In this paper, a novel algorithm is proposed to design sparse FIR filters. It is known that this design problem is highly nonconvex due to the existence of -norm of a filter coefficient vector in its objective function. To tackle this difficulty, an iterative procedure is developed to search a potential sparsity pattern, which is then used to compute the final solution by solving a convex optimization problem. In each iterative step, the original sparse filter design problem is successively transformed to a simpler subproblem. It can be proved that under a weak condition, globally optimal solutions of these subproblems can be attained by solving their dual problems. In this case, the overall iterative procedure converges to a locally optimal solution of the original design problem. The design procedure described above can be repeated for several times to further improve the sparsity of design results. The output of the previous stage can be used as the initial point of the subsequent design. The performance of the proposed algorithm is evaluated by two sets of design examples, and compared to other sparse FIR filter design algorithms.Index Terms-Finite impulse response (FIR) filters, secondorder cone programming (SOCP), sparse filter design.

No abstract

The construction risk of deep foundation pit (DFP) engineering is high, and accidents occur frequently. It is necessary to evaluate the risk of deep foundation pits before construction. At present, although there are many risk assessment methods, there is not one with strong applicability and high accuracy. Based on expert scoring, this paper analyses the risk from two aspects (the severity of consequences and the probability of occurrence), divides the severity of the consequences into five indexes, calculates the risk by using the analytic hierarchy process (AHP), and sets the expert weight index so that the subjective expert scoring result can obtain the best possible objective calculation result. In addition, this paper uses the membership function from fuzzy mathematics to establish the level of risk and optimize the evaluation criteria of risk events. An engineering example is introduced, and the result of the risk assessment shows that the evaluation result R (risk value) obtained by the optimized risk assessment method in this paper is 7.9 and that the level of risk is grade III. The risk assessment method proposed in this paper has strong applicability and can obtain more accurate evaluation results. This method can provide a reference for the risk assessment of deep foundation pit engineering.

No abstract

No abstract