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Air balancing is an important technique in heating, ventilation, and air conditioning (HVAC) applications to achieve accurate air supply for satisfactory indoor air quality and better energy saving performance. The existing air balancing methods are usually based on a hybrid duct system model, which includes a data-driven duct system model between terminal flow and static pressure, and an American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) damper model between static pressure and terminal damper angle. Most of the existing methods just focus on how to improve the accuracy of the former part (i.e., the data-driven duct system model), whereas neglecting the latter. However, it is found that the ASHRAE damper model cannot exactly reflect the characteristics of the actual dampers in practice and may lead to unavoidable modeling errors. To fix this issue, this article develops a full data-driven duct system (FD3S) model to directly reveal the relationship between the terminal flow and terminal damper angle in the whole duct system. As a result, the desired terminal damper angle under the design flow conditions can be more accurately predicted. Besides, since the proposed method directly models the relationship between terminal flow and terminal damper angle, it avoids installing extra pressure sensors and reduces the operating cost. Besides, the proposed FD3S model greatly reduces the model complexity compared with the previous hybrid model. The proposed FD3S model-based air balancing method is fully tested on three real duct systems, and the results proved the effectiveness and generality of the proposed FD3S model-based air balancing method.

Estimation of the sintering state has importance for clinker quality improvements and the safe operation of the rotary kiln. Class imbalanced thermal signals usually pose challenges in feature extraction and abnormal state recognition. In this article, a novel framework that integrates prior knowledge and hidden information is developed for sintering state recognition in the class imbalance condition. For discriminative feature extraction of imbalanced data, a cascaded stack autoencoder (SAE) model is proposed to fuse our prior knowledge and hidden information. The model includes a feature extraction SAE and a deep fusion SAE: the former extracts hidden information from thermal signals, and the latter deeply fuses and compresses our prior knowledge and hidden information. For the class imbalance of sintering samples, we propose a data-dependent kernel modification optimal margin distribution machine (ddKMODM) as a sintering state recognition model. Modifying the original kernel function by a conformal function depending on the data distribution in kernel space, ddKMODM can change the local volume expansion coefficient of the feature space to eliminate the negative effects caused by imbalanced samples. Experiments on real data show that the proposed framework can balance the detection rate of each state in the class imbalanced condition, and its overall sintering state recognition accuracy exceeds 92%.

While the demand for quality power supply is increasing, the traditional power grid cannot meet with the users’ demand. Smart grid has become a new solution to quality power supply for its improved information sharing and intelligent power distribution. In the smart grid, the power load forecasting is the key to power distribution. So, this paper proposed a multiobjective deep belief ensemble network based on ensemble empirical mode decomposition (EEMD) to realize the high diversity and accuracy of the forecasting model. This method decomposes the data based on EEMD to reduce the complexity of the data and classifies the data with sample entropy, using a multiobjective evolutionary algorithm based on decomposition optimization algorithm to optimize network parameters with accuracy and diversity as objective functions. The comparison of this method with other intelligent prediction methods such as deep belief network (DBN) and deep belief network based on ensemble empirical mode decomposition (EEMD-DBN) on multiple datasets shows that this method can guarantee accuracy and has good generalization characteristics.

Air balancing is a key technology to reduce energy consumption of ventilation system and improve the quality of indoor living environment. So far, most of the existing data-driven non-iterative air balancing methods only focus on the prediction of terminal damper angle to supply appropriate airflow, but they do not pay attention to the energy-saving constraint of fan voltage and terminal damper. Therefore, their energy efficiencies are not high enough. In this paper, energy-saving constraint strategy of low fan voltage and small damper friction resistance is considered and a novel data-driven non-iterative air balancing model with energy-saving constraint strategy is proposed. The model parameters can be trained by the proposed optimization algorithm inputting acquisition data. Then, given a design airflow rate, the required fan voltage and terminal damper angle can be predicted by the trained model to achieve accurate air balancing control with high energy efficiency. The performance validation of the proposed method is executed on our experimental duct system with five terminals. Compared with the current air balancing method, the proposed method can improve energy saving potential up to 13.7%, while keeping accurate air balancing within 10% relative error standard. This work is supported by NSFC (61976005, 6177219, 61902167, 61871204), Natural Science Foundation of Anhui Province (1908085MF215, 1908085QE247), Open Research Fund of AnHui Key Laboratory of Detection Technology and Energy Saving Devices (DTESD2020A03), Open Research Fund of AnHui Polytechnic University (Xjky02201903).

An advanced deep learning-based method that employs transformer architecture is proposed to diagnose the simultaneous faults with time-series data. This method can be directly applied to transient data while maintaining the accuracy without a steady-state detector so that the fault can be diagnosed in its early stage. The transformer architecture adopts a novel multi-head attention mechanism without involving any convolutional and recurrent layers as in conventional deep learning methods. The model has been verified by an on-site air handling unit with 6 single-fault cases, 7 simultaneous-fault cases, and normal operating conditions with satisfactory performances of test accuracy of 99.87%, Jaccard score of 99.94%, and F1 score of 99.95%. Besides, the attention distribution reveals the correlations between features to the corresponding fault. It is found that the length of the sliding window is key to the model performance, and a trade-off is made for the window length between the model performance and the diagnosis time. Based on the similar idea, another sequence-to-vector model based on the gated recurrent unit (GRU) is proposed and benchmarked with the transformer model. The results show that the transformer model outperforms the GRU model with a better Jaccard score and F1 score in less training time.

In practical chiller systems, applying efficient fault diagnosis and Isolation (FDI) techniques can significantly reduce the energy consumption and keep the environment comfortable. The success of the existing methods for fault detection and diagnosis of chillers relies on the condition that sufficient labeled data are available for training. Generally, the number of labeled data is limited while abundant unlabeled normal data are available. To make effective use of the large number of unlabeled data to improve the fault detection (FD) performance and realize fault isolation (FI), a novel data driven FDI method based on the deep autoencoder (DAEFDI) is proposed. Specifically, DAEFDI method consists of two parts: fault detection (DAEFD) and fault isolation (DAEFI). For the DAEFD part, the unlabeled normal data is used to learn a DAE model to describe the chiller system. When the reconstruction error is higher than the threshold, it is considered that the system deviates from the normal state. For the DAEFI part, when it is detected that the system is in a fault state, the source variable caused the fault is found according to their proportion in the reconstruction error. Experimental results demonstrate the effectiveness of the DAEFDI method.

The stable operation of air handling units (AHU) is critical to ensure high efficiency and to extend the lifetime of the heating, ventilation, and air conditioning (HVAC) systems of buildings. In this paper, an online data-driven diagnosis method for AHU in an HVAC system is proposed and elaborated. The rule-based method can roughly detect the sensor condition by setting threshold values according to prior experience. Then, an efficient feature selection method using 1D convolutional neural networks (CNNs) is proposed for fault diagnosis of AHU in HVAC systems according to the system's historical data obtained from the building management system. The new framework combines the rule-based method and CNNs-based method (RACNN) for sensor fault and complicated fault. The fault type of AHU can be accurately identified via the offline test results with an accuracy of 99.15% and fast online detection within 2 min. In the lab, the proposed RACNN method was validated on a real AHU system. The experimental results show that the proposed RACNN improves the performance of fault diagnosis. Published version This research is supported under the RIE2020 Industry Alignment Fund — Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from Surbana Jurong Pte Ltd.

This paper mainly deduces a new stability criteria of the fractional-order HIV-1 system with delay on the basis of Wirtinger inequality, fractional-order Lyapunov method and integral mean value theorem. The Wirtinger inequality is rarely applied to stability analysis of fractional-order system. Nevertheless, this paper extends the general form of the Lyapunov-krasovskii function to a novel fractional expression form by applying definition of Caputo fractional derivative. Via the the integral mean value theorem, fractional-order Lyapunov method and Wirtinger inequality, the novel stability criteria is deduced. It is the integral mean value theorem that reduces the conservatism of the stability criteria. The simulation results show that the proposed criteria can satisfy different fractional-order operators.In addition, it can not only solve the stability problem of fractional-order HIV-1 system with the constant time delay, but also of the fractional-order HIV-1 system with time-varying time delay. Thus, the new stability criteria has generality and universality. So as to verify our theoretical results, many numerical simulations are provided.

Age estimation is a challenging research topic in recent years. Existing approaches usually use only appearance features for age estimation. Personalized aging patterns, i.e., sequences of personal features, which have been shown as an important factor for improving age estimation accuracy, however, are not considered in their researches. We propose a novel model named recurrent age estimation (RAE), to make full use of appearance features as well as personalized aging patterns. RAE uses the CNN-LSTM architecture. Convolutional neural networks (CNNs) are trained to extract discriminative appearance features from face images, and long short-term memory networks (LSTMs) are employed to learn personalized aging patterns from sequences of personal features. Furthermore, we integrate the label distribution learning (LDL) scheme into LSTMs to exploit ambiguity from the real age and adjacent ages. The superiority of the RAE compared with existing approaches is shown by experimental results.

This paper puts forward a novel stability criterion of all cases of the time-delay fractional-order financial systems(FFS) including FFS without time delay, FFS with constant time delay and FFS with time-varying delay. This novel stability criterion is mainly based on a new stability judgment method which contains the deduction of Wirtinger inequality, Integral mean value theorem, fractional-order Lyapunov method, and a new functional transformation lemma which we deduced. This new functional transformation lemma simplifies the structure of the novel stability criterion with fewer constraints. Thus, compared with the previous stability criterion of FFS, the novel stability criterion of FFS has clearer structure and lower conservatism. Moreover, the novel stability criterion of FFS can also satisfy all fractional-order operators from 0 to 1. Last but not least, some numerical simulation examples are provided to verify the effectiveness and the benefit of the proposed novel stability criterion of FFS.

The economic operation optimization of microgrid is an important research topic in the power system. Therefore, this paper proposes a surrogate model particle swarm optimization algorithm based on the global-local search mechanism. Firstly, aiming at the problem that the statistical information of Kriging model is difficult to guarantee the prediction accuracy, the dynamic transformation is carried out to enhance the robustness of the model; secondly, the global-local search mechanism is introduced to make the algorithm fully explore the fitness landscape near the Kriging model after quickly locating the current optimal particle position, so as to achieve the balance of convergence quality and convergence efficiency. The proposed method has been tested on numerous benchmark test functions from two test suites, and the results show that the proposed algorithm has more advantages than other comparison algorithms in optimization accuracy. Finally, simulations are carried out in two operating modes of microgrid islanding and grid-connected, which has verified the effectiveness of the proposed method.

This paper mainly analyzes the stability of high-dimensional fractional-order gene regulatory network systems with time delay. Based on the judgment of eigenvalues, this paper proposes sufficient information about the stability of high-dimensional fractional-order gene regulatory network systems with time delay. Conditions, and by analyzing the characteristic equations, the bifurcation conditions of the high-dimensional fractional-order gene regulatory network system with time delay are derived. Finally, the theoretical part of this paper is verified by numerical simulation.

In practical chiller systems, applying efficient fault diagnosis techniques can significantly reduce energy consumption and improve energy efficiency of buildings. The success of the existing methods for fault diagnosis of chillers relies on the condition that sufficient labeled data are available for training. However, label acquisition is laborious and costly in practice. Usually, the number of labeled data is limited and most data available are unlabeled. Most of the existing methods cannot exploit the information contained in unlabeled data, which significantly limits the improvement of fault diagnosis performance in chiller systems. To make effective use of unlabeled data to further improve fault diagnosis performance and reduce the dependency on labeled data, we proposed a novel semi-supervised data-driven fault diagnosis method for chiller systems based on the semi-generative adversarial network, which incorporates both unlabeled and labeled data into learning process. The semi-generative adversarial network can learn the information of data distribution from unlabeled data and this information can help to significantly improve the diagnostic performance. Experimental results demonstrate the effectiveness of the proposed method. Under the scenario that there are only 80 labeled samples and 16,000 unlabeled samples, the proposed method can improve the diagnostic accuracy to 84%, while the supervised baseline methods only reach the accuracy of 65% at most. Besides, compared with the supervised learning method based on the neural network, the proposed semi-supervised method can reduce the minimal required number of labeled samples by about 60% when there are enough unlabeled samples.

A novel decentralized non-integer order controller applied on nonlinear fractional-order composite system(NFOCS) is proposed. In addition, some novel results for the asymptotic stabilization are shown with fractional parameter α∈0,1. First, we derive certain novel results useful for the Mittag-Leffler function. Then, we design a new decentralized fractional-order controller for the NFOCS according to the novel results applied to Mittag-Leffler function. Next, this novel asymptotic stabilization condition has been proposed. Compared with other controllers our controller has wider control gain range and weaker requirements. Moreover, we solve the asymptotic stabilization problem of the NFOCS with time delays via the novel controller. In the end, four general examples are performed to show the progressiveness of the new fractional-order decentralized controller.

Sample mean is generally the simplest feasible description of samples.Margin distribution can characterize the generalization performance.Double Distribution Support Vector Machine (DDSVM) maximizes the margin distribution of two classes sample means.DDSVM can obtain efficient and more balanced classification performance. This paper studies the role of the sample mean in binary classifier based on the margin theory. Support Vector Machine (SVM) with maximized minimum margin is widely used in pattern recognition, but it sometimes induces the weak margin distribution which is negative for the generalization performance. Therefore Double Distribution Support Vector Machine (DDSVM) is proposed to obtain strong generalization performance by maximizing the margin distribution of two classes sample means and the minimum margin. The sample mean is usually a good description of samples, and DDSVM can increase the margin distribution and improve the generalization performance. DDSVM is a general learning approach, and its superiority is verified both theoretically and experimentally.

This paper develops cost-sensitive margin distribution learning and proposes Large Cost-Sensitive margin Distribution Machine (LCSDM) to get balanced detection rate on imbalanced training data. Recently, margin theory revealed that compared with a single margin, margin distribution is more critical to the generalization performance. Large margin Distribution Machine (LDM) is designed to get superior classification performance and strong generalization performance. However, LDM generally has imbalanced margin distribution between two classes on imbalanced training data. This generally leads to the lower detection rate of the minority class, which contradicts to the needs of high detection rate of the minority class in many real applications. Therefore, cost-sensitive margin distribution learning is brought forward to obtain balanced margin distribution and detection rate between two classes. What's more, this research deduces the relation between cost-sensitive parameter and in-class detection rate, and designs LCSDM to obtain balanced detection rate. Experimental results show that LCSDM can gradually increase the margin distribution of the minority class to obtain a more balanced detection rate. As a general learning method, LCSDM is especially applicable to imbalanced data classification.

Accurate sintering condition recognition (SCR) is an important precondition for optimal control of rotary kilns. However, the occurrence probability of abnormal conditions in the industrial field is much lower than normal, resulting in imbalanced class sintering samples in general. This significantly deteriorates the effectiveness of existing recognition models in abnormal condition detection. In this paper, an integrated framework considering class imbalance is proposed for sintering condition recognition. In the proposed framework, after analysing the characteristics of thermal signals by the Lipschitz method, four discriminant features are extracted to comprehensively describe different sintering conditions. In addition, focusing on the class imbalance of sintering samples, the kernel modification method is introduced to enhance the optimal marginal distribution machine (ODM), and a novel recognition model kernel modified the ODM (KMODM) is proposed for SCR. By constructing a new conformal transformation function to modify the ODM kernel function, KMODM optimizes the spatial distribution of training samples in the kernel space, thereby alleviating the detection accuracy deterioration of the minority class. The experimental results on real thermal signals and standard datasets show that the KMODM model can effectively handle imbalanced data. Based on this, the proposed SCR framework can reduce the misjudgement of abnormal conditions and balance the recognition accuracy of each condition.

This paper attempts to develop a delay three-variable fractional-order gene regulatory networks(FGRNs) model with an impulse input to control the state of of genes are transformed and translated. The formulas for determining the bifurcation points and the conditions of stability are derived by applying Lyapunov stability judgment method. Moreover, via the study of the dynamics, we design a novel controller that can able to be applied for the FGRNs, and it can make the FGRNs stable. Finally, some examples are shown the correctness of the controller we designed.

Given the importance of the class-imbalanced data and misclassified unequal costs in large wind turbine datasets, this paper proposes a cost-sensitive large margin distribution machine (CLDM) for fault detection of wind turbines. The margin mean and margin variance are use to characterize the margin distribution. The objective function and constraints of the large margin distribution machine (LDM) are modified to be cost-sensitive. The class-imbalanced data and misclassified unequal costs are solved by selecting the appropriately cost-sensitive parameters. Then CLDM is designed to train and test data from wind turbines in a wind farm. In order to verify the effectiveness of CLDM, it is compared with support vector machine (SVM), cost-sensitive SVM, and LDM. Comprehensive experiments on 7 datasets from a benchmark model of wind turbines and 5 datasets from a real wind farm show that CLDM has better sensitivity, gMean and average misclassified cost than the other methods.

The Internet of Things (IoT) is emerging as a new communication paradigm and has attracted a significant amount of attention from both academic and engineering communities. In this paper, we consider an IoT market where three roles exist: Wireless Sensor Networks (WSNs), two service providers (SPs) and end users. The WSNs are responsible for sensing and providing data to the two SPs. Based on the sensed data from WSNs, the two SPs compete to provide services to the end users. We model the relationship between the two SPs and end users as a two-stage Stackelberg game, where the two SPs set the prices for their services firstly, and then the end users decide which SP to choose. Specifically, we consider two price-competition scenarios of the two SPs, which are engaged in two games, one is a noncooperative strategic game (NSG) where the two SPs set the prices for services simultaneously, the other is a Stackelberg game (SG) where SP1 who sets the price first is the leader and SP2 who sets the price after is the follower. Each user decides whether and which SP to purchase services from based on prices and service rates. An equilibrium is achieved in each of the two scenarios. Numerical results are conducted to verify our theoretical analysis.

This paper proposes a novel fault detection and diagnosis (FDD) method using multiscale convolutional neural networks (MCNNs) for Air Handling Unit (AHU) in Heating, Ventilation, and Air conditioning (HVAC) system. In existing works, it is challenging to achieve high diagnosis performance on multiscale monitoring signals from AHU system since the feature extraction methods in these works are not powerful enough. Although the single-scale convolutional neural networks (CNNs) have been adopted to improve the ability of feature extraction in FDD, it remains difficult to extract strong discriminative feature from multiscale monitoring signals only using single-scale kernels. In this paper, a novel MCNNs-based FDD method is proposed with three different scale kernels to improve the ability of feature extraction and the end-to-end learning strategy is adopted to optimize the model of MCNNs. With strong representation ability, the proposed method can capture highly discriminative features, which can help to improve the diagnostic performance of AHU. The proposed method is compared with other five commonly used methods using the measured data from our AHU experiment platform. The comparison results demonstrate that the proposed MCNNs-based FDD method outperforms other FDD methods.

Large margin Distribution Machine (LDM) is not satisfactory on imbalanced training data.Cost-sensitive margin distribution is introduced to design a balanced classifier.Cost-sensitive LDM (CS-LDM) has a very strong generalization performance.CS-LDM can gradually improve the detection rate of the minority class.CS-LDM can obtain a balanced detection rate at the balance point. This paper proposes a new method to design a balanced classifier on imbalanced training data based on margin distribution theory. Recently, Large margin Distribution Machine (LDM) is put forward and it obtains superior classification performance compared with Support Vector Machine (SVM) and many state-of-the-art methods. However, one of the deficiencies of LDM is that it easily leads to the lower detection rate of the minority class than that of the majority class on imbalanced data which contradicts to the needs of high detection rate of the minority class in the real application. In this paper, Cost-Sensitive Large margin Distribution Machine (CS-LDM) is brought forward to improve the detection rate of the minority class by introducing cost-sensitive margin mean and cost-sensitive penalty. Theoretical and experimental results show that CS-LDM can gradually improve the detection rate of the minority class with the increasing of the cost parameter and obtain a balanced classifier when the cost parameter increases to a certain value. CS-LDM is superior to some popular cost-sensitive methods and can be used in many applications.

The research on the fractional-order network system (FONS, The derivative model of network system is fractional-order) has seen fruitful achievements, but ignores whether the fractional-order operator (The order of fractional derivatives α) in the FONS will affect its stability and dynamic characteristics. To tackle this problem, this paper adopts a new method to study the effect of fractional-operators in gamma functions on the dynamic state of the gamma function. This new method helps us to derive a novel dynamic principle of multidimensional FONS. We define it as the Whole Oscillation Principle. According to this principle, the choice of fractional operator reflects the dynamic oscillation characteristic of the multidimensional FONS in two dimensions of time and system state, thus better optimizing the complex case of the fractional-order system research process in the future. Furthermore, based on the auxiliary function-based integral inequality, the paper derives a new stability criterion for all dimensional FONS in the general form. Finally, the validity and correctness of the above theories are verified through numerical simulation to its good effect.

The imbalanced data classification problem is common in many real-world supervised learning tasks, and always leads to the lower class-prediction accuracy of the minority class. In this paper, a modified large margin distribution machine is proposed by adjust the kernel matrix based on the distribution of the data near the class boundary, to improve the class-prediction accuracy. Through theoretical analysis backed by empirical study, it shows that the proposed algorithm in this paper works effectively on several UCI datasets.

Optical Music Recognition (OMR) has received increasing attention in recent years. In this paper, we adopt the descriptor of Locality-constrained Linear Coding (LLC) and Double Distribution Support Vector Machine (DDSVM) to address music symbol classification in OMR. LLC can obtain stronger feature representation ability compared with original music symbol. Recently, DDSVM is presented to obtain stronger robustness and generalization performance. Therefore, DDSVM is adopted to improve the classification performance in OMR. Moreover, One Versus Rest Double Distribution Support Vector Machine (OVR-DDSVM) is proposed for multi-class music symbol classification. OVR-DDSVM can obtain high accuracy only using linear kernel due to LLC descriptor, and this speeds the classification process. OVR-DDSVM is tested on more than 10000 music symbol images of 20 classes, and experimental results verify the superiority of LLC+DDSVM to other algorithms.

Air balancing is an important means to reduce energy consumption and improve thermal comfort and indoor air quality for dedicated outdoor air system (DOAS). It effectively distributes the required amount of air to each conditioned zone through dynamic regulation of terminal/branch dampers and fan speed. Up to now, most of the existing air balancing methods are modeled by quadratic models that greatly rely on the accuracy of the collected data and are therefore difficult to obtain satisfactory forecasting results. Noise, outlier and model approximation error are likely to cause large prediction errors in air balancing, leading to increased demand for new methods to overcome these problems. In this paper, a robust air balancing method based on data-driven model is proposed to produce a more accurate prediction of pressure difference. With precise prediction, the proposed method obtains a more accurate balancing result and is more robust against noise and outlier. The proposed method includes three parts: building mathematical model for duct system based on steady-state pressure balance; training model parameters by robust air balancing learning algorithm; estimating damper positions by the damper characteristic curve. The performance of the proposed method is validated on a laboratory duct test-bed with five terminals. The relative error can be controlled with 5.5% in the test cases. Compared with the existing air balancing methods, the proposed method is more accurate in prediction and more robust in the balancing results. The proposed method offers the possibility to obtain a superior balancing performance when sensor accuracy cannot be guaranteed in practical applications.

This paper studies the impact of margin distribution on detection performance and proposes Diverse Margin Distribution Ensemble (DMDE) for pedestrian detection, based on HOG descriptor. Large margin Distribution Machine (LDM) introduces the margin mean and margin variance. Large margin mean is relevant to the strong generalization performance and large margin variance is relevant to the more balanced detection rate between two classes. Inspired by this recognition, DMDE is proposed to obtain greater robustness and balance for pedestrian detection. It is a blending of SVM and two LDMs with different parameter orders and can aggregate the merits of the three classifiers. Experimental results show that DMDE is more robust and balanced than single SVM or LDM for pedestrian detection.

Optical Music Recognition (OMR) has received increasing attention in recent years. In this paper, we propose a classifier based on a new method named Directed Acyclic Graph-Large margin Distribution Machine (DAG-LDM). The DAG-LDM is an improvement of the Large margin Distribution Machine (LDM), which is a binary classifier that optimizes the margin distribution by maximizing the margin mean and minimizing the margin variance simultaneously. We modify the LDM to the DAG-LDM to solve the multi-class music symbol classification problem. Tests are conducted on more than 10000 music symbol images, obtained from handwritten and printed images of music scores. The proposed method provides superior classification capability and achieves much higher classification accuracy than the state-of-the-art algorithms such as Support Vector Machines (SVMs) and Neural Networks (NNs).

Providing source privacy is a critical security service for sensor networks. However, privacy preserving in sensor networks is a challenging task, particularly due to the limited resources of sensor nodes and the threat of node capture attack. On the other hand, existing works use either random walk path or fake packets injection, both incurring tremendous overhead. In this work, we propose a new approach, which separates the sensor nodes into groups. The source packet is randomly forwarded within and between the groups with elaborate design to ensure communication anonymity; furthermore, members of each group exchange encrypted traffic of constant packet length to make it difficult for the adversary to trace back. One salient feature of the proposed scheme is its flexibility of trading transmission for higher anonymity requirement. We analyze the ability of our proposed scheme to withstand different attacks and demonstrate its efficiency in terms of overhead and functionality when compared to existing works.