Nonlinear Model Research Articles

Performance Evaluation of Fractional Proportional–Integral–Derivative Controllers Tuned by Heuristic Algorithms for Nonlinear Interconnected Tanks

This article presents an in-depth analysis of three advanced strategies to tune fractional PID (FOPID) controllers for a nonlinear system of interconnected tanks, simulated using MATLAB. The study focuses on evaluating the performance characteristics of system responses controlled by FOPID controllers tuned through three heuristic algorithms: Ant Colony Optimization (ACO), Grey Wolf Optimizer (GWO), and Flower Pollination Algorithm (FPA). Each algorithm aims to minimize its respective cost function using various performance metrics. The nonlinear model was linearized around an equilibrium point using Taylor Series expansion and Laplace transforms to facilitate control. The FPA algorithm performed better with the lowest Integral Square Error (ISE) criterion value (297.83) and faster convergence in constant values and fractional orders. This comprehensive evaluation underscores the importance of selecting the appropriate tuning strategy and performance index, demonstrating that the FPA provides the most efficient and robust tuning for FOPID controllers in nonlinear systems. The results highlight the efficacy of meta-heuristic algorithms in optimizing complex control systems, providing valuable insights for future research and practical applications, thereby contributing to the advancement of control systems engineering.

Cost-aware workflow offloading in edge-cloud computing using a genetic algorithm

AbstractThe edge-cloud computing continuum effectively uses fog and cloud servers to meet the quality of service (QoS) requirements of tasks when edge devices cannot meet those requirements. This paper focuses on the workflow offloading problem in edge-cloud computing and formulates this problem as a nonlinear mathematical programming model. The objective function is to minimize the monetary cost of executing a workflow while satisfying constraints related to data dependency among tasks and QoS requirements, including security and deadlines. Additionally, it presents a genetic algorithm for the workflow offloading problem to find near-optimal solutions with the cost minimization objective. The performance of the proposed mathematical model and genetic algorithm is evaluated on several real-world workflows. Experimental results demonstrate that the proposed genetic algorithm can find admissible solutions comparable to the mathematical model and outperforms particle swarm optimization, bee life algorithm, and a hybrid heuristic-genetic algorithm in terms of workflow execution costs.

Nonlinear finite element modelling of the bond behavior of near-surface mounted Fe-SMA bars

Strengthening of concrete members with near-surface-mounted (NSM) iron-based shape memory alloy (Fe-SMA) bars can increase the load-carrying capacity and reduce deflections/crack widths owing to the unique self-prestressing ability of the Fe-SMA. However, the bond behavior of Fe-SMA bars is critical for the effectiveness of the NSM strengthening method, as inadequate bond strength can result in premature bond failure, rendering the strengthening technique ineffective. This study presents the results of a non-linear finite element (FE) model that was developed and validated to simulate the bond behavior and failure patterns of NSM Fe-SMA bars grouted into concrete. The variable parameters of the study included the effect of the compressive strength of the grout and the concrete block, the effect of cover depth and the activation of the Fe-SMA bar on the bond behavior. Investigations showed that the bond resistance and failure patterns of the NSM bars were significantly affected by the compressive strength of the concrete block and grout. The results showed that increasing the compressive strength of the grout by two times resulted in a 35 % increase in bond strength while increasing the compressive strength of the concrete block by three times resulted in a 30 % increase in bond strength. Additionally, the load transfer between the grout and concrete block was strongly influenced by the grout's compressive strength, where a higher strength of the grout resulted in a stiffer bond and increased contribution of the concrete block to resisting loads. Similarly, increasing the cover depth by four times from 5 mm to 20 mm increased the bond strength by more than twice and ultimately led to a change in failure mode from a splitting crack in the grout to a splitting crack in the concrete block. The results of the study also show that prestressing the short NSM bond with Fe-SMA can induce an initial bar slip in the range of 0.025 to 0.14 mm for recovery stresses of 100 MPa to 350 MPa.

Numerical hybrid simulation assessment of E‐BRBF and E‐FBF systems for mitigating P‐delta effects and enhancing post‐earthquake performance

AbstractThis article investigates the seismic stability of E‐BRBF and E‐FBF systems previously proposed as stability‐enhanced alternatives to conventional BRBF and FBF systems. The E‐BRBF system is a buckling restrained braced frame with an inverted‐V brace configuration in which one of the two braces is a conventional brace designed to remain elastic during a strong earthquake. When the buckling restrained brace (BRB) yields, an unbalanced vertical force develops at the brace‐to‐beam connection, which imposes flexural demand on the beam and creates a positive post‐elastic storey shear stiffness. The E‐FBF system is identical except that the buckling restrained braces are replaced by conventional bracing members constructed with an end friction connection designed and detailed to slip at a predetermined load. At every storey, the beam and the elastic braces are designed such that this post‐elastic stiffness is sufficient to cancel the negative storey shear stiffness resulting from P‐delta effects and introduce a re‐centring mechanism to achieve an enhanced performance in steel buildings subjected to interface subduction earthquakes. Using distributed plasticity numerical models, past studies demonstrated the effectiveness of E‐BRBF and E‐FBF systems in mitigating P‐delta effects, emphasizing the importance of a stable and predictable response of the beam, which is a critical element in the scheme that provides the post‐elastic stiffness of the system. This beam is subjected to axial and flexural demands and must remain near elastic to ensure the global seismic stability of the structure. The response of the beam can be affected by localized yielding and local instability effects resulting from residual stresses, stress concentration near gusset plate connections and geometric imperfections. Employing a refined nonlinear finite element model of the beam element, this article assesses the performance of 10‐storey E‐BRBF and E‐FBF systems utilizing multi‐platform numerical hybrid simulations. The evaluation involves static‐monotonic and dynamic response history analyses, incorporating seismic excitations representing Vancouver, BC's seismic hazard (Crustal, In Slab, and Subduction Interface). In the hybrid simulation model, the most critical member for the proposed system (i.e., first‐storey beam) is sub‐structured in ABAQUS using solid elements, while the remaining frames are integrated using OpenSees using fiber‐based sections. Numerical hybrid simulation dynamic nonlinear response history analyses demonstrate the adequacy of the E‐BRBF and E‐FBF systems in mitigating P‐delta effects with residual drifts within repair limits, unlike conventional systems where instability or excessive drifting occurred. Monotonic Pushover hybrid simulations reveal a more ductile beam behavior compared to standalone models, in which frame members are entirely modeled in OpenSees. The analysis also indicates a ductile plastic hinging beam failure mechanism with no instability failure modes at extreme drifts.

Neural activity shaping in visual prostheses with deep learning.


The visual perception provided by retinal prostheses is limited by the overlapping current spread of adjacent electrodes. This reduces the spatial resolution attainable with unipolar stimulation. Conversely, simultaneous multipolar stimulation guided by the measured neural responses - Neural Activity Shaping (NAS) - can attenuate excessive spread of excitation allowing for more precise control over the pattern of neural activation. However, predicting the results of a multipolar stimulus pattern is a challenging task. Previous attempts focused on analytical solutions based on an assumed linear nonlinear model of retinal response; an Analytical Model Inversion (AMI) approach. Here, we propose a model-free solution for NAS, using Artificial Neural Networks (ANNs) that could be trained with data acquired from the implant. Our method consists of two ANNs trained sequentially. The Measurement Predictor Network (MPN) is trained on data from the implant and is used to predict how the retina responds to multipolar stimulation. The Stimulus Generator Network (STG) is trained on a large dataset of natural images and uses the trained MPN to determine efficient multipolar stimulus patterns by learning its inverse model. We validate our method in silico using a realistic model of retinal response to multipolar stimulation.
Main Results:
We show that our ANN-based NAS approach produces sharper retinal activations than the conventional unipolar stimulation strategy. As a theoretical bench-mark of optimal NAS results, we implemented AMI stimulation by inverting the model used to simulate the retina. Our ANN strategy produced equivalent results to AMI, while not being restricted to any specific type of retina model and being three orders of magnitude more computationally efficient. Our novel protocol provides a method for efficient and personalized retinal stimulation, which may improve the visual experience and quality of life of retinal prosthesis users.&#xD.

Neural activity shaping in visual prostheses with deep learning.


The visual perception provided by retinal prostheses is limited by the overlapping current spread of adjacent electrodes. This reduces the spatial resolution attainable with unipolar stimulation. Conversely, simultaneous multipolar stimulation guided by the measured neural responses - Neural Activity Shaping (NAS) - can attenuate excessive spread of excitation allowing for more precise control over the pattern of neural activation. However, predicting the results of a multipolar stimulus pattern is a challenging task. Previous attempts focused on analytical solutions based on an assumed linear nonlinear model of retinal response; an Analytical Model Inversion (AMI) approach. Here, we propose a model-free solution for NAS, using Artificial Neural Networks (ANNs) that could be trained with data acquired from the implant. Our method consists of two ANNs trained sequentially. The Measurement Predictor Network (MPN) is trained on data from the implant and is used to predict how the retina responds to multipolar stimulation. The Stimulus Generator Network (STG) is trained on a large dataset of natural images and uses the trained MPN to determine efficient multipolar stimulus patterns by learning its inverse model. We validate our method in silico using a realistic model of retinal response to multipolar stimulation.
Main Results:
We show that our ANN-based NAS approach produces sharper retinal activations than the conventional unipolar stimulation strategy. As a theoretical bench-mark of optimal NAS results, we implemented AMI stimulation by inverting the model used to simulate the retina. Our ANN strategy produced equivalent results to AMI, while not being restricted to any specific type of retina model and being three orders of magnitude more computationally efficient. Our novel protocol provides a method for efficient and personalized retinal stimulation, which may improve the visual experience and quality of life of retinal prosthesis users.&#xD.

Comparative assessment of growth curves in Brazilian white Morada Nova hair sheep breed.

The Morada Nova sheep breed is essential for the economy of the semi-arid region of Northeast Brazil, standing out for its adaptability, resistance to parasites and reproductive ability. However, the white variant is endangered, highlighting the importance of studies on its productivity to support conservation efforts. This study focuses on the growth curve of the Morada Nova sheep breed, using nonlinear models and analyzing flock profiles. Total of 764 observations of 165 animals from four farms in Ceará and Rio Grande do Norte, Brazil, were analyzed. Canonical discriminant analysis (CDA) was used for the exploratory analysis and four nonlinear models were used to study the growth curve. Weight from birth to 270days of age, absolute growth rate (AGR), and the impact of sex on growth curves were assessed. Sex and farm are significant discriminating variables (P < 0.05) for the studied effects (weight and age). Weight was the primary phenotypic biomarker that discriminated between the two indicators, while age was a discriminating indicator only for the core effect. The Gompertz model was the most efficient, presenting the lowest residuals and greatest convergence. The study reveals new information about the growth of Morada Nova sheep, the white variety, including weight differences between the sexes at all analyzed ages and an inflection point before 90days of age. These discoveries contribute to the understanding of the breed's growth and help in the formulation of conservation strategies.

Towards interpretable Cryo-EM: disentangling latent spaces of molecular conformations.

Molecules are essential building blocks of life and their different conformations (i.e., shapes) crucially determine the functional role that they play in living organisms. Cryogenic Electron Microscopy (cryo-EM) allows for acquisition of large image datasets of individual molecules. Recent advances in computational cryo-EM have made it possible to learn latent variable models of conformation landscapes. However, interpreting these latent spaces remains a challenge as their individual dimensions are often arbitrary. The key message of our work is that this interpretation challenge can be viewed as an Independent Component Analysis (ICA) problem where we seek models that have the property of identifiability. That means, they have an essentially unique solution, representing a conformational latent space that separates the different degrees of freedom a molecule is equipped with in nature. Thus, we aim to advance the computational field of cryo-EM beyond visualizations as we connect it with the theoretical framework of (nonlinear) ICA and discuss the need for identifiable models, improved metrics, and benchmarks. Moving forward, we propose future directions for enhancing the disentanglement of latent spaces in cryo-EM, refining evaluation metrics and exploring techniques that leverage physics-based decoders of biomolecular systems. Moreover, we discuss how future technological developments in time-resolved single particle imaging may enable the application of nonlinear ICA models that can discover the true conformation changes of molecules in nature. The pursuit of interpretable conformational latent spaces will empower researchers to unravel complex biological processes and facilitate targeted interventions. This has significant implications for drug discovery and structural biology more broadly. More generally, latent variable models are deployed widely across many scientific disciplines. Thus, the argument we present in this work has much broader applications in AI for science if we want to move from impressive nonlinear neural network models to mathematically grounded methods that can help us learn something new about nature.

Development of new numerical approach to the flow and segregation behaviors of fresh concrete considering rebar restraint and its application in reinforced lightweight aggregate concrete

Although there are many studies on flow simulation methods for fresh concrete, there are very few studies on casting simulation of reinforced concrete, and in these studies the reinforcing bars are treated only as static boundaries without their restraining effect on the concrete flowing between them. In this study, we first developed a new numerical method based on the MPS method for simulating the flow and segregation behaviors of fresh concrete during casting reinforced member, considering the restraint of reinforcing bars by applying a normal stress to the concrete. Fresh concrete was treated as the double-phase granular fluid that follows a non-linear rheological model, and was represented by matrix mortar, and coarse aggregate particles with actual sizes and random shapes. Then, as an application of this numerical method, the flow and segregation behaviors of lightweight aggregate concrete (LWAC) in an L-shaped box with rebars were numerically investigated in addition to measurement. The comparison of the numerical and experimental results shows that this numerical method allows the LCA volume fraction to be calculated within 3 % error in predicting the segregation behavior of LCA in reinforced LWAC, and improves the accuracy of the flow simulation of LWAC by about 1.5 times. Furthermore, this numerical method can double the accuracy of concrete flow prediction, compared to treating the reinforcement as a static boundary.

Exploring the chaotic structure and soliton solutions for (3 + 1)-dimensional generalized Kadomtsev–Petviashvili model

The study of the Kadomtsev–Petviashvili (KP) model is widely used for simulating several scientific phenomena, including the evolution of water wave surfaces, the processes of soliton diffusion, and the electromagnetic field of transmission. In current study, we explore some multiple soliton solutions of the (3+1)-dimensional generalized KP model via applying modified Sardar sub-equation approach (MSSEA). By extracting the novel soliton solutions, we can effectively obtain singular, dark, combo, periodic and plane wave solutions through a multiple physical regions. We also investigate the chaotic structure of governing model using the chaos theory. The behavior of the collected solutions is visually depicted to demonstrate the physical properties of the proposed model. The solutions obtained in this paper can expand the existing solutions of the (3+1)-dimensional KP model and enhance our understanding of the nonlinear dynamic behaviors. This approach allows for consistent and effective treatment of the computation process for nonlinear KP model.

Exploring the chaotic structure and soliton solutions for (3 + 1)-dimensional generalized Kadomtsev–Petviashvili model

The study of the Kadomtsev–Petviashvili (KP) model is widely used for simulating several scientific phenomena, including the evolution of water wave surfaces, the processes of soliton diffusion, and the electromagnetic field of transmission. In current study, we explore some multiple soliton solutions of the (3+1)-dimensional generalized KP model via applying modified Sardar sub-equation approach (MSSEA). By extracting the novel soliton solutions, we can effectively obtain singular, dark, combo, periodic and plane wave solutions through a multiple physical regions. We also investigate the chaotic structure of governing model using the chaos theory. The behavior of the collected solutions is visually depicted to demonstrate the physical properties of the proposed model. The solutions obtained in this paper can expand the existing solutions of the (3+1)-dimensional KP model and enhance our understanding of the nonlinear dynamic behaviors. This approach allows for consistent and effective treatment of the computation process for nonlinear KP model.

Optical soliton solutions and modulation instability for unstable conformable Schrödinger model

The unstable time fractional Schrödinger model (UTFSM) is studied through the development of disturbances in marginally stable or unstable media. A modified Sardar-sub equation technique (MSSE) for a conformable fractional-order nonlinear evolution model is presented in this paper. The objective here is to construct new wave solutions for UTFSM. These solutions have particular relevance in quantum physics and assume several forms such as rational, exponential, trigonometric and hyperbolic functions, as well as combo solutions. This technique produces various shapes of dark, kink-type solitons and periodic solitary waves by setting proper parametric values. These discrete physical frameworks contribute to an understanding from analysis of unstable dynamical models. Additionally, we investigate modulation instability and stability analysis to ensure that obtained solutions are highly stable. The multiplicity of waves and solutions emphasizes how this technique can be used for different nonlinear fractional models in quantum physics and other areas.

Nonlinear similarity characterisation and validation of dynamic response of ship stiffened plate structure under explosion load impacts

The similarity test of ship stiffened plate structures under underwater explosions is a cost-effective and efficient method to evaluate the vitality of ships and guide the design of their shock resistance. This study focuses on the nonlinear impact response model tests of ship stiffened plate structures and their similarity laws with actual ships. The vertical motion of the ship stiffened plate structure is characterized by the Hurst index, and an equivalent relationship between the Hurst index of the model and the prototype is derived from classical similarity law. Based on the Hurst index, a similarity transformation relationship between the strain signals of the model and prototype is established. To verify the conclusions, similarity experiments of underwater explosions were conducted on both the model and the prototype. The original signals were grouped by the natural vibration period to determine the variation of the Hurst index over time. The model experiment strain signals for each natural vibration period were converted and compared with the prototype experiment results to verify the method's effectiveness. Simultaneously, the Hurst index of the stiffened plate structure under explosive shock load and its similarity transformation relationship with the prototype were simulated and analyzed. This provides theoretical and technical support for conducting analogous nonlinear response experiments for ship underwater explosions.

Nonlinear similarity characterisation and validation of dynamic response of ship stiffened plate structure under explosion load impacts

The similarity test of ship stiffened plate structures under underwater explosions is a cost-effective and efficient method to evaluate the vitality of ships and guide the design of their shock resistance. This study focuses on the nonlinear impact response model tests of ship stiffened plate structures and their similarity laws with actual ships. The vertical motion of the ship stiffened plate structure is characterized by the Hurst index, and an equivalent relationship between the Hurst index of the model and the prototype is derived from classical similarity law. Based on the Hurst index, a similarity transformation relationship between the strain signals of the model and prototype is established. To verify the conclusions, similarity experiments of underwater explosions were conducted on both the model and the prototype. The original signals were grouped by the natural vibration period to determine the variation of the Hurst index over time. The model experiment strain signals for each natural vibration period were converted and compared with the prototype experiment results to verify the method's effectiveness. Simultaneously, the Hurst index of the stiffened plate structure under explosive shock load and its similarity transformation relationship with the prototype were simulated and analyzed. This provides theoretical and technical support for conducting analogous nonlinear response experiments for ship underwater explosions.

An improved dynamic bidirectional coupled hydrologic–hydrodynamic model for efficient flood inundation prediction

Abstract. To improve computational efficiency while maintaining numerical accuracy, coupled hydrologic–hydrodynamic models based on non-uniform grids are used for flood inundation prediction. In these models, a hydrodynamic model using a fine grid can be applied to flood-prone areas, and a hydrologic model using a coarse grid can be used for the remaining areas. However, it is challenging to deal with the separation and interface between the two types of areas because the boundaries of the flood-prone areas are time dependent. We present an improved Multigrid Dynamical Bidirectional Coupled hydrologic–hydrodynamic Model (IM-DBCM) with two major improvements: (1) automated non-uniform mesh generation based on the D-infinity algorithm was implemented to identify the flood-prone areas where high-resolution inundation conditions are needed and (2) ghost cells and bilinear interpolation were implemented to improve numerical accuracy in interpolating variables between the coarse and fine grids. A hydrologic model, the 2D nonlinear reservoir model, was bidirectionally coupled with a 2D hydrodynamic model that solves the shallow-water equations. Three cases were considered to demonstrate the effectiveness of the improvements. In all cases, the mesh generation algorithm was shown to efficiently and successfully generate high-resolution grids in those flood-prone areas. Compared to the original M-DBCM (OM-DBCM), the new model had lower root-mean square errors (RMSEs) and higher Nash–Sutcliffe efficiencies (NSEs), indicating that the proposed mesh generation and interpolation were reliable and stable. It can be adequately adapted to the real-life flood evolution process in watersheds and provide practical and reliable solutions for rapid flood prediction.

An improved dynamic bidirectional coupled hydrologic–hydrodynamic model for efficient flood inundation prediction

Abstract. To improve computational efficiency while maintaining numerical accuracy, coupled hydrologic–hydrodynamic models based on non-uniform grids are used for flood inundation prediction. In these models, a hydrodynamic model using a fine grid can be applied to flood-prone areas, and a hydrologic model using a coarse grid can be used for the remaining areas. However, it is challenging to deal with the separation and interface between the two types of areas because the boundaries of the flood-prone areas are time dependent. We present an improved Multigrid Dynamical Bidirectional Coupled hydrologic–hydrodynamic Model (IM-DBCM) with two major improvements: (1) automated non-uniform mesh generation based on the D-infinity algorithm was implemented to identify the flood-prone areas where high-resolution inundation conditions are needed and (2) ghost cells and bilinear interpolation were implemented to improve numerical accuracy in interpolating variables between the coarse and fine grids. A hydrologic model, the 2D nonlinear reservoir model, was bidirectionally coupled with a 2D hydrodynamic model that solves the shallow-water equations. Three cases were considered to demonstrate the effectiveness of the improvements. In all cases, the mesh generation algorithm was shown to efficiently and successfully generate high-resolution grids in those flood-prone areas. Compared to the original M-DBCM (OM-DBCM), the new model had lower root-mean square errors (RMSEs) and higher Nash–Sutcliffe efficiencies (NSEs), indicating that the proposed mesh generation and interpolation were reliable and stable. It can be adequately adapted to the real-life flood evolution process in watersheds and provide practical and reliable solutions for rapid flood prediction.

Assessing macroeconomic tail risk

Abstract Real GDP and industrial production in the US display substantial asymmetry and tail risk. Is this asymmetry driven by a specific structural shock? Our empirical approach, based on quantile regressions and local projections, suggests otherwise. We find that the 10th percentile of predictive growth distributions responds between three and six times more than the median to monetary policy shocks, financial shocks, uncertainty shocks, and oil price shocks, indicating a common transmission mechanism. We present two data-generating processes that are capable of matching this finding: A threshold VAR model and a nonlinear equilibrium model.

Supervised machine learning computing paradigm to measure melting and dissipative effects in entropy induced Darcy–Forchheimer flow with ternary-hybrid nanofluids

This study investigates the change in thermophysical characteristics of Darcy–Forchheimer flow of tri-hybrid nanofluid (THNF) over stretchable porous skin. Machine learning (ML) technique is employed to compare thermal exchange of water-based hybrid nanofluid (HNF), composed of aluminum oxide (Al2O3) and silicon dioxide (SiO2) with THNF by introducing copper oxide (CuO) nanoparticles in HNF. Flow rate profile, dissipation effect, and entropy generation are analyzed with novel, time, and cost-effective evaluation technique. By using similarity parameters, the governing system of partial differential equations (PDEs) is transformed to a system of ordinary differential equations (ODEs). Finite difference method is used for dataset generation by the aid of Python environment, then neural fitting computation technique is utilized for optimized results. Turbulence and randomness are incorporated in the present nonlinear mathematical model which is tackled by artificial intelligence (AI)-based Levenberg Marquardt Neural-Network Algorithms (LMNA), to produce optimized outputs. Velocity, temperature, and entropy profile are evaluated against various influencing factors, such as Forchheimer value, porosity, melting parameter, radiation, Prandtl, Eckert, and Brinkmann coefficient. Numerical and AI-generated outputs and errors graphs with complete neural network training scheme, are portrayed to draw the effective concluding inferences. Enhanced results are beneficial for industrial and engineering production units, for efficient thermal management.

Hamiltonian shocks

AbstractWave propagation in the form of fronts or kinks, a common occurrence in a wide range of physical phenomena, is studied in the context of models defined by their Hamiltonian structure. Motivated, for dispersive wave evolution equations such as a strongly nonlinear model of two‐layer internal waves in the Boussinesq limit, by the symmetric properties of a class of front‐propagating solutions, known as conjugate states or solibores, a generalized formulation based purely on the dispersionless reduction of a system is introduced, and a class of undercompressive shock solutions, here referred to as “Hamiltonian shocks,” is defined. This analysis determines whether a Hamiltonian shock, representing locally a kink for the parent dispersive equations, will interact with a sufficiently smooth background wave without inducing loss of regularity, which would take the form of a classical dispersive shock for the parent equations. This property is also related to an infinitude of conservation laws, drawing a parallel to the case of completely integrable systems.

Hamiltonian shocks

AbstractWave propagation in the form of fronts or kinks, a common occurrence in a wide range of physical phenomena, is studied in the context of models defined by their Hamiltonian structure. Motivated, for dispersive wave evolution equations such as a strongly nonlinear model of two‐layer internal waves in the Boussinesq limit, by the symmetric properties of a class of front‐propagating solutions, known as conjugate states or solibores, a generalized formulation based purely on the dispersionless reduction of a system is introduced, and a class of undercompressive shock solutions, here referred to as “Hamiltonian shocks,” is defined. This analysis determines whether a Hamiltonian shock, representing locally a kink for the parent dispersive equations, will interact with a sufficiently smooth background wave without inducing loss of regularity, which would take the form of a classical dispersive shock for the parent equations. This property is also related to an infinitude of conservation laws, drawing a parallel to the case of completely integrable systems.