Functional Constraints Research Articles

Life-cycle production optimization with nonlinear constraints using a least-squares support-vector regression proxy

When nonlinear constraints such as field liquid or water production rate, injection pressures, etc., as functions of time need to be honored in addition to linear ones, the life-cycle production optimization problem, a component of a closed loop reservoir management, becomes challenging and computationally expensive to perform using a high-fidelity reservoir simulator with the existing gradient-based methods using the adjoint or stochastic approximate gradient methods. Therefore, the objective of this study is to present computationally efficient methods for deterministic production optimization under nonlinear constraints using a kernel-based machine learning method where the cost function is the net present value (NPV). We use the least-squares support-vector regression (LSSVR) to approximate the NPV function. To achieve computational efficiency, we generate a set of output values of the NPV and nonlinear constraint functions, which are field liquid production rate (FLPR) and water production rate (FWPR) in this study, by running the high-fidelity simulator for a broad set of input design variables (well controls) and then using the collection of input/output data to train LSSVR proxy models to replace the high-fidelity simulator to compute NPV and nonlinear state constraint functions during iterations of sequential quadratic programming (SQP). To obtain improved (higher) estimated optimal NPV values, we use the existing so-called iterative sampling refinement (ISR) method to update the LSSVR proxy so that the updated proxy remains predictive toward promising regions of search space during the optimization. Direct and indirect ways of constructing LSSVR-based NPVs as well as different combinations of input data, including nonlinear state constraints and/or the bottomhole pressures (BHPs) and water injection rates, are tested as alternative feature spaces. The results obtained from our proposed LSSVR-based optimization methods are compared with those obtained from our in-house stochastic simplex approximate gradient (StoSAG)-based line-search SQP programming (LS-SQP-StoSAG) algorithm that uses directly a high-fidelity simulator to compute the gradients of the objective function and the nonlinear state functions with StoSAG for the Brugge reservoir model. The results show that nonlinear constrained optimization with the LSSVR ISR with SQP is computationally 3.25 fold more efficient than LS-SQP-StoSAG. In addition, the results show that constructing NPV indirectly using the field liquid and water rates for a waterflooding problem where inputs come from LSSVR proxies of the nonlinear state constraints requires significantly fewer training samples than the method constructing NPV directly from the NPVs computed from a high-fidelity simulator. LSSVR has advantages for its computational efficiency which is the main goal in our research, and robustness against overfitting especially for the cases where we have limited data. However, DNNs and random forest require large training size and require much more computational resources and longer training times. Also, Random Forests and Gradient Boosting Machines can be prone to overfitting and become computationally intensive.

Impact of Urban Morphology on High-Density Commercial Block Energy Consumption in Severe Cold Regions

In sustainable city development, urban form plays an important role in block energy consumption, and as different environmental contexts and block functions create differences in energy use, it is necessary to study the relationship between morphology and energy consumption under the dual constraints of special environments and special block functions. Urban high-density blocks have concentrated energy consumption, high energy intensity, and complex morphological layout, but the influencing mechanism of the block’s morphology on its energy consumption remains unclear. Accordingly, this study focuses on the mechanism and evaluation method of the influence of morphology on the energy consumption of high-density commercial blocks in severe cold regions. Through Grasshopper model extraction, EnergyPlus performance simulation, Pearson correlation analysis, and linear regression analysis, this study extracts and classifies high-density commercial blocks in Harbin, China, into six basic layout types (Courtyard, Courtyard-T, Slab, Slab-T, Point, Point-T) according to their horizontal and vertical morphology, analyzes the energy consumption characteristics of each basic type, examines the relationships between energy use intensity (EUI) and building density (BD) and between floor area ratio (FAR) and building height standard deviation (BHSD), and constructs theoretical models by controlling variables to study the effect of a single form parameter on block EUI. The research findings are as follows: (1) The annual energy consumption of Point and Slab blocks is relatively low, whereas that of Courtyard and Courtyard-T blocks is higher due to the lack of open space in Courtyards and the poor ventilation in summer. (2) FAR is significantly correlated with the energy consumption of high-density commercial blocks in severe cold regions, while the effects of BD and BHSD are weaker than those of FAR. For every 0.1 increase in BD, every 1 increase in FAR, and every 1(m) increase in BHSD, the Winter Daily EUI of the Slab block changes by +0.87, −2.26, and −0.22 (kWh/m2), respectively, whereas that of the Slab-T block changes by −0.38, +0.68, and +0.08 (kWh/m2), respectively. (3) Controlling other variables, a large BD is theoretically beneficial to energy performance in the blocks, and increasing BD in the range of 0.4–0.55 has a significant effect on lowering energy consumption in Point blocks. EUI increases with the increase in FAR, while the change depends on different block types with the increase in BHSD. This study provides design strategies for high-density commercial blocks in severe cold regions. Under different layout types, though EUI shows different relationships with BD, FAR, and BHSD, Slab-T and Point-T blocks can achieve excellent energy performance by appropriately increasing BD and decreasing FAR, whereas Slab blocks need to decrease BD while increasing FAR. The patterns found in this paper can provide strategic help for policymaking and early urban design.

Topology Optimization of Anisotropic Materials with Smooth Fiber Orientation

In the concurrent optimization of topology and fiber orientation, the design of smooth fiber helps to maintain the stability of numerical calculation and the compatibility of the manufacturing process. However, the improvement of fiber continuity is often accompanied by a significant decrease in the overall structural stiffness. Aiming at this problem, this paper proposes a topology optimization method for anisotropic materials with smooth fiber orientation. This method improves the smoothness of fiber orientation and reduces stiffness loss by introducing a fiber angle constraint strategy and adaptive filtering technology. The fiber angle constraint strategy integrates the created angle constraint function into the Method of Moving Asymptotes (MMA) to complete the strong constraint of the angle. This strategy quantifies the continuity of the fiber and effectively improves the continuity of the fiber. At the same time, the application of adaptive filtering technology can adjust a reasonable fiber angle distribution on the basis of smoothing fibers, thereby enhancing the stiffness of the overall structure. In addition, this paper shows the complete optimization process and MATLAB code implementation and verifies the effectiveness of the method through a series of numerical examples, that is, on the basis of improving fiber continuity, the stiffness of the whole structure is guaranteed, and then the effective balance between the two is realized.

Dressing fields for supersymmetry: the cases of the Rarita-Schwinger and gravitino fields

In this paper we argue that the gauge-fixing conditions typically used to extract the (off-shell) degrees of freedom of the Rarita-Schwinger spinor-vector and gravitino, respectively in rigid supersymmetric field theory and supergravity, are actually instances of the dressing field method of symmetry reduction. Since the latter has a natural relation interpretation, solving the “gauge-fixing condition” — or, better, “dressing functional constraints” — actually realises the Rarita-Schwinger spinor-vector and the gravitino fields as (non-local) relational variables. To the best of our knowledge, this is the first application of the dressing field method to supersymmetric theories.

Grid-Connected Inverter Grid Voltage Feedforward Control Strategy Based on Multi-Objective Constraint in Weak Grid

In weak grid, feedforward of grid voltage control is widely used to effectively suppress grid-side current distortion of inverters caused by harmonics in point of common coupling (PCC) voltage. However, due to its introduction of a positive feedback loop related to the grid impedance, it results in a significant reduction in the system phase margin. In view of this, in this paper, the output impedance of a three-phase LCL grid-connected inverter under a quasi-proportional resonant (QPR) controller is first modeled. Instead of the traditional grid voltage feedforward control strategy, a band-pass filter is added to the grid voltage feedforward channel. Secondly, a multi-objective constraint method is proposed to make improvements to the feedforward function. Then, a multi-objective constraint function is established with the constraints of base-wave current tracking performance, system stability margin, and low-frequency amplitude, and the feasibility of its function optimization design method is verified. Theoretical analysis shows that the optimized grid voltage feedforward control strategy can effectively reshape the phase characteristics of the system output impedance, which greatly broadens the adaptation range of the system to the grid impedance. Finally, the effectiveness of the proposed control strategy is verified by building a semi-physical simulation experimental platform based on RT-LAB OP4510.

Research on reliability mapping of 5G low orbit constellation network slice based on deep reinforcement learning

Reliability mapping of 5G low orbit constellation network slice is an important means to ensure link network communication. The problem of state space explosion is a typical problem. The deep reinforcement learning method is introduced. Under the 5G low orbit constellation integrated network architecture based on software definition network (SDN) and network function virtualization (NFV), the resource requirements and resource constraints of the virtual network function (VNF) are comprehensively considered to build the 5G low orbit constellation network slice reliability mapping model, and the reliability mapping model parameters are trained and learned by using deep reinforcement learning, solve the problem of state space explosion in the reliability mapping process of 5G low orbit constellation network slices. In addition, node backup and link backup strategies based on importance are adopted to solve the problem that VNF/link reliability is difficult to meet in the reliability mapping process of 5G low orbit constellation network slice. The experimental results show that this method improves the network throughput, packet loss rate and intra slice traffic of 5G low orbit constellation, and can completely repair network faults within 0.3 s; For different number of 5G low orbit constellation network slicing requests, the reliability of this method remains above 98%; For SFC with different lengths, the average network delay of this method is less than 0.15 s.

Adaptive finite‐time tracking control of nonlinear systems subject to input hysteresis and multiple objective constraints

AbstractIn this article, the problem of adaptive finite‐time tracking control for a class of nonlinear systems subject to backlash‐like input hysteresis and multiple objective constraints is investigated. For the purpose of realizing multiple objective constraints, a new time‐varying barrier function (TVBF) is introduced to ensure that all objective constraint functions are always within the defined range. Meanwhile, based on the combination of the command filter approach and adaptive backstepping control, an error compensation system (ECS) is supplied to reduce the impact of filter error on control performance. Additionally, the problem of “singularity” caused by hysteresis is avoided by linearizing the backlash‐like hysteresis model, and Nussbaum‐type function is also applied to reduce the influence of hysteresis on the stability of the system. Then, by combining multi‐dimensional Taylor network (MTN) technology and command filter backstepping approach, an adaptive finite‐time control strategy is designed. The proposed control strategy ensures that all the signals in the closed‐loop system realize finite‐time semi‐globally uniformly ultimately bounded (SGUUB), and the output signal of the system can track the reference signal greatly while adhering to multiple objective constraints. Finally, the effectiveness of the proposed control strategy is verified by a practical simulation example.

Kinematic of dart-throwing: virtual reality (functional and structural constraints) vs. real-world

ABSTRACT Using virtual reality tools can improve performance and learning motor skills. In a way, active practice in a virtual environment can be a good alternative to real practice and create a better learning opportunity. This study compared the kinematic variables of dart-throwing skills in virtual and real-world environments. For this purpose, 36 male high school students (mean age 13.66 ± .07) without experience in dart-throwing skills were divided into three groups: Functional and Structural constraints and the Real-world practice group. The kinematic variables of the skill were recorded using a high-speed Casio camera at 240 frames per second. Mixed ANOVA was used to analyse the data. The significance level was p ≤ 0.05. The difference between time and group interaction was not statistically significant for all dependent variables. There were significant differences within the groups in throwing time, preparation time, angular velocity, and elbow release angle (p < 0.05). There were no significant differences between the groups in the variables of throwing time (p = .163), preparation time (p = .366), maximum flexion angle (p = .717), and elbow release angle (p = .083). According to the results, the study suggests that training and practicing through VR in discrete dart-throwing skills will create a similar movement pattern to real-world training and have similar benefits.

A systems approach for characterizing human deep space mission anomaly response capabilities and functional constraints

Human exploration of Mars and beyond will demand unprecedented levels of onboard self-sufficiency due to the exceedingly far distances from Earth and lengthy mission durations. This paradigm shift will require the development of novel anomaly response architectures to protect future crews adequately from anomalies and failures. In this paper we outline and demonstrate a process to identify and evaluate key factors that affect the anomaly response process for deep space operations. It builds on established frameworks, illustrating how incredibly complex and interdependent this activity is. Relevant factors of the current state-of-the-art anomaly response were established through a literature review in combination with an established taxonomy process. These factors were then assessed for their Earth-reliance specific attributes through a case study. In this paper we have identified over 120 relevant anomaly response factors and developed a process that allows for identifying system capabilities that need to be integrated into future habitat designs to provide a minimum level self-sufficiency to protect crews from catastrophic outcomes stemming from communications delays and compounding co-dependency of factors. While this process was demonstrated using notional Mars mission constraints and evaluated against current ISS processes as the baseline, the outlined approach can be adapted for anomaly response designs that require different forms of system autonomy by modifying the relevant mission constraints and operational capability attributes accordingly.

Modulation of biophysical properties of nucleocapsid protein in the mutant spectrum of SARS-CoV-2.

Genetic diversity is a hallmark of RNA viruses and the basis for their evolutionary success. Taking advantage of the uniquely large genomic database of SARS-CoV-2, we examine the impact of mutations across the spectrum of viable amino acid sequences on the biophysical phenotypes of the highly expressed and multifunctional nucleocapsid protein. We find variation in the physicochemical parameters of its extended intrinsically disordered regions (IDRs) sufficient to allow local plasticity, but also observe functional constraints that similarly occur in related coronaviruses. In biophysical experiments with several N-protein species carrying mutations associated with major variants, we find that point mutations in the IDRs can have nonlocal impact and modulate thermodynamic stability, secondary structure, protein oligomeric state, particle formation, and liquid-liquid phase separation. In the Omicron variant, distant mutations in different IDRs have compensatory effects in shifting a delicate balance of interactions controlling protein assembly properties, and include the creation of a new protein-protein interaction interface in the N-terminal IDR through the defining P13L mutation. A picture emerges where genetic diversity is accompanied by significant variation in biophysical characteristics of functional N-protein species, in particular in the IDRs.

Modulation of biophysical properties of nucleocapsid protein in the mutant spectrum of SARS-CoV-2

Genetic diversity is a hallmark of RNA viruses and the basis for their evolutionary success. Taking advantage of the uniquely large genomic database of SARS-CoV-2, we examine the impact of mutations across the spectrum of viable amino acid sequences on the biophysical phenotypes of the highly expressed and multifunctional nucleocapsid protein. We find variation in the physicochemical parameters of its extended intrinsically disordered regions (IDRs) sufficient to allow local plasticity, but also observe functional constraints that similarly occur in related coronaviruses. In biophysical experiments with several N-protein species carrying mutations associated with major variants, we find that point mutations in the IDRs can have nonlocal impact and modulate thermodynamic stability, secondary structure, protein oligomeric state, particle formation, and liquid-liquid phase separation. In the Omicron variant, distant mutations in different IDRs have compensatory effects in shifting a delicate balance of interactions controlling protein assembly properties, and include the creation of a new protein-protein interaction interface in the N-terminal IDR through the defining P13L mutation. A picture emerges where genetic diversity is accompanied by significant variation in biophysical characteristics of functional N-protein species, in particular in the IDRs.

Pervasive conservation of intron number and other genetic elements revealed by a chromosome-level genomic assembly of the hyper-polymorphic nematode Caenorhabditis brenneri.

With within-species genetic diversity estimates that span the gambit of that seen across the entirety of animals, the Caenorhabditis genus of nematodes holds unique potential to provide insights into how population size and reproductive strategies influence gene and genome organization and evolution. Our study focuses on Caenorhabditis brenneri, currently known as one of the most genetically diverse nematodes within its genus and metazoan phyla. Here, we present a high-quality gapless genome assembly and annotation for C. brenneri, revealing a common nematode chromosome arrangement characterized by gene-dense central regions and repeat rich peripheral parts. Comparison of C. brenneri with other nematodes from the 'Elegans' group revealed conserved macrosynteny but a lack of microsynteny, characterized by frequent rearrangements and low correlation iof orthogroup sizes, indicative of high rates of gene turnover. We also assessed genome organization within corresponding syntenic blocks in selfing and outcrossing species, affirming that selfing species predominantly experience loss of both genes and intergenic DNA. Comparison of gene structures revealed strikingly small number of shared introns across species, yet consistent distributions of intron number and length, regardless of population size or reproductive mode, suggesting that their evolutionary dynamics are primarily reflective of functional constraints. Our study provides valuable insights into genome evolution and expands the nematode genome resources with the highly genetically diverse C. brenneri, facilitating research into various aspects of nematode biology and evolutionary processes.

Finite variation sensitivity analysis in the design of isotropic metamaterials through discrete topology optimization

AbstractThis article extends recently developed finite variation sensitivity analysis (FVSA) approaches to an inverse homogenization problem. The design of metamaterials with prescribed mechanical properties is stated as a discrete density‐based topology optimization problem, in which the design variables define the microstructure of the periodic base cell. The FVSA consists in estimating the finite variations of the objective and constraint functions after independently switching the state of each variable. It is used to properly linearize the functions of binary variables so the optimization problem can be solved through sequential integer linear programming. Novel sensitivity expressions were developed and it was shown that they are more accurate than the ones conventionally used in literature. Referred to as the conjugate gradient sensitivity (CGS) approach, the proposed strategy was quantitatively evaluated through numerical examples. In these examples, metamaterials with prescribed homogenized Poisson's ratios and minimal homogenized Young's moduli were obtained. A hexagonal base cell with dihedral symmetry was used to produce only metamaterials with isotropic properties. It was shown that, by using the CGS approach instead of the conventional sensitivity analysis, the sensitivity error was substantially reduced for the considered problem. The proposed developments effectively improved the stability and robustness of the discrete optimization procedures. In all the considered examples, when more accurate sensitivity analyses were performed, the parameters of the topology optimization method could be tuned more easily, yielding effective solutions even if the settings were not ideal.

The evolution of mammalian Rem2: unraveling the impact of purifying selection and coevolution on protein function, and implications for human disorders.

Rad And Gem-Like GTP-Binding Protein 2 (Rem2), a member of the RGK family of Ras-like GTPases, is implicated in Huntington's disease and Long QT Syndrome and is highly expressed in the brain and endocrine cells. We examine the evolutionary history of Rem2 identified in various mammalian species, focusing on the role of purifying selection and coevolution in shaping its sequence and protein structural constraints. Our analysis of Rem2 sequences across 175 mammalian species found evidence for strong purifying selection in 70% of non-invariant codon sites which is characteristic of essential proteins that play critical roles in biological processes and is consistent with Rem2's role in the regulation of neuronal development and function. We inferred epistatic effects in 50 pairs of codon sites in Rem2, some of which are predicted to have deleterious effects on human health. Additionally, we reconstructed the ancestral evolutionary history of mammalian Rem2 using protein structure prediction of extinct and extant sequences which revealed the dynamics of how substitutions that change the gene sequence of Rem2 can impact protein structure in variable regions while maintaining core functional mechanisms. By understanding the selective pressures, protein- and gene - interactions that have shaped the sequence and structure of the Rem2 protein, we gain a stronger understanding of its biological and functional constraints.

Multi-response multi-parameter optimization of CoCrFeNiMo0.2 HEA coatings prepared by internal laser cladding and tribological behaviors

The process parameters of internal laser cladding have a significant influence on the dilution rate and hardness of CoCrFeNiMo0.2 high entropy alloy (HEA) coatings. In this paper, the influence of the key parameters for preparing CoCrFeNiMo0.2 coatings, namely laser power, scanning speed, and powder feeding rate on dilution rate and microhardness were systematically investigated. Polynomial mathematical models of the dilution and the microhardness were designed using the Response Surface Methodology (RSM), and the effects of each parameter on the objective response were investigated in depth. Then the quadratic models were used as the constraint functions and the multi-parameter multi-objective optimization algorithm was applied to find the minimum dilution rate and maximum microhardness. The algorithm was then utilized to predict the optimal combination of parameters to manufacture the internal HEA coating. Finally, the tribological behaviors of the coating were analyzed. The internal CoCrFeNiMo0.2 coating consisted of a single FCC solid solution phase. Only a small amount of hybrid texture phenomenon appeared in the coating. The coefficient of friction was approximately stable around 0.61, and the wear mechanism consisted of abrasive, adhesive, and oxidative wear. The coating has excellent tribological properties. The reliability of the RSM for the optimization of the internal HEA coating was demonstrated.

Mitigation Strategy of Neutral-Point DC for Transformer Caused by Metro Stray Currents

Metro stray currents flowing into neutral-point-grounded transformers can cause serious direct current (DC) bias. Affected by both metro train and urban power grid operations, transformer neutral-point DC caused by metro stray current is complex, dynamic, and time-varying, which changes the DC bias risk level of transformers. Thus, just installing blocking devices (BDs) at transformer neutral points with high instantaneous DC may make it difficult to comprehensively mitigate DC bias and lead to increased BD installation. To solve this, through optimizing BD installation placements, a mitigation method for transformer DC bias is proposed. In the proposed method, the DC bias risk level and BD installation number are included in the constraint and objective functions. To evaluate the risk level of transformer DC bias, four indicators are proposed considering the distribution characteristics of neutral DC. To optimize the BD installation placements, the effects of both the metro train dynamic operation and the operation topology of the urban power grid on neutral DCs are considered. The Monte Carlo method is used to sample the train operation conditions and a relation matrix among transformers is established. Applying the method to a certain power system, the result of BD installation placements shows that the transformers supplying the metro system must have BDs installed at their neutral points.

Improved scheduling model for a multistage biopharmaceutical process in a multiproduct facility

This study critically evaluates deterministic and stochastic/evolutionary strategies for long-term scheduling of multiproduct facilities in batch and continuous biopharmaceutical manufacturing, as reported in existing literature using discrete-time and continuous-time models. It identifies key limitations in literature model/algorithm, including (i) real-time storage violation, (ii) real-time violation of shelf-life due to its calculation over a single event, (iii) minimum campaign length calculated over single events leading to suboptimal use of resources, and (iv) early product deliveries. To overcome these limitations, a deterministic mathematical model is proposed extending the existing unit-specific event-based model(s) with additional features including (i) modified material balances, (ii) new minimum campaign length constraints captured over multiple events, (iii) new shelf-life constraints captured over multiple events, (iv) new setup constraints based on product sequencing, (v) updated tightening constraints, (vi) updated sales and penalty constraints for late deliveries, (vii) updated bounds, and (viii) updated objective function. These improved features lead to better modeling in terms of handling intermediate and final product storage without real-time violations of storage and shelf-life, handling of initial setup in production tasks, and timely delivery of final products. The proposed improved model yields up to 36 % increase in profit when applied on four literature examples.

Bi-Level Planning of Electric Vehicle Charging Stations Considering Spatial–Temporal Distribution Characteristics of Charging Loads in Uncertain Environments

With the increase in the number of distributed energy resources (DERs) and electric vehicles (EVs), it is particularly important to solve the problem of EV charging station siting and capacity determination under the distribution network considering a large proportion of DERs. This paper proposes a bi-level planning model for EV charging stations that takes into account the characteristics of the spatial–temporal distribution of charging loads under an uncertain environment. First, the Origin–Destination (OD) matrix analysis method and the real-time Dijkstra dynamic path search algorithm are introduced and combined with the Larin Hypercube Sampling (LHS) method to establish the EV charging load prediction model considering the spatial and temporal distribution characteristics. Second, the upper objective function with the objective of minimizing the cost of EV charging station planning and user charging behavior is constructed, while the lower objective function with the objective of minimizing the cost of distribution network operation and carbon emission cost considering the uncertainty of wind power and photovoltaics is constructed. The constraints of the lower-layer objective function are transformed into the upper-layer objective function through Karush–Kuhn–Tucker (KKT) conditions, the optimal location and capacity of charging stations are finally determined, and the model of EV charging station siting and capacity determination is established. Finally, the validity of the model was verified by planning the coupled IEEE 33-node distribution network with the traffic road map of a city in southeastern South Dakota, USA.

Functional effects of mutations in proteins can be predicted and interpreted by guided selection of sequence covariation information

Predicting the effects of one or more mutations to the in vivo or in vitro properties of a wild-type protein is a major computational challenge, due to the presence of epistasis, that is, of interactions between amino acids in the sequence. We introduce a computationally efficient procedure to build minimal epistatic models to predict mutational effects by combining evolutionary (homologous sequence) and few mutational-scan data. Mutagenesis measurements guide the selection of links in a sparse graphical model, while the parameters on the nodes and the edges are inferred from sequence data. We show, on 10 mutational scans, that our pipeline exhibits performances comparable to state-of-the-art deep networks trained on many more data, while requiring much less parameters and being hence more interpretable. In particular, the identified interactions adapt to the wild-type protein and to the fitness or biochemical property experimentally measured, mostly focus on key functional sites, and are not necessarily related to structural contacts. Therefore, our method is able to extract information relevant for one mutational experiment from homologous sequence data reflecting the multitude of structural and functional constraints acting on proteins throughout evolution.

Nonlinear fatigue damage constrained topology optimization

In engineering applications, plenty of components are subjected to variable-amplitude cyclic loading, resulting in fatigue damage, which is one of the main forms of structural damage. While the linear damage rule has long served as a fundamental approach, its limitations necessitate advancements for more accurate fatigue life predictions. Hence, this paper introduces a pioneering method termed nonlinear fatigue damage constrained topology optimization (NFDCTO). This method integrates several key components: the rainflow counting method to evaluate the non-proportional cyclic load levels, Basquin's equation to describe the S-N curve, and Morrow's plastic work interaction rule to calculate the nonlinear cumulative damage of the structure. Consequently, we establish a mathematical model for the NFDCTO method based on these components. The incorporation of penalized damage aggregation with the P-Normal function is used to address significant constraints and singularity challenges. Furthermore, by employing the adjoint method, we derive sensitivity equations for both the objective function and fatigue constraint function concerning the design variables. Subsequently, the superiority of the NFDCTO method over traditional linear fatigue damage method were verified applying 2D l-shaped beam and simply supported structures as examples. Concurrently, bridge structures were employed to investigate the effect of the sensitivity index of the material to the history of variable amplitude stresses on the optimization results. In addition, the influence of the fatigue penalty factor on the topology optimization results was assessed using a 2D cantilever beam. Finaly, we verify the effectiveness and feasibility of the NFDCTO method in addressing fatigue optimization challenges for 3D structures utilizing two 3D examples.