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The present paper studies the efficient prediction of effective mechanical properties of heterogeneous material by the FCA (FEM-Cluster based reduced order model Analysis) method proposed in Cheng et al. (Comput Methods Appl Mech Eng 348:157–168, 2019 ). The principle of minimum complementary energy and its cluster form for the RUC subjected to applied uniform eigenstrains and the PHBCs (Periodic Homogeneous Boundary Conditions) are developed. By using the known interaction matrix, an alternative form of the principle of cluster minimum complementary energy is constructed and proved very efficient for updating the interaction matrix and the effective elastic modulus when the material properties of clusters change. Moreover, the proposed principle of cluster minimum complementary energy is applied for the incremental nonlinear analysis of the cluster reduced order model, and thus greatly improves the prediction of nonlinear effective properties of the RUC in online stage computed in Cheng et al. (Comput Methods Appl Mech Eng 348:157–168, 2019 ). A number of numerical examples illustrate the effectiveness and efficiency of the FCA approach with the proposed principle of cluster minimum complementary energy.

A representative cluster-based model of the batch process of ethanol production by Kluyveromyces sp. is proposed. Experimental data from fermentation processes of 17 different strains of K. marxianus are used; each of them potentially exhibits different metabolic and kinetic behavior. Three algorithms for clustering are applied. Two modifications of Principal Component Analysis (PCA)—hierarchical clustering and k-means clustering; and InterCriteria Analysis (ICrA) are used to simplify a large dataset into a smaller set while preserving as much information as possible. The experimental data are organized into two main clusters. As a result, the most representative fermentation processes are identified. For each of the fermentation processes in the clusters, structural and parameter identification are performed. Four different structures describing the specific substrate (glucose) consumption rate are applied. The best structure is used to derive the representative model using the data from the first cluster. Verification of the derived model is performed using experimental data of the second cluster. Model parameter identification is performed by applying an evolutionary optimization algorithm.

In wireless sensor networks (WSNs), the creation of energy holes is extremely difficult to be avoided because the data flow usually follows a many-to-one and multi-hop pattern. Since energy holes exhaust their energy faster than other nodes, network partitions might be created, which might lead to failure of the network. Cluster-based WSNs have been widely used because of their good performance, and power control strategies are an effective way to improve energy efficiency in WSNs. In this paper, we first propose a power-based energy consumption model and a cluster-based coronal model for analyzing the energy hole problem in WSNs. Then, on the basis of the proposed models, we investigate the feasibility and effectiveness of the existing approaches for solving the energy hole problem in WSNs. Furthermore, an immune clone selection-based power control (ICSPC) strategy for alleviating the energy hole problem in WSNs is proposed. In the ICSPC strategy, the immune clone selection algorithm is used to optimize the transmission ranges of sensors in various coronas to balance the energy consumption rates of the coronas. Finally, simulation results are analyzed to show that the energy hole problem in WSNs has been largely alleviated by the ICSPC strategy, and the network lifetime is greatly prolonged.

As a reduced order homogenization approach, the FEM-Cluster based reduced order Analysis method (FCA) proposed by Cheng et al. provides an efficient approach to predict the nonlinear effective properties of heterogeneous materials. In its improved version, the clustered Minimum Complementary Energy (MCE) approach is adopted for the computations of incremental strain–stress relation. This work mainly focuses on the mathematical foundations of FCA with clustered MCE. The completeness of the interaction matrix as the clustered self-equilibrium stress space is proved, and the prediction error of FCA solution is analyzed. The deductions also reveal that some bases of the clustered self-equilibrium stress space denoted by the interaction matrix may contradict the basic hypothesis of the cluster-based reduce order methods, and they are mainly responsible for the error of FCA. According to this observation, a spectral analysis algorithm is developed to refine the interaction matrix and improve the accuracy of FCA.

In present decade, wireless sensor networks is applied in a variety of applications such as health monitoring, agriculture, traffic management, security domains, pollution management, and so on. Owing to the node density, the same data are collected by multiple sensors that introduce redundancy, which should be avoided by means of proper data aggregation methodology. With that note, this paper presents a cluster-based systematic data aggregation model (CSDAM) for real-time data processing. First, the network is formed into a cluster with active and sleep state nodes and cluster-head (CH) is selected based on ranking given to sensors with two criteria: existing energy level (EEL) and geographic-location (GL) to base station (BS), [i.e., Rank(EEL,GL)]. Here, the CH is the aggregator. Second, Aggregation is carried out in 3 levels where the data processing of level 3 has been reduced by aggregating the data at level 1 and level 2. If the energy of aggregator goes below the threshold, we choose another aggregator. Third, Real time application should be given more precedence than other applications, so additionally an application type field is added to each sensor node from which the priority of data processing is given first to real time applications. The simulation results show that CSDAM minimizes the consumption of energy and transmission delay effectively, thereby increasing the network lifespan.

The hybrid flow shop (HFS) scheduling, typically found in a variety of real-world industries, is an NP-hard combinatorial optimisation problem. Consideration of uncertainties hugely aggravates its complexity. This paper considers makespan minimisation of dynamic HFS scheduling problems under machine breakdown and stochastic processing times. It presents a novel cluster-based scheduling model (CBSM) that combines the good features of the shortest processing time (SPT) algorithm and the simulated annealing (SA) heuristic to synergise HFS scheduling under uncertainties. In this model, a neighbouring agglomerative hierarchical clustering algorithm is firstly developed. This algorithm decomposes an HFS into an appropriate number of machine clusters with different stochastic natures. The CBSM then performs a decision-tree-based assignment procedure using the classification and regression trees to determine an appropriate approach, either SPT or SA, for each machine cluster. Finally, the machine clusters are scheduled by their assigned approaches. To validate the effectiveness of the CBSM, a discrete-event simulator is conducted to evaluate its performance. The simulation results show that the CBSM outperforms all the compared algorithms in solving the dynamic HFS scheduling problems.

An analytic model for cluster-based wireless sensor network (WSN) is developed for traffic flow analysis and network performance evaluation in this paper. The traffic flow path is modeled by a number of tandem linked parallel-queues with single-server and finite capacity, where channels of control data and message data are distinguished. Traffic of the tandem-cluster path is analyzed by dividing it into individual clusters. Through development of a stochastic model for this model, the explicit results of several important quality-of-service (QoS) metrics, such as the data blocking probability (DBP), successful data delivery rate (DDR), network throughput, source-to-destination delay (SDD) for both control and message traffic flows, and the network lifetime, of the proposed WSN are derived. A dynamic traffic allocation algorithm aiming to maintain the QoS of the whole WSN and two energy/consumption distribution schemes aiming to optimize the WSN's energy utilization are further proposed, respectively. The accuracy of the analytic model and QoS evaluation, as well as the effectiveness of the proposed algorithm and schemes are also validated through numerical analysis and simulation.

In this study, the authors propose a cluster-based trust management model that efficiently detects the malicious nodes and restricts them to be on a route in wireless ad hoc networks. In contrast to previous works, the trust of a node is calculated using various trust attributes having substantial effect on reliable routing in the networks. In the proposed model, each node periodically predicts the value of each trust attribute about other nodes using autoregression. Subsequently, the direct trust is estimated using the weighted combination of trust attributes and it is fine tuned using proportional–integral model. All these recommendation trusts, from common neighbours, are collected and combined by the clusterhead to quantify the trust, and hence the routing is reliable and secure in the proposed model. Simulation results show that the proposed trust model provides better throughput and packet delivery ratio in presence of malicious nodes compared to other existing schemes.