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As the limited energy of wireless sensor networks (WSNs), energy-efficient data-gathering algorithms are required. This paper proposes a compressive data-gathering algorithm based on double sparse structure dictionary learning (DSSDL). The purpose of this paper is to reduce the energy consumption of WSNs.

The historical data is used to construct a sparse representation base. In the dictionary-learning stage, the sparse representation matrix is decomposed into the product of double sparse matrices. Then, in the update stage of the dictionary, the sparse representation matrix is orthogonalized and unitized. The finally obtained double sparse structure dictionary is applied to the compressive data gathering in WSNs.

The dictionary obtained by the proposed algorithm has better sparse representation ability. The experimental results show that, the sparse representation error can be reduced by at least 3.6% compared with other dictionaries. In addition, the better sparse representation ability makes the WSNs achieve less measurement times under the same accuracy of data gathering, which means more energy saving. According to the results of simulation, the proposed algorithm can reduce the energy consumption by at least 2.7% compared with other compressive data-gathering methods under the same data-gathering accuracy.

In this paper, the double sparse structure dictionary is introduced into the compressive data-gathering algorithm in WSNs. The experimental results indicate that the proposed algorithm has good performance on energy consumption and sparse representation.

The success of public–private partnership (PPP) projects is highly correlated to the successful management of risks encountered during the operation phase. PPP projects are especially exposed to risk due to the long operation period over which revenues need to be generated to recoup substantial initial investment and operational running costs. Despite the critical impact of risk exposure, limited research has been specifically undertaken on the matter of operational risk management. This study seeks to address this oversight by identifying and evaluating operational risk management strategies for PPPs.

Vulnerability theory is the theoretical lens used, with context drawn from Chinese PPP projects. Based on the data collected from expert interviews and questionnaires, 28 operational risk management strategies are identified. A fuzzy synthetic method is employed to analyze the effectiveness of the 28 strategies.

The findings reveal that providing an exit mechanism clause into the contract, establishing a comprehensive performance evaluation mechanism and developing a clear compensation mechanism are the top three effective strategies. This study also reveals that risk mitigation approaches that reduce vulnerability prove more effective than attempts to reduce external threats. Specifically, strategies aimed at managing contract, political, technical and financial risk are the most effective.

The findings of this study extend current knowledge regarding the risk management of PPP projects. They also offer a reference by which practitioners may select effective operational risk management pathways and thereby, galvanize the sustainable development of PPPs.