment, situated in the northeastern region of Romania, within a transitional zone between mountains and plateaus. The analysis focused on assessing the likelihood of geo-hazards like floods, landslides, and earthquakes, utilizing the weights obtained through the implementation of the Analytical Hierarchy Process (AHP). Subsequently, the obtained results were utilized to generate a multi-hazard map, which facilitated the identification of areas that are suitable for territorial development. The results were validated in two ways: by sensitivity analysis in which two minimum and maximum scenarios were proposed concerning the result obtained and by validation using the receiver operating characteristic (ROC) curve method. The areas with high susceptibility to geo-hazards triggers are located in the southeastern part of the region, in the proximity of the hydrographic network. Flood risk is the hazard with the highest recurrence. Localities with high suitability for spatial development have a central-western distribution. According to the applied model, sites for each locality included in the study area can be identified. The high and very high suitability classes account for 54% of the total area, while the unsuitable classes represent 15% of the area. However, the vulnerability of the area and the need for the study are generated by 35% of the settlements being located in areas with high susceptibility. NaturThe term “multi-hazard” was first introduced in Agenda 21 for Sustainable Development in International Policy, which states the relevance of “comprehensive multi-hazard research” in human settlement planning and management of exposed areas . The conThere are two distinct approaches in the analysis of natural hazards: independent multi-hazard analysis  and multMost studies have concentrated on the detailed analysis of a single potentially destructive natural phenomenon: floods , landsliMulti-hazard studies are based on the Multi-Criteria Decision Making (MCDM) technique, which combines information from multiple levels to result in a single evaluation index . To condIn Central European countries, Romania is one of the most affected by natural hazards  with a significant economic and social impact . Recent This research was performed in the Moldova River catchment. Its versatility in relief conditions and territorial suitability has led to the concentration of communities in areas exposed to natural hazards. Over time, extreme events have been recorded within the basin . Non-comThe aim of the paper is to estimate the suitable areas for spatial development in relation to the natural geo-hazards occurring in the study area . Associated to this aim, the paper has the following objectives: i) identification of causal factors and their standardization; ii) application of the AHP method for each hazard and obtaining susceptibility maps; iii) obtaining the multi-hazard map and estimation of areas suitable for territorial development; iv) validation of the results using sensitivity analysis and ROC curve method.The novelty of the study results from applying the analysis to a hydrologically undeveloped watershed, representative of the eastern part of the Eastern Carpathians, affected by many natural hazards. The multi-hazard analysis of a medium-sized catchment in an area with low data availability is a novelty in Romania.The results will allow modeling and identifying suitable areas for territorial expansion with reduced risk. The utilization of cartographic materials, statistical data, methodologies, and specialized programs will be essential in obtaining the final results. These outcomes will serve as a prerequisite for elaborating valuable materials for development strategies in the Northeast Region of Romania.22.12 extends over a wide altitudinal range between 180 m  and 1858 m , together with the specific geological conditions of the mountainous and submontane areas developed in the flysch zone and crystalline rocks. Climatic conditions generate a hydrological regime with high values of river runoff :(1):(1)49]:(·I.) Eq. :(2)C.I.=The consistency ratio is calculated to verify the weights obtained and avoid discrepancies within the matrices. According to Saaty (1977) , when thThe relevance of each thematic layer in relation to the other identified layers on the assessment of each hazard was provided by assigning weights. This was done using the relevant literature, observations made during the field phases, and expert judgments to complete the related matrices.In order to obtain the result of the multi-hazard analysis for the Moldova river catchment, three matrices were made in the first phase for each hazard , followed by a comparative analysis of the results obtained to estimate the areas with optimal suitability for territorial sprawl. Based on the result (multi-hazard map), a sensitivity analysis was carried out in which spatial variations in development areas were tracked, considering the related degree of uncertainty.The spatial database was created using ArcGIS Pro 3.0.3 software (ESRI 2022), and all parameters, were standardized and converted from vector to raster at a spatial resolution of 30 × 30 m per pixel.2.4The study can be analyzed from two perspectives. The initial section focuses on the analysis of natural hazards and the identification of areas with high susceptibility. In the second part, the analysis aims at identifying suitable areas for spatial development using multi-hazard mapping and sensitivity analysis.In order to develop a model to assess and identify areas exposed to natural hazards with the potential to occur, a set of conditioning factors must be identified .According to the current literature and the environmental characteristics of the study region, 13 causal factors were identified. The first step is to classify all factors by standardizing them to a uniform scale for comparison. The standardization used in the study is based on integers from 1 to 5 . Therefo2.5The analysis is based on the fact that more than 88 extreme hydrological events have been identified in the Moldova river catchment, affecting communities from 1950 until now. For many of these events, data on the flooded area are available, but not other hydraulic parameters such as runoff velocity and water depth; therefore, it was necessary to develop the flood hazard map by applying the indicator-based AHP.A multi-criteria model based on the following control factors was applied to produce the flood hazard assessment map:Slope (Sl). Slope distribution significantly impacts the evaluation of floods, flash-floods and associated landslide occurrence . T. THydro-Land use (LU). Land use is essential to flood occurrence due to the negative correlation between vegetation density and rainfall :,89:23,89After calculating the ΔS error, the raster file obtained was multiplied by 1.96 to achieve a 95% confidence interval . The resUncertainties can be due to inherent natural variability and statistical uncertainties model, leading to different levels of natural hazard uncertainty. Integrating uncertainty into analyses is necessary for probabilistic risk assessment .3A GIS-based MCDM analysis generated a map of flood hazard spatialization within the Moldova catchment. Five flood hazard classes have been derived using the standard deviation as a classification method of the obtained file . Based oThe moderate hazard class is predominant in distribution within the urban area, with a percentage of 47%. It is distributed from the contact with the mountain area, related to the Moldavia Subcarpathians and the Suceava Plateau.The landslide susceptibility distribution was generated by integrating the weights obtained from the AHP methodology into the GIS environment. The same classification method was used, the standard deviation highlighting the oscillations from the mean value. The representation of five hazard classes allows the analysis of the hazard distribution .Fig. 8LaHence, it is evident that the northeastern part of the area displays a greater susceptibility to landslide hazards, particularly on the hillsides near the rivers within the mountainous region, as well as in the contact area of the Subcarpathians. The highest degree of hazard covers 4.87% of the analyzed area and 3.1% of the locality area . The higIn terms of seismic hazard analysis, upon implementing the methodology and categorizing the results, it becomes apparent that the areas situated in the southern part of the basin are most impacted owing to their proximity to the Vrancea seismic region. . FurtherThe multi-hazard analysis carried out is a novelty in Romania and can be used as guidance on the territorial development directions of the localities in the study area. In addition to the result obtained from the direct application of the AHP methodology and the integration of the three geo-hazards, a calibration of the model was performed through sensitivity analysis which includes the consideration of the uncertainties that may occur in the assignment of the value, in the representation of the result a. Thus, The obtained map was classified using the same number of classes, and the analysis aims to identify the directions of territorial development concerning the three representations.Regarding the distribution of areas suitable for territorial expansion, the northwestern part of the basin predominantly exhibits favorable classes, whereas the southeastern portion, specifically the lower course area, demonstrates low suitability. This is principally caused by floods near the confluence with the Siret River, Subcarpathians that have developed on the molasse deposits that provide instability, and the seismic hazard due to the proximity of the seismic epicenter on the Romanian territory.A comparative analysis of the results shows that within the very high suitability class, there is a difference of 8% of the area analyzed between minimum and maximum suitability . Within The areas with low suitability zones class have a 5% difference between the minimum and maximum. They are controlled by geological structure, slope and the fact that these areas are located close to the river network, therefore flood hazard areas. According to Furthermore, to validate the obtained results, a comprehensive inventory of hydrological events and landslides in the Moldova catchment was conducted. This inventory relied on field observations, satellite images, and relevant literature.The receiver operating characteristic (ROC) curve method validated the multi-hazard map obtained. The ROC curve for the proposed model was performed to validate the model in terms of both flooding and landslides. ROC is a graphical representation of the true-positive and false-negative rates, considering all possible variants of existing flood and landslide data against the model prediction results . The resThrough the application of this validation method, it can be concluded that the GIS-based MCDM application is a suitable model for estimating and assessing the susceptibility to natural hazards in areas where data availability is limited.4The results derived from this study could be an essential contribution to land-use planning by integrating risk categories that generate particular problems for anthropized areas. The sprawl of these spaces in areas where natural hazards occur without adequate spatial planning implies the occurrence of events that affect local communities.Romania's territorial development strategy, Polycentric Romania 2035 is the long-term programmatic document that defines the territorial development vision of the national territory for the time horizon 2035 and sets development objectives, measures, actions, and concrete projects at the territorial level.The Ministry of Environment is the coordinator, and the County Councils are legally required to produce risk maps. Given the situation in recent years, the flood risk maps are among the most sensitive, and there has been an urgent need to produce them following legal obligations. All these measures also came as an obligation of the introduction of European directives (Directive 2007/60/EC).For example, floods are one of the most destructive natural hazards at the European level. Despite early warning systems developed in recent decades, the damage has increased substantially as flood-vulnerable areas have been included in urbanized spaces . The hig2 in the lower basin to 51–120 landslides per 100 km2 in the upper basin [Following historical floods in the Moldova river basin, landslides were reactivated in significant areas. The phenomenon is specific to the transition areas from the Carpathian to the plateau in the eastern part of the Carpathians, being generated by the geological structure favorable to the production of these processes and by the reactivation of some areas due to the increase in rainfall intensity generated by regional climate change . The laner basin . Most ofDifferent neotectonic uplift movements affect eastern Romania's Carpathian, sub-Carpathian, and neighboring areas . These iThis region also includes the Carpathians and Moldavia Subcarpathians and the central and southern sectors of the Moldavian Plateau. Following major earthquakes in 1940 (Mw7.7) and 1977 (Mw7.4), shallow landslides, rock falls, and rock slides have been triggered as co-seismic and post-seismic processes at distances of up to 100–200 km from the epicenter. These past earthquakes have generated significant landslides ,103, sucThe analysis of geo-hazards is an important issue when identifying spatial development directions. Thus, the methodology and methods used to reduce the degree of uncertainty through the two scenarios of minimum and maximum and the determination of the ROC curve validate the proposed model.Within the regional, county, or local spatial development plans, the types of risk are analyzed individually by presenting diagnostic elements and sub-objectives referring to some structural measures concerning the development of protective infrastructure, as well as non-structural measures referring to increasing the awareness of the population about the risks they are exposed to. Risk maps are required for urban and spatial planning studies, which will be used to determine the direction of development of settlements and the positioning of economic objectives. However, realizing individual maps by type of risk may produce inconsistencies when territorial development directions are proposed and require a larger number of maps with different hazard distribution information. Thus, synthesizing in a single map supports decision-makers by applying sustainable planning strategies . StrategThe map of the distribution of the suitability of territorial development can be a tool for institutions involved in planning and urban development .According to the statistical data obtained, 35% of the areas of the localities in this area are situated in areas with a high and very high susceptibility to natural hazards, and 42% are located in non-hazardous areas.The multi-hazard distribution map can be a valuable tool in early spatial planning as it provides a comprehensive view of the distribution of hazards associated with the area. The synthesis of hazards in a single material is a method that facilitates the decision-making process to implement sustainable strategies .Geomorphological conditions, the hydrographic network, land use, and spatial accessibility are all factors that question the suitability for inhabitation within the area. However, climate change, land use change, deforestation, and uncontrolled building have increased the vulnerability of settlements and the necessity to carry out these studies.The limitations of the study are that although the assessment of each parameter in the AHP methodology was carried out by standard agreement in terms of weight scores, a slightly different result can be obtained if specialists on a domain-by-domain analysis analyze them. Therefore, it can be recommended that all these natural hazard mappings be done in parallel by specialists from different fields, which would increase the reliability of the results. Another area for improvement is the need for complete spatial data to validate the results. Most of the localities in the catchment are located along the river network, which exposes them more to hydrological risks and less to landslide and earthquake risks.The requirement for natural hazard studies arises from the need to mitigate impacts on communities. Uncontrolled spatial sprawl, chaotic distribution of buildings, lack of a coherent spatial development policy, lack of a substantiated and validated risk study makes it necessary to study these aspects for efficient risk management.The political factor is the deciding factor. Promoting these results would make it easier for decision-makers to understand the issue's importance. Increasing resilience is vital in these types of risk situations, and thorough preparation at the government level to react accordingly is vital for both the population and institutions.The consequences of climate change negatively impact communities, and regional sustainability and spatial development planning are directly affected by natural hazards. These changes raise complex issues and require approaches to interrelated factors that promote the development of a governance system that enables effective mitigation and planning strategies. There is discussion of decentralization, but steps to achieve it are slow. Decentralization would make governance work and improve resilience to crises. In other words, exactly what is needed to solve problems affecting communities. It is a political philosophy that can provide the basis for vital strategies and actions for local authorities. Governance would improve responsiveness and resilience to risks. After the abolition of collectivization, land use has suffered significant changes because the rigor of the communist regime, driven by appropriate agro-techniques, has been weakened. Against the backdrop of subsistence farming, it is difficult to control the proper use of land, so the emphasis should be on awareness, permissiveness, and not coercion..The present study could serve as a basis for the current analyses on land expansion and the introduction of more specific variables on how to analyze in relation to area-specific geo-hazards. This approach can contribute to implementing an administrative-territorial reform initiated at a local or regional level, always postponed for various reasons .In Romania, the high population density in certain areas leads to an expansion of built-up areas near areas with a high degree of vulnerability, such as near riverbeds. Therefore, measures can be taken to limit land concessions and issue building permits in areas at high risk of natural hazards.Possible strategies to reduce future vulnerability to this risk identify several application directions: increasing public awareness, establishing an early warning system and site analysis for future infrastructure and civil construction projects, including existing ones.However, the study provides a reliable assessment of multiple hazards carried out individually and collectively for the Moldova catchment.5When discussing the territorial development of a specific region, this study has focused on two key aspects to be considered. The first is the spatialization of geo-hazards relevant to the studied area, namely for floods, landslides and earthquakes, based on the analysis of some conditioning/triggering factors. The second approach integrates the maps obtained for each natural hazard analyzed into a multi-hazard map.Through the implementation of this approach, it becomes possible to generate results that can be incorporated into spatial planning documentation, taking into account the geo-hazards that communities may encounter. With the help of this cartographic material, it is possible to identify the suitable directions of territorial development for each settlement in the analyzed area, which is extremely useful in future spatial planning actions.The GIS-based MCDM method implemented in the present study is based on the standardization and analysis of triggers and assigning weights to each factor by applying AHP. Since the criteria and the way of assigning weights can generate uncertainty, sensitivity analysis was applied by performing two scenarios.The study results highlighted that the areas located in the southeastern part of the Moldova catchment are the most susceptible to natural geo-hazards being overlapped over the contact zone and the plateau . The high vulnerability of the settlements is because most of them are distributed close to the hydrographic network, which provides a major risk of flooding, the transition zone of the Moldavia Subcarpathians being considered a dynamic area with frequent landslides. The southeastern end of the basin is the most prone to earthquakes (due to the direction of seismic wave propagation). In this context, 14% of the basin area is distributed in low and very low suitability classes, and 35% is situated within the settlement limits.Areas suitable for land development are predominantly located in higher areas, with low and low natural hazards. Moreover, the application of this methodology enables the identification of areas with minimal exposure to natural hazards. Sensitivity analysis revealed minor differences in the spatial distribution of the two scenarios (minimum and maximum). The area with the most remarkable changes was located in the southwest of the basin and belonging to the Ozana river.The obtained multi-hazard map was validated by correlating the results with the recorded events. The values of 0.95 for floods and 0.76 for landslides obtained from the ROC curves indicate that the proposed model is adequate.Disaster risk management is an essential aspect of building resilient communities. The current study meets this objective by identifying areas that are suitable for territorial development, thereby reducing the impact of natural risks. At national level, this type of methodology meets the needs of the new National Recovery and Resilience Plan. At local level, the utilization of this type of tool, which integrates the geo-hazards specific to a particular area, assists the relevant authorities in identifying areas that are suitable for territorial development.Oana-Elena Chelariu: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.Ionuț Minea: Conceived and designed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.Corneliu Iațu: Conceived and designed the experiments; Analyzed and interpreted the data; Wrote the paper.10.13039/100005186CNCS – 10.13039/501100006595UEFISCDI, project number PN–III–P1-1.1-PD-2019-0577, within PNCDI III.This work was supported by a grant of the Ministry of Research, Innovation and Digitization, Data will be made available on request.No additional information is available for this study.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.