Structures composed of spatially-varying architected materials have great potential for targeted mechanical and/or multifunctional behavior, but lack of structural integrity at the interfaces between different architecture geometries can degrade the expected performance. While smooth transitions between functionally-defined architected materials can be designed easily using mathematical interpolation, a robust transitioning scheme is less apparent for architectures without a simple mathematical description. Here we focus on periodic, strut-based lattices exhibiting cubic symmetry of their nodes and propose an algorithm that automates the design of smoothly-varying transitions between any finite set of these lattices embedded in a macroscale structure. The algorithm takes in lattice existence and relative density fields indicating which lattice and associated relative density exists at each point in the macroscale structure, and an ordered set of m key lattices to be embedded. We define a transitional skeleton (i.e., nodes and connectivity) that encapsulates all m key lattices via a continuous morphing between different nodal configurations, and use it to spatially transition between the different lattice geometries. Material is added after manipulating the skeletons according to the given relative density distribution. We explain details of the algorithm in 2D using a multi-lattice design obtained from topology optimization and show the flexibility and robustness of the algorithm by generating a lattice-embedded rendering of The Starry Night by Vincent Van Gogh. In 3D, we explore the effect of the transition radius and demonstrate manufacturability of the spatially-varying lattice-embedded structures by 3D printing a multi-lattice canopy obtained from topology optimization.
Purpose This paper aims to address the instability issue of water-rich layered rock mass tunnels under blasting and swelling effects, lateral confinement swelling tests on water-rich slate are conducted to reveal the argillization and swelling characteristics as well as the variation laws of slate. Based on the surrounding rock instability characteristics of water-rich layered rock, a tunnel mechanical model is established. Design/methodology/approach In this paper, the swelling characteristics of water-rich slate are studied by laterally constrained swelling test. Based on the mechanical model of layered rock, the instability criterion of tunnel blasting is established, and the reliability of the criterion is verified by engineering application. Findings The smaller the layer inclination angle, the larger the contact area between clay minerals in the slate and water, and the stronger the water absorption capacity of the rock sample, which leads to greater swelling pressure and swelling deformation. Based on the mechanical model of layered rock, the instability criterion of tunnel blasting is established, and the reliability of the criterion is verified by engineering application. Originality/value Based on the layered rock mechanics model, considering the expansion effect of the rock mass and the deterioration effect of blasting, the criterion for tunnel blasting instability in water-rich layered rock masses was constructed using the point singularity theory. The influences of tunnel width, the expansion effect of slate, and the blasting deterioration effect on the stability of the tunnel were discussed.
Purpose This study focuses on understanding species population dynamics through a (3 + 1)-dimensional biological population model governed by Verhulst's logistic growth law. The main objective is to explore how nonlinear growth and spatial diffusion mechanisms influence the evolution of populations over time and space. By modeling the system with a nonlinear degenerate parabolic partial differential equation (PDE), the research seeks to provide a deeper theoretical framework for interpreting complex biological and ecological processes. Design/methodology/approach The investigation is carried out using Lie symmetry analysis as the principal analytical tool. The symmetry properties of the governing nonlinear PDE are systematically determined, followed by the construction of one-dimensional optimal subalgebras. These subalgebras enable the reduction of the original high-dimensional PDE into ordinary differential equations (ODEs), making the problem more tractable. Exact invariant solutions are then derived from the reduced equations and further expanded using symmetry group transformations to generate broader classes of solutions and visual interpretations of the system's dynamics. Findings The study successfully obtains several invariant solutions that describe the behavior of the Verhulst population model under different symmetry reductions. These solutions reveal important dynamical features of population spread, interaction and regulation under nonlinear and degenerate diffusion effects. The visual and analytical results demonstrate how successive symmetry reductions can simplify complex PDE models while preserving essential biological characteristics, thereby offering meaningful insight into the spatial–temporal evolution of populations. Originality/value The originality of this work lies in the application of Lie symmetry methods to a high-dimensional, degenerate biological population model incorporating logistic growth. The systematic use of optimal subalgebras and successive reductions provides a structured pathway from complex PDEs to exact analytical solutions. This approach not only advances the mathematical treatment of nonlinear population models but also strengthens the connection between symmetry analysis and practical ecological modeling, offering new perspectives for population control and environmental management strategies.
Purpose The purpose of this study is to assess the technical and economic feasibility of integrating a Francis-type micro-hydropower turbine into a pressurized drinking water pipeline using data-driven performance prediction. Daily flow rate time series are forecast using deep learning models to capture the dynamic operating conditions of the system. The predicted flow data are then used to construct flow-duration curves and head–discharge relationships for turbine selection and annual energy estimation. The study aims to demonstrate the applicability of machine learning–based forecasting for reliable micro-hydropower feasibility assessments. Design/methodology/approach Daily flow rate data obtained from a pressurized drinking water transmission pipeline were analyzed as time-series. Flow-duration curves and head–discharge relationships were derived using classical hydraulic methods. To predict future operating conditions, deep learning–based long short-term memory (LSTM) and gated recurrent unit (GRU) models were developed and optimized through hyperparameter tuning. The forecasted flow series were then used to evaluate turbine operating conditions, estimate annual energy production, and assess the technical and economic feasibility of integrating a Francis-type in-pipe micro-hydropower turbine. Findings The optimized LSTM model achieved a prediction accuracy exceeding R2 = 0.90, demonstrating strong capability in capturing the short-term memory behavior of the pipeline flow system. Based on the predicted flow series, the optimal design discharge and head were identified as approximately 550 L/s and 70 m, respectively. The feasibility analysis indicates that installing a Francis-type in-pipe turbine with an installed capacity of about 290 kW is technically viable. The system is expected to generate approximately 2.01 GWh of electrical energy annually, yielding favorable economic returns. Research limitations/implications The study is based on historical flow data from a single pressurized drinking water pipeline, which may limit the generalizability of the results to other network configurations. Future operating conditions were estimated using data-driven models rather than real measured values. Nevertheless, the proposed methodology provides a transferable framework for preliminary feasibility assessments in similar water infrastructure systems. Future research may incorporate longer datasets, multiple pipeline cases, transient hydraulic effects and alternative deep learning architectures to improve prediction robustness and broader applicability. Practical implications The proposed approach offers a practical decision-support tool for water utilities and engineers to evaluate the feasibility of micro-hydropower installations in pressurized pipeline systems. By combining machine learning–based flow forecasting with classical hydraulic analysis, turbine selection and energy production can be assessed without extensive field testing. The methodology enables efficient identification of suitable operating conditions, supports energy recovery from excess pressure and facilitates cost-effective integration of Francis-type turbines into existing water infrastructure, contributing to sustainable energy generation and reduced operational losses. Social implications The implementation of micro-hydropower systems in existing water infrastructure supports the transition toward cleaner and more sustainable energy production without additional environmental or land-use impacts. Recovering energy from excess pressure in drinking water pipelines can reduce carbon emissions, lower operational costs for water utilities and contribute indirectly to more affordable public services. By promoting energy efficiency and renewable energy integration within urban infrastructure, the proposed approach supports broader societal goals related to sustainability, climate resilience and responsible resource management. Originality/value This study presents a novel integration of deep learning–based time-series forecasting with classical hydraulic feasibility analysis for micro-hydropower applications in pressurized water pipelines. Unlike existing studies that rely on static or short-term data, the proposed approach uses long-term daily flow predictions to support turbine selection and energy estimation. The application of LSTM and GRU models to a Francis-type in-pipe turbine feasibility problem provides a data-driven framework that enhances reliability, reduces uncertainty and extends the methodological toolkit for sustainable energy recovery in water infrastructure systems.
Purpose To solve the poor real-time performance of active control systems for ultra-high-speed elevator horizontal vibration suppression, which is caused by sensor signal delays and unknown external disturbances. Design/methodology/approach First, a nonlinear 8-degree-of-freedom dynamic model of elevator horizontal vibration with a state delay mechanism was established. Then, a GRU-based state estimator was developed and a modified DDPG-NoisePER algorithm was proposed, integrated into GRU-DDPG-NoisePER to train the optimal delayed-state control strategy. Findings The GRU-DDPG-NoisePER-based strategy reduces the root mean square of car vibration acceleration by over 59%, outperforming DDPG-NoisePER by more than 1.02 times and DDPG-PER by more than 1.32 times. Practical implications The GRU-DDPG-NoisePER algorithm can be directly applied to ultra-high-speed elevator horizontal vibration control. It solves real-time issues caused by state delays, reduces equipment wear from excessive vibration, lowers maintenance costs, and provides a feasible technical solution for elevator manufacturers to optimize product performance in practical engineering scenarios. Social implications As a core transportation tool in high-rise buildings, stabilized ultra-high-speed elevators improve passengers' travel comfort (reducing vibration discomfort) and safety. The technology also drives technical upgrading of the elevator industry, aligns with smart city transportation needs and indirectly guarantees efficient and reliable urban vertical transportation. Originality/value This study innovatively integrates GRU with a modified DDPG (DDPG-NoisePER) to form GRU-DDPG-NoisePER. It effectively addresses state delay issues, improves DRL training efficiency, enhances vibration control effect and has strong practical application potential.
