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Figure 7. The ANN model was trained using data points from B1, B3, B4 and BS, and then it was employed to investigate the load prediction for B7. a) Comparison of the experimental forces with the prediction of the ANN model where recorded number for data points represents n expressed in Equation 7. b) Comparison of the second cycle of the force-displacement curve for both the experiment and the ANN model. c) Histogram of errors between experimental load and the ANN model. d) The regression model, the experimental results, and the prediction of the ANN model. A major improvement in the accuracy of the ANN model was found with consideration of more samples from both two and three-year-old age groups.

Figure 7 The ANN model was trained using data points from B1, B3, B4 and BS, and then it was employed to investigate the load prediction for B7. a) Comparison of the experimental forces with the prediction of the ANN model where recorded number for data points represents n expressed in Equation 7. b) Comparison of the second cycle of the force-displacement curve for both the experiment and the ANN model. c) Histogram of errors between experimental load and the ANN model. d) The regression model, the experimental results, and the prediction of the ANN model. A major improvement in the accuracy of the ANN model was found with consideration of more samples from both two and three-year-old age groups.

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Table 1. The sample number, age group, and the length of the third metacarpal bones used in this study. The tota number of recorded experimental data points (maximum value of n in the Equations 6 and 7) was also reported herein.
Table 1. The sample number, age group, and the length of the third metacarpal bones used in this study. The tota number of recorded experimental data points (maximum value of n in the Equations 6 and 7) was also reported herein.
Figure 1. The process of bone preparation for the experiment. The output of the experiment was imported into MATLAB to train neural networks and to develop the cyclic load prediction algorithm. The distal and proximal ends of the MC3 bones were surrounded by metal cups into which slow-curing fiberglass resin was poured. Due to the resin, both ends of the bones became flat parallel surfaces and were perpendicular to the shaft of the bones. Recorded number for data points represents n in Equation 7.
Figure 1. The process of bone preparation for the experiment. The output of the experiment was imported into MATLAB to train neural networks and to develop the cyclic load prediction algorithm. The distal and proximal ends of the MC3 bones were surrounded by metal cups into which slow-curing fiberglass resin was poured. Due to the resin, both ends of the bones became flat parallel surfaces and were perpendicular to the shaft of the bones. Recorded number for data points represents n in Equation 7.
Figure 2. a) The structure of artificial neurons developed for this study to introduce the feed forward neural network. b) The architecture of an artificial neuron being tested. x; is an introduced input to each neuron, Wn; is the weight assigned to the corresponding neuron, Am=2(X;X Wini)+Dm aNd Ym=f(Am), where f is the activation function.
Figure 2. a) The structure of artificial neurons developed for this study to introduce the feed forward neural network. b) The architecture of an artificial neuron being tested. x; is an introduced input to each neuron, Wn; is the weight assigned to the corresponding neuron, Am=2(X;X Wini)+Dm aNd Ym=f(Am), where f is the activation function.
The ANN was first trained using experimental data points from B1 and B3. These bones are representative of the two-year-old group (Table 1). There is a very good agreement between the output and target for both training (R=0.9999) and testing (R=0.9999) (Figure 3). The regression plot (R) depicts the relevance between the target (the desired output) and the ANN output (the actual output). R=0.9999 shows that the output of ANN in load prediction is in a good agreement with the ex-vivo measurements. In general, when R approaches 1, this indicates a precise linear relevance between the targets and the desired outputs. On the contrary, when R approaches zero, only a slight linear relevance between the targets and the outputs exists. Since the values of R are promising, the response of the network is favourable (Figure 3). Hence, the ANN model can be employed to import new inputs. Figure 3. The three scatter plots represent a) the training, b) testing, c) all data points. The ANN was trained with data points from BI and B3. The dashed line in each plot represents the perfect result which is outputs = targets. The solid line represents the best fit linear regression line between the outputs of ANN and targets (the experimental data points). The value of R (coefficient of correlation) is approximately 1, which indicates that there is an exact linear relationship between outputs and targets. As such, the fitted curve in each sub-plot overlaps the dashed line contributing to the invisibility of the dashed lines in these sub-plots. The training data indicates a good fit. The test results also show a high value for R.
The ANN was first trained using experimental data points from B1 and B3. These bones are representative of the two-year-old group (Table 1). There is a very good agreement between the output and target for both training (R=0.9999) and testing (R=0.9999) (Figure 3). The regression plot (R) depicts the relevance between the target (the desired output) and the ANN output (the actual output). R=0.9999 shows that the output of ANN in load prediction is in a good agreement with the ex-vivo measurements. In general, when R approaches 1, this indicates a precise linear relevance between the targets and the desired outputs. On the contrary, when R approaches zero, only a slight linear relevance between the targets and the outputs exists. Since the values of R are promising, the response of the network is favourable (Figure 3). Hence, the ANN model can be employed to import new inputs. Figure 3. The three scatter plots represent a) the training, b) testing, c) all data points. The ANN was trained with data points from BI and B3. The dashed line in each plot represents the perfect result which is outputs = targets. The solid line represents the best fit linear regression line between the outputs of ANN and targets (the experimental data points). The value of R (coefficient of correlation) is approximately 1, which indicates that there is an exact linear relationship between outputs and targets. As such, the fitted curve in each sub-plot overlaps the dashed line contributing to the invisibility of the dashed lines in these sub-plots. The training data indicates a good fit. The test results also show a high value for R.
Figure 4. The ANN was trained with data points from B1 and B3. a) The training curve of the ANN. b) The identification errors for the train and test datasets are presented in the histogram.
Figure 4. The ANN was trained with data points from B1 and B3. a) The training curve of the ANN. b) The identification errors for the train and test datasets are presented in the histogram.
Figure 5. The ANN model was trained using data points from BI and B3, and then it was employed in order to investigate the load prediction for B2. a) Comparison of the experimental force with the prediction of the ANN model where recorded number for data points represents n expressed in Equation 7. b) Comparison of the second cycle of the force-displacement curve for both the experiment and the ANN model. c) Histogram of errors between experimental load and the load predicted by ANN model. d) The regression model, the experimental results, and the prediction of the ANN model.
Figure 5. The ANN model was trained using data points from BI and B3, and then it was employed in order to investigate the load prediction for B2. a) Comparison of the experimental force with the prediction of the ANN model where recorded number for data points represents n expressed in Equation 7. b) Comparison of the second cycle of the force-displacement curve for both the experiment and the ANN model. c) Histogram of errors between experimental load and the load predicted by ANN model. d) The regression model, the experimental results, and the prediction of the ANN model.
Figure 6. The ANN model was trained using data points from B1 and B3, and then it was employed in order to investigate the load prediction for B7. a) Comparison of the experimental forces with the prediction of the ANN model where recorded number for data points represents n expressed in Equation 7. b) Comparison of the second cycle of the force-displacement curve for both the experiment and the ANN model. c) Histogram of errors between experimental load and the ANN model. d) The regression model, the experimental results, and the prediction of the ANN model.
Figure 6. The ANN model was trained using data points from B1 and B3, and then it was employed in order to investigate the load prediction for B7. a) Comparison of the experimental forces with the prediction of the ANN model where recorded number for data points represents n expressed in Equation 7. b) Comparison of the second cycle of the force-displacement curve for both the experiment and the ANN model. c) Histogram of errors between experimental load and the ANN model. d) The regression model, the experimental results, and the prediction of the ANN model.
Figure 8. The ANN model was trained using data points from two and three-year-olds (B1, B2, B3, B4, BS and Bo) and then it was employed to predict the responses of a) B7 which belongs to a three-year-old horse and b) B9 from a two-month-old foal. Recorded number for data points represents n in Equation 7. maturation (a comparison between foals and the rest of the samples) (Mouloodi et al., 2019c). A variety of geometrical parameters within the midshaft of MC3 bones was measured anc compared in that study. Immaturity, horse training history, lack of exercise, and bone shape are all closely tied to bone function (and its response under load that we recorded in this study). These factors, along with a decrease in quasi-static fracture toughness with age (Kulin et al.. 2011), contribute to the lower magnitudes and cycles of loads that bones (at the whole level) from foals can tolerate prior to failure. Increasing the sample size and range of ages of foals ir the experiments to acquire more data is recommended, so that the ANN is trained using more data points during loading/unloading of foal samples. The majority of growth in length of the MC3 in horses occurs in the first 6 weeks of life while the majority of the overall growth of body height and weight continues to around 15 to 18 months of age and complete maturity in body size is reached between the ages of 5 to 8 years. Hence it might be expected that immaturity would have a large and complex effect on the responses of the MC3 to loading, especially in horses less than 18 months of age.
Figure 8. The ANN model was trained using data points from two and three-year-olds (B1, B2, B3, B4, BS and Bo) and then it was employed to predict the responses of a) B7 which belongs to a three-year-old horse and b) B9 from a two-month-old foal. Recorded number for data points represents n in Equation 7. maturation (a comparison between foals and the rest of the samples) (Mouloodi et al., 2019c). A variety of geometrical parameters within the midshaft of MC3 bones was measured anc compared in that study. Immaturity, horse training history, lack of exercise, and bone shape are all closely tied to bone function (and its response under load that we recorded in this study). These factors, along with a decrease in quasi-static fracture toughness with age (Kulin et al.. 2011), contribute to the lower magnitudes and cycles of loads that bones (at the whole level) from foals can tolerate prior to failure. Increasing the sample size and range of ages of foals ir the experiments to acquire more data is recommended, so that the ANN is trained using more data points during loading/unloading of foal samples. The majority of growth in length of the MC3 in horses occurs in the first 6 weeks of life while the majority of the overall growth of body height and weight continues to around 15 to 18 months of age and complete maturity in body size is reached between the ages of 5 to 8 years. Hence it might be expected that immaturity would have a large and complex effect on the responses of the MC3 to loading, especially in horses less than 18 months of age.
Figure 9 a) Confusion Matrices for age Prediction: the ANN trained using all input features from B1, B3, B5, BO, B7, and B9 then the ANN model was employed to classify data points including time, displacement, and strains from B2, B4, and B8. The bottom right corner cells contain the overall accuracy of the results. b) Receiver operating characteristic (ROC) curve.
Figure 9 a) Confusion Matrices for age Prediction: the ANN trained using all input features from B1, B3, B5, BO, B7, and B9 then the ANN model was employed to classify data points including time, displacement, and strains from B2, B4, and B8. The bottom right corner cells contain the overall accuracy of the results. b) Receiver operating characteristic (ROC) curve.
Table 2. The percentage of relative importance for the individual input variables using the connection weigh approach. The ANN input variables were defined in the Equations 4 and 5. fhe basic advantage of artificial neural networks lies in the fact that they are able to utomatically map a relationship from the supplied input and output parameters. Hence, omplicated relationships between various parameters can be found out by an ANN. ANN is a nodel-free estimator, as such, parameters that are difficult to be measured experimentally can be Sti ini mated via the ANN model. ANNs are particularly useful in cases where solving a forward e element model is time consuming (Hambli et al., 2006; Mouloodi et al., 2019b; Unger and <Gnke, 2008), particularly when the model is comprised of a high number of nodes and elements Mouloodi et al., 2019a), or when the loading condition on a model is not straightforward. In uc. ro h cases, ANNs bring enormous benefits in reducing the time required for predicting the load, ause the generation of the training dataset which involves solving the forward finite element blem needs to be performed just once. Afterwards, the trained ANN can be employed to edict the load without any need to solve the forward problem again. Solving inverse problems ften involves a solution of several forward problems. Therefore, it is generally more omputationally expensive to solve an inverse problem than to solve a forward one. The main vantage of artificial neural networks is that they are more efficient than the methods (such as lirect optimization) where the results of previously solved forward problems cannot be used Su ng, 1998). These are the merits of using ANNs in predicting loading of complex engineering tructures with exotic mechanical properties.
Table 2. The percentage of relative importance for the individual input variables using the connection weigh approach. The ANN input variables were defined in the Equations 4 and 5. fhe basic advantage of artificial neural networks lies in the fact that they are able to utomatically map a relationship from the supplied input and output parameters. Hence, omplicated relationships between various parameters can be found out by an ANN. ANN is a nodel-free estimator, as such, parameters that are difficult to be measured experimentally can be Sti ini mated via the ANN model. ANNs are particularly useful in cases where solving a forward e element model is time consuming (Hambli et al., 2006; Mouloodi et al., 2019b; Unger and <Gnke, 2008), particularly when the model is comprised of a high number of nodes and elements Mouloodi et al., 2019a), or when the loading condition on a model is not straightforward. In uc. ro h cases, ANNs bring enormous benefits in reducing the time required for predicting the load, ause the generation of the training dataset which involves solving the forward finite element blem needs to be performed just once. Afterwards, the trained ANN can be employed to edict the load without any need to solve the forward problem again. Solving inverse problems ften involves a solution of several forward problems. Therefore, it is generally more omputationally expensive to solve an inverse problem than to solve a forward one. The main vantage of artificial neural networks is that they are more efficient than the methods (such as lirect optimization) where the results of previously solved forward problems cannot be used Su ng, 1998). These are the merits of using ANNs in predicting loading of complex engineering tructures with exotic mechanical properties.
Related topics:
Materials EngineeringMechanical EngineeringComputer ScienceBiomedical EngineeringStructural EngineeringPattern recognition (Engineering)MedicineStrain GaugeArtifcial neural network (ANN)Load prediction
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