In the process of solving the Traveling Salesman Problem (TSP), both Ant Colony Optimization and simulated annealing exhibit different limitations depending on the dataset. This article aims to address these limitations by improving and combining these two algorithms using the clustering method. The problems tackled include Ant Colony Optimization’s susceptibility to stagnation, slow convergence, excessive computations, and local optima, as well as simulated annealing’s slow convergence and limited local search capability. By conducting tests on various TSPLIB datasets, the algorithm proposed in this article demonstrates improved convergence speed and solution quality compared to traditional algorithms. Furthermore, it exhibits certain advantages over other existing improved algorithms. Finally, this article applies this algorithm to logistics transportation, yielding excellent results. Since the Traveling Salesman Problem (TSP) is widely used in artificial intelligence, logistics transportation, circuit board design, and other fields , it has The bionic algorithm is a heuristic algorithm that simulates natural phenomena or processes. Many research scholars have used bionic algorithms, such as the genetic algorithm, particle swarm optimization and so on to approximate the solution of TSP instances . Ant ColIn nature, the foraging habits of ants served as the basis principle for the Ant Colony Optimization (ACO) . The ItaPhysical annealing served as the basis for the simulated annealing (SA)  concept.Firstly, in this article, we introduce two strategies to address slow convergence and susceptibility to local optima of the ACO, which effectively accelerate its convergence and enhance the accuracy to a considerable extent. Secondly, we propose two strategies to overcome the accuracy limitations of the simulated annealing, which traditionally lacked optimization ability. Subsequently, we analyze the shortcomings of the two improved algorithms and synergistically combine their advantages to devise a new hybrid algorithm. We thoroughly test this algorithm using 22 different TSP instances. Additionally, we conduct a comprehensive comparison with other traditional algorithms and state-of-the-art techniques from the literature. Finally, we apply this novel algorithm to the domain of logistics and transportation, showcasing its potential and practicality in real-world scenarios.V represents the set of vertices and E represents the set of edges. The distance between vertices In the DFJ formulation, the TSP can be represented by an assignment-complete graph Subject to the following constraints. Each city must be visited exactly once:Each city must be left exactly once:Subtour elimination constraints to prevent subtours:S represents a subset of cities, and |S| denotes the cardinality of set S. The subtour elimination constraints ensure that the solution does not contain any subtours .In these constraints, The K-Medoids algorithm  is an exThe ACO has been under development for over 20 years, and numerous researchers have been continuously improving and refining ACOs. Some notable improved ACO include the Maximum-Minimum Ant Colony Optimization, Elite Ant Colony Optimization, Sorting-Based Ant Colony Optimization, and others. Among them, the Elite Ant Colony Optimization (EACO)  introduc(1) Transition probabilityThe ant colony uses a probabilistic selection method to decide to transfer from the current city (2) Update of pheromonesThe pheromones on each road are updated once all the ants have traveled through all the cities. The three steps of the EACO’s pheromone update are pheromone volatilization, ant release of pheromones along their separate paths, and pheromone reward for elite ants.Pheromone volatilization equation:The number of pheromones remains on the path at the current iteration for ant Q is the pheromone augmentation factor, Update formula for additional pheromones awarded to elite ants:The pheromones for all ants are updated using the following equation:The EACO exhibits similar robustness to the ACO and can be easily integrated with other algorithms. While the EACO improves upon the number of iterations required by the ACO, it still inherits the limitations of slow convergence and susceptibility to local optima. Therefore, this article proposes two improvement strategies for the slow convergence of the EACO.The optimal path between a colony’s exploration of a nest and a food source relies heavily on the information transmitted through pheromones. If the ant colony already knows the starting city This strategy changes the initial pheromone concentration of the EACO and focuses on the distance between the current city and the ending city, which provides directional guidance for the initial ant colony and avoids blind searches of the ant colony, thus improving the speed of solution and accuracy of the solution.The method for ants to select the next city from the current city is primarily based on the roulette wheel betting method. This method ensures a well-balanced algorithm, where ants with higher fitness values are more likely to be selected, while ants with lower fitness values still have a chance to be chosen. This approach allows the ant colony to explore and experiment within the solution space, allowing all unvisited cities to be selected. However, in the actual solution process, it is important to avoid consecutively visiting two cities that are particularly far apart. If the ant colony selects a distant city as the next destination from its current location, it would result in wasted iterations, leading to increased solution time for the algorithm. More critically, it could significantly affect the overall direction of the algorithm’s solution and potentially trap it in a local optimal solution. Therefore, this article restricts the city selection process to the roulette wheel betting method. Ants are not allowed to choose a more distant city as the next visited destination. This constraint is expressed mathematically as follows:R is the maximum distance from other cities that can be visited, SD is the error rate and calculated by Our algorithm called the Adaptive Elite Ant Colony Optimization (AEACO) is an efficient optimization-seeking algorithm for small-scale TSP instances, which will automatically adjust the number of iterations and the number of ants for different small-scale instances. Meanwhile, a comparison test with the ACO and the AEACO is run to evaluate the performance of the AEACO. The AEACO, ACO, and AEACO are put to the test 30 times, with each algorithm’s optimal solution, average error rate, and solution time is provided. Parameter setting of ACO: Parameter setting of EACO: Parameter setting of AEACO: From According to The SA commences from an initial solution, denoted as The SA receives worse solutions with a certain probability. Therefore, the climbing ability is strong and it is not easy to fall into the local optimum, but the SA is slow to converge and has poor local search ability.The SA is a powerful global optimization algorithm known for its excellent hill-climbing ability. However, the SA is heavily dependent on the initial temperature and a single optimization search method. As a result, the algorithm can fall into premature convergence and become trapped in local optimal solutions. Therefore, this article proposes two strategies to improve the deficiencies of the SA.The traditional simulated annealing, which primarily employs perturbation operations to perturb the solution sequence, uses a random exchange of the positions of a specific pair of cities as its perturbation mechanism in the TSP instances, which is the primary cause of the algorithm’s slow convergence. The perturbation mechanism, however, plays a critical role in the algorithm’s superiority. As the perturbation approach for the SA process cannot be overly complicated, we will employ three conventional perturbation operations to change the old solution sequence.(1) Swap method: randomly swap two positions in the solution sequence.(2) Random insert method: randomly swap two adjacent positions in the solution sequence.(3) 2-opt method: two positions in the solution sequence are randomly selected and arranged in reverse order from these two positions.The traditional SA typically employ a sufficiently large initial temperature to enhance the search performance. However, there is no universally recommended method for determining the initial temperature. Selecting an inappropriate initial temperature not only results in wasted time but also hampers the effectiveness of the solution search. According to the method described in literature , we emplK is the number of temperature changes, The MSA-1 is randomly selected to perturb the solution sequence by the swap method, random insertion method, and 2-opt method. The MSA-1 means that the MSA uses only strategy 1 and not strategy 2. In this article, three instances of pr76, tsp225, and pcb1173 are used to test the MSA-1 for four different proportions of perturbations of the swap method, random insertion method, and 2-opt method. The experimental results are shown in As shown in By utilizing the swap method, random insertion method, and 2-opt method to enhance perturbation in the SA. The perturbation capabilities of the SA can be improved, which can leading to more accurate solutions. Using strategy 2 to improve the initialization temperature of the SA has the advantage of avoiding too high or too low a temperature that would cause the algorithm to fall into a local optimal solution. In this study, comparison tests between the MSA-1 and the conventional the SA are carried out using the same initial solution sequence, initial temperature, termination temperature, cooling factor, and the maximum number of iterations. The MSA does not use the same initial temperature. A total of 30 tests are carried out, and the experimental results are displayed in The parameters were set as follows: initial temperature: 300, termination temperature 1, cooling factor: 0.998, and the maximum number of iterations: 100.Experiments show that the solution accuracy of the MSA-1 is much higher than that of the SA in the same environment. The main reason is that Strategy 1 improves the exploration pattern of the SA. Comparing the MSA-1 and the MSA, MSA has strategy 2 which provides an effective initial temperature, leading to a high convergence accuracy of the MSA. But MSA of the average time is longer than the SA, resulting in the inability of the SA to improve the solution accuracy and reduce the solution time, mainly because the MSA is not sufficient in local search capability.After improving Ant Colony Optimization and simulated annealing, the AEACO helps the initial ant colony form a good search path and rewards the elite ant colony that finds the optimal path with extra pheromones. However, this algorithm cannot be used for the larger TSP instances, mainly because the AEACO cannot get rid of the inherent defects of the ACO. While the enhanced simulated annealing increases the algorithm’s perturbation of the solution sequence and improves its climbing ability and solution accuracy, it also leads to an increase in solution time. These two algorithms can work together as a complement. From an overall perspective, these two algorithms can complement each other, with the AEACO responsible for rapid search of small-scale TSP instances and the MSA responsible for the overall TSP instances to jump out the local optimal solution problem. Based on the above analysis, this article will use the clustering algorithm to combine the advantages of the AEACO and the MSA with each other.The algorithm in this article will be carried out in three processes.Initialization process: Formation of small cluster classes and cluster sequences, intra-cluster optimization.First annealing process: Optimizing the sequence of clusters and intra-cluster optimization.Second annealing process: Global optimization.TSP instances can be fundamentally viewed as sorting problems, allowing large-scale TSP instances to be decomposed into multiple smaller ones. Solving the TSP involves determining the sequence in which the salesman selects the next city from the current city, typically focusing on cities around the current location. This approach is preferred over selecting cities across significant distances to maintain precision. To address this, as shown in Steps for forming small cluster classes:Step 1: Randomly select Step 2: The remaining cities of the data are divided into cluster classes according to the principle of closest to the Step 3: Update: for each cluster formed by the assigned data points, select a new Step 4: Evaluate whether each cluster exceeds its maximum member capacity and consider reclassifying any surplus members from the exceeding clusters to other appropriate clusters.Step 5: Repeat the process of 2–4 until all Step 6: Forming cluster sequence: using the greedy algorithm and cluster centroids to sort the clusters.The AEACO is an efficient algorithm for solving small-scale TSP instances with known starting city and ending city. Therefore, in this article’s algorithm, the AEACO is used to find the best solution found for the TSP instances that are split into small-scale ones. As shown in Steps for finding the best solution founds and solution sequences within the cluster class:Q, the maximal number of iterations Step 1: Parameter initialization: the number of Step 2: Initialization of pheromones: initialize the pheromone concentrations on each path according to Step 3: Construct the solution space:Select the set of of AEACO .Each ant in the population selects the next city from Repeat the process until all ants have visited all cities, ensuring that each city is visited exactly once.Calculate the path length each ant and identify the ant with the best path (elite ant).Step 4: Pheromone update: leave pheromones on each ant’s passing edge and reward elite ants with a certain amount of extra pheromones on their passing edge.Step 5: Termination condition: if The split into small-scale clusters needs to be recombined into a solution to the large-scale TSP instances, however, in the process of combination, a suitable sequence is needed for sorting. Therefore, the algorithm in this article uses the MSA to find the optimal ordering of this cluster. To obtain a better solution, the received sequence of clusters is first perturbed to produce a new sequence of clusters. Next, the optimal sequence of clusters is internally searched for each cluster in the new sequence of clusters, and the optimal solution and sequence of clusters are obtained by using the table of the nearest cities and the optimal solution of clusters obtained from the internal search of clusters. Lastly, the decision of whether to accept the new cluster sequence is made using the Metropolis criterion, as shown in As illustrated in the Pheromone update of SE strategy:Steps to optimize the sequence of clusters:Step 1: Parameter initialization: temperature initialization Step 2: Initialization of pheromones: set the same pheromone on each path.Step 3: The initialization process of the cluster sequence: perform the internal cluster search for each cluster, and build up the optimal solution table of each cluster and the internal sequence table of each cluster according to the sequence of clusters.Step 4: Perturbation of cluster sequence: perturbation of cluster sequence using swap method, random insertion method and 2-opt method with a probability of Step 5: Calculate the results after the perturbation:Using SE strategy to find the starting city and the ending city of the perturbed part of the clusters.Using an intra-cluster optimization search for the clusters in the perturbed part.Update the optimal solution table and the internal sequence table of the clusters.Step 6: The Metropolis criterion: use the Metropolis criterion to determine whether to receive a new cluster sequence.Step 7: Determine if the maximum number of iterations has been reached: if so, exit the current loop, otherwise return to Step 3.Step 8: Pheromone update: leave pheromones on each ant’s passing edge and reward elite ants with a certain amount of extra pheromones on their passing edge.Step 9: Cooling: Step 10: Stop condition: determine whether the termination temperature Step 11: Formation of a quality solution: connect all clusters.Since the clustering algorithm splits the TSP instances into several small TSP instances, mainly based on the nearest principle, resulting in the solution of this algorithm is not necessarily the optimal solution, due to the strong climbing ability of the MSA can jump out of the local optimal solution, so the global search for the sequence after experiencing the clustered sequence seeking is performed to increase the quality of the solution of the algorithm in this article.Steps for global optimization search:Step 1: Parameter initialization: initial temperature Step 2: Solution sequence perturbation: the solution sequence is perturbed using the swap method, random insertion method, and 2-opt method with a probability of Step 3: The Metropolis criterion: the Metropolis criterion is used to determine whether to receive new sequences and new solutions.Step 4: Determine if the maximum number of iterations has been reached: if so, exit the current loop, otherwise return to Step 2.Step 5: Cooling: Step 6: Stop condition: determine whether the termination temperature Step 7: Output the best solution found: output the best solution found and solution sequence.As shown in The process of initializationStep 1: The Step 2: Using the greedy algorithm and cluster centroids, create a cluster sequence.Step 3: The starting and ending cities of each cluster are selected using the SE strategy. The AEACO is then employed to find the best solution found and sort each cluster based on the cluster class order. Finally, the optimal solution table and the internal sequential table are constructed.First annealing processStep 4: Initial temperature, termination temperature, number of iterations, and cooling factor of intra-cluster optimization are initialized for the operation.Step 5: Perturb the cluster sequence and perform intra-cluster optimization search for the cities in the perturbed part of the cluster to calculate the solution value of the perturbed part.Step 6: If the new solution sequence is accepted, determine using the Metropolis acceptance criterion: whether to update the optimal solution table for each cluster and the internal sequence table for each cluster; if not, do not update these two tables.Step 7: Judge whether the number of iterations is reached, if not, return to Step 5, otherwise, execute the next step.Step 8: Judge whether the termination temperature is reached, if not, return to Step 5, otherwise find out the solution sequence and solution based on the optimal solution table of each cluster and the internal sequence table of each cluster, and execute the next step.Second annealing processStep 9: Initial temperature, termination temperature, number of iterations, and cooling factor of global optimization are initialized for the operation.Step 10: Perturb the solution sequence and calculate the new solution.Step 11: Use the Metropolis acceptance criterion to judge whether the new solution sequence is received, if so, update the solution sequence; otherwise, do not update the solution sequence.Step 12: Judge whether the number of iterations is reached, if not, return to Step 10, otherwise, execute the next step.Step 13: Judge whether the termination temperature is reached, if not, return to Step 10, otherwise, output the solution sequence and the best solution found.To test the effectiveness of the ACO-DSA, experiments will be conducted using TSP instance of different sizes from the TSPLIB database, which are arranged as follows:(1) The ACO-DSA is used to find the optimal solution for different TSP instance sizes.(2) The effect of varying clusters of clusters on the first annealing at the same TSP scale and temperature control.(3) The ACO-DSA is compared with other algorithms.This article experiments in the following environment: Python 3.8, Win11 operating system, Intel(R) Core(TM) i7-8550U processor, 8 GB RAM.SD is the error rate and calculated by To verify the operational effectiveness of the ACO-DSA, 30 tests are run on TSP instances of different sizes. In particular, According to experiments, when using the ACO-DSA to solve instances of various sizes, the solution accuracy increases at the end of each process and converges to a specific range of accuracy. Decomposing the instance into numerous small clusters and effectively ranking each cluster is the primary priority of the first annealing process of the ACO-DSA. The effect of the number of clusters on the time and accuracy of the ACO-DSA is investigated by varying the number of clusters and the number of iterations while maintaining the same termination temperature and cooling factor. As depicted in The formula for calculating the number of cities in the cluster is shown below:Parameter settings for the pr299 instances: termination temperature: 10, cooling factor: 0.998, The results indicate that increasing the number of cities in the cluster leads to longer optimization times. However, it also achieves better optimization results for the same case. Similarly, when maintaining the same number of cities in the cluster, a higher number of iterations results in superior optimization outcomes, albeit with a significant increase in processing time. Specifically, when using 20 cities in the cluster and 25 iterations, the solution accuracy reaches its peak. Nevertheless, it is not recommended to choose a configuration with a large number of cities in the cluster and a high number of iterations due to the considerable time consumption.The path planning for this company’s problem is carried out by the ACO, EACO, AEACO, SA, MSA, and this article’s algorithm based on the customer points indicated above. The approximate iterative trajectories of the SA, MSA, and the algorithm in this article are shown for better comparison. The ACO-DSA can achieve good results in solving TSP instances. All of them can converge to good accuracy and have some robustness when facing small to medium TSP instance sizes. The ACO-DSA can give a good result when faced with large scales, but the time consumed can be exceptionally long. In addition, both the algorithm in this article and the traditional algorithm are applied to logistics, and the algorithm in this article performs optimally.As shown in 10.7717/peerj-cs.1609/supp-1Supplemental Information 1Click here for additional data file.10.7717/peerj-cs.1609/supp-2Supplemental Information 2Click here for additional data file.


The features of measurement and process noise are directly related to the optimal performance of the cubature Kalman filter. The maneuvering target model’s high level of uncertainty and non-Gaussian mean noise are typical issues that the radar tracking system must deal with, making it impossible to obtain the appropriate estimation. How to strike a compromise between high robustness and estimation accuracy while designing filters has always been challenging. The H-infinity filter is a widely used robust algorithm. Based on the H-infinity cubature Kalman filter (HCKF), a novel adaptive robust cubature Kalman filter (ARCKF) is suggested in this paper. There are two adaptable components in the algorithm. First, an adaptive fading factor addresses the model uncertainty issue brought on by the target’s maneuvering turn. Second, an improved Sage–Husa estimation based on the Mahalanobis distance (MD) is suggested to estimate the measurement noise covariance matrix adaptively. The new approach significantly increases the robustness and estimation precision of the HCKF. According to the simulation results, the suggested algorithm is more effective than the conventional HCKF at handling system model errors and abnormal observations. Target tracking is estimating motion parameters such as the tracked target’s position and velocity in real time through measurement data . It is aThe Kalman filter, an ideal recursive estimator created for linear Gaussian systems, is the approach for target tracking that is most frequently used . HoweverAn H-infinity filter not based on the assumption of signal spectral characteristics is proposed in  to increAcademics have presented some adaptive techniques to further enhance the filtering algorithm’s estimation performance. Zhou proposed a strong tracking filter (STF) that can maintain the residual sequence orthogonal to solve the system model uncertainty problem . The STFA low-cost strong tracking fading factor is proposed. This method avoids the calculation of the Jacobian matrix and additional sampling operations, significantly reducing the algorithm’s time complexity. At the same time, it also solves the problem of STF failure caused by the large difference in the order of magnitude of each dimension of the measurement system. An MD-based method is proposed to correct the noise covariance of the Sage–Husa estimate. Sage–Husa estimation decreases measuring system error by estimating measurement noise in real time, but this method can easily lead to non-positive definite matrices and filter divergence. The MD approach is used in this study to construct the expansion factor, which is used to correct the measurement noise updated by the Sage–Husa estimate, limit the interference of outliers on the filter results, and improve the algorithm’s robustness.For the composite problems of model mismatch and measurement noise anomaly that may occur in maneuvering target tracking, a new robust adaptive cubature Kalman filter is proposed. The new method, which is based on the HCKF algorithm, introduces the two new, enhanced methods mentioned above, and suppresses the influence of system mutation and non-Gaussian noise. The simulation results show that the proposed method achieves a similar impact as the interacting-multiple model CKF (IMMCKF) algorithm in the face of a sudden change in maneuvering target motion. It also exhibits improved robustness and tracking accuracy in the presence of anomalous measurement noise compared with the CKF, HCKF, and Sage–Husa CKF.The research presented in this paper develops an adaptive fading factor and noise covariance estimation method with a robust strategy based on the traditional HCKF to solve the issues mentioned earlier. A low-cost STF calculation method is adopted to solve the problem of insufficient tracking accuracy caused by model errors. The MD-improved Sage–Husa estimation method is used to estimate abnormal or non-Gaussian measurement noise, further improving the robustness and tracking accuracy of the HCKF. The major contributions of this paper can be summarized as follows:The rest of this article is organized as follows. k; k; Consider the following nonlinear discrete system:According to the classic CKF, the system must be accurately modeled, and the process and measurement noise must be Gaussian white noise with well-known statistical properties. The process state equation will unavoidably vary in the radar monitoring system due to the maneuvering target’s easily modifiable trajectory. The measurement noise is typically non-standard Gaussian noise due to external environment disturbance, and its statistical features cannot be recognized in real time. The traditional filter algorithm will not be able to estimate the state accurately in this situation, and divergence issues may even arise.The high-speed maneuvering target has uncertain reentry motion, which is the main reason for the significant decrease in tracking accuracy. An improved algorithm is needed to solve the model error caused by maneuvering motion.The statistical characteristics of non-Gaussian noise cannot be accurately estimated in real time, and it is necessary to improve the system’s resistance to unknown noise as much as possible.Due to parameter settings, the proposed improvement approaches would interact with one another during implementation, necessitating specific designs to avoid system interference.The problems solved in this paper are described as follows:The H-infinity filter is based on game theory, which aims to minimize the estimation error for all disturbances with bounded energy. It is a particular form of Kalman filter . For theminimize :(3)J∞=∑kThe purpose of the H-infinity filter is to estimate y sought . In the The cubature Kalman filter is a nonlinear filter based on the third-order spherical-radial cubature rule proposed by Arasaratnam . The CKF(1)n cubature points The system’s initial predictive value and covariance matrix are set to Prediction Update:n-dimensional unit matrix.(2)The prior prediction state value The obtained cubature points (3)The cubature points are calculated again according to the prior prediction Measurement Update:(4)The autocorrelation covariance matrix (5)Calculate the Kalman gain (6)Finally, the update state The threshold The HCKF requires that all parameters and noise statistics of the system model must be known, which is almost impossible in actual maneuvering target tracking. The trajectory of a maneuvering target usually cannot be represented by a single kinematic model, and the measurement system’s noise is usually heavy tailed. The above problems will lead to a decrease in the estimation accuracy of the filter.In order to compensate for the modeling error and improve the ability of the filter to deal with abnormal measurements, we introduce the STF and the Sage–Husa noise estimator method based on k, k, and k. Equations (18) and (19) are sufficient conditions for STF. These two conditions are called the orthogonality principle. The filtering performance index under the minimum variance estimation criterion is given by Equation (18), which states that the output of the filter must meet the minimal mean square error; Equation (19) shows that the residual sequence is orthogonal. That is, the residual sequences at different times are not related. When the filter has a model mismatch problem, the estimated value of the system state deviates from the actual state of the system, which is reflected in the residual sequence. By adjusting the Kalman gain in real time to meet Equation (19), it can ensure that the residual sequence always has Gaussian white noise characteristics and improve the tracking ability of the system; when the system model is accurate, Equation (19) is satisfied, and the filter is equivalent to the original filter.The strong tracking filter  is an alEquation (19) is the core of the orthogonality principle. Equation (18) represents the design standard the original filter must meet. When the original filter is combined with the criteria of Equation (19), it exhibits the features of the STF. The STF modifies the prediction covariance matrix to update the Kalman gain using the adaptive fading factorn method :(20)λk=mApplying statistical linearization to the nonlinear observation equation , we can According to the theorem in , the sufUsing the definition of the cross-correlation covariance matrix Equation (26) is rewritten as:It is known that the autocorrelation covariance matrix has the formThe fading factor Redefining Therefore, rather than using Equations (22) and (23), we can determine the fading factor k and its estimated value. The recursive formula of the measurement noise is expressed as  and matrix inversion [see (15) and (17)]. When working with high-precision measurement systems, numerically ill-conditioned is another possibility that could lead to a non-positive definite covariance matrix. The most widely utilized methods to lessen the negative consequences that could cause unstable or even divergent behavior include swapping out the CKF algorithm for SCKF and substituting Cholesky decomposition with SVD decomposition. This paper does not examine this section of the content because it is outside the purview of the work.In summary, we give the adaptive robust correction strategy of the HCKF, and the specific process steps of the algorithm are shown in In order to verify the robustness and accuracy of the ARCKF algorithm proposed in this paper, three possible situations in maneuvering target tracking are simulated and compared with the estimation results of the CKF , HCKF 2, and SagIn the simulation experiment, the radar position is set as the origin of the rectangular coordinate system, and the measurement information of the radar is distance and azimuth; then, the corresponding measurement equation isThe state vector of the system is N is the number of Monte Carlo simulations, j is the jth Monte Carlo simulation, and k is the simulation time. The values The relevant parameters of the simulation experiment are given in k, respectively. If For filters, consistency is equally as crucial as accuracy because it can help us gauge the algorithm’s robustness. The average normalized estimation error square (ANEES), the consistency analysis index, can be calculated as follows :(45) ANEA single kinematic model usually cannot express the motion characteristics of maneuvering targets, which may lead to the loss of targets in the target tracking system when maneuvering orbit changes occur. The interacting-multiple model is a widely used and effective method of dealing with model mismatch issues. As a result, we incorporated IMMCKF as one of the comparison algorithms in this experiment. In this case, the maneuvering target maintains an alternating motion state in 0~250 s, and the periods of uniform motion are 0~70 s, 121~145 s, 161~200 s, and 226~250 s; the periods of maneuver turning are 71~120 s, 146~160 s, and 201~225 s. Among these, the uniform motion section satisfies Equation (43), the maneuvering turning section’s motion equation satisfies Equation (46), and the maneuvering turning rate The RMSE of the position estimate and velocity estimation for various filtering algorithms in Case 5.1 is shown in In general, the measurement system is susceptible to abnormal noise pollution. The noise distribution cannot meet the Gaussian distribution and usually presents a heavy-tailed distribution. Contaminated Gaussian distribution noise can be expressed as :(47)wk~1t represents the simulation time.When the measurement system tracks the target, sometimes the signal is unstable, which will cause the noise covariance error to change. In this case, we mainly discuss when the noise covariance matrix suddenly increases significantly. The measurement noise is assumed to satisfy the Gaussian distribution, but it will sometimes change:An adaptive robust cubature Kalman filter is proposed in this study to address the problems of system model uncertainty and abnormal measurement noise in maneuvering target tracking. Based on the traditional HCKF, the algorithm introduces a simplified adaptive fading factor to solve the problem of system model uncertainty. Sage–Husa estimation is used to update


Three-axis atomic magnetometers have great advantages for interpreting information conveyed by magnetic fields. Here, we demonstrate a compact construction of a three-axis vector atomic magnetometer. The magnetometer is operated with a single laser beam and with a specially designed triangular  Atomic magnetometers (AM) have seen rapid development and have shown great potential in widespread applications ranging from fundamental physics  and biomVarious configurations of AMs have been proposed and realized to meet specific requirements in practical applications. Among them, AMs operated in the condition of the spin-exchange relaxation-free (SERF) regime enable the highest sensitivity , comparaVector property is one of the main driving forces for extracting information about the object from its magnetic field. Especially for biomagnetism, vector measurement provides more information for the source inversion problem or focal diagnosis. The accuracy of spatial inversion can be improved using the direction information of the magnetic field . Great eon field . In thison field . In thisHere, a new compact triaxial SERF AM is proposed and experimentally demonstrated. A triangular prism-shaped vapor cell is used as the sensing element. Vectorial measurement is achieved by reflecting a single beam once inside the cell and, respectively, applying modulation magnetic fields to all three axes. Only one photodetector is required in the scheme. The atomic spin dynamics are numerically investigated to understand the principle of the AM. In the experiment, vectorial measurement of magnetic fields is performed with high sensitivity in all three axes PxSimilarly, for atoms of the P2 part, the atomic polarization along the direction of light propagation isIgnoring the higher-order term and keeping the zero-order and the first-order term of the Taylor expansion of e obtainPprobe=P0Two approximations are introduced for the analytical solution (Equation ). First,Equation . The comUnder the condition of strong modulation, in In the experiment, we successively applied a 200 pT magnetic field with a duration of 5 s along the x, y, and z axes, and measured the response signals of the AM with a triaxial-signal synchronous acquisition system. Here, the modulation frequencies are chosen as 2000 Hz, 1000 Hz and 1000 Hz for x, y and z directions, respectively. The amplitudes of the modulation fields are chosen as 100 nT, 50 nT and 50 nT for the x, y and z directions, respectively. The recorded response signals are shown in The response signal is the strongest to the magnetic field along the y direction and is the weakest to the magnetic field along the x direction. It thus leads to different sensitivities related to different directions. As shown in e result a also inWe also verified the measurement accuracy of the vectorial AM. We applied magnetic fields with magnitudes of 400 pT with various spatial orientations. The magnetic fields are generated with three pairs of mutually orthogonal coils. The relationships between the magnetic field and the input current of the coils have been calibrated. The comparison between the experimental and expected values of the applied magnetic fields is shown on a sphere . The expHere, a novel scheme of a vectorial atomic magnetometer is described and experimentally verified. Highly sensitive vectorial measurement is realized by reflecting the light beam inside the cell in the SERF regime. Our scheme relaxes the requirement for the light and photodetector, facilitating the realization of a compact vectorial magnetic sensor or a sensor array. It has great potential in biomagnetism measurements, such as MCG and MEG.


The physical examination of the newborn is essential in diagnosing neurological or neurosurgical conditions in the newborn. This article focuses on three clinical assessments of newborns and infants that are especially important if neurological problems are suspected: The Ballard score, the examination of the head in a baby with (suspected) hydrocephalus, and the neurological and developmental evaluation of an infant in an ambulatory setting. A textual description and a link to a video describe each assessment. Neonates and infants could not communicate their symptoms to healthcare professionals, rendering a close observation and good physical examination essential in neonatal care. The neonatal brain is very fragile and perinatal events such as difficult delivery or prematurity pose a significant risk to the developing brain. Hypoxic ischaemic brain injury in both term and preterm neonates and intraventricular hemorrhages, mainly in preterm neonates, are common complications in the neonatal intensive care unit (NICU). Hydrocephalus, either congenital or as a consequence of the complications mentioned earlier, is a serious condition requiring adequate assessment of the baby.Most high-risk neonates admitted to the NICU for a prolonged time require close follow-up as outpatients. Again, a thorough physical examination by an experienced doctor is vital to detect early neurological problems or developmental delays. This article focuses on three important areas of the neurological assessment of neonates: i) maturational assessment of gestational age using the Ballard score, ii) neurological examination of the infant’s head with suspected hydrocephalus and iii) neurological examination in a clinical setting.Gestational age describes the time elapsed between the first day of the last normal menstrual period and the delivery of the baby . It is chttps://youtu.be/xlcWbH3Ym_g) and explained in detail as follows.However, certainty about the first day of the last menses and early antenatal ultrasound is often unavailable, especially in low- and middle-income countries. That is when one can fully appreciate the usefulness of a scoring system, such as the new Ballard maturation score , 4. The The first assessment for physical maturity is the skin. The maturation involves the development of its intrinsic structures concurrent with the gradual loss of its protective coating, the vernix caseosa. As foetal maturation progresses, the skin becomes thickened, wrinkled, and starts peeling. At term and post-term, the skin started to dry, causing further peeling and cracking with a leathery appearance.Lanugo is the fine, soft, and unpigmented hair resembling ‘peach fuzz’ covering the body of the fetus. Premature infants of 24 weeks–32 weeks gestation frequently display this fine coat of lanugo hair. The bald area starts to occur at the lumbosacral area and term babies will be devoid of lanugo.The plantar surface of the foot is scored, mainly based on its creases. At 28 weeks gestation, the sole appears smooth. The creases start to appear at the ball or anterior one-third of the foot and accelerate with increasing maturity. In a very immature infant, the heel-toe distance should be measured.The breast areola and bud should be felt and measured, with a value in millimeters. At 28 weeks gestation, the breast tissue is absent and the areola is barely visible. By 32 weeks gestation, the areola is stippled with a raised bud that can be measured.The eye/ear involves looking at the changes in configuration/curving of the pinna, thickness of cartilage, and state of development of eyelids as maturity increases. For example, at 26 weeks gestation, the ear has less cartilage and is pliable; hence, folding of the pinna will cause a slow release or it will remain folded. However, in term babies, the ear is firm with a well-formed margin. The pinna will instantly recoil.Genitals  involve an examination of the scrotal area. At 28 weeks gestation, the testicles are still high in the scrotum. The left testicle precedes the right, descends and enters the scrotum during 32 weeks gestation. The scrotal rugae can be appreciated at this stage. The scrotal skin becomes thicker and pigmented, and at 36 weeks gestation, both testicles are well-descended and palpable.Genitals  involve an examination of the clitoris, labia minora and majora. The neonate is positioned supine with the hips abducted to approximately 45°. At 28 weeks gestation, the labia are flat and the clitoris is prominent. Increasing fat deposit in labia majora occurs at 32 weeks gestation, and during this stage, both clitoris and labia minora recede. By 36 weeks gestation, labia majora will envelop and cover the labia minora and clitoris.Posture reflects body muscle tone at rest. The maturation starts in a centripetal direction, and the lower extremity is ahead of the upper extremity.The square window test determines the wrist flexibility and/or resistance to extensor stretch. The examiner straightens the fingers and applies pressure to the dorsum of the hand. The angle when the neonate’s wrist is flexed progresses from 90° to 0° with advancing gestational age. The 45° angle is consistent with a gestational age of 30–32 weeks.The arm recoil maneuver looks at the passive flexor tone of the biceps muscle by measuring the recoil after a brief arm extension. The examiner should place one hand under the neonate’s elbow for support. Arm recoil measures from 180° to < 90°. Score 4 should be given when the arm recoils and the fist touch the face.The popliteal angle is measured when the infant’s thigh is flexed at the hip and placed at the abdomen. The examiner should support the thigh from the side and avoid excessive pressure on the flexor being tested. Then, the examiner holds the foot and extends the leg below the knee until resistance is felt. The angle progresses from 180° to < 90° with increasing gestational age.The scarf sign is performed to test the passive tone of the shoulder girdle. The head should stay in the midline, and the examiner takes the infant’s hand and places it around the neck as far as possible while feeling the resistance of the muscle. The score is based on the point of the elbow on the chest when the resistance occurs.The heel-to-ear test measures the resistance of the flexor muscles at the hip. The hip girdle is stabilised and the hip is flexed so that it rests on the sheets alongside the neonate’s trunk. Then, the leg is drawn towards the ear to see the resistance to the maneuver.Again, each assessment is given a score between −1 and a maximum of 5. In the end, all scores are added up to determine the corresponding gestational age.https://youtu.be/YADjepw_5mk) shows the clinical evaluation of the head of a child that was born with or who was developing signs of hydrocephalus within the first month of life. Details on the process of the physical examination are given in the text below.The second video  and lateral bulging of the parietal bones. The shape of the head may vary based on the cause of hydrocephalus and the underlying condition of the skull bones. A disproportionately large forehead is common in aqueductal stenosis. A combination of other features, such as midface retrusion or hypoplasia, hyper- or hypotelorism, softening of the skull (craniotabes), and/or skeletal abnormalities, may suggest an underlying genetic syndrome . OccipitPalpation of the neonatal head starts with general palpation to feel for bruising, abrasion or swelling, such as caput succedaneum, cephalohematoma, or subaponeurotic haemorrhage (SAH). Clinical differentiation of these three scalp-swelling types is essential since each has different clinical implications. Cephalohematoma does not cross suture lines but fluctuates (boggy) on palpation. SAH is also fluctuant on palpation but crosses the suture lines. Meanwhile, caput succedaneum crosses the suture lines but is not fluctuant.Palpation along the suture line allows the doctor to appreciate widely spaced or split sutures. The sutures, namely the sagittal, coronal, lambdoid and metopic are separated by connective tissue junctions to allow growth along the edges of the two bones and permit adequate space for the growth of the brain during the development of the infant into childhood . The palFour palpable fontanels are noted in a quiet infant, i.e. anterior, posterior, sphenoidal and mastoid. They should be soft and flat. Upon uncertainty of whether the fontanel is flat or bulging, the infant should be placed in an upright, sitting position for further palpation. Palpation of the anterior fontanel feels like the shape of a diamond, with an average size of 2.1 cm. The posterior fontanel feels like a triangle and is small enough to admit the tip of a finger. Variations in the size and closure time of the fontanels depend on gender and ethnicity –17. HoweUpon the presence of hydrocephalus, the examiner may feel for a full, bulging and non-pulsating anterior fontanel. The fontanel tends to bulge when the infant cries. However, due to the easy expansion of the skull, the fontanel may not bulge or feel tense. The only sign may be an increased size of the fontanel.The head circumference or occipital frontal circumference (OFC) should be measured using a flexible non-stretchable measuring tape. The following should be considered to improve the reading and prevent discrepancies in measurements:The infant and examiner are in a comfortable position.Any hair decorations that interfere with the measurement must be excluded.The tape must be snug over the most prominent part on the back of the head (occiput) and just above the eyebrows .Two measures are to be taken, and the tape has to be repositioned each time. The largest value is recorded upon 0.2 cm differences in measurement. If the measurements exceed the tolerance value, a third measurement is taken, and the average of the two closest measures is recorded.According to the standard growth curves for head circumference by the World Health Organization (WHO), microcephaly at term is described as the OFC < 32.1 cm for boys and < 31.7 cm for girls, whereas macrocephaly is when the OFC > 36.9 cm for boys and > 36.1 cm for girls . The MalAn abnormal fluid-filled intracranial cavity can be transilluminated using a strong torchlight. The transillumination test should be performed in total darkness and starts against the infant’s forehead (midline near the hairline or at the anterior fontanel), occiput to forehead, and side to side. A faint glowing subcutaneous halo around the circumference of the flashlight is normal. Larger, irregular and brighter areas may indicate the presence of an abnormality, especially in a thin skull. When the transillumination is seen from the side opposite of a flashlight, an appearance of total glowing is usually suggestive of hydranencephaly. An asymmetrical cranial transillumination of one side may reveal the abnormal area of enlarging cystic or cerebrospinal fluid spaces .On percussion, a ‘cracked pot’ resonance sound (first described by William Macewen in 1893) can be heard when percussing near the junction of the frontal, temporal and parietal bones. This happens as the bone becomes thin due to increased distance between the sutures of the bones and the ready vibration of the bone when the content is more fluid . Next, tAfter completing the examination around the scalp, the examiner should proceed with checking the eyes for position and pupillary sizes. Common abnormal eye positions in infants with hydrocephalus are either deviating downwards (setting sun sign) due to pressure on the suprapineal recess or deviating medially (convergent squint) due to weakness on the lateral rectus muscle. Sometimes, the observations might not be obvious and require the oculocephalic or vestibulo-ocular reflexes, whereby the baby’s head is turned from side to side or up and down , 25. TheNext, the reaction of the pupils to light should be tested for both direct and indirect reflexes. Even when the eyes are closed, the blink reflex to light can still be tested unless the baby is crying, when the eyes are already held maximally closed. General depression from CNS, such as anoxia, sedation from anesthesia or a comatose baby, causes a diminished reflex. A fundoscopic exam is also important to search for papilledema. The examination of an infant with (suspected) hydrocephalus should be completed by examination of the other cranial nerves, a complete neurological assessment and examination of the body of the child for the presence of deformations and/or malformations, determination of the tone of the baby and testing of reflexes.The neurological examination of an infant should be tailored to their developmental level and cooperation. The examiner must acquire knowledge and appreciate the normal and abnormal findings. Sometimes, the neurological exam is performed with the infant on the parent’s lap to overcome shyness and stranger anxiety. Serial examinations may be necessary to establish accurate findings or diagnoses. In a busy clinic, a gross examination is performed to detect an abnormal pattern of neurological deficits. Once detected, further thorough assessment and referral to specific services are required. Children born preterm are expected to have developmental milestones and anthropometric measurements according to their corrected gestational age. The corrected gestational age is obtained by subtracting the number of weeks they were born before 40 weeks from their chronological age. Meanwhile, the chronological age is used only for immunisation and feeding practice for preterm babies.At 1 year old of age, most of the gross motor milestones have appeared, and the concerned neurological findings such as hypo- or hypertonia, hypo- or hyperreflexia, and pathological and primitive reflexes observed in earlier testing should no longer be present to a significant degree . This seThe ambience of the environment is vital during an examination of an infant. It is best performed in a warm room and during the infant’s quiet alert state, which most frequently occurs between feedings. The infant should lie down unclothed and in unconfined boundaries. This position enables accurate observation of facial and limb positions during the resting posture and spontaneous movements of the head and limb. The level of alertness can be viewed in Below are some of the less rare syndromic features to be looked at on a routine basis, without any intention to give a complete list of syndromic features.The shape and size of the infant’s skull require careful inspection and palpation of the sutures and fontanel, followed by measurement of the OFC (please see the previous section).The facial features involve observation and appreciation of the relationships of the facial components; ears, eyes, nose, mouth and mandible. An unusual facial characteristic may alert the examiner of certain syndromes or neurological injuries. For example, a pale-pink macular lesion (port-wine stain) over the face may signify Sturge-Weber syndrome . Facial The position of the eyes is important. The distance between the outer canthi can be divided into equal thirds and the length between the canthus of one eye should cover the distance between the two eyes. Hypertelorism is a wide-set eye and hypotelorism is a close-set eye. Upslanting palpebral fissures mean that the outer canthus of the eye is higher than the inner canthus, while downslanting palpebral fissures are when the outer canthus is lower than the inner canthus. An example is an infant with Apert syndrome showing hypertelorism and downslanting palpebral fissures. Blepharoptosis or ptosis is the drooping of the upper eyelid below its normal position (1 mm–2 mm of upper limbus). This can be congenital, such as in the levator palpebrae muscle, or secondary to neurological injury, including third nerve palsy and Horner’s syndrome. Further assessment should be performed for other cranial nerves.The ear position is assessed by extending an imaginary line from the inner to the outer canthus of the eye toward the ear. The ear should be 1/3 above the imaginary line. Evidence of pits, tags, or periauricular sinus tract is assessed, as this may require further follow-up treatment. A poorly formed external ear should alert the examiner to a possible syndromic infant such as Down syndrome, whereby the ears are small with an overfolded helix. Hence, other positive clinical findings should also be assessed. Infants usually respond to the sound of their mother’s voice. The examiner may might the mother if the child turned their head to sounds or familiar voices. Subsequently, younger infants may blink or become startled by clapping or a bell.The optimal visualisation of the skin and spine requires the infant to turn prone or side-lying. The evidence of hair tufts, dimples, or tracts along the spine is inspected, which might indicate the presence of a spinal dysraphism. A light brown to dark brown café-au-lait macules ≥ 0.5 cm in diameter or > 6, particularly in the presence of axillary freckling, requires evaluation for neurofibromatosis (NF) . MeanwhiGeneral observation of the infant gives much information on cranial nerve functions. The examiners have to be opportunistic in their approach during the examination according to the infant’s temperament and leave the stressful tests for last. The olfactory nerve for smell is rarely tested. However, one can still appreciate it by testing using a strong scent, such as mint or clove, and observing for grimacing. The eye examination starts with a general inspection of the eyes to look for ptosis, squint, or stationary nystagmus. Next is the test for direct and indirect pupillary reflexes. The vision is checked by moving a bright object side to side and in an H shape 10 in–12 in from the infant’s eye. The examiner should observe for spontaneous eye movement, symmetry and nystagmus. When there is a weakness in muscle movement, the doll’s eye maneuver may be useful to differentiate the weakness of the lateral rectus (for the abducens nerve). The rooting reflex, if still present, allows appreciation of the sensory test for the trigeminal nerve. The effective sucking and swallowing of the child provide some information about the cranial nerves V, VII, IX, X, and XII. During the interaction, the examiner should notice the facial expression and response to the parent’s voice. When the baby is being fed or crying, forehead wrinkling, nasolabial fold, sucking movement and crying quality are also noted.Testing the eighth nerve is not easy in small children, and the startle reflex can be used. Children below the age of 4 months–6 months do often not turn to sounds during the hearing distraction test since they lack attention to sounds. In many places, children are now universally screened for hearing deficit shortly after birth by otoacoustic emission (OAE) or automated auditory brain stem response (AABR) .The auditory response requires the sternocleidomastoid muscle range of motion for rotation and lateral flexion, which is innervated by the spinal accessory nerve. The infant’s head must be in a neutral position, and the muscle must be palpated and compared on each side. A screening test by turning the infants’ head side to side and comparing the shoulder height is the initial evaluation in the clinic. Muscle function of the lateral flexor muscles of the neck is assessed using the muscle function scale for an infant. Further testing using an arthrodial protractor is needed when there is a lack of muscular strength or an imbalance in muscle function .Some tests can be stressful and require parents to be around to keep the infant comfortable. If the infant is quiet, a fundoscopic exam is necessary. Vestibular reflex may be performed, although it is seldom included in the routine neurologic examination. The parent can assist by holding the infant and turning them around. During the test, the eye will follow the direction of rotation. Upon stopping, the eye will turn in the opposite direction. Sometimes, horizontal nystagmus is observed.Next, an inspection of the mouth is required. The parent may have to hold the infant’s head steady. The tongue is inspected for symmetry and fasciculation using a wooden tongue blade and a good light source. The palate is checked for a cleft or a high arch by inserting the finger. Simultaneously, the sucking reflex is tested. Most of the time, the gag reflex is not routinely tested if the examiner is confident that the rest of the lower cranial nerve tests are normal, has observed the infants during bottle feeding and the parent does not report any trouble during feeding.Assessment of the tone and muscle strength in infants requires good observation of the resting posture followed by assessment of the passive, active and axial tones. Diminished or lack of resistance to muscle movement or stretch indicates hypotonia, while increased muscle contractility and resistance to passive muscle movement or stretch indicate hypertonia. The primitive reflexes are useful in assessing the motor component of the limbs and trunk. In infants younger than 2 months, the palmar grasp reflex helps assess the distal power and the Moro reflex for the proximal power. As the child gets older, the upper limbs can be tested by giving a small object and watching how the infant reaches overhead and how they manipulate small objects.Most newborn infants, either premature or full-term, have a head turn preference toward the right side . This isThe passive tone assesses the resistance of the appendicular muscles of the upper and lower limbs, with arm and leg tractions being commonly tested. The infant should remain supine and quiet when the movement is applied. Sometimes, clinical assessment can be difficult when the infant is stressed or crying, and interpretation may err towards hypertonia rather than a normal tone. Arm traction is when the examiner holds the infant’s wrist and attempts to pull the arm to a vertical position. The infant will flex the elbow to keep muscle resistance as the shoulder lifts off the surface. Leg traction is when the examiner holds the infant’s ankle and attempts to pull the leg to a vertical position. The infant will flex the knee and maintain this position as the buttocks lift off the surface. There will be too little resistance (extension) to traction in hypotonia.The assessment of the active axial tone involves four tests: i) pull-to-sit (head lag), ii) head and trunk tone, iii) horizontal suspension and iv) vertical suspension.Pull-to-sit manoeuver (traction response) requires the baby to lie supine. The examiner grasps the infant’s wrists and slowly pulls them to a sitting position. At 2 months–3 months, an infant could activate the neck flexor muscles and hold the head in line with the trunk. The hip will flex to brace the impact of sitting. Following further encouragement, such as toys or an animated face, the infant will hold the head for a short while. However, an infant with axial hypotonia does not have anticipatory neck flexor muscle activity, and the head lags behind the trunk. Meanwhile, in axial hypertonia, the head pulls in front of the trunk . AsymmetHead and trunk tone. Head control is established by 3 months old of age, followed by the progressive development of trunk control . HoweverHorizontal  suspension requires turning the infant to a prone position. The examiner will hold and support the infant at the chest and abdominal area and let the arms and legs loose. A normal infant could maintain the back straight with the head erect and in line with the back. The arms and legs are in the flexed position. Hypotonia is when the back is curved, the head flops down and the limbs hang straight .Vertical suspension requires the examiner to place both hands in the infant’s axillae and lift them upright. In a normal infant, the shoulder muscles should have sufficient strength against the examiner’s hand to allow the infant to maintain vertically with the head in line with the back. However, in hypotonia, the infant’s head will fall forward, and the infant slips through at the shoulder. During this manoeuver, the child tends to flex the legs. In children with peripheral hypertonia, fixed extension and scissoring of the lower limbs may be observed.Deep tendon reflexes (DTR) are performed later in the exam to prevent the infant from getting stressed. Very premature infants of < 33 weeks old had an overall diminished reflex intensity compared to late premature infants of 33–36 weeks old . The refThe biceps, brachioradialis and triceps reflexes are commonly tested for the upper limb, while the hip adductor, knee and ankle reflexes are for the lower limb. Tendon reflexes diminish with repeated stimulation, a phenomenon called ‘habituation’ . If the There are some differences when comparing DTR between infants and adults. Term neonates or infants can have brisk reflexes and still be normal. The absence of DTR is a more worrying finding than brisk reflexes. A crossed adductor reflex is a contraction of the contralateral adductors causing extension of the thigh following the tapping of the ipsilateral patella tendon. This is a normal finding in infants; as they grow, it is still present in < 10% after 8 months old .Primitive reflexes provide information about the development of the brainstem and cortical function. Around 4–6 months, the maturation of the CNS progresses and the primitive reflexes begin to diminish . The perCapute and colleagues  classifyPlantar grasp disappears by 7 months to 9 months to allow the infant to start standing. The stepping reflex is provoked by holding the infant under the axilla in an upright position and placing the anterior tibia or dorsum of the infant’s foot under or against the edge of a table. The infant’s hip and knee will flex, simulating walking. The response diminishes by the end of the first year . Asymmethttps://youtu.be/CkNHxnhI8PY) serves as a general summary that one should look for in the clinic setting.The above examination may not be assessed in detail, particularly by other clinicians outside the pediatric clinical setting; hence, Video 3  . TypicalThe neurological examination techniques for neonates to infants require skills and a lot of patience and practice. Observing the infants alone does give many clues, nevertheless, perfecting the examination is a requisite. Modification is needed to correspond to different developmental stages and one cannot avoid examining temperamental infants. Hopefully, this article and videos will be useful to the students and other clinicians in helping them with their decision-making.


The impact performance and compression after impact characteristics of 2D and 3D fiber metal laminates (FMLs) are investigated both experimentally and numerically. Commercial-grade GLARE3A-3/2-0.3, and a recently developed FML, which incorporates a unique 3D glass fabric, are used in the study. Both FMLs have similar areal densities. The specimens are subjected to impact loading at three energy levels—low, intermediate, and high. The test results indicate that GLARE is slightly more resilient under impact compared to the 3DFML. However, since GLARE is much thinner than the 3DFML, the two-material systems exhibit very different failure modes. GLARE and 3DFML lost up to 62.6% and 41.5% of their original compressive load-bearing capacity, respectively. Robust and accurate finite element models are developed that can predict the damage evolution and failure modes of both FMLs. Knowing the level of reduction in the residual load-bearing capacity of a material resulting from an impact is of practical importance when assessing the service life of materials. However, further exploration would be required to determine how the information obtained through testing relatively small-sized specimens in a laboratory environment can be extrapolated to larger real-life structural components. Fiber metal laminate (FML) is a hybrid laminated material system consisting of layers of fiber-reinforced plastics (FRPs) and thin sheets of metal. FML was developed with the aim of taking advantage of the positive attributes of the metallic and FRP constituents. Since their introduction, various types of FMLs have been developed . FMLs offer outstanding static properties, impact resistance and fatigue resistance, and they have primarily been used in the aerospace industry. For example, glass-laminated aluminum-reinforced epoxy (GLARE), possibly the most widely used FML type, has been successfully incorporated in the fuselage of the Airbus A380 airliner . A few yAerospace and transport vehicles’ structural components are susceptible to low-velocity impact (LVI) loadings during their fabrication, assembly, operation and maintenance ; exampleThe residual load-carrying capacity of a composite after impact loading is usually evaluated using the standardized testing method, referred to as the compression after impact (CAI) tests, such as those outlined in ASTM D7137 and ISO 18352 ,15. ThesIt should be noted that the majority of the literature on this topic has focused on the CAI performance of composite materials (mainly CFRP), and only a few works have investigated the CAI performance of FMLs. For instance, Wang et al.  investignd Newaz  studied All in all, limited data are available regarding the CAI response of FMLs  and are virtually non-existent for 3DFMLs. As a potential candidate for applications in aerospace and other transport industries, the CAI characteristics of 3DFMLs would have to be investigated and compared to the current commercial-grade FMLs . Therefore, in this study, LVI and CAI responses of 3DFML and GLARE are experimentally investigated and compared. To complement the investigation, models based on the finite element method (FEM) are developed to simulate the two experimental procedures. The integrity of the models is validated against the experimental results. These models could be effectively utilized to examine the influence of various parameters that influence the response of such complex hybrid material configurations and optimize their performance.It is believed that the in-depth experimental and numerical investigations presented in this paper serve as a valuable attempt to fill this knowledge gap in the literature. Moreover, knowledge about the reduction in the residual load capacity of such materials after an impact would be beneficial to practicing engineers. It will also be demonstrated that micro-CT scanning is a highly effective technique for gaining insight into the performance of hybrid composites with complex configurations.The first step of producing the 3DFML panels involved impregnating a First, a layer of epoxy resin was applied evenly onto a peel-ply that hosted the 3DFGF. Then, epoxy resin was brushed onto the 3DFGF against the pillar yarn’s direction; this brushing process was repeated after flipping the fabric over. Finally, a layer of peel-ply was placed on top of the fabric, and the whole assembly was lightly brushed against the pillar yarn direction, before being cured at room temperature for In the second step, a two-part liquid polyurethane foam with a density of Since most applications that utilize FMLs are weight-sensitive, a lightweight grade of GLARE was selected to match the areal density of the 3DFML. Specifically, a commercial-grade GLARE3A-3/2-0.3  or rebounds back (for non-perforation cases), giving the pendulum a chance to hit the impactor a second time. This is critically harmful to this experiment because additional energy would be transferred to the specimen, adversely affecting the consistency of the subsequent phase residual strength evaluation. The second hit between the pendulum and the impactor usually occurs so quickly after the initial impact that the naked eye cannot observe it; this event could only be detected by the joint observation of the high-speed camera footage and the force response data. The unwanted second impact was effectively eliminated after implementing a suitable pendulum stopper. The pendulum stopper is a steel piece that limits the pendulum’s travel beyond hitting the impactor. As a result, the pendulum stops swaying forward after transferring energy to the impactor, and the impactor hits the specimen only once and bounces back to its initial position.Additionally, a load reducer made of rubber and a steel protector were fitted to the back of the impactor. Initially, it was observed that the peak load occurred when the pendulum hit the impactor, rather than when the impactor hit the specimen (due to the steel-to-steel impact). This phenomenon is problematic for two reasons. Firstly, the maximum impact load that can be accurately measured is limited by the working limit of the load cell. Moreover, in an event when an impact load exerts an excessive peak, its load would compromise the impact energy capacity of the testing equipment. Secondly, it was observed that the metal-to-metal impact excited the impactor and caused “rougher” load signals. Adding the load reducer significantly decreased the peak load and made the load curve smoother. An advantage of using this pendulum-type setup over the commonly used drop-weight impact setup is that the energy is singular to height, and no additional treatment is required for correcting the gravitational force. Therefore, the refined test setup is believed to be equivalent to (if not more effective than) the drop-weight impact testing setup, as per ASTM D7136.Furthermore, an impact fixture with a circular opening was adopted instead of the standard fixture with a rectangular opening. A circular opening ensures uniformly distanced boundary conditions with respect to the point of impact, thereby eliminating the edge effect; in other words, the support would potentially enhance the consistency in capturing the anisotropic response of the composite panels. The specimens were sandwiched between the front and back fixture plates, which were bolted together at all four corners. The circular opening had a diameter of In this study, the considered energy levels were The impact energies can be determined using Equation (1) for the given experimental setup.In the above equation, All specimen groups were assessed for damage after impact before each specimen was subjected to the compression test. There are many non-destructive inspection methods for assessing damage in composite materials, including visual inspection (VI) and other techniques, such as ultrasonic, thermography, radiography, electromagnetic, acoustic emission, and stereography, which require specialized equipment . This stAfter the impacted specimens were scanned, they were subjected to quasi-static compression tests to establish their residual performance. According to ASTM D7137, the CAI test requires a unique compression fixture, as shown in The ultimate strength of the damaged specimen can be determined using Equation (4) .(4)FCAIIn total, 13 3DFML and 9 GLARE specimens with dimensions of The compressive response of the virgin specimens was also evaluated following ASTM D6641. All specimens were The minimum thickness of each material category was established based on the layup. In the standard, the thickness of specimens must satisfy Equation (6) to preclude the Euler buckling of the specimen.The special fixture used to support the specimen in the compression test has two halves, gripping the top and bottom sections of the specimen. The two halves are aligned concentrically by two rails (see ASTM D6641). The upper half slides on the rails effortlessly via bearings, thereby subjecting the specimen to a concentric compressive load with buckling prevented by the established gauge length. A laser extensometer was used to record the resulting strain in the gauge length. Five specimens of each system were prepared for the compression tests.The LS-DYNA commercial software package was used to conduct the numerical simulations. Specifically, LS-PrePost V4.9.10 and solver R13.1.1 were used in this study. In addition, the Message Passing Parallel (MPP) solver was used for all the analyses to optimize the running time. The analyses were run using 150 cores and 4 gigabits of memory for each core on the Cedar cluster provided by Digital Research Alliance of Canada.x, y, and z directions, and the impactor was restrained in the x and y directions. The impactor’s material density was selected to match the actual impactor’s mass. The mesh of the impactor’s nose is shown in The FE models of the FMLs are shown in The metal and FRP constituents of both FMLs were modeled using MAT_24 and MAT_54 of LS-DYNA, respectively. MAT_24 uses a piecewise linear function to define the elastic-plastic behavior of metals and uses a plastic strain-based failure criterion to facilitate element erosion (deletion). The material parameters used in the models are given in —When the DFAILT parameter is set to zero, the element is deemed to have failed when the tension failure mode is met based on the Chang-Chang stress-based criteria.—When DFAILT is set to a non-zero value, the element is deemed to have failed if the strain in any direction becomes greater than the defined DFAILT, DFAILC, DFAILM, and DFAILS limits.—When EFS is set to a positive value, the element is deemed to have failed if the effective strain in the element becomes larger than the set effective failure strain (EFS). EFS is calculated using the ultimate normal and shearing strains.—When the timestep size criteria for element deletion (TFAIL) is set to a positive value (0 < TFAIL ≤ 1), the element is deemed to have failed when the element timestep is smaller than TFAIL. Conversely, if TFAIL is set greater than 1, the element is deleted when the ratio of the original timestep over the current timestep becomes less than TFAIL.MAT_54 models the response of an arbitrary orthotropic material effectively in conjunction with the Chang-Chang failure criterion. Notice that the element erosion in MAT_54 is not purely failure-based; instead, element erosion is declared when one of the following criteria is met:To correctly model the failure of an FRP part in LS-DYNA, it is essential to define the failure strains of the material. Furthermore, when the second criterion is met, the first criterion (Chang-Chang criterion) would still affect the element’s strength. In such cases, the Chang-Chang criterion parameters define the maximum strengths of the element. In other words, the element would not be eroded (deleted) when the criterion is satisfied; instead, the stress value will hold the element steady at that prescribed maximum strength until the element erodes based on the defined failure strains. For further insight into the definitions of the specific terms, the user is referred to LS-DYNA’s theory manual . The mecLastly, the elastic model, MAT_1, was used for the foam, and an effective strain-based erosion card was adopted to enable the erosion/deletion of the foam elements. The foam has a density of The specimen was tied to the two rigid impact specimen-restraining fixtures using TIED_SURFACE_TO_SURFACE_OFFSET, where the “_OFFSET” keyword switches the default constrain-based contact to a penalty-based contact to make tied contact compatible with the rigid material model. When using this option, it is essential to ensure that the slave segment is within the orthogonal projection of the master segment.s = intfor” must be included in the command line when executing the analysis. These two steps will produce a series of binary output files named “intfor”. Subsequently, these “intfor” files can be viewed in LS-PREPOST, and the delaminated region can be discerned by fringing the nodal contact gap.In CAI testing, the resulting damaged region of the specimens (the delaminated region) is used to establish the residual strength of the tested specimen. The cohesive zone modelling approach (CZM) is incorporated in this study to model the interfacial delamination growth. The customary method to incorporate CZM in LS-DYNA is to use CZM elements at the region of interest. CZM can also be incorporated by modelling the interface using the surface-to-surface tiebreak contact algorithm. This method enables visualization of the delaminated region during post-processing. To do so, a BINARY_INTFOR card must be included in the input deck, and “In LS-DYNA, the CZM model MAT_138 (a bilinear mixed-mode relative displacement CZM model) has been adapted into surface-to-surface tiebreak contact as OPTION 9 . CompareUnderstandably, the most realistic debonding would be that caused by the combination of both modes. The mixed-mode bilinear model would consist of a proportion of each mode; this is graphically illustrated in The CZM tiebreak contacts were applied to the interfaces between metallic and FRP layers because these interfaces are prone to delamination based on the literature and our experience. The parameters used in the model are summarized in z-direction was applied to the impactor using the INITIAL_VELOCITY_GENERATION card, reflecting the velocity observed in the experiment.The interfaces between FRP layers and 3DFGF and foam were merged because based on our experience, delamination is less likely to occur in these interfaces. Next, eroding contact was defined between the impactor and the specimen. Eroding contacts were also defined within the specimen between different layers to model the internal interactions more realistically. Lastly, an initial velocity in the negative It should be noted that the solution of such a complex system involves an intensive CPU time, which is primarily due to the small contact timestep necessary to ensure solution convergence. To stabilize contacts with a practical global timestep, the SOFT options 1 and 2 were used for cohesive tiebreak contacts and all other contacts, respectively.The dynamic impact analysis was explicitly solved. The quasi-static compression test is a rather lengthy process in real-life; thus, simulating it numerically using the actual loading rate would consume an unfeasibly large CPU. As a result, it would be efficient to use the implicit solver for this phase of the analysis. As mentioned in , an effeThe described method, however, could not be used because the scheme would not be able to initialize the contact forces, given the fact that bonding interfaces were modelled using “cohesive tiebreak contact” in the current study. Consequently, the static analysis was explicitly continued after the impact simulation to model the compressive loading phase.z-direction. Next, the knife edges of vertical sliders were modeled as rails and were restrained y direction. Then, a prescribed motion was applied to the nodes forming the top edge of the specimen to simulate the compression loading. Lastly, the nodes at the bottom left corner of the specimen were restrained in the x direction for the rigid body stability of the model. Ideally, the compressive load (simulated as applied downward displacement here) should be applied using the same rate as in the experimental tests; however, since this phase of the analysis was also solved explicitly , the adaptation of the actual loading rate in this phase would be extremely CPU intensive, thus impractical. Therefore, the downward (compressive) motion (loading) was applied relatively quickly and as smoothly as possible to make the compression loading phase very short, while minimizing the dynamic inertia effect. Although modelling the applied load based on the actual loading rate would be more accurate, the adopted method has been proven to be viable and effective by other researchers [At a specific time during an impact simulation, the impact force reduces to zero, indicating the end of the event. This time was used to define the death time for contacts between the impactor and the specimen and between the specimen and the impact fixtures. Boundary conditions associated with the CAI test were then applied to the specimen. First, the regions near the specimen’s top and bottom were all restrained in the etup see a. Furtheearchers . Note thCompression tests conducted on virgin specimens were modelled by reducing the full model to a smaller size to reflect the ASTM D6641 specimen dimensions. Subsequently, appropriate boundary conditions were applied to the model in conformance with the actual specimen gauge length.Elements can undergo significant deformation during an impact simulation. When the characteristic length of some of the elements decreases during the analysis, the element’s timestep decreases accordingly and causes a decrease in the global timestep. In some cases, the severe deformation of an element can yield a negative volume numerically, attributing a negative timestep to the element and the global system, thus disrupting the progress of the simulation. In simple terms, the severely distorted elements could either dramatically slow down the simulation or cause premature termination of the simulation. To overcome this issue, the ERODE key was set to 1, and the DTMIN was set to 0.01. As a result, the solver would erode the severely distorted elements that require a solution timestep smaller than 1% of the initial timestep used for solving the global model, facilitating the successful completion of the analysis. The timestep scale factor, TSSFAC in the CONTROL_TIMESTEP card, was set at The computation time for these analyses ranged between 5 and 13 h. The analyses that involved energy levels close to the perforation limit of the materials had longer running times, likely because the elements were more severely deformed, resulting in smaller global timesteps. It should be noted that the above time range can only be achieved using a supercomputer facility similar to that used in this study. Based on our experience, the same analyses are estimated to take much longer  when conducted on a workstation with an AMD Ryzen-7 CPU, consisting of 8 cores and 3600 Mhz.As mentioned earlier, the real-time force-displacement data were recorded using a dynamic load cell and a dynamic linear variable differential transformer (LVDT) during the impact experiments, and the representative data have been plotted in Under LVI, a larger impact energy induces a more significant deformation to the specimen and, in turn, causes a larger peak impact force. As the impact energy surpasses a critical value that causes the system to lose integrity, the rate of change of the peak impact force slows down, approaching a plateau, which can be observed in For the low-impact energy, the smooth responses of GLARE and 3DFML specimens, as shown in Examination of Since the high-impact energy level selected for 3DFML specimens was slightly above the system’s perforation limit, the penetration depth differs from specimen to specimen. However, all specimens managed to stop the impactor successfully. Therefore, the damage and failure modes in the specimens were similar, but relatively different post-penetration responses were observed. The response at this stage in the events is believed to be highly dependent on the impactor shape. As shown in As can be observed through the results presented in The numerical models could also capture the partial perforation that resulted from the high-energy impacts; however, the models underestimated the force response after the onset of the perforations. This may be because the incorporated element size was larger than the crack width, so the numerically predicted crack (mimicked by element erosion) was larger than the real crack width. The underestimated impact force response in turn caused the impactor to maintain its velocity more effectively in the numerical models compared to that observed in the experiments see b.Micro computerized tomography (micro-CT) scanning was used to generate a series of images of the cross-section along the longitudinal and lateral axis of the specimens. Images that illustrate the cross-sectional deformation of typical specimens under different impact energies are presented in As discussed previously, the impacted GLARE specimens exhibited noticeable flexural deformations compared to their counterparts. The low- and intermediate-impact energies did not cause major material failure, besides the bending deformation in the GLARE specimens; however, interlaminar delamination could be observed through the darker gaps observed between the layers. In contrast, the high-impact energy caused the fracture of all the metallic layers and fiber breakage of all the FRP layers, indicating that the impact energy was near the specimen’s perforation threshold. Moreover, the interlaminar damage was also significantly more extensive.As for the 3DFML specimens, the low-impact energy caused an indentation on the impacted side and very minor deformation on the unimpacted side. Despite the minor damage on the surface and no obvious sign of delamination, fiber breakage could be observed in the pillars in the vicinity of the impact. Under the intermediate-energy level, both the impacted and unimpacted sides experienced cracking, and the pillars were buckled or broken, rendering the through-thickness collapse of the 3DFRP core. Furthermore, fiber breakage in 3DFRP plies could also be observed. Lastly, under high-impact energy, the specimen suffered severe damage. Significant cracks formed on the metallic layers, and breakages in the plies and collapse of the foam and pillars were substantial. In addition, the specimens showed minor global bending deformation due to the sufficient flexural rigidity of the material system, even under high-impact energy. Moreover, delamination in the lower metal/FRP interface was more prevalent since the impactor seemed to have pressed that layer after perforating through the FML. Lastly, an asymmetric failure response was observed in the 3DFML specimens impacted at the high-energy level. This is postulated to be due to the impactor contacting a region between two rows of supporting pillars, as opposed to directly contacting the spot above a row of pillars.The delamination length was measured from both the micro-CT scan images and numerical results and was plotted with respect to the energy levels in The CAI tests were carried out according to ASTM D7137, which recommended a specimen thickness of The failure modes were similar in both material systems, regardless of the applied impact energy levels; therefore, the response of a representative specimen per material system is presented in The 3DFMLs did not show any noticeable global buckling during the tests, and CAI failure occurred on both sides of the specimens at the impacted region. The failure mode can be assessed as local buckling-induced delamination. Looking closely at the failed regions, one can observe that the 3DFGF plies also buckled, evidencing fiber breakage on both sides of the specimen. The foam was also noticeably locally compressed, and its failure can be clearly observed near the buckled region. Furthermore, the width of the buckling band in the magnesium skin on the impacted side is greater than that on the unimpacted side. Material sections near the side rails were restrained in the out-of-plane direction, thus dodging the buckling stresses and shifting the stresses and causing local failure on the magnesium skin near the side rails. It is, therefore, assumed that this failure mode should not have any bearing on the measured residual strengths. The numerical models predicted similar failure modes. All the local failed phenomena were correctly predicted by the numerical models, indicating the reliability of the numerical modelling framework. This included the buckling of magnesium layers at the impacted region, the higher local buckling amplitude on one side, the slightly tilted buckling shape, the side rails-induced localized failures, and the delamination and fiber breakage of the 3DFGF plies.The impact tests induced significant local bending deformation  at the center of the GLARE specimens. This promoted the global buckling of the GLARE specimens during the CAI tests. Nevertheless, the compressive load caused failure to occur closer to the upper edge, away from the locally impacted and deformed region. It is believed that the failure was affected by the complex deformed shapes of the GLARE specimens. Similar to the failure mode observed in the 3DFML specimens, the CAI-induced failure mode in the GLARE specimens could also be identified as local buckling-induced delamination, with fiber breakage observed in the picture showing the side view of the failed region. The buckled region was smaller than that of 3DFMLs, likely because of the smaller overall thickness of GLARE. Similarly, the side rails also caused concentrated failure to the GLARE skins. The numerical predictions, shown in Detailed internal damage in both materials during the compression testing can be observed through the numerical results. One can also notice that the compression failure was initiated from different locations within the specimens. In the case of the 3DFML specimens, the impact caused severe damage to the pillars situated at the location of impact (center of the specimen), leading to the instabilities of the 3DFML walls. Furthermore, the applied compressive load during the CAI test caused additional stress on the already damaged pillars, causing compression failure from the impact damage at the center of the specimen.In contrast, GLARE’s failure originated from the specimen edges and propagated laterally toward the center. The impact caused a dimple at the center of the GLARE specimen. Once the specimen was subjected to the axial compressive load, the dimpled region deformed further out-of-plane, thereby ununiformly shrinking the damage footprint in the longitudinal direction, causing the failure of the transverse fiber  due to the extensive shear stress and the pre-existing compressive stress. Subsequently, the failure progressed toward the dimpled region, and their advancing trajectories turned slightly towards the impact-damaged region and finally joined somewhere near the center of the specimen. Thus, it is believed that the inherent thin configuration of GLARE caused the unexpected failure shift from the center of the specimen  to a different location. Furthermore, the described progressive failure theory can also justify the phenomenon of failure shifting from the region damaged by the initial impact toward the upper edges of GLARE specimens.The experimentally measured load vs. the displacement results of the CAI tests are shown in As a comparative investigation, the compressive strengths of the virgin FMLs were evaluated following ASTM D6641. The virgin specimens showed a similar failure mode to the impacted specimens. The failure of the pillars of the 3DFMLs led to the buckling of 3DFGF plies and magnesium layers of 3DFMLs, causing larger scale delamination. The comparison of the compressive residual strength of the impacted specimens and non-impacted specimens is graphically illustrated in As observed, despite the fact that the virgin GLARE specimens preserved a significantly higher load capacity than their 3DFML counterparts, the impacted GLARE exhibited comparable residual capacity compared to 3DFML. This was expected due to the developed impact-induced dimple on GLARE specimens, which was found to adversely affect their residual load capacity. On the other hand, 3DFML specimens maintained their configuration more effectively. Furthermore, the relatively small thickness of GLARE makes the larger size GLARE specimens significantly prone to buckling during a CAI test, thus substantially lowering its compressive capacity compared to the strength exhibited by the virgin test coupons tested at a much shorter gauge length.Comparison of the post intermediate- and high-energy impact residual load capacities of both material systems revealed that the residual capacity of the 3DFML significantly decreased, while GLARE maintained its capacity quite well. This is likely due to the more severe damage caused by the high-energy impacts on the 3DFML specimens . This is because, as stated earlier, the numerically estimated high-impact energy level for 3DFML happened to be slightly greater than the actual perforation threshold of the material system. Overall, however, it can be observed that 3DFML offers better tolerance to impact damage, even though it showed slightly lower impact resistance compared to GLARE.Furthermore, a relatively larger inconsistency can be observed in the 3DFML experimental results shown in Additionally, the numerical models’ results were fairly accurate in predicting the CAI residual capacity and failure modes of both material systems. The predicted capacity for all cases is within 10% of the experimentally measured values. Interestingly, the trends in the curves illustrated in The Residual Reduction Index  with similar areal densities through a comprehensive coupled experimental and numerical study. The outcomes of this study and suggestions for further research are summarized as follows.The CAI performance of GLARE and 3DFML was successfully evaluated using ASTM D7137 guidelines; however, minor modifications had to be applied to the standard test fixture.Micro-CT scans were found to be an effective and worthy non-destructive inspection technique for observing internal damage in such complex hybrid material systems.The impact energy levels ranged from low to high, with the selection of high-impact energy close to each material system’s perforation threshold, which was established by numerical simulations.The impacted GLARE and 3DFML specimens lost approximately 60% and 40% of their original compressive load-carrying capacity, respectively. GLARE’s significant loss of load capacity is attributed to its relatively small thickness.The developed numerical models predicted the impact and post-impact responses of both material systems accurately and effectively. In addition, the predicted failure modes closely matched the experimental results, confirming the integrity of the numerical models.The GLARE specimens showed better impact resistance and post-impact compressive load capacity compared to 3DFML; however, due to their large impact-induced deformations, their CAI residual capacity was closely comparable with 3DFMLs. Given the fact that 3DFML possesses comparatively significantly higher flexural properties, 3DFML is deemed to be an effective alternative to GLARE in various engineering applications.The developed numerical models were successfully used to establish the influences of the critical and limiting parameters that govern the post-impact compressive load capacity of 3DFML. The developed modelling framework can be effectively used to evaluate the response of different 3DFML configurations and optimize their impact resistance and CAI performance in the future.Two equations were proposed for calculating the Reduction in Residual Capacity and Residual Reduction Index. These simple equations can be used to relate the post-impact residual load capacity of real-world FML panels to the CAI performance of laboratory-size specimens. However, the universality of these equations should be further investigated.